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<!-- Creation Date      : 2020-10-20T06:15:19.8189819+00:00 -->
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<!-- Copyright (c) 2020 Donnelley Financial Solutions, Inc. All Rights Reserved. -->
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  <xsd:element id="pstv_PreferredStockAbstract" name="PreferredStockAbstract" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="pstv_SeriesAConvertiblePreferredStockMember" name="SeriesAConvertiblePreferredStockMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="pstv_TwoThousandEighteenRightsOfferingMember" name="TwoThousandEighteenRightsOfferingMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="pstv_NumberOfPreferredStockSharesExercised" name="NumberOfPreferredStockSharesExercised" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="pstv_ConversionPricePerShare" name="ConversionPricePerShare" type="num:perShareItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" />
  <xsd:element id="pstv_ChargeOnNonTransferableSubscriptionRights" name="ChargeOnNonTransferableSubscriptionRights" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit" />
  <xsd:element id="pstv_GrossProceedsFromIssuanceOfPrivatePlacement" name="GrossProceedsFromIssuanceOfPrivatePlacement" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" xbrli:balance="debit" />
  <xsd:element id="pstv_CommonStockAndSeriesBConvertiblePreferredStockMember" name="CommonStockAndSeriesBConvertiblePreferredStockMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="pstv_SeriesTWarrantsMember" name="SeriesTWarrantsMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="pstv_RepresentativeSeriesUWarrantMember" name="RepresentativeSeriesUWarrantMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="pstv_NumberOfWarrantsExercised" name="NumberOfWarrantsExercised" type="xbrli:sharesItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="pstv_PeriodExercisableFromTheDateOfIssuance" name="PeriodExercisableFromTheDateOfIssuance" type="xbrli:durationItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="pstv_CommonStockSalesAvailableForIssuance" name="CommonStockSalesAvailableForIssuance" type="xbrli:monetaryItemType" substitutionGroup="xbrli:item" xbrli:periodType="instant" nillable="true" abstract="false" xbrli:balance="credit" />
  <xsd:element id="pstv_PurchaseAgreementMember" name="PurchaseAgreementMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="pstv_LincolnParkCapitalFundLLCMember" name="LincolnParkCapitalFundLLCMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="pstv_TwentyTwentyRepurchaseAgreementMember" name="TwentyTwentyRepurchaseAgreementMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="pstv_PercentageIssuanceOfCommonStock" name="PercentageIssuanceOfCommonStock" type="num:percentItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="false" />
  <xsd:element id="pstv_StockBasedCompensation2015EquityIncentivePlan1Member" name="StockBasedCompensation2015EquityIncentivePlan1Member" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="pstv_StockBasedCompensation2020EquityIncentivePlanMember" name="StockBasedCompensation2020EquityIncentivePlanMember" type="nonnum:domainItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
  <xsd:element id="pstv_ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsAggregateIntrinsicValueRollForward1" name="ShareBasedCompensationArrangementByShareBasedPaymentAwardOptionsAggregateIntrinsicValueRollForward1" type="xbrli:stringItemType" substitutionGroup="xbrli:item" xbrli:periodType="duration" nillable="true" abstract="true" />
</xsd:schema>
