Exhibit 4.1

    

     

    

    BIOCRYST PHARMACEUTICALS, INC.

    

    

    FORM OF PRE-FUNDED WARRANT TO PURCHASE COMMON STOCK

    

    

    

    

    

    

     Number of Shares: [           ]

    (subject to adjustment)

    

    

    Warrant No. [   ]

    Original Issue Date: May [   ], 2020

    

    

    BioCryst Pharmaceuticals, Inc., a Delaware corporation (the “Company”),
      hereby certifies that, for good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, [Baker Brothers Life Sciences, L.P.][667, L.P.] or its permitted registered assigns (the “Holder”), is entitled, subject to the terms set forth below, to purchase from the Company up to a total of [                ] shares of common stock, $0.01 par value per
      share (the “Common Stock”), of the Company (each such share, a “Warrant Share” and all such shares, the “Warrant Shares”) at an exercise price per share equal to $0.01 per share
      (as adjusted from time to time as provided in Section 9 herein, the “Exercise Price”), upon surrender of this Warrant to Purchase Common Stock (including any Warrants to Purchase Common Stock issued in exchange, transfer or replacement hereof, the “Warrant”) at any time and from time to time on or after the date hereof (the “Original Issue Date”), subject to the
      following terms and conditions:

    

    

    1.  Definitions. For purposes of this Warrant, the following terms
      shall have the following meanings:

    

    

    (a) “Affiliate” means any Person directly or indirectly controlled by, controlling or under common control with, a Holder, but only for so
      long as such control shall continue. For purposes of this definition, “control” (including, with correlative meanings, “controlled by”, “controlling” and “under common control with”) means, with respect to a Person, possession, direct or indirect, of
      (a) the power to direct or cause direction of the management and policies of such Person (whether through ownership of securities or partnership or other ownership interests, by contract or otherwise), or (b) at least 50% of the voting securities
      (whether directly or pursuant to any option, warrant or other similar arrangement) or other comparable equity interests.

    

    

    (b) “Commission” means the United
      States Securities and Exchange Commission.

    

    

    (c) “Closing Sale Price” means, for
      any security as of any date, the last trade price for such security on the Principal Trading Market for such security, as reported by Bloomberg Financial Markets, or, if such Principal Trading Market begins to operate on an extended hours basis and
      does not designate the last trade price, then the last trade price of such security prior to 4:00 P.M., New York City time, as reported by Bloomberg Financial Markets, or if the foregoing do not apply, the last trade price of such security in the
      over-the-counter market on the electronic bulletin board for such security as reported by Bloomberg Financial Markets, or, if no last trade price is reported for such security by Bloomberg Financial Markets, the average of the bid and ask prices, of
      any market makers for such security as reported in the “pink sheets” by Pink Sheets LLC. If the Closing Sale Price cannot be calculated for a security on a particular date on any of the foregoing bases, the Closing Sale Price of such security on such
      date shall be the fair market value as mutually determined by the Company and the Holder. If the Company and the Holder are unable to agree upon the fair market value of such security, then the Board of Directors of the Company shall use its good
      faith judgment to determine the fair market value. The Board of Directors’ determination shall be binding upon all parties absent demonstrable error. All such determinations shall be appropriately adjusted for any stock dividend, stock split, stock
      combination or other similar transaction during the applicable calculation period.

    

    

    (d) “Principal Trading Market”
      means the national securities exchange or other trading market on which the Common Stock is primarily listed on and quoted for trading, which, as of the Original Issue Date, shall be the Nasdaq Global Select Market.

    

    

    (e) “Registration Statement” means
      the Company’s Registration Statement on Form S-3 (File No. 333-237820)), as amended, declared effective on May 14, 2020.

    

    

    
      
        


    

    (f) “Securities Act” means the
      Securities Act of 1933, as amended.

    

    

    (g) “Trading Day” means any weekday
      on which the Principal Trading Market is open for trading.

    

    

    (h) “Transfer Agent” means American
      Stock Transfer & Trust Company, LLC, the Company’s transfer agent and registrar for the Common Stock, and any successor appointed in such capacity.

    

    

    2.  Issuance of Securities; Registration of Warrants. The Warrant,
      as initially issued by the Company, is offered and sold pursuant to the Registration Statement. The Company shall register ownership of this Warrant, upon records to be maintained by the Company for that purpose (the “Warrant Register”), in the name of the record Holder (which shall include the initial Holder or, as the case may be, any assignee to which this Warrant is assigned hereunder)
      from time to time. The Company may deem and treat the registered Holder of this Warrant as the absolute owner hereof for the purpose of any exercise hereof or any distribution to the Holder, and for all other purposes, absent actual notice to the
      contrary.

    

    

    3.  Registration of Transfers. Subject to compliance with all
      applicable securities laws, the Company shall, or will cause its Transfer Agent to, register the transfer of all or any portion of this Warrant in the Warrant Register, upon surrender of this Warrant, and payment for all applicable transfer taxes (if
      any). Upon any such registration or transfer, a new warrant to purchase Common Stock in substantially the form of this Warrant (any such new warrant, a “New
        Warrant”) evidencing the portion of this Warrant so transferred shall be issued to the transferee, and a New Warrant evidencing the remaining portion of this Warrant not so transferred, if any, shall be issued to the transferring Holder. The
      acceptance of the New Warrant by the transferee thereof shall be deemed the acceptance by such transferee of all of the rights and obligations in respect of the New Warrant that the Holder has in respect of this Warrant. The Company shall, or will
      cause its Transfer Agent to, prepare, issue and deliver at the Company’s own expense any New Warrant under this Section 3. Until due presentment for
      registration of transfer, the Company may treat the registered Holder hereof as the owner and holder for all purposes, and the Company shall not be affected by any notice to the contrary.

    

    

    4.  Exercise and Duration of Warrants.

    

    

    (a) All or any part of this Warrant shall be exercisable by the registered Holder in any manner permitted by this Warrant at any time and
      from time to time on or after the Original Issue Date.

    

    

    (b) The Holder may exercise this Warrant by delivering (as determined in accordance with the notice provisions hereof) to the Company an
      exercise notice, in the form attached as Schedule 1 hereto (the “Exercise Notice”), completed and duly signed.  Within one (1) Trading Day following the date of delivery of the Exercise Notice, the Holder shall make payment of the Exercise Price for the number of Warrant Shares as to which this
      Warrant is being exercised (which may take the form of a “cashless exercise” if so indicated in the Exercise Notice pursuant to Section 10 below).  The date
      on which the Notice of Exercise is delivered to the Company (as determined in accordance with the notice provisions hereof) is an “Exercise Date”
      provided, that if the Exercise Price is not delivered on or before one (1) Trading Day following the date of delivery of the Exercise Notice, the Exercise Date shall be deemed to be one (1) Trading Day following the date of that the Exercise Price is
      delivered to the Company. No ink-original Notice of Exercise shall be required, nor shall any medallion guarantee (or other type of guarantee or notarization) of any Notice of Exercise be required.  The Holder shall not be required to deliver the
      original Warrant in order to effect an exercise hereunder. Execution and delivery of the Exercise Notice shall have the same effect as cancellation of the original Warrant and issuance of a New Warrant evidencing the right to purchase the remaining
      number of Warrant Shares, if any.  The aggregate exercise price of this Warrant, except for the Exercise Price, was pre-funded to the Company on or before the Original Issue Date, and consequently no additional consideration (other than the Exercise
      Price) shall be required by to be paid by the Holder to effect any exercise of this Warrant.  The Holder shall not be entitled to the return or refund of all, or any portion, of such pre-funded exercise price under any circumstance or for any reason
      whatsoever.

    

    

    
      
        


    

    5.  Delivery of Warrant Shares.

    

    

    (a) Upon exercise of this Warrant, the Company shall promptly (but in no event later than two (2) Trading Days after the Exercise Date),
      upon the request of the Holder, credit such aggregate number of shares of Common Stock to which the Holder is entitled pursuant to such exercise to the Holder’s or its designee’s balance account with The Depository Trust Company (“DTC”) through its Deposit / Withdrawal At Custodian system, or if the Transfer Agent is not participating in the Fast Automated Securities Transfer
      Program (the “FAST Program”) or if the certificates are required to bear a legend regarding restriction on transferability, issue and dispatch by
      overnight courier to the address as specified in the Exercise Notice, a certificate, registered in the Company’s share register in the name of the Holder or its designee, for the number of shares of Common Stock to which the Holder is entitled
      pursuant to such exercise. The Holder, or any natural person or legal entity (each, a “Person”) so designated by the Holder to receive Warrant Shares, shall be deemed to have become the holder of record of such Warrant Shares as of the time of
      delivery of the Exercise Notice on the Exercise Date, irrespective of the date such Warrant Shares are credited to the Holder’s DTC account or the date of delivery of the certificates evidencing such Warrant Shares, as the case may be.  While this
      Warrant remains outstanding, the Company shall maintain a transfer agent that participates in the FAST Program.

    

    

    (b) If by the close of the fifth (5th) Trading Day after the Exercise Date, the Company fails to deliver to the Holder a certificate
      representing the required number of Warrant Shares in the manner required pursuant to Section 5(a) or fails to credit the Holder’s balance account with DTC
      for such number of Warrant Shares to which the Holder is entitled, and if after such second (2nd) Trading Day and prior to the receipt of such Warrant Shares, the Holder purchases (in an open market transaction or otherwise) shares of Common Stock to
      deliver in satisfaction of a sale by the Holder of the Warrant Shares which the Holder anticipated receiving upon such exercise (a “Buy-In”), then
      the Company shall, within two (2) Trading Days after the Holder’s request and in the Holder’s sole and absolute discretion, either (1) pay in cash to the Holder an amount equal to the Holder’s total purchase price (including brokerage commissions, if
      any) for the shares of Common Stock so purchased, at which point the Company’s obligation to deliver such certificate (and to issue such Warrant Shares) shall terminate or (2) promptly honor its obligation to deliver to the Holder a certificate or
      certificates representing such Warrant Shares and pay cash to the Holder in an amount equal to the excess (if any) of Holder’s total purchase price (including brokerage commissions, if any) for the shares of Common Stock so purchased in the Buy-In
      over the product of (A) the number of shares of Common Stock purchased in the Buy-In, times (B) the Closing Sale Price of a share of Common Stock on the Exercise Date.

    

    

    (c) To the extent permitted by law and subject to Section
          5(b), the Company’s obligations to issue and deliver Warrant Shares in accordance with and subject to the terms hereof (including the limitations set forth in Section 11 below) are absolute and unconditional, irrespective of any action or inaction by the Holder to enforce the same, any waiver or consent with respect to any provision hereof, the recovery of any judgment against any
      Person or any action to enforce the same, or any setoff, counterclaim, recoupment, limitation or termination, or any breach or alleged breach by the Holder or any other Person of any obligation to the Company or any violation or alleged violation of
      law by the Holder or any other Person, and irrespective of any other circumstance that might otherwise limit such obligation of the Company to the Holder in connection with the issuance of Warrant Shares. Subject to Section 5(b), nothing herein shall limit the Holder’s right to pursue any other remedies available to it hereunder, at law or in equity including, without limitation, a decree of specific
      performance and/or injunctive relief with respect to the Company’s failure to timely deliver certificates representing shares of Common Stock upon exercise of the Warrant as required pursuant to the terms hereof.

    

    

    6.  Charges, Taxes and Expenses. Issuance and delivery of
      certificates for shares of Common Stock upon exercise of this Warrant shall be made without charge to the Holder for any issue or transfer tax, transfer agent fee or other incidental tax or expense (excluding any applicable stamp duties) in respect
      of the issuance of such certificates, all of which taxes and expenses shall be paid by the Company; provided, however, that the Company shall not
      be required to pay any tax that may be payable in respect of any transfer involved in the registration of any certificates for Warrant Shares or the Warrants in a name other than that of the Holder or an Affiliate thereof. The Holder shall be
      responsible for all other tax liability that may arise as a result of holding or transferring this Warrant or receiving Warrant Shares upon exercise hereof.

    

    

    7.  Replacement of Warrant. If this Warrant is mutilated, lost,
      stolen or destroyed, the Company shall issue or cause to be issued in exchange and substitution for and upon cancellation hereof, or in lieu of and substitution for this Warrant, a New Warrant, but only upon receipt of evidence reasonably
      satisfactory to the Company of such loss, theft or destruction (in such case) and, in each case, a customary and reasonable indemnity (but not the posting of any surety or other bond), if requested by the Company. Applicants for a New Warrant under
      such circumstances shall also comply with such other reasonable regulations and procedures and pay such other reasonable third party costs as the Company may prescribe.  If a New Warrant is requested as a result of a mutilation of this Warrant, then
      the Holder shall deliver such mutilated Warrant to the Company as a condition precedent to the Company’s obligation to issue the New Warrant.

    

    

    
      
        


    

    8.  Reservation of Warrant Shares. The Company covenants that it
      will, at all times while this Warrant is outstanding, reserve and keep available out of the aggregate of its authorized but unissued and otherwise unreserved Common Stock, solely for the purpose of enabling it to issue Warrant Shares upon exercise of
      this Warrant as herein provided, the number of Warrant Shares that are initially issuable and deliverable upon the exercise of this entire Warrant, free from preemptive rights or any other contingent purchase rights of persons other than the Holder
      (taking into account the adjustments and restrictions of Section 9). The Company covenants that all Warrant Shares so issuable and deliverable shall, upon
      issuance and the payment of the applicable Exercise Price in accordance with the terms hereof, be duly and validly authorized, issued and fully paid and non-assessable. The Company will take all such action as may be reasonably necessary to assure
      that such shares of Common Stock may be issued as provided herein without violation of any applicable law or regulation, or of any requirements of any securities exchange or automated quotation system upon which the Common Stock may be listed.  The
      Company further covenants that it will not, without the prior written consent of the Holder, take any actions to increase the par value of the Common Stock at any time while this Warrant is outstanding.

    

    

    9.  Certain Adjustments. The Exercise Price and number of Warrant
      Shares issuable upon exercise of this Warrant are subject to adjustment from time to time as set forth in this Section 9.

    

    

    (a) Stock Dividends and Splits. If the Company,
      at any time while this Warrant is outstanding, (i) pays a stock dividend on its Common Stock or otherwise makes a distribution on any class of capital stock issued and outstanding on the Original Issue Date and in accordance with the terms of such
      stock on the Original Issue Date or as amended, as described in the Registration Statement, that is payable in shares of Common Stock, (ii) subdivides its outstanding shares of Common Stock into a larger number of shares of Common Stock, (iii)
      combines its outstanding shares of Common Stock into a smaller number of shares of Common Stock or (iv) issues by reclassification of shares of capital stock any additional shares of Common Stock of the Company, then in each such case the Exercise
      Price shall be multiplied by a fraction, the numerator of which shall be the number of shares of Common Stock outstanding immediately before such event and the denominator of which shall be the number of shares of Common Stock outstanding immediately
      after such event. Any adjustment made pursuant to clause (i) of this paragraph shall become effective immediately after the record date for the determination of stockholders entitled to receive such dividend or distribution, provided, however, that
      if such record date shall have been fixed and such dividend is not fully paid on the date fixed therefor, the Exercise Price shall be recomputed accordingly as of the close of business on such record date and thereafter the Exercise Price shall be
      adjusted pursuant to this paragraph as of the time of actual payment of such dividends. Any adjustment pursuant to clause (ii) or (iii) of this paragraph shall become effective immediately after the effective date of such subdivision or combination.

    

    

    (b) Pro Rata Distributions. If the Company, at
      any time while this Warrant is outstanding, distributes to all holders of Common Stock for no consideration (i) evidences of its indebtedness, (ii) any security (other than a distribution of Common Stock covered by the preceding paragraph) or (iii)
      rights or warrants to subscribe for or purchase any security, or (iv) cash or any other asset (in each case, “Distributed Property”), then, upon
      any exercise of this Warrant that occurs after the record date fixed for determination of stockholders entitled to receive such distribution, the Holder shall be entitled to receive, in addition to the Warrant Shares otherwise issuable upon such
      exercise (if applicable), the Distributed Property that such Holder would have been entitled to receive in respect of such number of Warrant Shares had the Holder been the record holder of such Warrant Shares immediately prior to such record date
      without regard to any limitation on exercise contained therein. The Company covenants that it will, at all times while this Warrant is outstanding, reserve and keep available all Distributed Property that the Holder shall be entitled to receive
      hereunder, solely for the purpose of fulfilling its obligations pursuant to this Section 9(b).

    

    

    (c) Fundamental Transactions. If, at any time
      while this Warrant is outstanding (i) the Company effects any merger or consolidation of the Company with or into another Person, in which the Company is not the surviving entity and in which the stockholders of the Company immediately prior to such
      merger or consolidation do not own, directly or indirectly, at least 50% of the voting power of the surviving entity immediately after such merger or consolidation, (ii) the Company effects any sale to another Person of all or substantially all of
      its assets in one transaction or a series of related transactions, (iii) pursuant to any tender offer or exchange offer (whether by the Company or another Person), holders of capital stock tender shares representing more than 50% of the voting power
      of the capital stock of the Company and the Company or such other Person, as applicable, accepts such tender for payment, (iv) the Company consummates a stock purchase agreement or other business combination (including, without limitation, a
      reorganization, recapitalization, spin-off or scheme of arrangement) with another Person whereby such other Person acquires more than the 50% of the voting power of the capital stock of the Company (except for any such transaction in which the
      stockholders of the Company immediately prior to such transaction maintain, in substantially the same proportions, the voting power of such Person immediately after the transaction) or (v) the Company effects any reclassification of the Common Stock
      or any compulsory share exchange pursuant to which the Common Stock is effectively converted into or exchanged for other securities, cash or property (other than as a result of a subdivision or combination of shares of Common Stock covered by Section 9(a) above) (in any such case, a “Fundamental Transaction”),
      then following such Fundamental Transaction the Holder shall have the right to receive, upon exercise of this Warrant, the same amount and kind of securities, cash or property as it would have been entitled to receive upon the occurrence of such
      Fundamental Transaction if it had been, immediately prior to such Fundamental Transaction, the holder of the number of Warrant Shares then issuable upon exercise in full of this Warrant without regard to any limitations on exercise contained herein
      (the “Alternate Consideration”). The Company shall not effect any Fundamental Transaction in which the Company is not the surviving entity or the
      Alternate Consideration includes securities of another Person unless (i) the Alternate Consideration is solely cash and the Company provides for the simultaneous “cashless exercise” of this Warrant pursuant to Section 10 below or (ii) prior to or simultaneously with the consummation thereof, any successor to the Company, surviving entity or other Person (including any purchaser of assets of the
      Company) shall assume the obligation to deliver to the Holder such Alternate Consideration as, in accordance with the foregoing provisions, the Holder may be entitled to receive, and the other obligations under this Warrant. The provisions of this
      paragraph (c) shall similarly apply to subsequent transactions analogous of a Fundamental Transaction type.

    

    

    
      
        


    

    (d) Number of Warrant Shares. Simultaneously
      with any adjustment to the Exercise Price pursuant to Section 9, the number of Warrant Shares that may be purchased upon exercise of this Warrant shall be
      increased or decreased proportionately, so that after such adjustment the aggregate Exercise Price payable hereunder for the increased or decreased number of Warrant Shares shall be the same as the aggregate Exercise Price in effect immediately prior
      to such adjustment.

    

    

    (e) Calculations. All calculations under this Section 9 shall be made to the nearest one-tenth of one cent or the nearest share, as applicable.

    

    

    (f) Notice of Adjustments. Upon the occurrence
      of each adjustment pursuant to this Section 9, the Company at its expense will, at the written request of the Holder, promptly compute such adjustment, in
      good faith, in accordance with the terms of this Warrant and prepare a certificate setting forth such adjustment, including a statement of the adjusted Exercise Price and adjusted number or type of Warrant Shares or other securities issuable upon
      exercise of this Warrant (as applicable), describing the transactions giving rise to such adjustments and showing in detail the facts upon which such adjustment is based. Upon written request, the Company will promptly deliver a copy of each such
      certificate to the Holder and to the Company’s transfer agent.

    

    

    (g) Notice of Corporate Events. If, while this
      Warrant is outstanding, the Company (i) declares a dividend or any other distribution of cash, securities or other property in respect of its Common Stock, including, without limitation, any granting of rights or warrants to subscribe for or purchase
      any capital stock of the Company or any subsidiary, (ii) authorizes or approves, enters into any agreement contemplating or solicits stockholder approval for any Fundamental Transaction or (iii) authorizes the voluntary dissolution, liquidation or
      winding up of the affairs of the Company, then, except if such notice and the contents thereof shall be deemed to constitute material non-public information, the Company shall deliver to the Holder a notice of such transaction at least ten (10) days
      prior to the applicable record or effective date on which a Person would need to hold Common Stock in order to participate in or vote with respect to such transaction; provided, however, that the failure to deliver such notice or any defect therein shall not affect the validity of the corporate action required to be described in such notice. In the event such notice and the contents
      thereof shall be deemed to constitute material non-public information, the Company shall (on the same time frame set forth in the immediately prior sentence) offer the Holder the ability to sign a confidentiality agreement related thereto sufficient
      to allow the Holder to receive such notice, and the Company shall deliver such notice immediately upon execution of such confidentiality agreement.  In addition, if while this Warrant is outstanding, the Company authorizes or approves, enters into
      any agreement contemplating or solicits stockholder approval for any Fundamental Transaction contemplated by Section 9(c), other than a Fundamental
      Transaction under clause (iii) of Section 9(c), the Company shall
      deliver to the Holder a notice of such Fundamental Transaction at least thirty (30) days prior to the date such Fundamental Transaction is consummated. Holder agrees to maintain any information disclosed pursuant to this Section 9(g) in confidence until such information is publicly available, and shall comply with applicable law with respect to trading in the Company’s securities following receipt
      any such information.

    

    

    
      
        


    

    10.  Payment of Exercise Price. Notwithstanding anything contained
      herein to the contrary, the Holder may, in its sole discretion, satisfy its obligation to pay the Exercise Price through a “cashless exercise”, in which event the Company shall issue to the Holder the number of Warrant Shares determined as follows:

    

    

    X = Y [(A-B)/A]

    

    

    where:

    

    

    “X” equals the number of Warrant Shares to be issued to the Holder;

    

    

    “Y” equals the total number of Warrant Shares with respect to which this Warrant is then being exercised;

    

    

    “A” equals  (i) the last Closing Sale Price of the shares of Common Stock (as reported by Bloomberg Financial Markets) on the Trading Day immediately
      preceding the Exercise Date if the Exercise Notice is delivered prior to market close on the Exercise Date, or (ii) the last Closing Sale Price of the shares of Common Stock (as reported by Bloomberg Financial Markets) on the Exercise Date if the
      Exercise Notice is delivered following market close on the Exercise Date; and

    

    

    “B” equals the Exercise Price then in effect for the applicable Warrant Shares at the time of such exercise.

    

    

    For purposes of Rule 144 promulgated under the Securities Act, it is intended, understood and acknowledged that the Warrant Shares issued in a “cashless
      exercise” transaction shall be deemed to have been acquired by the Holder, the Warrant Shares shall take on the registered characteristics of the Warrants being exercised, and the holding period for the Warrant Shares shall be deemed to have
      commenced, on the date this Warrant was originally issued (provided that the Commission continues to take the position that such treatment is proper at the time of such exercise). In the event that the Registration Statement or another registration
      statement registering the issuance of Warrant Shares is, for any reason, not effective at the time of exercise of this Warrant, then the Warrant may only be exercised through a cashless exercise, as set forth in this Section 10. Except as set forth in Section 5(b) (Buy-In remedy) and Section 12 (payment of cash in lieu of fractional shares), in no event will the exercise of this Warrant be settled in cash.

    

    

    11.  Limitations on Exercise.

    

    

    (a)          Notwithstanding anything to
        the contrary contained herein, the Company shall not effect any exercise of this Warrant, and the Holder shall not be entitled to exercise this Warrant for a number of Warrant Shares in excess of that number of Warrant Shares which, upon giving
        effect or immediately prior to such exercise, would cause (i) the aggregate number of shares of Common Stock beneficially owned by the Holder and its Affiliates and any other Persons whose beneficial ownership of Common Stock would be aggregated
        with the Holder’s for purposes of Section 13(d) of the Exchange Act, to exceed 9.99% (the “Maximum Percentage”) of the total number of issued and outstanding shares of Common Stock of the Company following such exercise, or (ii) the combined voting
        power of the securities of the Company beneficially owned by the Holder and its Affiliates and any other Persons whose beneficial ownership of Common Stock would be aggregated with the Holder’s for purposes of Section 13(d) of the Exchange Act to
        exceed 9.99% of the combined voting power of all of the securities of the Company then outstanding following such exercise. For purposes of this Warrant, in determining the number of outstanding shares of Common Stock, the Holder may rely on the
        number of outstanding shares of Common Stock as reflected in (x) the Company’s most recent Form 10-Q or Form 10-K, as the case may be, filed with the Commission prior to the date hereof, (y) a more recent public announcement by the Company or (z)
        any other notice by the Company or the Transfer Agent setting forth the number of shares of Common Stock outstanding. Upon the written request of the Holder, the Company shall within three (3) Trading Days confirm in writing or by electronic mail
        to the Holder the number of shares of Common Stock then outstanding. In any case, the number of outstanding shares of Common Stock shall be determined after giving effect to the conversion or exercise of securities of the Company, including this
        Warrant, by the Holder since the date as of which such number of outstanding shares of Common Stock was reported. By written notice to the Company, the Holder may from time to time increase or decrease the Maximum Percentage to any other percentage
        not in excess of 19.99% specified in such notice; provided that any such increase will not be effective until the sixty-first (61st) day after such notice is delivered to the Company. For purposes of this Section 11(a), the aggregate number of shares of Common Stock or voting securities beneficially owned by the Holder and its Affiliates and any other Persons whose beneficial ownership of Common
        Stock would be aggregated with the Holder’s for purposes of Section 13(d) of the Exchange Act shall include the shares of Common Stock issuable upon the exercise of this Warrant with respect to which such determination is being made, but shall
        exclude the number of shares of Common Stock which would be issuable upon (x) exercise of the remaining unexercised and non-cancelled portion of this Warrant by the Holder and (y) exercise or conversion of the unexercised, non-converted or
        non-cancelled portion of any other securities of the Company that do not have voting power (including without limitation any securities of the Company which would entitle the holder thereof to acquire at any time Common Stock, including without
        limitation any debt, preferred stock, right, option, warrant or other instrument that is at any time convertible into or exercisable or exchangeable for, or otherwise entitles the holder thereof to receive, Common Stock), is subject to a limitation
        on conversion or exercise analogous to the limitation contained herein and is beneficially owned by the Holder or any of its Affiliates and other Persons whose beneficial ownership of Common Stock would be aggregated with the Holder’s for purposes
        of Section 13(d) of the Exchange Act.

    

    

    (b)          This Section 11 shall not restrict the number of shares of Common Stock which a Holder may receive or beneficially own in order to determine the amount of securities
        or other consideration that such Holder may receive in the event of a Fundamental Transaction as contemplated in Section 9(c) of this Warrant.

    

    

    
      
        


    

    12.  No Fractional Shares. No fractional Warrant Shares will be
      issued in connection with any exercise of this Warrant. In lieu of any fractional shares that would otherwise be issuable, the number of Warrant Shares to be issued shall be rounded down to the next whole number and the Company shall pay the Holder
      in cash the fair market value (based on the Closing Sale Price) for any such fractional shares.

    

    

    13.  Notices. Any and all notices or other communications or
      deliveries hereunder (including, without limitation, any Exercise Notice) shall be in writing and shall be deemed given and effective on the earliest of (i) the time of transmission, if such notice or communication is delivered via facsimile or
      e-mail at the facsimile number or e-mail address specified in the books and records of the Transfer Agent prior to 5:30 P.M., New York City time, on a Trading Day so long as the sender of an e-mail has not received an automated notice of delivery
      failure from the proposed recipient's computer server, (ii) the next Trading Day after the date of transmission, if such notice or communication is delivered via facsimile or e-mail at the facsimile number or e-mail address specified in the books and
      records of the Transfer Agent on a day that is not a Trading Day or later than 5:30 P.M., New York City time, on any Trading Day so long as the sender of an e-mail has not received an automated notice of delivery failure from the proposed recipient's
      computer server, (iii) the Trading Day following the date of mailing, if sent by nationally recognized overnight courier service specifying next business day delivery, or (iv) upon actual receipt by the Person to whom such notice is required to be
      given, if by hand delivery.  To the extent that any notice provided hereunder constitutes, or contains, material, non-public information regarding the Company or any subsidiaries, the Company shall simultaneously file such notice with the Commission
      pursuant to a Current Report on Form 8-K.

    

    

    14.  Warrant Agent. The Company shall initially serve as warrant
      agent under this Warrant. Upon thirty (30) days’ notice to the Holder, the Company may appoint a new warrant agent. Any corporation into which the Company or any new warrant agent may be merged or any corporation resulting from any consolidation to
      which the Company or any new warrant agent shall be a party or any corporation to which the Company or any new warrant agent transfers substantially all of its corporate trust or shareholders services business shall be a successor warrant agent under
      this Warrant without any further act. Any such successor warrant agent shall promptly cause notice of its succession as warrant agent to be mailed (by first class mail, postage prepaid) to the Holder at the Holder’s last address as shown on the
      Warrant Register. Notwithstanding anything to the contrary contained herein or in any warrant agency agreement that the Company may enter into in the future, the Holder shall be entitled to elect to receive, or continue to hold, this Warrant in
      certificated form, in which case the terms set forth in any such warrant agency agreement shall not apply to this Warrant.

    

    

    15.  Miscellaneous.

    

    

    (a) No Rights as a Stockholder. The Holder,
      solely in such Person’s capacity as a holder of this Warrant, shall not be entitled to vote or receive dividends or be deemed the holder of share capital of the Company for any purpose, nor shall anything contained in this Warrant be construed to
      confer upon the Holder, solely in such Person’s capacity as the Holder of this Warrant, any of the rights of a stockholder of the Company or any right to vote, give or withhold consent to any corporate action (whether any reorganization, issue of
      stock, reclassification of stock, consolidation, merger, amalgamation, conveyance or otherwise), receive notice of meetings, receive dividends or subscription rights, or otherwise, prior to the issuance to the Holder of the Warrant Shares which such
      Person is then entitled to receive upon the due exercise of this Warrant. In addition, nothing contained in this Warrant shall be construed as imposing any liabilities on the Holder to purchase any securities (upon exercise of this Warrant or
      otherwise) or as a stockholder of the Company, whether such liabilities are asserted by the Company or by creditors of the Company.

    

    

    (b) Authorized Shares.

    

    

    (i) Except and to the extent as waived or consented to by the Holder, the Company shall not by any action, including,
      without limitation, amending its certificate or articles of incorporation or through any reorganization, transfer of assets, consolidation, merger, dissolution, issue or sale of securities or any other voluntary action, avoid or seek to avoid the
      observance or performance of any of the terms of this Warrant, but will at all times in good faith assist in the carrying out of all such terms and in the taking of all such actions as may be necessary or appropriate to protect the rights of Holder
      as set forth in this Warrant against impairment. Without limiting the generality of the foregoing, the Company will (a) not increase the par value of any Warrant Shares above the amount payable therefor upon such exercise immediately prior to such
      increase in par value, (b) take all such action as may be necessary or appropriate in order that the Company may validly and legally issue fully paid and non-assessable Warrant Shares upon the exercise of this Warrant, and (c) use commercially
      reasonable efforts to obtain all such authorizations, exemptions or consents from any public regulatory body having jurisdiction thereof as may be necessary to enable the Company to perform its obligations under this Warrant.

    

    

    (ii) Before taking any action which would result in an adjustment in the number of Warrant Shares for which this Warrant
      is exercisable or in the Exercise Price, the Company shall obtain all such authorizations or exemptions thereof, or consents thereto, as may be necessary from any public regulatory body or bodies having jurisdiction thereof.

    

    

    
      
        


    

    (c) Successors and Assigns. Subject to the
      restrictions on transfer set forth in this Warrant and compliance with applicable securities laws, this Warrant may be assigned by the Holder. This Warrant may not be assigned by the Company without the written consent of the Holder, except to a
      successor in the event of a Fundamental Transaction. This Warrant shall be binding on and inure to the benefit of the Company and the Holder and their respective successors and assigns. Subject to the preceding sentence, nothing in this Warrant shall
      be construed to give to any Person other than the Company and the Holder any legal or equitable right, remedy or cause of action under this Warrant. This Warrant may be amended only in writing signed by the Company and the Holder, or their successors
      and assigns.

    

    

    (d) Amendment and Waiver. Except as otherwise
      provided herein, the provisions of the Warrants may be amended and the Company may take any action herein prohibited, or omit to perform any act herein required to be performed by it, only if the Company has obtained the written consent of the
      Holders of Warrants representing no less than a majority of the Warrant Shares obtainable upon exercise of the Warrants then outstanding.

    

    

    (e) Acceptance. Receipt of this Warrant by the
      Holder shall constitute acceptance of and agreement to all of the terms and conditions contained herein.

    

    

    (f) Governing Law; Jurisdiction. ALL QUESTIONS
      CONCERNING THE CONSTRUCTION, VALIDITY, ENFORCEMENT AND INTERPRETATION OF THIS WARRANT SHALL BE GOVERNED BY AND CONSTRUED AND ENFORCED IN ACCORDANCE WITH THE LAWS OF THE STATE OF NEW YORK WITHOUT REGARD TO THE PRINCIPLES OF CONFLICTS OF LAW THEREOF.
      EACH OF THE COMPANY AND THE HOLDER HEREBY IRREVOCABLY SUBMITS TO THE EXCLUSIVE JURISDICTION OF THE STATE AND FEDERAL COURTS SITTING IN THE CITY OF NEW YORK, BOROUGH OF MANHATTAN, FOR THE ADJUDICATION OF ANY DISPUTE HEREUNDER OR IN CONNECTION HEREWITH
      OR WITH ANY TRANSACTION CONTEMPLATED HEREBY OR DISCUSSED HEREIN (INCLUDING WITH RESPECT TO THE ENFORCEMENT OF ANY OF THE TRANSACTION DOCUMENTS), AND HEREBY IRREVOCABLY WAIVES, AND AGREES NOT TO ASSERT IN ANY SUIT, ACTION OR PROCEEDING, ANY CLAIM THAT
      IT IS NOT PERSONALLY SUBJECT TO THE JURISDICTION OF ANY SUCH COURT. EACH OF THE COMPANY AND THE HOLDER HEREBY IRREVOCABLY WAIVES PERSONAL SERVICE OF PROCESS AND CONSENTS TO PROCESS BEING SERVED IN ANY SUCH SUIT, ACTION OR PROCEEDING BY MAILING A COPY
      THEREOF VIA REGISTERED OR CERTIFIED MAIL OR OVERNIGHT DELIVERY (WITH EVIDENCE OF DELIVERY) TO SUCH PERSON AT THE ADDRESS IN EFFECT FOR NOTICES TO IT AND AGREES THAT SUCH SERVICE SHALL CONSTITUTE GOOD AND SUFFICIENT SERVICE OF PROCESS AND NOTICE
      THEREOF. NOTHING CONTAINED HEREIN SHALL BE DEEMED TO LIMIT IN ANY WAY ANY RIGHT TO SERVE PROCESS IN ANY MANNER PERMITTED BY LAW. EACH OF THE COMPANY AND THE HOLDER HEREBY WAIVES ALL RIGHTS TO A TRIAL BY JURY.

    

    

    (g) Headings. The headings herein are for
      convenience only, do not constitute a part of this Warrant and shall not be deemed to limit or affect any of the provisions hereof.

    

    

    (h) Severability. In case any one or more of
      the provisions of this Warrant shall be invalid or unenforceable in any respect, the validity and enforceability of the remaining terms and provisions of this Warrant shall not in any way be affected or impaired thereby, and the Company and the
      Holder will attempt in good faith to agree upon a valid and enforceable provision which shall be a commercially reasonable substitute therefor, and upon so agreeing, shall incorporate such substitute provision in this Warrant.

    

    

    (i) Interpretation. For purposes of this
      Warrant, (a) the words “include,” “includes” and “including” are deemed to be followed by the words “without limitation”; (b) the word “or” is not exclusive; and (c) the words “herein,” “hereof, “hereby,” “hereto” and “hereunder” refer to this
      Warrant as a whole. Unless the context otherwise requires, references herein: (x) to sections and schedules mean the sections of, and schedules attached to, this Warrant; (y) to an agreement, instrument, or other document means such agreement,
      instrument, or other document (as amended, supplemented and modified from time to time to the extent permitted by the provisions thereof/without regard to subsequent amendments, supplements, and modifications thereto); and (z) to a statute means such
      statute (as amended from time to time and includes/enforced at the time and date of this Warrant becoming effective) and does not include any successor legislation thereto and any regulations promulgated thereunder. This Warrant shall be construed
      without regard to any presumption or rule requiring construction or interpretation against the party drafting an instrument or causing any instrument to be drafted. The schedules referred to herein shall be construed with, and as an integral part of,
      this Warrant to the same extent as if they were set forth verbatim herein. All references to “$” or “dollars” mean the lawful currency of the United States of America. Whenever the singular is used in this Warrant, the same shall include the plural,
      and whenever the plural is used herein, the same shall include the singular, where appropriate.

    

    

    [REMAINDER OF PAGE INTENTIONALLY LEFT BLANK]

    

    

    
      
        


    

    IN WITNESS WHEREOF, the undersigned has caused this Warrant to be duly executed by its authorized officer as of the date first indicated above.

     

    

    
      	
               

            	
               COMPANY:

            
	
               

            	
               

            
	
               

            	
               BIOCRYST PHARMACEUTICALS, INC.

            
	
               

            	
               

            
	
               

            	
               By:

            	
               

            
	
               

            	
               Name:

            	
              
                Alane Barnes

              

            
	
               

            	
               Title:

            	
              
                Senior Vice President and Chief Legal Officer

              

            
	
               

            	
               

            	
               

            


    

     

    

    
      
        


    

    

    

    SCHEDULE 1

    

    

    FORM OF EXERCISE NOTICE

    

    

    [To be executed by the Holder to purchase shares of Common Stock under the Warrant]

    

    

    Ladies and Gentlemen:

    

    

    (1) The undersigned is the Holder of Warrant No. __ (the “Warrant”)
      issued by BioCryst Pharmaceuticals, Inc., a Delaware corporation (the “Company”). Capitalized terms used herein and not otherwise defined herein
      have the respective meanings set forth in the Warrant.

    

    

    (2) The undersigned hereby exercises its right to purchase Warrant Shares pursuant to the Warrant.

    

    

    (3) The Holder intends that payment of the Exercise Price shall be made as (check one):

     

    

    	 	
            ☐

          	
            Cash Exercise

          


     

    

    	 	
            ☐

          	
            “Cashless Exercise” under Section 10
              of the Warrant

          


     

    

    (4) If the Holder has elected a Cash Exercise, the Holder shall pay the sum of $ in immediately available funds to the Company in accordance with the terms of
      the Warrant.

    

    

    (5) Pursuant to this Exercise Notice, the Company shall deliver to the Holder Warrant Shares determined in accordance with the terms of the Warrant.

    

    

    (6) By its delivery of this Exercise Notice, the undersigned represents and warrants to the Company that in giving effect to the exercise evidenced hereby the
      Holder will not beneficially own in excess of the number of shares of Common Stock (as determined in accordance with Section 13(d) of the Securities Exchange Act of 1934, as amended) permitted to be owned under Section 11(a) of the Warrant to which this notice relates.

    

    

     

    

    	 	 	 
	
            Dated:

          	 	 
	 	 
	
            Name of Holder:

          	 	 
	 	 
	
            By:

          	 	 
	
            Name:

          	 	 
	
            Title:

          	 	 


    (Signature must conform in all respects to name of Holder as specified on the face of the Warrant)