Warrant to Purchase Shares of Capital Stock, dated February 22, 2018

Exhibit 4.4

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.

EIDOS THERAPEUTICS, INC.

WARRANT TO PURCHASE SHARES OF CAPITAL STOCK

For valued received, pursuant to the that certain Note and Warrant Purchase Agreement (the “Purchase Agreement”) dated as of February 22, 2018, by and among the Company and the purchasers listed on Exhibit A thereto, this Warrant is issued to BridgeBio Pharma LLC, or its assigns (the “Holder”) by Eidos Therapeutics, Inc., a Delaware corporation (the “Company”). Capitalized terms not defined herein shall have the meaning set forth in the Purchase Agreement.

1. Purchase of Shares.

(a) Number of Warrant Shares. Subject to the terms and conditions set forth herein and in the Purchase Agreement, the Holder is entitled, upon surrender of this Warrant at the principal office of the Company (or at such other place as the Company shall notify the Holder in writing), to purchase from the Company up to a number of fully paid and nonassessable Warrant Shares equal to $4,000,000, divided by the applicable Exercise Price (as defined below), rounded down to the nearest whole share, subject to adjustment pursuant to Section 7 hereof. As used herein, “Warrant Shares” shall mean:

(i) if the Exercise Period commences upon a Qualified Financing as set forth in clause (a) of Section 2 below, shares of New Preferred Stock (as defined in the Notes); and

(ii) if the Exercise Period commences immediately prior to the consummation of a Deemed Liquidation Event (as defined in the Company’s Certificate of Incorporation) as set forth in clause (b) of Section 2 below, shares of the Company’s Series Seed Preferred Stock, par value $0.001 per share (the “Series Seed Preferred Stock”).

(b) Exercise Price. The purchase price for the Warrant Shares issuable pursuant to this Section 1 shall be:

(i) if the Warrant is exercisable for shares of New Preferred Stock in accordance with Section 1(a)(i), the lowest per share purchase price at which shares of the New Preferred Stock are or have been sold in the Qualified Financing at the time of conversion of the Notes; and

(ii) if the Warrant is exercisable for shares of Series Seed Preferred Stock in accordance with Section 1(a)(ii), $1.3248 per share.

Such purchase price, subject to adjustment pursuant to Section 7 hereof from time to time, is herein referred to as the “Exercise Price.”

2. Exercise Period. This Warrant shall be exercisable, in whole or in part, during the term commencing on the earlier to occur of: (a) the consummation of a Qualified Financing and (b) immediately prior to the consummation of a Deemed Liquidation Event (but subject to and contingent upon the consummation of such Deemed Liquidation Event) and ending on the earlier to occur of (x) three (3) years after the commencement of exercisability or (y) the consummation of a Deemed Liquidation Event or IPO, as set forth in Section 2(d) (the “Exercise Period”).

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 number and type of Warrant Shares being purchased.

(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 the Warrant Shares 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 Warrant Shares represented by such certificate.

(c) As soon as practicable 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:

(i) a certificate or certificates for the number of Warrant Shares to which such Holder shall be entitled, and

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(ii) in case such exercise is in part only, a new warrant or warrants (dated the date hereof) of like tenor, calling in the aggregate on the face or faces thereof for the number of Warrant Shares equal to the number of such Warrant Shares called for on the face of this Warrant minus the number of Warrant Shares purchased by the Holder upon all exercises made in accordance with Section 3(a) above or Section 4 below.

(d) Notwithstanding the provisions of Section 2 and subject to the provisions of Section 5, if the Holder has not exercised this Warrant prior to the closing of a Deemed Liquidation Event or an IPO (as defined below), this Warrant shall automatically be deemed to be exercised in full in the manner set forth in Section 4, without any further action on behalf of the Holder, immediately prior to such closing (and in the case of a Deemed Liquidation Event, subject to and contingent upon such Deemed Liquidation Event), and thereafter, this Warrant shall be automatically cancelled on the books of the Company and shall be of no further force or effect, except as to the Holder’s right to receive Warrant Shares in accordance with the terms and conditions of Section 4. For purposes hereof, an “IPO” shall mean the first firm-commitment underwritten public offering of Common Stock pursuant to an effective registration statement under the Securities Act.

4. Net Exercise. In lieu of exercising this Warrant for cash, 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 Sections 3(b) and 3(c) hereof, and the Company shall issue to such Holder a number of Warrant Shares computed using the following formula:

Where

For purposes of this Section 4, (a) in the event that this Warrant is exercised pursuant to this Section 4 in connection with and contingent upon the closing of an IPO, the fair market value per Warrant Share shall be (i) the per share offering price to the public of the Common Stock in the IPO if the Warrant is exercisable for Common Stock and (ii) the per share offering price to the public of the Common Stock in the IPO, multiplied by the number of shares of Common Stock into which each Warrant Share is then convertible, if the Warrant is exercisable for New Preferred Stock or Series Seed Preferred Stock, as applicable, and (b) in all other instances in which this Warrant is exercised pursuant to this Section 4, the fair market value per Warrant Share shall be the price per share of the class and series of such Warrant Share, as such price shall be determined in good faith by the Company’s Board of Directors.

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5. [Reserved].

6. Covenants of the Company.

(a) Notices of Record Date, Deemed Liquidation Event or IPO. In the event of any (i) 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 a stock dividend) or other distribution, (ii) Deemed Liquidation Event or (iii) IPO, the Company shall mail to the Holder, at least ten (10) days prior to such record date or the anticipated closing date of such Deemed Liquidation Event or IPO, a notice specifying the date on which any such record is to be taken for the purpose of such dividend or distribution or such anticipated closing date, as the case may be.

(b) Covenants as to Warrant Shares. The Company covenants and agrees that all Warrant Shares 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. The Company further covenants and agrees that the Company will at all times during the Exercise Period have authorized and reserved, free from preemptive rights, a sufficient number of shares of New Preferred Stock or Series Seed Preferred Stock, as applicable, to provide for the exercise of the rights represented by this Warrant and, if the Warrant is exercisable for New Preferred Stock, a sufficient number of shares of Series Seed Preferred Stock to provide for the conversion of the Warrant Shares. If at any time during the Exercise Period the number of authorized but unissued shares of New Preferred Stock or Series Seed Preferred Stock shall not be sufficient to permit exercise of this Warrant, the Company will take such corporate action as may be necessary to increase its authorized but unissued shares of New Preferred Stock or Series Seed Preferred Stock to such number of shares as shall be sufficient for such purposes, together with any necessary increase in the number of shares of Common Stock reserved for the conversion of such shares of New Preferred Stock or Series Seed Preferred Stock, and the Holder shall cooperate with the Company in connection therewith, including by executing and delivering such consents and other agreements or documents in the Holder’s capacity as a stockholder of the Company as may be necessary for the Company to effect such actions.

7. Adjustment of Exercise Price and Number of Warrant Shares. The number of Warrant Shares 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 issuance but prior to the expiration of this Warrant subdivide, by split-up or otherwise, or combine, the shares of the class or series of capital stock corresponding to the Warrant Shares, or issue additional shares of capital stock as a dividend with respect to any shares of the class or series of capital stock corresponding to the Warrant Shares, the number of Warrant Shares 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

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share, but the aggregate Exercise Price payable for the total number of Warrant Shares purchasable under this Warrant (as adjusted) shall remain the same. Any adjustment under this Section 7(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 7(a) above), 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 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 other securities or property receivable in connection with such reclassification, reorganization or change by a holder of the same number and type of securities as were purchasable as Warrant Shares 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 per Warrant Share payable hereunder, provided the aggregate Exercise Price shall remain the same.

(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 Warrant Shares or other securities or property thereafter purchasable upon exercise of this Warrant.

8. No Fractional Shares or Scrip. No fractional shares or scrip representing fractional shares shall be issued upon the exercise of this Warrant, but in lieu of such fractional shares the Company shall make a cash payment therefor on the basis of the Exercise Price then in effect.

9. 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 Warrant Shares, including (without limitation) the right to vote such Warrant Shares, 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.

10. Governing Law. This Warrant shall be governed by and construed in accordance with the Delaware General Corporation Law as to matters within the scope thereof, and as to all other matters shall be governed by, and construed in accordance with, the internal laws of the State of California, without reference to principles of conflict of laws or choice of laws.

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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. Notices. Any notice required or permitted hereunder shall be given in writing and shall be conclusively deemed effectively given (a) upon personal delivery or delivery by courier, (b) when sent, if sent by electronic mail or facsimile during normal business hours of the recipient, and if not sent during normal business hours, then on the next business day after transmission if sent by confirmed electronic mail or facsimile transmission, (c) for domestic United States deliveries, four (4) business days after deposit in the United States mail, by registered or certified mail, postage prepaid, or (d) for international deliveries, four (4) business days after deposit with an internationally recognized overnight delivery service, specifying two-(2-) day delivery, postage prepaid, addressed (i) if to the Company, at the principal offices of the Company and (ii) if to the Holder, at the Holder’s address as set forth on Exhibit A to the Purchase Agreement, or at such other address as the Company or the Holder may designate by advance written notice to the other party hereto. For purposes of this Section 13, a “business day” means a weekday on which banks are open for general banking business in San Francisco, California.

14. Amendment. This Warrant may not be amended or modified, or any provision hereof waived, except by a written instrument signed in accordance with the amendment and waiver provisions set forth in Section 6.02 of the Purchase Agreement.

15. 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.

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IN WITNESS WHEREOF, the parties have executed this Warrant as of the date first written above.

Acknowledged and agreed by the Holder:

[SIGNATURE PAGE TO WARRANT]

NOTICE OF EXERCISE

Attention: Corporate Secretary

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

The undersigned hereby represents and warrants that the representations and warranties in Article 4 of the Purchase Agreement are true and correct as to the undersigned as of the date hereof.

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.