AMBIT BIOSCIENCES CORPORATION WARRANT TO PURCHASE STOCK

Exhibit 4.13

THIS WARRANT AND THE UNDERLYING SECURITIES HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE “ACT”), OR UNDER THE SECURITIES LAWS OF CERTAIN STATES AND MAY NOT BE OFFERED, SOLD OR OTHERWISE TRANSFERRED, PLEDGED OR HYPOTHECATED EXCEPT AS PERMITTED UNDER THE ACT AND APPLICABLE STATE SECURITIES LAWS PURSUANT TO AN EFFECTIVE REGISTRATION STATEMENT OR AN EXEMPTION THEREFROM. THE ISSUER OF THESE SECURITIES MAY REQUIRE AN OPINION OF COUNSEL REASONABLY SATISFACTORY TO THE ISSUER THAT SUCH OFFER, SALE OR TRANSFER, PLEDGE OR HYPOTHECATION OTHERWISE COMPLIES WITH THE ACT AND ANY APPLICABLE STATE SECURITIES LAWS.

AMBIT BIOSCIENCES CORPORATION

WARRANT TO PURCHASE STOCK

THIS CERTIFIES THAT, for value received, [                    ] (the “Holder”), is entitled to subscribe for and purchase at the Warrant Price (defined below) from Ambit Biosciences Corporation, a Delaware corporation (the “Company”), all or any portion of the Shares (as defined below) during the Exercise Period (as defined below).

This Warrant is issued as one of a series of warrants (the “Series D-2 Warrants”) pursuant to the Series D-2 and Series D-3 Preferred Stock and Warrant Purchase Agreement (the “Purchase Agreement”) dated as of May 9, 2011, as may be amended from time to time, by and among the Company and the persons and entities listed on Exhibit A thereto (the “Purchasers”). Capitalized terms used and not otherwise defined herein shall have the meanings given them in the Purchase Agreement.

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

(a) “Astellas License” shall mean that certain Exclusive License and Collaborative Research, Co-Development and Commercialization Agreement, dated December 18, 2009, by and among the Company, Astellas Pharma Inc., a Japanese corporation, and Astellas US LLC, a Delaware limited liability company.

(b) “Astellas Milestone Deadline” shall mean 5:00 p.m. Pacific time on the later of (i) March 31, 2012 or (ii) a date, the number of business days following March 31, 2012 equal to the number of business days elapsed between (A) August 31, 2011 and (B) the date on which the Company receives from the United States Food and Drug Administration approval of the Special Protocol Assessment for the Company’s proposed phase 3 clinical trial of AC220 to the extent such date occurs following August 31, 2011.

(c) “Astellas Milestone Payment” shall mean the payment to which the Company is entitled upon initiation of a phase 3 clinical trial for AC220 under Section 4.2.1 of the Astellas License.

2. EXERCISE OF WARRANT. The terms and conditions upon which this Warrant may be exercised, and upon which the Shares covered hereby may be purchased, are as follows:

(a) Term. Subject to the terms and conditions hereof, this Warrant may be exercised at any time, or from time to time, in whole or in part, on or after the date on which this Warrant first becomes exercisable for Shares in accordance with Section 2(b) below; provided, however, that in no event may this Warrant be exercised after May 18, 2021 (the “Exercise Period”).

(b) Shares. For purposes of this Warrant, the “Shares” shall mean up to a maximum of [                    ] fully paid and nonassessable shares of the Series D-2 Preferred Stock of the Company (“Series D-2 Preferred”) calculated as follows (or such other number, class and kind of shares as may be issuable hereunder pursuant to Section 5 below):

(i) if, as of 5:00 p.m. Pacific time on January 31, 2012, (A) the Company has not delivered to the Major Investors draft tables, listings and figures showing top-line results of the phase 2 pivotal trial of AC220 or (B) the Company’s cash balance is less than $9,000,000, then, at such time, this Warrant shall become exercisable for [                ] shares of Series D-2 Preferred; and

(ii) if, as of the Astellas Milestone Deadline, the Company has not received the Astellas Milestone Payment, then, at such time, this Warrant shall become exercisable for [                ] shares of Series D-2 Preferred in addition to the number of shares for which this Warrant is exercisable under clause (i) above, if any.

(c) Warrant Price. For purposes of this Warrant, the “Warrant Price” shall mean $0.001 per Share, subject to adjustment pursuant to Section 5 below.

3. METHOD OF EXERCISE.

(a) 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 Company at its address set forth in the Purchase Agreement (or at such other address as it may designate by notice in writing to the Holder):

(i) An executed Notice of Exercise in the form attached hereto as Exhibit A;

(ii) Payment of the Warrant Price either (i) in cash or by check or (ii) by cancellation of indebtedness or (iii) by any combination thereof; and

(iii) This Warrant.

Upon the exercise of the rights represented by this Warrant, a certificate or certificates for the 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 promptly after the rights represented by this Warrant shall have been so exercised.

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The person in whose name any certificate or certificates for 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 Warrant 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 Company 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.

(b) Net Exercise. Notwithstanding any provisions herein to the contrary, if the Fair Market Value (as defined below) of one Share is greater than the Warrant Price (at the date of calculation as set forth below), in lieu of exercising this Warrant by payment of cash, the Holder may elect to receive Shares equal to the value (as determined below) of this Warrant (or the portion thereof being canceled) by surrender of this Warrant at the principal office of the Company together with the properly endorsed Notice of Exercise, in which event the Company shall issue to the Holder a number of Shares computed using the following formula:

X = Y (A-B)

A

For purposes of this Warrant, the fair market value of one Share (the “Fair Market Value”) shall mean, with respect to each such Share, the value as determined by the Company’s Board of Directors in good faith; provided, however, that in the event that this Warrant is exercised pursuant to this Section 3(b) in connection with the Company’s initial public offering of its Common Stock, the Fair Market Value of one Share shall be the product of (i) the per share offering price to the public of the Company’s initial public offering, and (ii) the number of shares of Common Stock into which each Share is convertible at the time of such exercise.

4. COVENANTS OF THE COMPANY. The Company covenants and agrees that all 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 (other than taxes, liens or charges created by or imposed upon the Holder through no action of the Company). The Company further covenants and agrees that the Company will at all times during the Exercise Period have authorized and

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reserved a sufficient number of shares of Preferred 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 Preferred Stock shall not be sufficient to permit exercise of this Warrant, the Company will take such corporate action as may, in the opinion of its counsel, be necessary to increase its authorized but unissued shares of Preferred Stock to such number of shares as shall be sufficient for such purposes.

5. ADJUSTMENT. In the event of changes in the outstanding shares of the Series D-2 Preferred by reason of stock dividends, split-ups, recapitalizations, reclassifications, conversions, mergers, combinations or exchanges of shares, separations, reorganizations, liquidations, or the like, the number and class of shares available under this Warrant in the aggregate and the Warrant Price and Shares shall be correspondingly adjusted to give the Holder of the Warrant, on exercise for the same aggregate Warrant 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.

6. FRACTIONAL SHARES. No fractional shares shall be issued upon the exercise of this Warrant as a consequence of any adjustment pursuant hereto. All 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 Company 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 a Share by such fraction.

7. EARLY TERMINATION. Notwithstanding Section 2(a), in the event of an Acquisition or Asset Transfer (each as defined in the Company’s Amended and Restated Certificate of Incorporation) at any time during the Exercise Period, the Company shall provide to the Holder at least 10 days advance written notice of the closing of such Acquisition or Asset Transfer and, if not exercised prior the closing of such Acquisition or Asset Transfer, this Warrant shall terminate immediately prior to the closing of such Acquisition or Asset Transfer. This Warrant shall terminate immediately upon the Second Tranche Closing Date if the Holder fails to purchase the Holder’s Second Tranche Closing Amount in the Second Tranche Closing.

8. 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 Company.

9. TRANSFER OF WARRANT. Subject to applicable laws and the restrictions on transfer set forth in the Purchase Agreement, 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. The transferee shall sign an investment letter in form and substance satisfactory to the Company and shall agree to assume the obligations of the Holder described in this Warrant.

10. LOST, STOLEN, MUTILATED OR DESTROYED WARRANT. If this Warrant is lost, stolen, mutilated or destroyed, the Company shall, on such terms as to indemnity or otherwise as it may

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reasonably impose (which shall, in the case of a mutilated Warrant, include the surrender thereof), issue a new Warrant of like denomination and tenor as the Warrant so lost, stolen, mutilated or destroyed. Any such new Warrant shall constitute an original contractual obligation of the Company, whether or not the allegedly lost, stolen, mutilated or destroyed Warrant shall be at any time enforceable by anyone.

11. GOVERNING LAW. This Warrant and all rights, obligations and liabilities hereunder shall be governed by the laws of the State of California.

12. AMENDMENT; WAIVER. Any term of this Warrant may be amended or waived with the written consent of the Company and the Requisite Purchasers; provided, however, if any amendment of this Warrant by its terms materially and adversely affects the rights or obligations under this Warrant of any Holder then holding securities purchased under the Purchase Agreement, in a manner different than such amendment affects such rights or obligations of other Purchasers, then such amendment shall not be effective with respect to such adversely affected Holder without the written consent of such adversely affected Holder. Notwithstanding the foregoing, nothing provided in this Section 12 shall limit an individual Holder’s right to waive, solely on such Holder’s own behalf, any obligation of the Company under this Warrant.

13. SEVERABILITY. Wherever possible, each provision of this Warrant shall be interpreted in such manner as to be effective and valid under applicable law, but if any provision of this Warrant shall be prohibited by or invalid under applicable law, such provision shall be ineffective to the extent of such prohibition or invalidity, without invalidating the remainder of such provisions or the remaining provisions of this Warrant.

14. COUNTERPARTS. This Warrant may be executed in two or more counterparts, each of which shall be deemed an original, but all of which together shall constitute one and the same instrument.

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IN WITNESS WHEREOF, the Company has caused this WARRANT to be executed by its duly authorized officer as of the date first written above.

Acknowledged and Accepted:

HOLDER

[WARRANT SIGNATURE PAGE]

EXHIBIT A

NOTICE OF EXERCISE

TO: AMBIT BIOSCIENCES CORPORATION

(1) ¨ The undersigned hereby elects to purchase                  Shares (the “Exercise Shares”) of Ambit Biosciences Corporation (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 (the “Exercise Shares”) of Ambit Biosciences Corporation (the “Company”) pursuant to the terms of the net exercise provisions set forth in Section 3(b) of the attached Warrant, and shall tender payment of all applicable transfer taxes, if any.

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

(Name)

(Address)

(3) The undersigned represents that (i) the aforesaid Exercise Shares are being acquired for the account of the undersigned for investment and not with a view to, or for resale in connection with, the distribution thereof and that the undersigned has no present intention of distributing or reselling such shares; (ii) the undersigned is aware of the Company’s business affairs and financial condition and has acquired sufficient information about the Company to reach an informed and knowledgeable decision regarding its investment in the Company; (iii) the undersigned is experienced in making investments of this type and has such knowledge and background in financial and business matters that the undersigned is capable of evaluating the merits and risks of this investment and protecting the undersigned’s own interests; (iv) the undersigned understands that Exercise Shares issuable upon exercise of this Warrant have not been registered under the Securities Act of 1933, as amended (the “Securities Act”), by reason of a specific exemption from the registration provisions of the Securities Act, which exemption depends upon, among other things, the bona fide nature of the investment intent as expressed herein, and, because such securities have not been registered under the Securities Act, they must be held indefinitely unless subsequently registered under the Securities Act or an exemption from such registration is available; (v) the undersigned is aware that the aforesaid Exercise Shares may not be sold pursuant to Rule 144 adopted under the Securities Act unless certain conditions are met and until the undersigned has held the shares for the period of time prescribed by Rule 144, that among the conditions for use of the Rule is the availability of current information to the public about the Company and the Company has not made such information available and has no present plans to do so; and (vi) the undersigned agrees not to make any disposition of all or any part of the aforesaid shares of Exercise Shares unless and until there is then in effect a registration statement under the Securities Act covering such proposed

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disposition and such disposition is made in accordance with said registration statement, or, if reasonably requested by the Company, the undersigned has provided the Company with an opinion of counsel satisfactory to the Company, stating that such registration is not required.

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EXHIBIT B

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

Dated:             , 20    

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 whatever. Officers of corporations and those acting in a fiduciary or other representative capacity should file proper evidence of authority to assign the foregoing Warrant.

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