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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInAccountsPayableAndOtherOperatingLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accounts payable and other liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BasisOfPresentationAndSignificantAccountingPoliciesTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Basis of Presentation and Summary of Significant Accounting Policies</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_BasisOfPresentationAndSignificantAccountingPoliciesTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Basis of Presentation and Significant Accounting Policies [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockCapitalSharesReservedForFutureIssuance_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock reserved for issuance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockCapitalSharesReservedForFutureIssuance_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Capital Shares Reserved for Future Issuance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockCapitalSharesReservedForFutureIssuance_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Common stock reserved for issuance</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Unrealized Losses 12 Months or Greater</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPosition12MonthsOrLongerAccumulatedLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale, Continuous Unrealized Loss Position, 12 Months or Longer, Accumulated Loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfAccruedLiabilitiesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Accrued Expenses and Current Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfAccruedLiabilitiesTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Accrued Liabilities [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Operating lease liabilities</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiability_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating lease liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommitmentsAndContingencies_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Commitments and Contingencies</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommitmentsAndContingencies_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Commitments and contingencies (See Note 8)</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Weighted Average Number of Shares Outstanding, Diluted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfDilutedSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Weighted Average Number of Shares Outstanding, Diluted, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock-based compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">APIC, Share-Based Payment Arrangement, Increase for Cost Recognition</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsToAdditionalPaidInCapitalSharebasedCompensationRequisiteServicePeriodRecognitionValue_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">APIC, Share-based Payment Arrangement, Increase for Cost Recognition, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestReceivableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest receivable</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseTermOfContract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Lease term</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_MinimumMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Minimum</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_MinimumMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Minimum [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_InvestigationNewDrugMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Investigation New Drug (IND)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_InvestigationNewDrugMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Investigation New Drug [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_InvestigationNewDrugMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Investigation new drug.</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_DebtSecuritiesAvailableForSaleMaturity_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Debt securities, available-for-sale, maturity.</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_BasisOfPresentationAndUseOfEstimatesPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Basis Of Presentation And Use Of Estimates Policy [Text Block]</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesIssued_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Common Stock, Shares, Issued, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingInformationLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other segment items</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_RepurchaseAgreementCounterpartyNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Counterparty Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_RepurchaseAgreementCounterpartyNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Counterparty Name [Domain]</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyTransactionLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Related Party Transaction [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyTransactionLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Related Party Transaction [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_TwoThousandTwentyOneEmployeeStockPurchasePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2021 Employee Stock Purchase Plan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_TwoThousandTwentyOneEmployeeStockPurchasePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Two Thousand Twenty One Employee Stock Purchase Plan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_TwoThousandTwentyOneEmployeeStockPurchasePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Two thousand twenty one employee stock purchase plan.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_TwoThousandTwentyOneEmployeeStockPurchasePlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">2021 Employee Stock Purchase Plan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingSegmentsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Segments [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingSegmentsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Segment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsMajorClassNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Intangible Asset, Finite-Lived, Class [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Debt securities, Amortized Cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleDebtSecuritiesAmortizedCostBasis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale, Amortized Cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Liability, Undiscounted Excess Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityUndiscountedExcessAmount_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedTerseLabel">Less: Present value adjustment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GeneralAndAdministrativeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">General and Administrative Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GeneralAndAdministrativeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">General and Administrative Expense, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GeneralAndAdministrativeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">General and administrative</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_GeneralAndAdministrativeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">General and administrative (including related party amounts of $60, $131, $145 and $265, respectively)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncomeStatementAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Income Statement [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_StockholdersDeficitTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stockholders Deficit [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_StockholdersDeficitTable_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Stockholders deficit.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_MonthlyFeeForConsultancyServices_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Monthly fee for consultancy services</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_MonthlyFeeForConsultancyServices_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Monthly Fee For Consultancy Services</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_MonthlyFeeForConsultancyServices_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Monthly fee for consultancy services.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_IncreaseInRightOfUseAssetAndOperatingLeaseLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase In Right of Use Asset And Operating Lease Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_IncreaseInRightOfUseAssetAndOperatingLeaseLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Increase in right of use asset and operating lease liabilities.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_IncreaseInRightOfUseAssetAndOperatingLeaseLiabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Increase in right of use asset and operating lease liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfAvailableForSaleSecuritiesReconciliationTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Amortized Cost, Unrealized Gains and Losses, Allowances for Credit Losses and Fair Value of Available-for-Sale Investments Aggregated by Maturity and Security Type</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfAvailableForSaleSecuritiesReconciliationTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Available-for-Sale Securities Reconciliation [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Related Party</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Related and Nonrelated Parties [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net loss per share, basic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings Per Share, Basic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Earnings Per Share, Basic, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentPeriodEndDate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Document Period End Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentPeriodEndDate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Period End Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_NonCashLeaseExpenseIncome_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Non Cash Lease Expense Income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_NonCashLeaseExpenseIncome_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Non-cash lease expense (income).</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_NonCashLeaseExpenseIncome_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Non-cash lease expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Purchases of property and equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Payments to Acquire Property, Plant, and Equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PaymentsToAcquirePropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Payments to Acquire Property, Plant, and Equipment, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted-Average Exercise Price, Granted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsGrantsInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangements by Share-Based Payment Award, Options, Grants in Period, Weighted Average Exercise Price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock, shares authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesAuthorized_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Shares Authorized</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementOfStockholdersEquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Stockholders' Equity [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilitiesPaymentsDueAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Liability, to be Paid, Fiscal Year Maturity [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidExpenseAndOtherAssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Prepaid expenses and other current assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidExpenseAndOtherAssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidExpenseAndOtherAssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Prepaid Expense and Other Assets, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CostsAndExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CostsAndExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Costs and Expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfShareBasedCompensationArrangementsByShareBasedPaymentAwardTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Share-Based Compensation Arrangements by Share-Based Payment Award [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Assets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Assets_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_Security12bTitle_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Title of 12(b) Security</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_Security12bTitle_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Title of 12(b) Security</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyTransactionAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Related Party Transaction</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyTransactionAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Related Party Transaction [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period, Value, Stock Options Exercised</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueStockOptionsExercised_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Exercises of stock options</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfEmployeeServiceShareBasedCompensationAllocationOfRecognizedPeriodCostsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Stock-based Compensation Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfEmployeeServiceShareBasedCompensationAllocationOfRecognizedPeriodCostsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Expensed and Capitalized, Amount [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfEmployeeServiceShareBasedCompensationAllocationOfRecognizedPeriodCostsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Stock-Based Compensation Expense Reported in Condensed Statements of Operations</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_AccruedExpensesAndOtherCurrentLiabilitiesRelatedPartiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued expenses and other current liabilities, related party amounts</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_AccruedExpensesAndOtherCurrentLiabilitiesRelatedPartiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Accrued expenses and other current liabilities Related Parties, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_AccruedExpensesAndOtherCurrentLiabilitiesRelatedPartiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accrued expenses and other current liabilities Related Parties, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Stock options granted to purchase common stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Grants in Period, Gross</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsGrantsInPeriodGross_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of Options and Awards Outstanding, Granted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Antidilutive Securities, Name [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Liability, to be Paid, Remainder of Fiscal Year</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2026 (remaining six months)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_LicenseAgreementAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">License Agreement [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_LicenseAgreementAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">License agreement.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Liability, to be Paid, Year One</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2027</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestrictedCashAndCashEquivalentsCashAndCashEquivalentsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash and Cash Equivalents</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RestrictedCashAndCashEquivalentsCashAndCashEquivalentsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash and Cash Equivalents [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NatureOfOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Organization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NatureOfOperations_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Nature of Operations [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Segment Reporting Information</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfSegmentReportingInformationBySegmentTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_ScheduleOfLicenseAgreementTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule Of License Agreement [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_ScheduleOfLicenseAgreementTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule Of License Agreement [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_ScheduleOfLicenseAgreementTable_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Schedule of license agreement.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeasesTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Leases</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeasesTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Leases [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_StockIssuedDuringPeriodValueStockOptionsExercisedAndVestingOfEarlyExercisedCommonStockOptions_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Vesting of restricted stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_StockIssuedDuringPeriodValueStockOptionsExercisedAndVestingOfEarlyExercisedCommonStockOptions_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period Value Stock Options Exercised And Vesting Of Early Exercised Common Stock Options</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_StockIssuedDuringPeriodValueStockOptionsExercisedAndVestingOfEarlyExercisedCommonStockOptions_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Stock issued during period value stock options exercised and vesting of early exercised common stock options.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_StockIssuedDuringPeriodValueStockOptionsExercisedAndVestingOfEarlyExercisedCommonStockOptions_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Exercises of stock options and vesting of restricted stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedPeriodEndLabel">Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total stockholders' equity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity, Attributable to Parent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressAddressLine2_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Address, Address Line Two</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressAddressLine2_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address, Address Line Two</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ArrangementsAndNonarrangementTransactionsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Collaborative Arrangement and Arrangement Other than Collaborative</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ArrangementsAndNonarrangementTransactionsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Collaborative Arrangement and Arrangement Other than Collaborative [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net Loss Per Share</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NumberOfReportableSegments_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Number of Reportable Segments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NumberOfReportableSegments_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of reportable segment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt securities, Unrealized Gains</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedGainBeforeTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale, Accumulated Gross Unrealized Gain, before Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromStockOptionsExercised_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds from Stock Options Exercised</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_RangeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Statistical Measurement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_RangeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statistical Measurement [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_PercentageOfAnnualIncreaseInLeasePayments_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Percentage of annual increase in lease payments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_PercentageOfAnnualIncreaseInLeasePayments_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Percentage Of Annual Increase In Lease Payments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_PercentageOfAnnualIncreaseInLeasePayments_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Percentage of annual increase in lease payments.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MoneyMarketFundsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Money market funds</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_MoneyMarketFundsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Money Market Funds [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPosition_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Estimated Fair Market Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPosition_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale, Unrealized Loss Position</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityInteractiveDataCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Interactive Data Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityInteractiveDataCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Interactive Data Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Liability, to be Paid, Year Three</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2029</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Value, Issued</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Common Stock, Value, Issued, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Common Stock, Value, Issued, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Common Stock, Value, Issued, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockValue_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock, $0.0001 par value; 200,000,000 shares authorized at June 30, 2026 and December 31, 2025; 62,580,096 and 60,398,051 shares issued and outstanding at June 30, 2026 and December 31, 2025, respectively</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Liabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Liabilities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accumulated deficit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Retained Earnings (Accumulated Deficit)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Retained Earnings (Accumulated Deficit), Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Retained Earnings (Accumulated Deficit), Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Retained Earnings (Accumulated Deficit), Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsAccumulatedDeficit_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Accumulated deficit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_AreaOfLeasedProperty_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Area of lease space</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_AreaOfLeasedProperty_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Area Of Leased Property</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_AreaOfLeasedProperty_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Area of leased property.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel3Member_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Significant Unobservable Inputs (Level 3)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel3Member_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Inputs, Level 3 [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total operating expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Change in operating assets and liabilities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInOperatingCapitalAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Adjustment to Reconcile Net Income to Cash Provided by (Used in) Operating Activity, Increase (Decrease) in Operating Capital [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesNewIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Number of shares sold</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesNewIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Initial public offering of common shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesNewIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Issuance of common stock in at-the-market offering, net of issuance costs, Shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_TypeOfStockOptionsGrantedToPurchaseCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Type of stock options granted to purchase common stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_TypeOfStockOptionsGrantedToPurchaseCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Type of Stock Options Granted to Purchase Common Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_TypeOfStockOptionsGrantedToPurchaseCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Type of stock options granted to purchase common stock.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_CrossingHoldingsLLCMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Crossing Holdings, LLC</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_CrossingHoldingsLLCMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Crossing Holdings L L C [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_CrossingHoldingsLLCMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Crossing Holdings LLC.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CertificatesOfDepositMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Certificates of Deposit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CertificatesOfDepositMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Certificates of deposit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CertificatesOfDepositMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Certificates of Deposit [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant, and Equipment, Accumulated Depreciation, Depletion, and Amortization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Less accumulated depreciation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Accumulated Depreciation, Depletion and Amortization, Property, Plant, and Equipment, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Accumulated Depreciation, Depletion and Amortization, Property, Plant, and Equipment, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedDepreciationDepletionAndAmortizationPropertyPlantAndEquipment_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Accumulated Depreciation, Depletion and Amortization, Property, Plant, and Equipment, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingCostsAndExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Operating Costs and Expenses, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingCostsAndExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Costs and Expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingCostsAndExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Research and development expenses related party amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyTransactionsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Related Party Transactions [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseCost_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Rent expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseCost_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Cost</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentByTypeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Long-Lived Tangible Asset</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentByTypeAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Long-Lived Asset, Class [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueByFairValueHierarchyLevelAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value Hierarchy and NAV</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueByFairValueHierarchyLevelAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value Hierarchy and NAV [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_NoticePeriodForTerminationOfAgreement_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Written notice period for termination of agreement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_NoticePeriodForTerminationOfAgreement_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Notice Period For Termination Of Agreement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_NoticePeriodForTerminationOfAgreement_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Notice period for termination of agreement.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Property Plant And Equipment [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant, and Equipment [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_AccruedInterestReceivableOnAvailableForSaleInvestmentSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued interest receivable on available-for-sale investment securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_AccruedInterestReceivableOnAvailableForSaleInvestmentSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accrued Interest Receivable On Available For Sale Investment Securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_AccruedInterestReceivableOnAvailableForSaleInvestmentSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Accrued interest receivable on available-for-sale investment securities.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_ExpectedMilestonePaymentOnAchievingCertainRegulatoryAndCommercialMilestones_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Expected milestone payment on achieving certain regulatory and commercial milestones</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_ExpectedMilestonePaymentOnAchievingCertainRegulatoryAndCommercialMilestones_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Expected Milestone Payment On Achieving Certain Regulatory And Commercial Milestones</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_ExpectedMilestonePaymentOnAchievingCertainRegulatoryAndCommercialMilestones_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Expected milestone payment on achieving certain regulatory and commercial milestones.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Liability, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current portion of operating lease liability (including related party amounts of $890 as of December 31, 2025)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Current portion of operating lease liability, related party</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseExistenceOfOptionToExtend_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Lessee, Operating Lease, Existence of Option to Extend [true false]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseExistenceOfOptionToExtend_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Existence of Option to Extend [true false]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesAndStockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities and Equity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesAndStockholdersEquity_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total liabilities and stockholders' equity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Liability, to be Paid, Year Two</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2028</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ResearchAndDevelopmentExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Research and Development Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ResearchAndDevelopmentExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Research and Development Expense, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ResearchAndDevelopmentExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Research and development</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ResearchAndDevelopmentExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Research and development (including related party amounts of $0, $230, $72 and $458, respectively)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_IncreaseInRight-Of-Use-AssetAndOperatingLeaseLiabilityRelatedToLeaseAmendment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase In Right-of-Use-Asset And Operating Lease Liability Related To Lease Amendment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_IncreaseInRight-Of-Use-AssetAndOperatingLeaseLiabilityRelatedToLeaseAmendment_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Increase in right-of-use-asset and operating lease liability related to lease amendment.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_IncreaseInRight-Of-Use-AssetAndOperatingLeaseLiabilityRelatedToLeaseAmendment_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Increase in right-of-use-asset and operating lease liability related to lease amendment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FiniteLivedIntangibleAssetsByMajorClassAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Intangible Asset, Finite-Lived, Class [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeLeaseDescriptionTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Lease, Description [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentFiscalPeriodFocus_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Document Fiscal Period Focus</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentFiscalPeriodFocus_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Fiscal Period Focus</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidExpenseAndOtherAssetsCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Prepaid Expense and Other Assets, Current [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfPropertyPlantAndEquipmentTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule Of Property Plant And Equipment [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfPropertyPlantAndEquipmentTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant, and Equipment [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_TerminationFee_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Termination fee</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_TerminationFee_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Termination Fee</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_TerminationFee_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Termination fee.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsidiarySaleOfStockAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Sale of Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SubsidiarySaleOfStockAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sale of Stock [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Period Increase (Decrease), Including Exchange Rate Effect and Discontinued Operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalentsPeriodIncreaseDecreaseIncludingExchangeRateEffect_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net decrease in cash and cash equivalents</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCurrentReportingStatus_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Current Reporting Status</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCurrentReportingStatus_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Current Reporting Status</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel1Member_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Quoted Prices in Active Markets for Identical Assets (Level 1)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel1Member_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Inputs, Level 1 [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounts Payable, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Accounts Payable, Current, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsPayableCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accounts payable</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Antidilutive Securities Excluded from Computation of Earnings Per Share [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule of Antidilutive Securities Excluded in Calculation of Diluted Net Loss Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FinancialInstrumentAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Financial Instrument [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestIncomeOperating_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestIncomeOperating_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Interest Income, Operating</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InterestIncomeOperating_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Interest Income, Operating, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentTransitionReport_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Transition Report</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentTransitionReport_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Document Transition Report</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionAccumulatedLoss_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedTotalLabel">Unrealized Losses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionAccumulatedLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Unrealized Losses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionAccumulatedLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale, Unrealized Loss Position, Accumulated Loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommitmentsAndContingenciesDisclosureAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Commitments and Contingencies Disclosure [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ExtinguishmentOfDebtAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Extinguishment of Debt</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ExtinguishmentOfDebtAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Extinguishment of Debt [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TypeOfAdoptionMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounting Standards Update [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfUnrealizedLossOnInvestmentsTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Available-for-Sale Investments in an Unrealized Loss Position</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfUnrealizedLossOnInvestmentsTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule of Unrealized Loss on Investments [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current liabilities:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities, Current [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisclosureOfCompensationRelatedCostsSharebasedPaymentsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdjustmentsForNewAccountingPronouncementsAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounting Standards Update [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_RangeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Statistical Measurement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_RangeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statistical Measurement [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidExpenseCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Prepaid expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidExpenseCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Prepaid Expense, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PrepaidExpenseCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Prepaid Expense, Current, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule Of Available For Sale Securities [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfAvailableForSaleSecuritiesLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity, Attributable to Parent [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stockholders' equity:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted-average shares of common stock outstanding, basic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Weighted Average Number of Shares Outstanding, Basic</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_WeightedAverageNumberOfSharesOutstandingBasic_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Weighted Average Number of Shares Outstanding, Basic, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant, and Equipment [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCentralIndexKey_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Central Index Key</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCentralIndexKey_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Central Index Key</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_DisclosureOfLicenseAgreementsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">License Agreements</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_DisclosureOfLicenseAgreementsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Disclosure Of License Agreements [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_DisclosureOfLicenseAgreementsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Disclosure of license agreements.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareByAntidilutiveSecuritiesAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Antidilutive Securities [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ConsolidationItemsAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Consolidation Items [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CurrentFiscalYearEndDate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current Fiscal Year End Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CurrentFiscalYearEndDate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Current Fiscal Year End Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentQuarterlyReport_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Document Quarterly Report</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentQuarterlyReport_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Quarterly Report</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_AreaOfOffice_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Area of office space</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_AreaOfOffice_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Area Of Office</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_AreaOfOffice_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Area of office.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt Securities Available For Sale [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashAndCashEquivalentsAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash and Cash Equivalents</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel2Member_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Significant Other Observable Inputs (Level 2)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueInputsLevel2Member_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Inputs, Level 2 [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Weighted-Average Exercise Price, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Weighted Average Exercise Price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Weighted Average Exercise Price, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net cash used in operating activities</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityIncorporationStateCountryCode_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Incorporation, State or Country Code</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityIncorporationStateCountryCode_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Incorporation, State or Country Code</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_LicenseFees_lbl" xlink:role="http://www.xbrl.org/2003/role/label">License fees</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_LicenseFees_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">License fees</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseWeightedAverageDiscountRatePercent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Weighted average operating lease right-of-use asset discount rate</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_ResearchConsultingAgreementsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Research consulting agreements.</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash flows from investing activities</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementsByShareBasedPaymentAwardOptionsExercisesInPeriodWeightedAverageExercisePrice_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangements by Share-Based Payment Award, Options, Exercises in Period, Weighted Average Exercise Price</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12MonthsAccumulatedLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Unrealized Losses, Less than 12 Months</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12MonthsAccumulatedLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale, Continuous Unrealized Loss Position, Less than 12 Months, Accumulated Loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Prepaid expense and other assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Increase (Decrease) in Prepaid Expense and Other Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_IncreaseDecreaseInPrepaidDeferredExpenseAndOtherAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Increase (Decrease) in Prepaid Expense and Other Assets, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueDisclosuresTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value Measurements</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueDisclosuresTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value Disclosures [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodNetOfTax_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Unrealized loss on investments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Unrealized gain on investments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Unrealized loss on available-for-sale securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeUnrealizedHoldingGainLossOnSecuritiesArisingDuringPeriodNetOfTax_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Unrealized loss on investments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Antidilutive securities excluded from calculation of diluted net loss per share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareAmount_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Antidilutive Securities Excluded from Computation of Earnings Per Share, Amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_CounterpartyNameAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Counterparty Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_CounterpartyNameAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Counterparty Name [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NumberOfOperatingSegments_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Number of Operating Segments</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtSecuritiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt securities, Estimated Fair Value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtSecuritiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleSecuritiesDebtSecuritiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Debt Securities, Available-for-sale, Current, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">AOCI Attributable to Parent [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccumulatedOtherComprehensiveIncomeMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accumulated Other Comprehensive Income (Loss)</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Number of Shares Available for Grant</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardNumberOfSharesAvailableForGrant_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Common stock remained available for issuance</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_UpfrontPaymentUponExecutionOfAgreement_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Upfront Payment Upon Execution Of Agreement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_UpfrontPaymentUponExecutionOfAgreement_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Upfront payment upon execution of agreement.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_NumberOfStockOptionsGrantedToEachTypeOfIncentivePlansToPurchaseCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Option to purchase</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_NumberOfStockOptionsGrantedToEachTypeOfIncentivePlansToPurchaseCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Number of Stock Options Granted to Each Type of Incentive Plans to Purchase Common Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_NumberOfStockOptionsGrantedToEachTypeOfIncentivePlansToPurchaseCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Number of stock options granted to each type of incentive plans to purchase common stock</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossNetOfTaxPeriodIncreaseDecreaseAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Comprehensive Income (Loss), Net of Tax [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherComprehensiveIncomeLossNetOfTaxPeriodIncreaseDecreaseAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other comprehensive loss:</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccruedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Outstanding, Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Number of Options and Awards Outstanding, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsOutstandingNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Number of Options and Awards Outstanding, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTax_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Debt securities, Unrealized Losses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AvailableForSaleDebtSecuritiesAccumulatedGrossUnrealizedLossBeforeTax_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale, Accumulated Gross Unrealized Loss, before Tax</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentType_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Document Type</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentType_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Type</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInOperatingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash flows from operating activities</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesAndStockholdersEquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities and Equity [Abstract]</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeLeaseDescriptionLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Lease, Description [Line Items]</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_LicenseAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">License agreement.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingIncomeLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Income (Loss)</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EquipmentMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Laboratory Equipment</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementOfIncomeLocationBalanceAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Location, Statement of Income, Balance [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accumulated Deficit</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RetainedEarningsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Retained Earnings [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Investment Securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentsInDebtAndMarketableEquitySecuritiesAndCertainTradingAssetsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Investment in Debt and Equity Securities and Other Trading Assets [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_NoncashGeneralAndAdministrativeExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Noncash General And Administrative Expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_NoncashGeneralAndAdministrativeExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Noncash general and administrative expenses.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_NoncashGeneralAndAdministrativeExpenses_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Noncash general and administrative expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_AugustTwentyThreeStockOptionsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">August 2023 Stock Options</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_AugustTwentyThreeStockOptionsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">August Twenty Three Stock Options [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_AugustTwentyThreeStockOptionsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">August Twenty Three Stock Options [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityRegistrantName_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Registrant Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityRegistrantName_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Registrant Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountingPoliciesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounting Policies [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Depreciation_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Depreciation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Depreciation_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Depreciation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Depreciation_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Depreciation, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProfitLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Net loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProfitLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Net Income (Loss), Including Portion Attributable to Noncontrolling Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProfitLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net Income (Loss), Including Portion Attributable to Noncontrolling Interest, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardPlanModificationDescriptionAndTerms_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock issuance, description and terms</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardPlanModificationDescriptionAndTerms_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Plan Modification, Description and Terms</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ShareBasedCompensationArrangementByShareBasedPaymentAwardPlanModificationDescriptionAndTerms_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Common stock issuance, description and terms</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SellingGeneralAndAdministrativeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Selling, General and Administrative Expense, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SellingGeneralAndAdministrativeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Selling, General and Administrative Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SellingGeneralAndAdministrativeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">General and administrative expenses related party amount</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressAddressLine1_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Address, Address Line One</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressAddressLine1_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address, Address Line One</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_StockholdersDeficitLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stockholders Deficit [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_StockholdersDeficitLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Stockholders deficit.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Compensation Arrangement by Share-Based Payment Award, Options, Exercises in Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of Options Outstanding, Exercised</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Exercises of stock options, Shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesStockOptionsExercised_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Number of Options and Awards Outstanding, Exercised</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_AggregateOfferingPriceFromEquityFinancing_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Aggregate offering price</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_AggregateOfferingPriceFromEquityFinancing_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Aggregate Offering Price From Equity Financing</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_AggregateOfferingPriceFromEquityFinancing_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Aggregate offering price from equity financing.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_ScheduleOfLicenseAgreementLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Schedule Of License Agreement [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_ScheduleOfLicenseAgreementLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Schedule Of License Agreement [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_ScheduleOfLicenseAgreementLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Schedule of license agreement.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total current assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FurnitureAndFixturesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Furniture and Fixtures [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FurnitureAndFixturesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Furniture and Fixtures</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value Assets And Liabilities Measured On Recurring And Nonrecurring Basis [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Recurring and Nonrecurring [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_DebtSecuritiesAvailableForSaleUnrealizedLossPositionFairValueAndAccumulatedLossTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Available-for-Sale Investments in an Unrealized Loss Position</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_DebtSecuritiesAvailableForSaleUnrealizedLossPositionFairValueAndAccumulatedLossTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities Available-for-Sale Unrealized Loss Position Fair Value and Accumulated Loss [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_DebtSecuritiesAvailableForSaleUnrealizedLossPositionFairValueAndAccumulatedLossTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Debt securities available-for-sale unrealized loss position fair value and accumulated loss.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SupplementalCashFlowInformationAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Supplemental disclosures</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SupplementalCashFlowInformationAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Supplemental Cash Flow Information [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyTransactionsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Related Party Transactions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyTransactionsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Related Party Transactions Disclosure [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntitySmallBusiness_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Small Business</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntitySmallBusiness_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Small Business</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_DeferredFinancingCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Financing Costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_DeferredFinancingCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Deferred financing costs.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_DeferredFinancingCosts_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Deferred financing costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromSaleAndMaturityOfAvailableForSaleSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Proceeds from maturities of investment securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromSaleAndMaturityOfAvailableForSaleSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds from Sale and Maturity of Debt Securities, Available-for-Sale</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromSaleAndMaturityOfAvailableForSaleSecurities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Proceeds from Sale and Maturity of Debt Securities, Available-for-sale, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_ConsolidationItemsDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Consolidation Items [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ChangeInAccountingPrincipleAccountingStandardsUpdateAdoptionDate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Change in Accounting Principle, Accounting Standards Update, Adoption Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAssets_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Other Assets, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeRelatedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued personnel costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeRelatedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Employee-related Liabilities, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EmployeeRelatedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Employee-related Liabilities, Current, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Antidilutive Securities Excluded from Computation of Earnings Per Share [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EarningsPerShareAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Earnings Per Share [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfShareBasedCompensationStockOptionsActivityTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Option, Activity [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfShareBasedCompensationStockOptionsActivityTableTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Stock Option Activity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_NumberOfDomesticCertificatesOfDepositHeld_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Number Of Domestic Certificates Of Deposit Held</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_NumberOfDomesticCertificatesOfDepositHeld_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Number of domestic certificates of deposit held.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_NumberOfDomesticCertificatesOfDepositHeld_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of domestic certificate of deposits held</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PlanNameAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Plan Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PlanNameAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Plan Name [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EquityAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityNoteDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stockholders' Equity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityNoteDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockholdersEquityNoteDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Stockholders' Equity</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_MilestonePayment_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Milestone payment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_MilestonePayment_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Milestone payment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_LesseeOperatingLeaseTermOfExpirationMonthAndYear_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee Operating Lease Term Of Expiration Month And Year</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_LesseeOperatingLeaseTermOfExpirationMonthAndYear_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Lessee operating lease term of expiration month and year.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_LesseeOperatingLeaseTermOfExpirationMonthAndYear_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Lease term, expiration month and year</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Cash flows from financing activities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInFinancingActivitiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Provided by (Used in) Financing Activity, Including Discontinued Operation [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccruedLiabilitiesCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accrued Liabilities, Current [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityTaxIdentificationNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Tax Identification Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityTaxIdentificationNumber_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Tax Identification Number</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_TwoThousandTwentyOneEquityIncentiveAwardPlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2021 Equity Incentive Award Plan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_TwoThousandTwentyOneEquityIncentiveAwardPlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Two Thousand Twenty One Equity Incentive Award Plan [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_TwoThousandTwentyOneEquityIncentiveAwardPlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Two thousand twenty one equity incentive award plan.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_TwoThousandTwentyOneEquityIncentiveAwardPlanMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">2021 Equity Incentive Award Plan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EquityComponentDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Equity Component</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_EquityComponentDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Equity Component [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressCityOrTown_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Address, City or Town</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressCityOrTown_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address, City or Town</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_WithinOneYearMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Within 1 Year</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_WithinOneYearMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Within One Year [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_WithinOneYearMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Within 1 year.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CapitalExpendituresIncurredButNotYetPaid_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Capital Expenditures Incurred but Not yet Paid</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CapitalExpendituresIncurredButNotYetPaid_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Purchases of property and equipment included in accounts payable and accrued expenses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueNewIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Issuance of common stock in at-the-market offering, net of issuance costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueNewIssues_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period, Value, New Issues</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentsFairValueDisclosure_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Investments, fair value disclosure</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentsFairValueDisclosure_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Investments, Fair Value Disclosure</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentsFairValueDisclosure_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Investments, Fair Value Disclosure, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Common Stock, Shares Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityCommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Common Stock, Shares Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ScheduleOfAntidilutiveSecuritiesExcludedFromComputationOfEarningsPerShareTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Antidilutive Security, Excluded EPS Calculation [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseOptionToExtend_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Lease term, option to extend period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseOptionToExtend_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Option to Extend</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementTable_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Statement [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AllocatedShareBasedCompensationExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement, Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AllocatedShareBasedCompensationExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock-based compensation expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityShellCompany_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Shell Company</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityShellCompany_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Shell Company</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsPayableAndOtherAccruedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accounts Payable and Other Accrued Liabilities, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccountsPayableAndOtherAccruedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued expenses and other current liabilities (including related party amounts of $890 as of December 31, 2025)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash Provided by (Used in) Investing Activity, Including Discontinued Operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NetCashProvidedByUsedInInvestingActivities_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Net cash provided by investing activities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Statement [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Fair Value Assets And Liabilities Measured On Recurring And Nonrecurring Basis [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueAssetsAndLiabilitiesMeasuredOnRecurringAndNonrecurringBasisLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_MaximumMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Maximum</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="srt_MaximumMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Maximum [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_MarlinspikeGroupLLCMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Marlinspike Group, LLC</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_MarlinspikeGroupLLCMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Marlinspike Group L L C [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_MarlinspikeGroupLLCMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Marlinspike Group, LLC.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SaleOfStockNameOfTransactionDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Sale of Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SaleOfStockNameOfTransactionDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Sale of Stock [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentIncomeInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Interest income</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentIncomeInterest_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Investment Income, Interest</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_PotentialMilestonePayments_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Potential milestone payments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_PotentialMilestonePayments_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Potential Milestone Payments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_PotentialMilestonePayments_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Potential milestone payments.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConstructionInProgressMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Construction in Progress</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ConstructionInProgressMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Construction in Progress [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_NoticePeriodDescription_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Termination period Description</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_NoticePeriodDescription_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Notice Period Description</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_NoticePeriodDescription_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Notice period description.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_InvestmentsDebtAndEquitySecuritiesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Investments, Debt and Equity Securities [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_DirectProgramExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Direct program expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_DirectProgramExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Direct Program Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_DirectProgramExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Direct program expense.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ExtinguishmentOfDebtTypeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Extinguishment of Debt, Type</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ExtinguishmentOfDebtTypeDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Extinguishment of Debt, Type [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_ComputerEquipmentAndSoftwareMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Computer Equipment and Software</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_ComputerEquipmentAndSoftwareMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Computer Equipment And Software [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_ComputerEquipmentAndSoftwareMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Computer equipment and software.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Current assets:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AssetsCurrentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Assets, Current [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_PersonnelExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Personnel Expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_PersonnelExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Personnel expense.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_PersonnelExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Personnel expense</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyTransactionDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Related Party Transaction</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyTransactionDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Related Party Transaction [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LeasesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Leases [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentFiscalYearFocus_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Document Fiscal Year Focus</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_DocumentFiscalYearFocus_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Document Fiscal Year Focus</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments_lbl" xlink:role="http://www.xbrl.org/2009/role/negatedLabel">Amortization of premiums on investment securities, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AccretionAmortizationOfDiscountsAndPremiumsInvestments_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accretion (Amortization) of Discounts and Premiums, Investments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_AccruedExpensesAndCurrentLiabilitiesLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accrued Expenses and Current Liabilities [Line Items]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_AccruedExpensesAndCurrentLiabilitiesLineItems_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Accrued expenses and current liabilities.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Common Stock, Shares, Outstanding, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Common Stock, Shares, Outstanding, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock, shares outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockSharesOutstanding_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Shares, Outstanding</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_UncuredPeriodOfAgreementInEventOfBreachOfAgreementNotice_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Uncured period of agreement in event of breach of agreement notice</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_UncuredPeriodOfAgreementInEventOfBreachOfAgreementNotice_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Uncured Period of Agreement in Event of Breach of Agreement Notice</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_UncuredPeriodOfAgreementInEventOfBreachOfAgreementNotice_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Uncured period of agreement in event of breach of agreement notice.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TransfersAndServicingOfFinancialInstrumentsTypesOfFinancialInstrumentsDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Financial Instruments [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StatementOfIncomeAndComprehensiveIncomeAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Statement of Comprehensive Income [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Related Party [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Related Party</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityExTransitionPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Ex Transition Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityExTransitionPeriod_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Ex Transition Period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ChangeInAccountingPrincipleAccountingStandardsUpdateAdopted_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Change in Accounting Principle, Accounting Standards Update, Adopted [true false]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Liability, Noncurrent</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityNoncurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating lease liability</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleAllowanceForCreditLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Debt securities, Allowance for Credit Losses</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleAllowanceForCreditLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale, Allowance for Credit Loss</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleAllowanceForCreditLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Debt Securities, Available-for-sale, Allowance for Credit Loss, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleAllowanceForCreditLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Debt Securities, Available-for-sale, Allowance for Credit Loss, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleAllowanceForCreditLoss_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Debt Securities, Available-for-sale, Allowance for Credit Loss, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee, Operating Lease, Liability, to be Paid</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total future minimum lease payments</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12Months_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Estimated Fair Market Value, Less than 12 Months</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleContinuousUnrealizedLossPositionLessThan12Months_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale, Continuous Unrealized Loss Position, Less than 12 Months</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAccruedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued other</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherAccruedLiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Accrued Liabilities, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapitalCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Additional paid-in capital</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapitalCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Additional Paid in Capital, Common Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapitalCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Additional Paid in Capital, Common Stock, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapitalCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Additional Paid in Capital, Common Stock, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_SecurityExchangeName_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Security Exchange Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_SecurityExchangeName_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Security Exchange Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Revenues_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Revenues</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_Revenues_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Revenues, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Related and Nonrelated Parties [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_RelatedPartyTransactionsByRelatedPartyAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Related and Nonrelated Parties [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">New Accounting Pronouncements, Policy [Policy Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_NewAccountingPronouncementsPolicyPolicyTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Issued Accounting Pronouncements Not Yet Adopted</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_LesseeOperatingLeaseCommencementDate_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Lessee Operating Lease Commencement Date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_LesseeOperatingLeaseCommencementDate_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Lessee operating lease commencement date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_LesseeOperatingLeaseCommencementDate_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Lease commencement date</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressStateOrProvince_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Address, State or Province</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityAddressStateOrProvince_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Address, State or Province</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseRightOfUseAsset_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Right-of-Use Asset</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseRightOfUseAsset_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Right-of-use asset</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_ConsultingAgreementsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Consulting Agreements</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_ConsultingAgreementsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Consulting Agreements [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_ConsultingAgreementsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Consulting agreements.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_AmendmentFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Amendment Flag</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_AmendmentFlag_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Amendment Flag</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Share-Based Payment Arrangement [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DisclosureOfCompensationRelatedCostsShareBasedPaymentsTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Stock-Based Compensation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherNonoperatingIncomeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Other Nonoperating Income (Expense)</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherNonoperatingIncomeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Other Nonoperating Income (Expense), Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OtherNonoperatingIncomeExpense_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Other income, net</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Cash and cash equivalents at beginning of period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Cash and cash equivalents at end of period</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cash, Cash Equivalent, Restricted Cash, and Restricted Cash Equivalent, Continuing Operation</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CashCashEquivalentsRestrictedCashAndRestrictedCashEquivalents_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Cash, Cash Equivalents, Restricted Cash and Restricted Cash Equivalents, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CityAreaCode_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">City Area Code</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CityAreaCode_lbl" xlink:role="http://www.xbrl.org/2003/role/label">City Area Code</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueEmployeeStockPurchasePlan_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period, Value, Employee Stock Purchase Plan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodValueEmployeeStockPurchasePlan_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Issuance of common stock under employee stock purchase plan</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueAssetsMeasuredOnRecurringBasisTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Company's Financial Instruments Measured at Fair Value on a Recurring Basis</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_FairValueAssetsMeasuredOnRecurringBasisTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Fair Value, Assets Measured on Recurring Basis [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingLeaseLiabilityCurrentStatementOfFinancialPositionExtensibleList_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Lease, Liability, Current, Statement of Financial Position [Extensible Enumeration]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OrganizationConsolidationAndPresentationOfFinancialStatementsAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Organization, Consolidation and Presentation of Financial Statements [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOfCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Proceeds from the issuance of common stock in at-the-market offering, net of issuance costs</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOfCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Proceeds from Issuance of Common Stock</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_ProceedsFromIssuanceOfCommonStock_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Aggregate net proceeds</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_GreaterThanOneYearMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Greater than 1 year</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_GreaterThanOneYearMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Greater Than One Year [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_GreaterThanOneYearMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Greater than one year.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_AccruedExpensesAndCurrentLiabilitiesTable_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Accrued Expenses and Current Liabilities [Table]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_AccruedExpensesAndCurrentLiabilitiesTable_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Accrued expenses and current liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionNumberOfPositions_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Debt Securities, Available-for-Sale, Unrealized Loss Position, Number of Positions</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DebtSecuritiesAvailableForSaleUnrealizedLossPositionNumberOfPositions_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Number of available-for-sale investment securities in continuous unrealized loss position</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingExpensesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Operating expenses:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingExpensesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Operating Expenses [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_OperatingExpensesAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Less:</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Common stock, par value</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_CommonStockParOrStatedValuePerShare_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Common Stock, Par or Stated Value Per Share</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Total current liabilities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LiabilitiesCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Liabilities, Current</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_USGovernmentCorporationsAndAgenciesSecuritiesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">US Government Corporations and Agencies Securities [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_USGovernmentCorporationsAndAgenciesSecuritiesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">U.S. Government agency securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LeaseholdImprovementsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Leasehold Improvements</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_LeaseholdImprovementsMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Leasehold Improvements [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentGross_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Property and equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentGross_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant, and Equipment, before Accumulated Depreciation, Depletion, and Amortization</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentGross_lbl" xlink:role="http://www.xbrl.org/2003/role/totalLabel">Property, Plant and Equipment, Gross, Total</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentGross_lbl" xlink:role="http://www.xbrl.org/2003/role/periodStartLabel">Property, Plant and Equipment, Gross, Beginning Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentGross_lbl" xlink:role="http://www.xbrl.org/2003/role/periodEndLabel">Property, Plant and Equipment, Gross, Ending Balance</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Segment Information</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_SegmentReportingDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Segment Reporting [Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TypeOfArrangementAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Collaborative Arrangement and Arrangement Other than Collaborative</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_TypeOfArrangementAxis_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Collaborative Arrangement and Arrangement Other than Collaborative [Axis]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_TradingSymbol_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Trading Symbol</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_TradingSymbol_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Trading Symbol</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Property and Equipment</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PropertyPlantAndEquipmentTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Property, Plant, and Equipment [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_BalanceSheetComponentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Balance Sheet Component [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_BalanceSheetComponentAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Balance sheet component.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityEmergingGrowthCompany_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Entity Emerging Growth Company</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_EntityEmergingGrowthCompany_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Entity Emerging Growth Company</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapitalMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Additional Paid-in Capital</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_AdditionalPaidInCapitalMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Additional Paid-in Capital [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredCostsCapitalizedPrepaidAndOtherAssetsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Summary of Prepaid Expenses and Other Current Assets</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_DeferredCostsCapitalizedPrepaidAndOtherAssetsDisclosureTextBlock_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Deferred Costs, Capitalized, Prepaid, and Other Assets Disclosure [Table Text Block]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PlanNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Plan Name</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_PlanNameDomain_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Plan Name [Domain]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_WrittenNoticePeriodToTerminatedAgreement_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Written Notice Period to Terminated Agreement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_WrittenNoticePeriodToTerminatedAgreement_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Written notice period to terminated agreement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_WrittenNoticePeriodToTerminatedAgreement_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Written Notice period to terminated agreement.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_AtTheMarketSalesAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">ATM Program</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_AtTheMarketSalesAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">At-the-market Sales Agreement [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_AtTheMarketSalesAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">At-the-market sales agreement.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_TwoThousandTwentyConsultingAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">2020 Consulting Agreement</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_TwoThousandTwentyConsultingAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Two Thousand Twenty Consulting Agreement [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_TwoThousandTwentyConsultingAgreementMember_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">2020 Consulting Agreement.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesEmployeeStockPurchasePlans_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Issuance of common stock under employee stock purchase plan, Shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_StockIssuedDuringPeriodSharesEmployeeStockPurchasePlans_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period, Shares, Employee Stock Purchase Plans</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_USTreasurySecuritiesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">U.S. Treasury Securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_USTreasurySecuritiesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">U.S. Treasury securities</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="us-gaap_USTreasurySecuritiesMember_lbl" xlink:role="http://www.xbrl.org/2003/role/label">US Treasury Securities [Member]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_StockIssuedDuringPeriodSharesStockOptionsExercisedAndVestingOfEarlyExercisedCommonStockOptions_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Vesting of restricted stock, Shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_StockIssuedDuringPeriodSharesStockOptionsExercisedAndVestingOfEarlyExercisedCommonStockOptions_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Stock Issued During Period Shares Stock Options Exercised And Vesting Of Early Exercised Common Stock Options</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_StockIssuedDuringPeriodSharesStockOptionsExercisedAndVestingOfEarlyExercisedCommonStockOptions_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Stock issued during period shares stock options exercised and vesting of early exercised common stock options.</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_StockIssuedDuringPeriodSharesStockOptionsExercisedAndVestingOfEarlyExercisedCommonStockOptions_lbl" xlink:role="http://www.xbrl.org/2003/role/verboseLabel">Exercises of stock options and vesting of restricted stock, Shares</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dei_CoverAbstract_lbl" xlink:role="http://www.xbrl.org/2003/role/label">Cover [Abstract]</link:label>
          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_AccruedResearchAndDevelopmentExpenseCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/terseLabel">Accrued research and development costs</link:label>
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          <link:label xml:lang="en-US" xlink:type="resource" xlink:label="dsgn_AccruedResearchAndDevelopmentExpenseCurrent_lbl" xlink:role="http://www.xbrl.org/2003/role/documentation">Accrued research and development expense current.</link:label>
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          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="us-gaap_CostsAndExpenses" xlink:to="us-gaap_ResearchAndDevelopmentExpense" order="0" weight="1" use="optional"/>
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="us-gaap_CostsAndExpenses" xlink:to="us-gaap_GeneralAndAdministrativeExpense" order="1" weight="1" use="optional"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_CostsAndExpenses" xlink:label="us-gaap_CostsAndExpenses"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_ResearchAndDevelopmentExpense" xlink:label="us-gaap_ResearchAndDevelopmentExpense"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_GeneralAndAdministrativeExpense" xlink:label="us-gaap_GeneralAndAdministrativeExpense"/>
        </link:calculationLink>
        <link:calculationLink xlink:type="extended" xlink:role="http://www.designtx.com/20260630/taxonomy/role/DisclosureLeasesSummaryOfMaturitiesOfOperatingLeaseLiabilitiesDetails">
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear" order="0" weight="1" use="optional"/>
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" order="1" weight="1" use="optional"/>
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" order="2" weight="1" use="optional"/>
          <link:calculationArc xlink:type="arc" xlink:arcrole="https://xbrl.org/2023/arcrole/summation-item" xlink:from="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:to="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" order="3" weight="1" use="optional"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDue"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsRemainderOfFiscalYear"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueNextTwelveMonths"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearTwo"/>
          <link:loc xlink:type="locator" xlink:href="https://xbrl.fasb.org/us-gaap/2026/elts/us-gaap-2026.xsd#us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree" xlink:label="us-gaap_LesseeOperatingLeaseLiabilityPaymentsDueYearThree"/>
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  <xsd:element id="dsgn_StockIssuedDuringPeriodValueStockOptionsExercisedAndVestingOfEarlyExercisedCommonStockOptions" name="StockIssuedDuringPeriodValueStockOptionsExercisedAndVestingOfEarlyExercisedCommonStockOptions" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="dsgn_NumberOfDomesticCertificatesOfDepositHeld" name="NumberOfDomesticCertificatesOfDepositHeld" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="dsgn_ExpectedRoyaltyPaymentsUponFirstCommercialProductSale" name="ExpectedRoyaltyPaymentsUponFirstCommercialProductSale" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="dsgn_AggregateOfferingPriceFromEquityFinancing" name="AggregateOfferingPriceFromEquityFinancing" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="dsgn_StockIssuedDuringPeriodSharesStockOptionsExercisedAndVestingOfEarlyExercisedCommonStockOptions" name="StockIssuedDuringPeriodSharesStockOptionsExercisedAndVestingOfEarlyExercisedCommonStockOptions" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="dsgn_TwoThousandTwentyOneEquityIncentiveAwardPlanMember" name="TwoThousandTwentyOneEquityIncentiveAwardPlanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="dsgn_GreaterThanOneYearMember" name="GreaterThanOneYearMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="dsgn_ResearchConsultingAgreementsMember" name="ResearchConsultingAgreementsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="dsgn_AccruedResearchAndDevelopmentExpenseCurrent" name="AccruedResearchAndDevelopmentExpenseCurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="dsgn_AccruedExpensesAndCurrentLiabilitiesTable" name="AccruedExpensesAndCurrentLiabilitiesTable" type="xbrli:stringItemType" substitutionGroup="xbrldt:hypercubeItem" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="dsgn_MilestonePayment" name="MilestonePayment" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="dsgn_AreaOfOffice" name="AreaOfOffice" type="dtr-types:areaItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="dsgn_UpfrontPaymentUponExecutionOfAgreement" name="UpfrontPaymentUponExecutionOfAgreement" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="dsgn_ComputerEquipmentAndSoftwareMember" name="ComputerEquipmentAndSoftwareMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="dsgn_WithinOneYearMember" name="WithinOneYearMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="dsgn_AugustTwentyThreeStockOptionsMember" name="AugustTwentyThreeStockOptionsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="dsgn_LesseeOperatingLeaseCommencementDate" name="LesseeOperatingLeaseCommencementDate" type="xbrli:dateItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="dsgn_AggregateOfferingPriceFromDebtAndEquityFinancing" name="AggregateOfferingPriceFromDebtAndEquityFinancing" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="dsgn_ConsultingAgreementsMember" name="ConsultingAgreementsMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="dsgn_StockOptionTwoMember" name="StockOptionTwoMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="dsgn_AccruedExpensesAndOtherCurrentLiabilitiesRelatedPartiesCurrent" name="AccruedExpensesAndOtherCurrentLiabilitiesRelatedPartiesCurrent" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="dsgn_DebtSecuritiesAvailableForSaleMaturity" name="DebtSecuritiesAvailableForSaleMaturity" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="dsgn_PotentialMilestonePayments" name="PotentialMilestonePayments" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="dsgn_NoticePeriodDescription" name="NoticePeriodDescription" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="dsgn_LicenseAgreementMember" name="LicenseAgreementMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="dsgn_TwoThousandTwentyOneEmployeeStockPurchasePlanMember" name="TwoThousandTwentyOneEmployeeStockPurchasePlanMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="dsgn_LicenseAgreementAbstract" name="LicenseAgreementAbstract" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="dsgn_NumberOfStockOptionsGrantedToEachTypeOfIncentivePlansToPurchaseCommonStock" name="NumberOfStockOptionsGrantedToEachTypeOfIncentivePlansToPurchaseCommonStock" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="dsgn_IssueOfCommonStockThroughEmployeeStockPurchasePlan" name="IssueOfCommonStockThroughEmployeeStockPurchasePlan" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="dsgn_StockholdersDeficitTable" name="StockholdersDeficitTable" type="xbrli:stringItemType" substitutionGroup="xbrldt:hypercubeItem" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="dsgn_PercentageOfAnnualIncreaseInLeasePayments" name="PercentageOfAnnualIncreaseInLeasePayments" type="dtr-types:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="dsgn_NoticePeriodForTerminationOfAgreement" name="NoticePeriodForTerminationOfAgreement" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="dsgn_NoncashGeneralAndAdministrativeExpenses" name="NoncashGeneralAndAdministrativeExpenses" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="dsgn_UncuredPeriodOfAgreementInEventOfBreachOfAgreementNotice" name="UncuredPeriodOfAgreementInEventOfBreachOfAgreementNotice" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="dsgn_BalanceSheetComponentAbstract" name="BalanceSheetComponentAbstract" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="dsgn_LesseeOperatingLeaseTermOfExpirationMonthAndYear" name="LesseeOperatingLeaseTermOfExpirationMonthAndYear" type="xbrli:gYearMonthItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="dsgn_IncreaseInRightOfUseAssetAndOperatingLeaseLiabilities" name="IncreaseInRightOfUseAssetAndOperatingLeaseLiabilities" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="dsgn_DirectProgramExpense" name="DirectProgramExpense" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="dsgn_TwoThousandTwentyConsultingAgreementMember" name="TwoThousandTwentyConsultingAgreementMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="dsgn_TerminationFee" name="TerminationFee" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="dsgn_ScheduleOfLicenseAgreementLineItems" name="ScheduleOfLicenseAgreementLineItems" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="dsgn_TypeOfStockOptionsGrantedToPurchaseCommonStock" name="TypeOfStockOptionsGrantedToPurchaseCommonStock" type="xbrli:integerItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="dsgn_AccruedExpensesAndCurrentLiabilitiesLineItems" name="AccruedExpensesAndCurrentLiabilitiesLineItems" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="dsgn_AreaOfLeasedProperty" name="AreaOfLeasedProperty" type="dtr-types:areaItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false"/>
  <xsd:element id="dsgn_MonthlyFeeForConsultancyServices" name="MonthlyFeeForConsultancyServices" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="dsgn_BasisOfPresentationAndUseOfEstimatesPolicyTextBlock" name="BasisOfPresentationAndUseOfEstimatesPolicyTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="dsgn_PersonnelExpense" name="PersonnelExpense" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="dsgn_DebtSecuritiesAvailableForSaleUnrealizedLossPositionFairValueAndAccumulatedLossTableTextBlock" name="DebtSecuritiesAvailableForSaleUnrealizedLossPositionFairValueAndAccumulatedLossTableTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="dsgn_AccruedInterestReceivableOnAvailableForSaleInvestmentSecurities" name="AccruedInterestReceivableOnAvailableForSaleInvestmentSecurities" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="dsgn_LesseeOperatingLeaseTermOfExpirationYear" name="LesseeOperatingLeaseTermOfExpirationYear" type="xbrli:gYearItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="dsgn_LicenseFees" name="LicenseFees" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="dsgn_WrittenNoticePeriodToTerminatedLicenseAgreementInEventOfBreachOfAgreement" name="WrittenNoticePeriodToTerminatedLicenseAgreementInEventOfBreachOfAgreement" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="dsgn_AtTheMarketSalesAgreementMember" name="AtTheMarketSalesAgreementMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="dsgn_ExpectedMilestonePaymentOnAchievingCertainRegulatoryAndCommercialMilestones" name="ExpectedMilestonePaymentOnAchievingCertainRegulatoryAndCommercialMilestones" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="dsgn_ScheduleOfLicenseAgreementTable" name="ScheduleOfLicenseAgreementTable" type="xbrli:stringItemType" substitutionGroup="xbrldt:hypercubeItem" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="dsgn_StockOptionOneMember" name="StockOptionOneMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="dsgn_StockholdersDeficitLineItems" name="StockholdersDeficitLineItems" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="dsgn_WrittenNoticePeriodToTerminatedAgreement" name="WrittenNoticePeriodToTerminatedAgreement" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="dsgn_DisclosureOfLicenseAgreementsTextBlock" name="DisclosureOfLicenseAgreementsTextBlock" type="dtr-types:textBlockItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false"/>
  <xsd:element id="dsgn_CrossingHoldingsLLCMember" name="CrossingHoldingsLLCMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="dsgn_NonCashLeaseExpenseIncome" name="NonCashLeaseExpenseIncome" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit"/>
  <xsd:element id="dsgn_IncreaseInRight-Of-Use-AssetAndOperatingLeaseLiabilityRelatedToLeaseAmendment" name="IncreaseInRight-Of-Use-AssetAndOperatingLeaseLiabilityRelatedToLeaseAmendment" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="credit"/>
  <xsd:element id="dsgn_InvestigationNewDrugMember" name="InvestigationNewDrugMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
  <xsd:element id="dsgn_MarlinspikeGroupLLCMember" name="MarlinspikeGroupLLCMember" type="dtr-types:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true"/>
</xsd:schema>
