ARCA BIOPHARMA, INC. WARRANT TO PURCHASE COMMON STOCK

Exhibit 4.13

THIS WARRANT AND THE UNDERLYING SECURITIES HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE “ACT”). THEY MAY NOT BE SOLD, OFFERED FOR SALE, PLEDGED OR HYPOTHECATED IN THE ABSENCE OF AN EFFECTIVE REGISTRATION STATEMENT AS TO SUCH SECURITIES UNDER THE ACT OR AN OPINION OF COUNSEL SATISFACTORY TO THE CORPORATION THAT SUCH REGISTRATION IS NOT REQUIRED.

ARCA BIOPHARMA, INC.

WARRANT TO PURCHASE COMMON STOCK

Void After October 10, 2013

This certifies that, for value received, Atlas Venture Fund VII, L.P., with its principal office at 890 Winter Street, Suite 320, Waltham, MA 02451, or its assigns (the “Holder” or “Purchaser”), is entitled to subscribe for and purchase at the Exercise Price (as defined below) from ARCA biopharma, Inc., a Delaware corporation, with its principal office at 8001 Arista Place, Suite 200, Broomfield, Colorado 80021 (the “Corporation”), up to a number of Exercise Shares (as defined below), upon the terms and subject to the adjustments as provided herein.

This Warrant is being issued pursuant to the terms of the Note and Warrant Purchase Agreement, dated September 24, 2008, as amended by the First Amendment thereto, dated as of the date hereof, (as amended, the “Note and Warrant Purchase Agreement”) by and among the Corporation and the Purchasers listed on the Schedule of Purchasers thereto, as the same may be further amended from time to time (the “Schedule of Purchasers”). Capitalized terms used herein but not otherwise defined shall have the meanings given to them in the Note and Warrant Purchase Agreement.

1. Definitions. As used herein, the following terms shall have the following respective meanings:

(a) “Exercise Period” shall mean the time period commencing with the date of this Warrant and ending five (5) years from date of this Warrant, unless sooner terminated as provided below.

(b) “Exercise Price” shall mean the lesser of (i) $3.253 or (ii) the product of (x) the Parent Trading Price (as defined in the Merger Agreement) and (y) the Exchange Ratio (as defined in the Merger Agreement and determined in accordance with the methodology reflected in the Spreadsheet (as defined in the Merger Agreement)); provided, however that in no event shall the Exercise Price be less than $1.6265; and provided, further that the Exercise Price shall be subject to adjustment pursuant to the terms herein, including Section 5 below. Notwithstanding the forgoing, if the Merger (as defined below) does not close on or before March 31, 2009, the Exercise Price shall be $1.6265, subject to adjustment pursuant to the terms herein, including Section 5 below.

(c) “Exercise Shares” shall mean a number of shares of common stock of the Corporation (the “Common Stock”) issuable upon exercise of this Warrant equal to (i) one-fifth (1/5^th ) of such Purchaser’s Total Purchase Price (as defined in the Note and Warrant Purchase Agreement) divided by (b) the Exercise Price, rounded up to the nearest share and subject to adjustment pursuant to the terms herein, including Section 5 below.

(d) “Merger Agreement” shall mean that certain Agreement and Plan of Merger and Reorganization dated September 24, 2008, by and among the Corporation, Nuvelo, Inc., a Delaware corporation (the “Parent”) and Dawn Acquisition Sub, Inc., a Delaware corporation (the “Merger Sub”), pursuant to which Merger Sub will merge with and into the Corporation and the stockholders of the Corporation will receive shares of the capital stock of Parent in exchange for their capital stock of the Corporation (the “Merger”).

2. EXERCISE OF WARRANT.

2.1 IN GENERAL. The rights represented by this Warrant may be exercised in whole or in part at any time during the Exercise Period, by delivery of the following to the Corporation at its address set forth above (or at such other address as it may designate by notice in writing to the Holder):

(a) an executed Notice of Exercise in the form attached hereto;

(b) payment of the Exercise Price either (i) in cash or by check, or (ii) by cancellation of indebtedness, or (iii) pursuant to Section 2.1 below; and

(c) this Warrant.

Upon the exercise of the rights represented by this Warrant, a certificate or certificates for the Exercise Shares so purchased, registered in the name of the Holder or persons affiliated with the Holder, if the Holder so designates, shall be issued and delivered to the Holder as soon as practicable after the rights represented by this Warrant shall have been so exercised.

The person in whose name any certificate or certificates for Exercise Shares are to be issued upon exercise of this Warrant shall be deemed to have become the holder of record of such shares on the date on which this Warrant was surrendered and payment of the Exercise Price was made, irrespective of the date of delivery of such certificate or certificates, except that, if the date of such surrender and payment is a date when the stock transfer books of the Corporation are closed, such person shall be deemed to have become the holder of such shares at the close of business on the next succeeding date on which the stock transfer books are open.

2.2 Net Exercise. Notwithstanding any provisions herein to the contrary, if the fair market value of one share of the Corporation’s Common Stock is greater than the Exercise Price (at the date of calculation as set forth below), in lieu of exercising this Warrant by payment of cash, the Holder may elect (the “Conversion Right”) to receive shares equal to the value (as

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determined below) of this Warrant (or the portion thereof being canceled) by surrender of this Warrant at the principal office of the Corporation together with the properly endorsed Notice of Exercise, in which event the Corporation shall issue to the Holder a number of shares of Common Stock computed using the following formula:

For purposes of the above calculation, the fair market value of one share of Common Stock shall be determined by the Corporation’s Board of Directors in good faith; provided, however, that in the event that this Warrant is exercised when the Corporation’s Common Stock is traded in a public market, the fair market value of each share of Common Stock shall be the closing price of a share of Common Stock for the business day immediately before the day the Holder delivers its Notice of Exercise to the Company.

3. COVENANTS OF THE CORPORATION.

3.1 Covenants as to Exercise Shares. The Corporation covenants and agrees that all Exercise Shares that may be issued upon the exercise of the rights represented by this Warrant will, upon issuance, be validly issued and outstanding, fully paid and nonassessable, and free from all taxes, liens and charges with respect to the issuance thereof. The Corporation further covenants and agrees that the Corporation shall at all times during the Exercise Period have authorized and reserved, free from preemptive rights, a sufficient number of shares of its Common Stock to provide for the exercise of the rights represented by this Warrant. If at any time during the Exercise Period the number of authorized but unissued shares of Common Stock shall not be sufficient to permit exercise of this Warrant, the Corporation will take such corporate action as may, in the opinion of its counsel, be necessary to increase its authorized but unissued shares of Common Stock to such number of shares as shall be sufficient for such purposes.

3.2 No Impairment. Except and to the extent as waived or consented to by the Holder, the Corporation will not, by amendment of its Certificate 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 to be observed or performed hereunder by the Corporation, but will at all times in good faith assist in the carrying out of all the provisions of this Warrant and in the taking of all such action as may be necessary or appropriate in order to protect the exercise rights of the Holder against impairment.

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3.3 Notices of Record Date. In the event of any taking by the Corporation of a record of the holders of any class of securities for the purpose of determining the holders thereof who are entitled to receive any dividend (other than a cash dividend which is the same as cash dividends paid in previous quarters) or other distribution, the Corporation shall mail to the Holder, at least ten (10) days prior to the date specified herein, a notice specifying the date on which any such record is to be taken for the purpose of such dividend or distribution.

3.4 Notice of Expiration. If this Warrant has not been fully exercised on or before the date thirty (30) days prior to the end of the Exercise Period, the Corporation shall thereafter provide Holder with at least twenty (20) days advance written notice of the date on which this Warrant is to expire. If the Corporation fails to provide such notice, the Exercise Period shall be extended until the date thirty (30) days after the date said notice is provided to Holder. If this Warrant would terminate when it could be net exercised pursuant to Section 2.2, it shall be deemed so exercised immediately prior to such termination, unless Holder states explicitly to the contrary in writing.

4. REPRESENTATIONS OF HOLDER.

4.1 Acquisition of Warrant for Personal Account. The Holder represents and warrants that it is acquiring the Warrant solely for his, her or its account for investment and not with a view to or for sale or distribution of said Warrant or any part thereof, other than potential transfers between affiliates (including affiliate funds). The Holder also represents that the entire legal and beneficial interests of the Warrant and Exercise Shares the Holder is acquiring is being acquired for, and will be held for, his, her or its account only.

4.2 Securities Are Not Registered.

(a) The Holder understands that the Warrant and the Exercise Shares have not been registered under the Securities Act of 1933, as amended (the “Act”) on the basis that no distribution or public offering of the stock of the Corporation is to be effected. The Holder realizes that the basis for the exemption may not be present if, notwithstanding his, her or its representations, the Holder has a present intention of acquiring the securities for a fixed or determinable period in the future, selling (in connection with a distribution or otherwise), granting any participation in, or otherwise distributing the securities. The Holder has no such present intention.

(b) The Holder recognizes that the Warrant and the Exercise Shares must be held indefinitely unless they are subsequently registered under the Act or an exemption from such registration is available.

(c) The Holder is aware that neither the Warrant nor the Exercise Shares may be sold pursuant to Rule 144 adopted under the Act unless certain conditions are met, including, among other things, the existence of a public market for the shares, the availability of certain current public information about the Corporation, the resale following the required holding period under Rule 144 and the number of shares being sold during any three month period not exceeding specified limitations. Holder is aware that the conditions for resale set forth in Rule 144 have not been satisfied and that the Corporation presently has no plans to satisfy these conditions in the foreseeable future.

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4.3 DISPOSITION OF WARRANT AND EXERCISE SHARES.

(a) The Holder further agrees not to make any disposition of all or any part of the Warrant or Exercise Shares in any event unless and until:

(i) The Corporation shall have received a letter secured by the Holder from the Securities and Exchange Commission stating that no action will be recommended to the Commission with respect to the proposed disposition; or

(ii) There is then in effect a registration statement under the Act covering such proposed disposition and such disposition is made in accordance with said registration statement; or

(iii) The Holder shall have notified the Corporation of the proposed disposition and shall have furnished the Corporation with a statement of the circumstances surrounding the proposed disposition; provided, however, that such statement will not be required if the disposition is permitted under Rule 144 of the Act, except in unusual circumstances.

(b) Notwithstanding the provisions of paragraphs (a) above, the Holder may assign this Warrant and the Exercise Shares to (i) any partner or retired partner of the Holder if Holder is a partnership, (ii) any member or former member of the Holder if Holder is a limited liability company, (iii) any affiliate, including affiliated funds or (iv) any family member or trust for the benefit of the Holder if the Holder is an individual; provided that the Corporation is given written notice thereof.

5. ADJUSTMENT OF EXERCISE PRICE AND EXERCISE SHARES; EFFECT OF ORGANIC CHANGES.

5.1 Adjustment of Exercise Price. In the event of changes in the outstanding Common Stock of the Corporation by reason of stock dividends, splits, recapitalizations, reclassifications, combinations or exchanges of shares, separations, reorganizations, liquidations, or the like, the number and class of shares available under the Warrant in the aggregate and the Exercise Price shall be correspondingly adjusted to give the Holder of the Warrant, on exercise for the same aggregate Exercise Price, the total number, class, and kind of shares as the Holder would have owned had the Warrant been exercised prior to the event and had the Holder continued to hold such shares until after the event requiring adjustment. The form of this Warrant need not be changed because of any adjustment in the number of Exercise Shares subject to this Warrant.

5.2 Reorganization, Reclassification, Consolidation, Merger or Sale. If any recapitalization, reclassification or reorganization of the capital stock of the Corporation, or any consolidation or merger of the Corporation with another corporation, or the sale of all or substantially all of its assets or other transaction shall be effected in such a way that holders of

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the Corporation’s Common Stock shall be entitled to receive stock, securities, or other assets or property, including, without limitation, upon conversion of such Common Stock (an “Organic Change”), then, as a condition of such Organic Change, lawful and adequate provisions shall be made by the Corporation whereby the Holder hereof shall thereafter have the right to purchase and receive (in lieu of the shares of the Common Stock of the Corporation immediately theretofore purchasable and receivable upon the exercise of the rights represented hereby) such shares of stock, securities or other assets or property as may be issued or payable with respect to or in exchange for a number of outstanding shares of such Common Stock equal to the number of shares of such stock immediately theretofore purchasable and receivable upon the exercise of the rights represented hereby. In the event of any Organic Change, appropriate provision shall be made by the Corporation with respect to the rights and interests of the Holder of this Warrant to the end that the provisions hereof (including, without limitation, provisions for adjustments of the Exercise Price and of the number of shares purchasable and receivable upon the exercise of this Warrant) shall thereafter be applicable, in relation to any shares of stock, securities or assets thereafter deliverable upon the exercise hereof and following such Organic Change the Corporation or its successor shall promptly issue to Holder an amendment to this Warrant reflecting such adjustments.

5.3 Certain Events. If any change in the outstanding Common Stock of the Corporation or any other event occurs as to which the other provisions of this Section 5 are not strictly applicable or if strictly applicable would not fairly protect the purchase rights of the Holder of the Warrant in accordance with such provisions, then the Board of Directors of the Corporation shall make an adjustment in the number and class of shares available under the Warrant, the Exercise Price or the application of such provisions, so as to protect such purchase rights as aforesaid. The adjustment shall be such as to give the Holder of the Warrant upon exercise for the same aggregate Exercise Price the total number, class and kind of shares as he would have owned had the Warrant been exercised prior to the event and had he continued to hold such shares until after the event requiring adjustment.

6. FRACTIONAL SHARES. No fractional shares shall be issued upon the exercise of this Warrant as a consequence of any adjustment pursuant hereto. All Exercise Shares (including fractions) issuable upon exercise of this Warrant may be aggregated for purposes of determining whether the exercise would result in the issuance of any fractional share. If, after aggregation, the exercise would result in the issuance of a fractional share, the Corporation shall, in lieu of issuance of any fractional share, pay the Holder otherwise entitled to such fraction a sum in cash equal to the product resulting from multiplying the then current fair market value of an Exercise Share by such fraction.

7. NO STOCKHOLDER RIGHTS. This Warrant in and of itself shall not entitle the Holder to any voting rights or other rights as a stockholder of the Corporation.

8. TRANSFER OF WARRANT. Subject to applicable laws and any restrictions on transfer set forth in this Warrant, this Warrant and all rights hereunder are transferable, by the Holder in person or by duly authorized attorney, upon delivery of this Warrant and the form of assignment attached hereto to any transferee designated by Holder.

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9. LOST, STOLEN, MUTILATED OR DESTROYED WARRANT. The Corporation covenants to the holder hereof that, upon receipt of evidence reasonably satisfactory to the Corporation of the loss, theft, destruction or mutilation of this Warrant or any stock certificate and, in the case of any such loss, theft or destruction, upon receipt of an indemnity reasonably satisfactory to the Corporation, or in the case of any such mutilation, upon surrender and cancellation of such Warrant or stock certificate, the Corporation will make and deliver a new Warrant or stock certificate, of like tenor, in lieu of the lost, stolen, destroyed or mutilated Warrant or stock certificate.

10. NOTICES, ETC. Any notice required or permitted under this Warrant shall be given in writing and shall be deemed effectively given: (a) upon personal delivery to the party to be notified, (b) when sent by confirmed facsimile if sent during normal business hours of the recipient; if not, then on the next business day, (c) five (5) business days after having been sent by registered or certified mail, return receipt requested, postage prepaid, or (d) one (1) business day after deposit with a nationally recognized overnight courier, specifying next day delivery, with written verification of receipt. All communications shall be sent to (i) the Corporation at ARCA biopharma, Inc., 8001 Arista Place, Suite 200, Broomfield, CO 80021, Attention: Chief Executive Officer and General Counsel; or to (ii) a Purchaser at his, her or its address shown on the Schedule of Purchasers, or at such other address as any such party may designate by ten (10) days advance written notice to the other parties hereto.

11. ACCEPTANCE. Receipt of this Warrant by the Holder shall constitute acceptance of and agreement to all of the terms and conditions contained herein.

12. GOVERNING LAW. This Warrant and all rights, obligations and liabilities hereunder shall be governed and construed under the laws of the State of Colorado in all respects as such laws are applied to agreements among Colorado residents entered into and performed entirely within Colorado, without giving effect to conflict of law principles thereof. The Corporation and Holder agree that any action brought by any party under or in relation to this Warrant, including without limitation to interpret or enforce any provision of this Warrant, shall be brought in, and each agrees to and does hereby submit to the jurisdiction and venue of, any state or federal court located in the County of Denver, Colorado.

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IN WITNESS WHEREOF, the Corporation has caused this Warrant to be executed by its duly authorized officer as of October 10, 2008.

SIGNATURE PAGE TO WARRANT

NOTICE OF EXERCISE

(1) ¨ The undersigned hereby elects to purchase              shares of the Common Stock of ARCA biopharama, Inc. (the “Company”) pursuant to the terms of the attached Warrant, and tenders herewith payment of the exercise price in full, together with all applicable transfer taxes, if any.

       ¨ The undersigned hereby elects to purchase              shares of the Common Stock of the Company pursuant to the terms of the net exercise provisions set forth in Section 2.1 of the attached Warrant, and shall tender payment of all applicable transfer taxes, if any.

(2) Please issue a certificate or certificates representing said shares of Common Stock in the name of the undersigned or in such other name as is specified below:

ASSIGNMENT FORM

(To assign the foregoing Warrant, execute this form and supply required

information. Do not use this form to purchase shares.)

FOR VALUE RECEIVED, the foregoing Warrant and all rights evidenced thereby are hereby assigned to

Name: ________________________________________________________________________________________________

(Please Print)

Address: ______________________________________________________________________________________________

(Please Print)

Dated:                             

Holder’s

Signature: _____________________________________________________________________________________________

Holder’s

Address: _____________________________________________________________________________________________

NOTE: The signature to this Assignment Form must correspond with the name as it appears on the face of the Warrant, without alteration or enlargement or any change whatsoever. Officers of corporations and those acting in a fiduciary or other representative capacity should file proper evidence of authority to assign the foregoing Warrant.