PREFERRED STOCK PURCHASE WARRANT Shares of Series D Convertible Preferred Stock Subject to determination as set for the below CERULEAN PHARMA INC. Effective as of December 6, 2011 Void after December 6, 2021

Exhibit 10.20

THIS WARRANT HAS NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE “1933 ACT”), OR ANY APPLICABLE STATE SECURITIES LAWS, AND MAY NOT BE SOLD OR TRANSFERRED UNLESS SUCH SALE OR TRANSFER IS IN ACCORDANCE WITH THE REGISTRATION REQUIREMENTS OF SUCH ACT AND APPLICABLE LAWS OR SOME OTHER EXEMPTION FROM THE REGISTRATION REQUIREMENTS OF SUCH ACT AND APPLICABLE LAWS IS AVAILABLE WITH RESPECT THERETO.

PREFERRED STOCK PURCHASE WARRANT

Shares of Series D Convertible Preferred Stock

Subject to determination as set for the below

CERULEAN PHARMA INC.

Effective as of December 6, 2011

Void after December 6, 2021

1. Issuance. This Preferred Stock Purchase Warrant (the “Warrant”) is issued to LIGHTHOUSE CAPITAL PARTNERS VI, L.P. by CERULEAN PHARMA INC., a Delaware corporation (hereinafter with its successors called the “Company”).

2. Purchase Price; Number of Shares.

(a) The registered holder of this Warrant (the “Holder”), is entitled upon surrender of this Warrant with the subscription form annexed hereto duly executed, at the principal office of the Company, to purchase from the Company, at a price per share of $0.83 (the “Purchase Price”), up to a maximum of 963,856 fully paid and non-assessable shares of the Company’s Series D Convertible Preferred Stock, $0.01 par value (the “Preferred Stock”). Commencing on the date hereof, 421,687 (the “Exercise Quantity”) of shares of Preferred Stock are immediately available for purchase hereunder.

(b) On the Commitment Termination Date, the Exercise Quantity shall automatically be increased by such additional number of shares as is equal to (A) 4.5% of the amount of Aggregate Advances funded under the Loan Agreement, if any, divided by (B) the Purchase Price.

In addition to other terms which may be defined herein, the following terms, as used in this Warrant, shall have the following meanings:

Any term not defined herein shall have the meaning as set forth in the Loan Agreement.

Until such time as this Warrant is exercised in full or expires, the Purchase Price and the securities issuable upon exercise of this Warrant are subject to adjustment as hereinafter provided. The person or persons in whose name or names any certificate representing shares of Preferred Stock is issued hereunder shall be deemed to have become the

holder of record of the shares represented thereby as at the close of business on the date this Warrant is exercised with respect to such shares, whether or not the transfer books of the Company shall be closed.

3. Payment of Purchase Price. The Purchase Price may be paid (i) in cash or by check, (ii) by the surrender by the Holder to the Company of any promissory notes or other obligations issued by the Company, with all such notes and obligations so surrendered being credited against the Purchase Price in an amount equal to the principal amount thereof plus accrued interest to the date of surrender, or (iii) by any combination of the foregoing.

4. Net Issue Election. The Holder may elect to receive, without the payment by the Holder of any additional consideration, shares of Preferred Stock equal to the value of this Warrant or any portion hereof by the surrender of this Warrant or such portion to the Company, with the net issue election notice annexed hereto duly executed, at the principal office of the Company. Thereupon, the Company shall issue to the Holder such number of fully paid and nonassessable shares of Preferred Stock as is computed using the following formula:

X=Y(A-B)

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where: X = the number of shares of Preferred Stock to be issued to the Holder pursuant to this Section 4.

“Fair Market Value” of a share of Preferred Stock (or a fully paid and non-assessable share of the Company’s common stock, $0.0001 par value (the “Common Stock”) if all the outstanding shares of Preferred Stock have been converted into Common Stock) as of the date that the net issue election is made (the “Determination Date”) shall mean:

(i) If the net issue election is made in connection with and contingent upon the closing of the sale of the Company’s Common Stock to the public in a public offering pursuant to a Registration Statement under the 1933 Act (a “Public Offering”), and if the Company’s Registration Statement relating to such Public Offering (“Registration Statement”) has been declared effective by the Securities and Exchange Commission, then the initial “Price to Public” specified in the final prospectus with respect to such offering multiplied by the number of shares of Common Stock into which each share of Preferred Stock is then convertible.

(ii) If the net issue election is not made in connection with and contingent upon a Public Offering, then as follows:

(a) If traded on a national securities exchange, the fair market value per share 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 trading day period ending five trading days prior to the Determination Date, and the fair market value per share of the Preferred Stock shall be deemed to be such fair market value per share of the Common Stock multiplied by the number of shares of Common Stock into which each share of Preferred Stock is then convertible;

(b) If otherwise traded in an over-the-counter market, the fair market value per share of the Common Stock shall be deemed to be the average of the closing ask prices of the Common Stock over

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the five trading day period ending five trading days prior to the Determination Date, and the fair market value per share of the Preferred Stock shall be deemed to be such fair market value per share of the Common Stock multiplied by the number of shares of Common Stock into which each share of Preferred Stock is then convertible; and

(c) If there is no public market for the Common Stock, then fair market value shall be determined in good faith by the Company’s Board of Directors.

5. Partial Exercise. This Warrant may be exercised in part, and the Holder shall be entitled to receive a new warrant, which shall be dated as of the date of this Warrant, covering the number of shares in respect of which this Warrant shall not have been exercised.

6. Fractional Shares. In no event shall any fractional share of Preferred Stock be issued upon any exercise of this Warrant. If, upon exercise of this Warrant in its entirety, the Holder would, except as provided in this Section 6, be entitled to receive a fractional share of Preferred Stock, then the Company shall pay the value thereof to the Holder in cash on the basis of the Fair Market Value per share of Preferred Stock, as determined pursuant to Section 4 above (for purposes of such determination, references in Section 4 to “net issue election” shall be deemed to refer to the “exercise” of this Warrant).

7. Expiration Date; Automatic Exercise. This Warrant shall expire at the close of business on December 6, 2021, and shall be void thereafter (the “Expiration Date”). Notwithstanding the term of this Warrant fixed pursuant to this Section 7, and provided Holder has received advance written notice of at least twenty (20) days and has not earlier exercised this Warrant, and provided this Warrant has not been assumed by the successor entity (or parent thereof), upon the consummation of a Merger (as defined below), this Warrant shall automatically be exercised in full pursuant to Section 4 hereof, without any action by Holder. “Merger” means: (i) a sale of all or substantially all of the Company’s assets to an Unaffiliated Entity (as defined below), or (ii) the merger, consolidation or acquisition of the Company with, into or by an Unaffiliated Entity (other than a merger or consolidation for the principal purpose of changing the domicile of the Company or a bona fide round of preferred stock equity financing), that results in the transfer of fifty percent (50%) or more of the outstanding voting power of the Company. “Unaffiliated Entity” means any entity that is owned or controlled by parties who own less than twenty percent (20%) of the combined voting power of the voting securities of the Company immediately prior to such merger, consolidation or acquisition. Notwithstanding the foregoing, in the event that any outstanding warrants to purchase equity securities of the Company are assumed by the successor entity of a Merger (or parent thereof), this Warrant shall also be similarly assumed. The Company agrees to promptly give the Holder written notice of any proposed Merger and written notice of termination of any proposed Merger. Notwithstanding anything to the contrary in this Warrant, the Holder may rescind any exercise of its purchase rights after a notice of termination of the proposed Merger if the exercise of this Warrant occurred after the Company notified the Holder that the Merger was proposed or if the exercise was otherwise precipitated by such proposed Merger, provided, however that such rescission right must be exercised within thirty (30) days of receipt of such written notice of termination of the proposed Merger. In the event of such rescission, this Warrant will continue to be exercisable on the same terms and conditions as prior to the exercise.

8. Reserved Shares; Valid Issuance. The Company covenants that it will at all times from and after the date hereof reserve and keep available such number of its authorized shares of Preferred Stock and Common Stock free from all preemptive or similar rights therein, as will be sufficient to permit, respectively, the exercise of this Warrant in full and the conversion into shares of Common Stock of all shares of Preferred Stock issuable upon such exercise. The Company further covenants that such shares as may be issued pursuant to such exercise and/or conversion will, upon issuance, be duly and validly issued, fully paid and non-assessable and free from all taxes, liens and charges with respect to the issuance thereof.

9. Stock Splits and Dividends. If after the date hereof the Company shall subdivide the Preferred Stock, by split-up or otherwise, or combine the Preferred Stock, or issue additional shares of Preferred Stock in payment of a stock dividend on the Preferred Stock, the number of shares of Preferred Stock issuable on the exercise of this Warrant shall forthwith be proportionately increased in the case of a subdivision or stock dividend, or

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proportionately decreased in the case of a combination, and the Purchase Price shall forthwith be proportionately decreased in the case of a subdivision or stock dividend, or proportionately increased in the case of a combination.

10. Adjustments for Diluting Issuances. The other anti-dilution rights applicable to the Preferred Stock are set forth in the Amended and Restated Certificate of Incorporation, as amended from time to time (the “Certificate”), a true and complete copy of which, in its current form, is attached hereto as Exhibit A. Such rights shall not be restated, amended or modified in any manner without the Holder’s prior written consent if the effect of such action would be more adverse to the Holder than, and substantially dissimilar to, the effect of such action on the other holders of the Preferred Stock. The Company shall promptly provide the Holder hereof with any restatement, amendment or modification to the Articles promptly after the same has been made.

11. Mergers and Reclassifications. Subject to Section 7, if after the date hereof the Company shall enter into any Reorganization (as hereinafter defined), then, as a condition of such Reorganization, unless the Company shall have complied with Section 7, lawful provisions 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 to purchase, at a total price not to exceed that payable upon the exercise of this Warrant in full, the kind and amount of shares of stock and other securities and property receivable upon such Reorganization by a holder of the number of shares of Preferred Stock which might have been purchased by the Holder immediately prior to such Reorganization, and in any such case appropriate provisions shall be made with respect to the rights and interest of the Holder to the end that the provisions hereof (including without limitation, provisions for the adjustment of the Purchase Price and the number of shares issuable hereunder and the provisions relating to the net issue election) shall thereafter be applicable in relation to any shares of stock or other securities and property thereafter deliverable upon exercise hereof. For the purposes of this Section 11, the term “Reorganization” shall mean any reclassification, capital reorganization or change of the Preferred Stock (other than as a result of a subdivision, combination or stock dividend provided for in Section 9 hereof), or any consolidation of the Company with, or merger of the Company into, another corporation or other business organization (other than a merger in which the Company is the surviving corporation and which does not result in any reclassification or change of the outstanding Preferred Stock), or any sale or conveyance to another corporation or other business organization of all or substantially all of the assets of the Company.

12. Certificate of Adjustment. Whenever the Purchase Price is adjusted, as herein provided, the Company shall promptly deliver to the Holder a certificate of the Company’s chief financial officer setting forth the Purchase Price after such adjustment and setting forth a brief statement of the facts requiring such adjustment.

13. Notices of Record Date, Etc. In the event of:

(a) 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 or other distribution, or any right to subscribe for, purchase, sell or otherwise acquire or dispose of any shares of stock of any class or any other securities or property, or to receive any other right;

(b) any reclassification of the Common Stock, Preferred Stock, or any other Series of stock of the Company, capital reorganization of the Company, consolidation or merger involving the Company, or sale or conveyance of all or substantially all of its assets; or

(c) any voluntary or involuntary dissolution, liquidation or winding-up of the Company;

then in each such event the Company will provide or cause to be provided to the Holder a written notice thereof. Such notice shall be provided at least twenty (20) days prior to the date specified in such notice on which any such action is to be taken.

14. Representations, Warranties and Covenants. This Warrant is issued and delivered by the Company and accepted by each Holder on the basis of the following representations, warranties and covenants made by the Company:

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(a) The Company has all necessary authority to issue, execute and deliver this Warrant and to perform its obligations hereunder. This Warrant has been duly authorized issued, executed and delivered by the Company and is the valid and binding obligation of the Company, enforceable in accordance with its terms.

(b) The shares of Preferred Stock issuable upon the exercise of this Warrant have been duly authorized and reserved for issuance by the Company and, when issued in accordance with the terms hereof, will be validly issued, fully paid and nonassessable.

(c) The issuance, execution and delivery of this Warrant do not, and the issuance of the shares of Preferred Stock upon the exercise of this Warrant in accordance with the terms hereof will not, (i) violate or contravene the Company’s Certificate or by-laws, or any law, statute, regulation, rule, judgment or order applicable to the Company, (ii) violate, contravene or result in a breach or default under any contract, agreement or instrument to which the Company is a party or by which the Company or any of its assets are bound or (iii) require the consent or approval of or the filing of any notice or registration with any person or entity, other than filings pursuant to Regulation D promulgated under the 1933 Act.

(d) As long as this Warrant is, or any shares of Preferred Stock issued upon exercise of this Warrant or any shares of Common Stock issued upon conversion of such shares of Preferred Stock are, issued and outstanding (but in no event after a Public Offering), the Company will provide to the Holder the financial and other information described in the Loan Agreement.

(e) As of the date hereof, the authorized capital stock of the Company consists of (i) 115,000,000 shares of Common Stock, of which 8,831,480 shares are issued and outstanding and 963,856 shares are reserved for issuance upon the exercise of this Warrant with respect to Common Stock and the conversion of the Preferred Stock into Common Stock if this Warrant is exercised with respect to Preferred Stock, (ii) 2,500,000 shares of Seed Convertible Preferred Stock, all of which are issued and outstanding shares, (iii) 9,307,692 shares of Series A Convertible Preferred Stock, all of which are issued and outstanding shares, (iv) 4,077,500 shares of Series B Convertible Preferred Stock, 4,062,500 of which are issued and outstanding shares, (v) 5,000,000 shares of Series B-1 Preferred Stock, all of which are issued and outstanding shares; (vi) 33,310,787 shares of Series C Preferred Stock, of which 32,432,417 are issued and outstanding shares; and (vii) 19,036,143 shares of Series D Preferred Stock, of which 18,072,287 are issued and outstanding shares, Attached hereto as Exhibit B is a capitalization table summarizing the capitalization of the Company. Upon request, not more than once per calendar quarter, the Company will provide Holder with a current capitalization table indicating changes, if any, to the number of outstanding shares of Common Stock, Preferred Stock, and any other series of stock outstanding, provided, however, that the Company shall not be considered in default of this Warrant unless the Holder has not received such capitalization table within ten (10) days of such request.

15. Registration Rights. The Company represents and warrants that is has granted to Holder certain registration rights under Section 8 that certain Series D Convertible Preferred Stock Purchase Agreement, dated as of December 2, 2011, among the Company and the Purchasers and Holders party thereto (the “Stock Purchase Agreement”), that the Holder hereunder shall be deemed a “Holder” for purposes of Section 8 of the Stock Purchase Agreement and as such that the shares of Common Stock issuable upon conversion of the shares of Preferred Stock issuable upon exercise of this Warrant, or issuable upon exercise of this Warrant (in the event this Warrant becomes exercisable for Common Stock), are deemed to be “Registrable Securities” for the purposes of Section 8 Stock Purchase Agreement; provided, however, that in no event shall Holder be permitted to be an Initiating Holder (as defined in the Stock Purchase Agreement) under Section 8.2 of the Stock Purchase Agreement, The Company shall not take, nor shall it permit to be taken, any action that would diminish, frustrate or limit the rights of Holder under Section 8 of the Stock Purchase Agreement in any manner in which the other “Holders” under the Stock Purchase Agreement are not likewise adversely affected.

16. Amendment. The terms of this Warrant may be amended, modified or waived only with the written consent of the Holder and the Company.

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17. Representations and Covenants of the Holder. This Warrant has been entered into by the Company in reliance upon the following representations and covenants of the Holder, which by its execution hereof the Holder hereby confirms:

(a) Investment Purpose. This Warrant and the securities issuable upon exercise of the Holder’s rights contained herein will be acquired for investment and not with a view to the sale or distribution of any part thereof, and the Holder has no present intention of selling or engaging in any public distribution of the same except pursuant to a registration or exemption.

(b) Accredited Investor. Holder is an “accredited investor” within the meaning of Regulation D promulgated under the 1933 Act, as presently in effect.

(c) Private Issue. The Holder understands (i) that the securities issuable upon exercise of the Holder’s rights contained herein is not registered under the 1933 Act or qualified under applicable state securities laws on the ground that the issuance contemplated by this Warrant will be exempt from the registration and qualification requirements thereof, and (ii) that the Company’s reliance on such exemption is predicated on the representations set forth in this Section 17.

(d) Financial Risk. The Holder has such knowledge and experience in financial and business matters as to be capable of evaluating the merits and risks of its investment and has the ability to bear the economic risks of its investment.

18. Notices, Transfers, Etc.

(a) Any notice or written communication required or permitted to be given to the Holder may be given by certified mail or delivered by reputable overnight courier or by hand to the Holder at the address most recently provided by the Holder to the Company.

(b) Prior to a Public Offering, neither this Warrant, nor the shares of capital stock issuable upon exercise of this Warrant (or upon conversion of the shares of Preferred Stock issuable upon exercise of this Warrant) shall be sold or transferred unless the Company first shall have been furnished with an opinion of legal counsel, reasonably satisfactory to the Company, to the effect that such sale or transfer is exempt from the registration requirements of the 1933 Act. The Company shall not require a legal opinion in connection with any transfer by Holder to an affiliate of Holder, provided that such transferee is an “accredited investor” within the meaning of Rule 501 of Regulation D, as in effect under the 1933 Act. Notwithstanding the foregoing, neither this Warrant nor the shares of capital stock issuable upon exercise of this Warrant (or upon conversion of the shares of Preferred Stock issuable upon exercise of this Warrant) may be transferred to a competitor of the Company (as determined in good faith by the Company’s Board of Directors) prior to a Public Offering. Upon surrender of this Warrant to the Company, together with the assignment notice annexed hereto duly executed, for transfer of this Warrant as an entirety by the Holder, the Company shall issue a new warrant of the same denomination to the assignee. Upon surrender of this Warrant to the Company, together with the assignment hereof properly endorsed, by the Holder for transfer with respect to a portion of the shares of Preferred Stock purchasable hereunder, the Company shall issue a new warrant to the assignee, in such denomination as shall be requested by the Holder hereof, and shall issue to such Holder a new warrant covering the number of shares in respect of which this Warrant shall not have been transferred.

(c) In case this Warrant shall be mutilated, lost, stolen or destroyed, the Company shall issue a new warrant of like tenor and denomination and deliver the same (i) in exchange and substitution for and upon surrender and cancellation of any mutilated Warrant, or (ii) in lieu of any Warrant lost, stolen or destroyed, upon receipt of an affidavit of the Holder or other evidence reasonably satisfactory to the Company of the loss, theft or destruction of such Warrant

19. No Impairment. The Company will not, without the prior written consent of the Holder, by amendment of its Certificate or through any reclassification, capital reorganization, consolidation, merger, sale or

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conveyance of assets, dissolution, liquidation, issue or sale of securities or any other voluntary action, avoid or seek to avoid the observance of 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 action as may be necessary or appropriate in order to protect the rights of the Holder.

20. Governing Law. The provisions and terms of this Warrant shall be governed by and construed in accordance with the internal laws of the State of California without giving effect to its principles regarding conflicts of laws.

21. Successors and Assigns. This Warrant shall be binding upon the Company’s successors and assigns and shall inure to the benefit of the Holder’s permitted successors, legal representatives and permitted assigns.

22. Business Days. If the last or appointed day for the taking of any action required or the expiration of any rights granted herein shall be a Saturday or Sunday or a legal holiday in California, then such action may be taken or right may be exercised on the next succeeding day which is not a Saturday or Sunday or such a legal holiday.

23. Conversion. If all of the outstanding shares of Preferred Stock are converted into Common Stock, effective upon such conversion, this Warrant shall change from the right to purchase shares of Preferred Stock to the right to purchase shares of Common Stock, and the Holder shall thereupon have the right to purchase, at a total price equal to that payable upon the exercise of this Warrant in full, the number of shares of Common Stock which would have been receivable by the Holder upon the exercise of this Warrant for shares of Preferred Stock immediately prior to such conversion of such shares of Preferred Stock into shares of Common Stock, and in such event appropriate provisions shall be made with respect to the rights and interest of the Holder to the end that the provisions hereof (including, without limitation, the provisions for the adjustment of the Purchase Price and of the number of shares purchasable upon exercise of this Warrant and the provisions relating to the net issue election) shall thereafter be applicable to any shares of Common Stock deliverable upon the exercise hereof, and all references in this Warrant to “Preferred Stock” shall thereafter be deemed to refer to “Common Stock.”

24. Value. The Company and the Holder agree that the value of this Warrant on the date of grant is $100.

25. Legends. Each certificate representing shares issuable upon exercise of this Warrant shall bear a legend substantially in the form set forth in Section 3.8 of the Series D Convertible Preferred Stock Purchase Agreement dated December 2, 2011.

26. Market Stand-Off Agreement. The Holder hereby agrees that, during a period of 180 days following the effective date of a registration statement of the Company filed under the 1933 Act relating to the initial Public Offering of the Company, plus up to an additional 34 days to the extent requested by the managing underwriter(s) for such offering in order to address Rule 2711(f) of the National Association of Securities Dealers, Inc. or any similar successor provision (such period, the “Lock-Up Period”), such Holder shall not, to the extent requested by the Company and such managing underwriter(s), directly or indirectly sell, offer to sell, contract to sell (including any short sale), grant any option to purchase, or otherwise transfer or dispose of (other than to donees who agree to be similarly bound) any securities of the Company held by it at any time during such period except Common Stock included in such registration; provided, however, that the Holder shall not be required to enter into such an agreement unless all officers and directors of the Company and stockholders holding in excess of one percent (1%) of the outstanding Common Stock (treating all Preferred Stock on an as-converted to Common Stock basis) enter into similar agreements.

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27. No Rights as a Stockholder. Until the exercise of this Warrant, the Holder shall not have or exercise any rights by virtue hereof as a stockholder of the Company.

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Subscription

The undersigned hereby subscribes for _____________ shares of Preferred Stock covered by this Warrant. The certificate(s) for such shares shall be issued in the name of the undersigned or as otherwise indicated below:

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Net Issue Election Notice

The undersigned hereby elects under Section 4 to surrender the right to purchase shares of Preferred Stock pursuant to this Warrant. The certificate(s) for such shares issuable upon such net issue election shall be issued in the name of the undersigned or as otherwise indicated below:

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Assignment

For value received ____________________________________________ hereby sells, assigns and transfers unto

[Please print or typewrite name and address of Assignee]

the within Warrant, and does hereby irrevocably constitute and appoint __________________________ its attorney to transfer the within Warrant on the books of the within named Company with full power of substitution on the premises.

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AMENDMENT NO. 01

Dated October 2, 2012

TO

that certain Preferred Stock Purchase Warrant, effective as of December 6, 2011 (“Warrant”)

issued to Lighthouse Capital Partners VI, L.P. (“Holder”)

by Cerulean Pharma Inc. (“Company”).

Without limiting or amending any other provisions of the Warrant, Holder and Company hereby agree to the following:

1. The first paragraph of Section 2(b) shall be deleted in its entirety and replaced with the following:

2. Except as specifically set forth herein, the Warrant remains unmodified and unchanged.

3. This Amendment may be executed in one or more counterparts, each of which shall for all purposes be deemed to be an original, and all of which together shall constitute one and the same document.

4. The provisions and terms of this Amendment shall be governed by and construed in accordance with the internal laws of the State of California without giving effect to its principles regarding conflicts of law.

5. All capitalized terms not otherwise defined herein shall have the meanings given to such terms in the Warrant.

[Remainder of Page Intentionally Left Blank.]

[Signature Page to Amendment No. 1 to Preferred Stock Purchase Warrant]