WARRANT TO PURCHASE SHARES OF COMMON STOCK

Exhibit 4.4

WARRANT TO PURCHASE SHARES OF COMMON STOCK

THIS WARRANT AND THE SECURITIES ISSUABLE UPON THE EXERCISE HEREOF HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED. THEY MAY NOT BE SOLD, OFFERED FOR SALE, PLEDGED, HYPOTHECATED OR OTHERWISE TRANSFERRED EXCEPT PURSUANT TO AN EFFECTIVE REGISTRATION STATEMENT UNDER THE SECURITIES ACT OF 1933, AS AMENDED, OR AN OPINION OF COUNSEL SATISFACTORY TO THE COMPANY THAT REGISTRATION IS NOT REQUIRED UNDER SUCH ACT OR UNLESS SOLD PURSUANT TO RULE 144 UNDER SUCH ACT.

HYPERION THERAPEUTICS, INC.

(a Delaware corporation)

For the consideration stipulated in that certain Convertible Note and Warrant Purchase Agreement dated «Date», 2011, by and among the Hyperion Therapeutics, Inc., a Delaware corporation (the “Company”), and the other parties named therein (the “Purchase Agreement”), the receipt and sufficiency of which is hereby acknowledged, this Warrant is issued to «Warrant_Holder» (the “Holder”) by the Company. Capitalized terms not defined herein shall have the meaning set forth in the Purchase Agreement.

1. Purchase of Shares of Common Stock.

(a) Number of Shares of Common Stock. Subject to the terms and conditions set forth herein and set forth in the Purchase Agreement, the Holder is entitled, upon surrender of this Warrant in accordance with Section 3(a)(i) and payment of the Exercise Price (as defined below) in accordance with Section 3(a)(ii) or Section 4 below, to purchase from the Company up to the number of fully paid and nonassessable shares of Common Stock (“Exercise Shares”) as follows:

(i) in the event that the Holder’s Note(s) have been converted into New Preferred Stock pursuant to Section 3.1 of the Purchase Agreement, the number of Exercise Shares shall be equal to the quotient of (A) thirty percent (30%) of the principal amount of the Note issued to such Holder at the Closing, divided by (B) the price per share paid by the New Investor for the New Preferred Stock in the Qualified Financing;

(ii) in the event that the Holder’s Note(s) have been converted into shares of Series C-2 Preferred pursuant to Section 3.2, 3.3 or 3.5 of the Purchase Agreement, the number of Exercise Shares shall be equal to the quotient of (A) thirty percent (30%) of the principal amount of the Note issued to such Purchaser at the

Closing, divided by (B) the Series C-2 Original Issue Price (as defined in the Company’s Amended and Restated Certificate of Incorporation, as may be amended from time to time (the “Restated Certificate”)); or

(iii) in the event that the Holder’s Note(s) have been converted into equity securities in a Non-Qualified Financing pursuant to Section 3.4 of the Purchase Agreement, the number of Exercise Shares shall be equal to the quotient of (A) thirty percent (30%) of the principal amount of the Note issued to such Holder at the Closing, divided by (B) the price per share paid by the investor for such equity securities in the Non-Qualified Financing;

provided, however, in each case, that the number of Exercise Shares shall be subject to adjustment pursuant to Section 5 below from and after the Issue Date.

(b) Purchase Price. The purchase price for each Exercise Share issuable pursuant to this Section 1 shall be $0.67; provided, however, that this purchase price shall be subject to adjustment pursuant to Section 5 hereof below from and after the Issue Date. Such purchase price, as adjusted from time to time, is herein referred to as the “Exercise Price.” For purposes of clarification and without modifying the foregoing or amending anything to the contrary herein, the Exercise Price is equal to the fair market value of one share of Common Stock as of the Effective Date (as set forth in the Purchase Agreement), as determined in good faith by the Company’s Board of Directors.

2. Exercise Period. This Warrant shall be exercisable, in whole or in part, during the term commencing on the date that the Holder’s Note(s) converts into equity securities of the Company pursuant to Section 3 of the Purchase Agreement and ending at 5:00 p.m. Pacific Time on [•], 2021 (the “Exercise Period”); provided, that, and subject to Section 3(d) below, this Warrant shall no longer be exercisable and shall become null and void upon the closing of either (i) an Initial Public Offering or (ii) a Change of Control in which the consideration received from the Company pursuant to such Change of Control consists solely of cash and/or securities listed and tradeable on a national securities exchange. In the event of an Initial Public Offering or a Change of Control, the Company shall notify the Holder at least ten (10) days prior to the closing of such Initial Public Offering or Change of Control, as applicable.

3. Method of Exercise.

(a) While this Warrant remains outstanding and exercisable in accordance with Section 2 above, the Holder may exercise, in whole or in part, the purchase rights evidenced hereby. Such exercise shall be effected by:

(i) the surrender of the Warrant, together with a duly executed copy of the Notice of Exercise attached hereto, to the Secretary of the Company at its principal office (or at such other place as the Company shall notify the Holder in writing); and

(ii) the payment to the Company of an amount equal to the aggregate Exercise Price for the Exercise Shares being purchased.

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(b) Each exercise of this Warrant shall be deemed to have been effected immediately prior to the close of business on the day on which this Warrant is surrendered to the Company as provided in Section 3(a) above. At such time, the person or persons in whose name or names any certificate for shares of Common Stock shall be issuable upon such exercise as provided in Section 3(c) below shall be deemed to have become the holder or holders of record of the shares of Common Stock represented by such certificate.

(c) Within a reasonable time after the exercise of this Warrant in whole or in part, the Company at its expense will cause to be issued in the name of, and delivered to, the Holder, or as such Holder (upon payment by such Holder of any applicable transfer taxes) may direct a certificate or certificates for the number of shares of Common Stock to which such Holder shall be entitled.

(d) If the Holder has not exercised this Warrant prior to an Initial Public Offering or a Change of Control in which the consideration received from the Company pursuant to such Change of Control consists solely of cash and/or securities listed and tradeable on a national securities exchange, this Warrant shall automatically and without any further action of the Holder convert into Exercise Shares pursuant to Section 4 prior to the occurrence of such event if not previously exercised or converted before such date.

4. Net Exercise. In lieu of exercising this Warrant for cash during the Exercise Period, from and after the Issue Date, the Holder may elect to receive shares equal to the value of this Warrant (or the portion thereof being exercised) by surrender of this Warrant at the principal office of the Company together with notice of such election (a “Net Exercise”). A Holder who Net Exercises shall have the rights described in Section 3(b) and Section 3(c) hereof, and the Company shall issue to such Holder a number of Exercise Shares computed using the following formula:

Where

For purposes of this Section 4, the fair market value of one share of Common Stock shall be determined as follows:

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(a) If traded on a securities exchange, the fair market value of the Common Stock shall be deemed to be the average of the closing or last reported sale prices of the Common Stock on such exchange over the five (5) day period ending five (5) trading days prior to the date the Net Exercise is made;

(b) If otherwise traded in an over-the-counter market, the fair market value of the Common Stock shall be deemed to be the average of the closing ask prices of the Common Stock over the five day period ending five trading days prior to the date the Net Exercise is made;

(c) If there is no public market for the Common Stock immediately prior to the date the Net Exercise is made, the fair market value shall be determined in good faith by the Company’s Board of Directors; and

(d) If the exercise is in connection with an Initial Public Offering, the fair market value of the Common Stock shall be the price to the public of the shares of Common Stock to be sold in the Initial Public Offering.

5. Adjustment of Exercise Price and Number of Shares of Common Stock. The number and kind of shares of Equity Securities purchasable upon exercise of this Warrant and the Exercise Price shall be subject to adjustment from time to time as follows:

(a) Subdivisions, Combinations and Other Issuances. If the Company shall at any time after the Issue Date but prior to the expiration of this Warrant subdivide its Common Stock, by split-up or otherwise, or combine such Common Stock, or issue additional shares of its Common Stock as a dividend on Common Stock, the number of shares of Common Stock issuable on the exercise of this Warrant shall forthwith be proportionately increased in the case of a subdivision or stock dividend, or proportionately decreased in the case of a combination. Appropriate adjustments shall also be made to the Exercise Price payable per share, but the aggregate Exercise Price payable for the total number of shares of Common Stock purchasable under this Warrant (as adjusted) shall remain the same. Any adjustment under this Section 5(a) shall become effective at the close of business on the date the subdivision or combination becomes effective, or as of the record date of such dividend, or in the event that no record date is fixed, upon the making of such dividend.

(b) Reclassification, Reorganization and Consolidation. In case of any reclassification, capital reorganization or change in the capital stock of the Company (other than as a result of a subdivision, combination or stock dividend provided for in Section 5(a) above) that occurs after the Issue Date, then, as a condition of such reclassification, reorganization or change, lawful provision shall be made, and duly executed documents evidencing the same from the Company or its successor shall be delivered to the Holder, so that the Holder shall thereafter have the right at any time prior to the expiration of this Warrant to purchase, at a total price equal to that payable upon the exercise of this Warrant, the kind and amount of shares of stock and/or other securities or property (including, if applicable, cash) receivable in connection with such

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reclassification, reorganization or change by a holder of the same number and type of securities as were purchasable as shares of Common Stock by the Holder immediately prior to such reclassification, reorganization or change. In any such case appropriate provisions shall be made with respect to the rights and interest of the Holder so that the provisions hereof shall thereafter be applicable with respect to any shares of stock or other securities or property deliverable upon exercise hereof, and appropriate adjustments shall be made to the Exercise Price payable hereunder, provided the aggregate Exercise Price shall remain the same (and, for the avoidance of doubt, this Warrant shall be exclusively exercisable for such shares of stock and/or other securities or property from and after the consummation of such reclassification or other change in the capital stock of the Company).

(c) Notice of Adjustment. When any adjustment is required to be made in the number or kind of shares purchasable upon exercise of the Warrant, or in the Exercise Price, the Company shall promptly notify the Holder of such event and of the number of shares of Common Stock or other securities or property thereafter purchasable upon exercise of this Warrant.

6. Covenants of the Company.

(a) Notices of Record Date. In the event of any taking by the Company 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 any stock dividend) or other distribution, the Company shall mail to the Holder, at least ten (10) days prior to such record date, a notice specifying the date on which any such record is to be taken for the purpose of such dividend or distribution.

(b) Covenants as to shares of Common Stock. The Company covenants and agrees that all shares of Common Stock that may be issued upon the exercise of the rights represented by this Warrant will, upon issuance in accordance with the terms hereof, be validly issued and outstanding, fully paid and nonassessable, and free from all taxes, liens and charges with respect to the issuance thereof.

(c) Registrable Securities. The Exercise Shares shall be considered Registrable Securities (as such term is defined in the Company’s Second Amended and Restated Investor Rights Agreement, dated as of June 29, 2009, as may be amended from time to time (the “IRA”)) and afforded the same rights as provided Registrable Securities in the IRA, including, but not limited to, registration rights.

7. No Fractional Shares or Scrip. No fractional shares or scrip representing fractional shares shall be issued upon the exercise of this Warrant, and any fraction of a share will be rounded down to the next whole share.

8. No Stockholder Rights. Prior to exercise of this Warrant, the Holder shall not be entitled to any rights of a stockholder with respect to the shares of Common Stock, including (without limitation) the right to vote such shares of Common Stock,

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receive dividends or other distributions thereon, exercise preemptive rights or be notified of stockholder meetings, and except as otherwise provided in this Warrant or the Purchase Agreement, such Holder shall not be entitled to any stockholder notice or other communication concerning the business or affairs of the Company.

9. Transfer of Warrant. Other than a surrender of this Warrant to the Company and reissuance of a new warrant to the transferee pursuant to Sections 3 or 4 of this Warrant, any attempted transfer, assignment, delegation or otherwise by the Holder of this Warrant, or of any right, interest or obligation hereunder, shall be null and void; provided, however, that no such restriction shall apply to a transfer by any Holder to (a) a parent, subsidiary or other affiliate of Holder that is a corporation, or (b) any of its partners, members or other equity owners, or retired partners, retired members or other equity owners, or to the estate of any of its partners, members or other equity owners or retired partners, retired members or other equity owners. Nothing in this Warrant, express or implied, is intended to confer upon any party other than the parties hereto or their respective successors and assigns any rights, remedies, obligations or liabilities under or by reason of this Warrant, except as expressly provided in this Warrant.

10. Governing Law. This Warrant shall be governed by and construed under the laws of the State of California as applied to agreements among California residents, made and to be performed entirely within the State of California.

11. Successors and Assigns. The terms and provisions of this Warrant and the Purchase Agreement shall inure to the benefit of, and be binding upon, the Company and the holders hereof and their respective successors and assigns.

12. Titles and Subtitles. The titles and subtitles used in this Warrant are used for convenience only and are not to be considered in construing or interpreting this Warrant.

13. Amendments and Waivers; Resolutions of Dispute; Notice. The amendment or waiver of any term of this Warrant, the resolution of any controversy or claim arising out of or relating to this Warrant and the provision of notice shall be conducted pursuant to the terms of the Purchase Agreement.

14. Severability. If any provision of this Warrant is held to be unenforceable under applicable law, such provision shall be excluded from this Warrant and the balance of the Warrant shall be interpreted as if such provision were so excluded and shall be enforceable in accordance with its terms.

[Signature Page Follows]

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IN WITNESS WHEREOF, the Company has executed this Warrant as of the Issue Date.

[SIGNATURE PAGE TO WARRANT TO PURCHASE COMMON STOCK]

NOTICE OF EXERCISE

HYPERION THERAPEUTICS, INC.

Attention: Corporate Secretary

The undersigned hereby elects to purchase, pursuant to the provisions of the Warrant, as follows:

q                        shares of Common Stock pursuant to the terms of the attached Warrant, and tenders herewith payment in cash of the Exercise Price of such shares in full, together with all applicable transfer taxes, if any.

q                        shares of Common Stock pursuant to the terms of the net exercise provisions set forth in Section 4 of the attached Warrant, and shall tender payment of all applicable transfer taxes, if any.

The undersigned hereby represents and warrants that Representations and warranties in Section 5 of the Purchase Agreement are true and correct as of the date hereof.

Name in which shares should be registered:

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

NOTE: The signature to this Assignment Form must correspond with the name as it appears on the face of the Warrant. Officers of corporations and those acting in a fiduciary or other representative capacity should provide proper evidence of authority to assign the foregoing Warrant.