WARRANT TO PURCHASE STOCK

Exhibit 4.1

THIS WARRANT AND THE SHARES ISSUABLE HEREUNDER HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE “ACT”), OR THE SECURITIES LAWS OF ANY STATE AND, EXCEPT AND PURSUANT TO THE PROVISIONS OF ARTICLE 5 BELOW, MAY NOT BE OFFERED, SOLD OR OTHERWISE TRANSFERRED, PLEDGED OR HYPOTHECATED UNLESS AND UNTIL REGISTERED UNDER SAID ACT AND APPLICABLE STATE SECURITIES LAW OR, IN THE OPINION OF LEGAL COUNSEL IN FORM AND SUBSTANCE SATISFACTORY TO THE ISSUER OF THESE SECURITIES, SUCH OFFER, SALE OR TRANSFER, PLEDGE OR HYPOTHECATION IS EXEMPT FROM REGISTRATION.

WARRANT TO PURCHASE STOCK

Company: MediciNova, Inc., a Delaware corporation

Number of Shares: 198,020, subject to adjustment

Class of Stock: Common Stock, $0.001 par value per share

Warrant Price: $6.06, subject to adjustment

Issue Date: May 10, 2010

Expiration Date: May 10, 2017

THIS WARRANT CERTIFIES THAT, for good and valuable consideration, OXFORD FINANCE CORPORATION (together with any successor or permitted assignee or transferee of this Warrant or of any Shares issued upon exercise or conversion hereof, “Holder”) is entitled to purchase the number of fully paid and non-assessable shares (the “Shares”) of the above-stated Class of Stock (the “Class”) of the above-named company (the “Company”) at the above-stated Warrant Price per Share, all as set forth above and as adjusted pursuant to Article 2 of this Warrant, subject to the provisions and upon the terms and conditions set forth in this Warrant.

ARTICLE 1. EXERCISE.

1.1 Method of Exercise. Holder may exercise this Warrant by delivering the original of this Warrant together with a duly executed Notice of Exercise in substantially the form attached as Appendix 1 to the principal office of the Company. Unless Holder is exercising the conversion right set forth in Article 1.2, Holder shall also deliver to the Company a check, wire transfer (to an account designated by the Company), or other form of payment acceptable to the Company for the aggregate Warrant Price for the Shares being purchased.

1.2 Conversion Right. In lieu of exercising this Warrant as specified in Article 1.1, Holder may from time to time convert this Warrant, in whole or in part, by surrendering this Warrant for that number of shares of the Class equal to the quotient obtained by dividing (x) the product of (i) the number of Shares underlying that portion of the Warrant to be surrendered, multiplied by (ii) the positive difference, if any, between the exercise price of such Warrant and the fair market value (as defined below), by (y) the fair market value.

1.3 Fair Market Value. If shares of the Class are then publicly listed or quoted on one or more securities exchanges, inter-dealer quotation systems or over-the-counter markets, the fair market value of a Share shall be the volume-weighted average of the closing prices of a share of the Class reported on the principal such exchange, system or market in the United States (or, if shares of the Class are not then publicly listed or quoted on one or more securities exchanges, inter-dealer quotation systems or over-the-counter markets in the United States, on the principal such non-US exchange, system or market) for the ten (10) consecutive trading days immediately prior to the date on which Holder delivers this Warrant together with its Notice of Exercise to the Company. If shares of the Class are not then publicly listed or quoted on one or more securities exchanges, inter-dealer quotation systems or over-the-counter markets, then the Board of Directors of the Company shall determine the fair market value of a Share in its reasonable good faith judgment.

1.4 Delivery of Certificate and New Warrant. Promptly after Holder exercises or converts this Warrant and, if applicable, the Company receives payment of the aggregate Warrant Price, the Company shall deliver to Holder certificates for the Shares acquired and, if this Warrant has not been fully exercised or converted and has not expired, a new warrant of like tenor representing the Shares not so acquired.

1.5 Replacement of Warrants. On receipt of evidence reasonably satisfactory to the Company of the loss, theft, destruction or mutilation of this Warrant and, in the case of loss, theft or destruction, on delivery of an indemnity agreement reasonably satisfactory in form and amount to the Company or, in the case of mutilation, on surrender and cancellation of this Warrant, the Company shall execute and deliver, in lieu of this Warrant, a new warrant of like tenor.

ARTICLE 2. ADJUSTMENTS TO THE SHARES.

2.1 Stock Dividends, Splits, Etc. If the Company declares or pays a dividend on the outstanding shares of the Class payable in additional shares of the Class or other securities, then upon exercise or conversion of this Warrant, for each Share acquired, Holder shall receive, without cost to Holder, the total number and kind of securities to which Holder would have been entitled had Holder owned the Shares of record as of the date the dividend occurred. If the Company subdivides the outstanding shares of the Class by reclassification or otherwise into a greater number of shares, the number of Shares purchasable hereunder shall be proportionately increased and the Warrant Price shall be proportionately decreased. If the outstanding shares of the Class are combined or consolidated, by reclassification or otherwise, into a lesser number of shares, the Warrant Price shall be proportionately increased and the number of Shares shall be proportionately decreased.

2.2 Reclassification, Reorganization, Merger, Etc. In case of any reclassification or reorganization of the Company’s Common Stock (other than a change otherwise covered by this Article 2 or that solely affects the par value of the Class), or in the case of any merger or consolidation of the Company into or with another entity (other than a consolidation or merger in which the Company is the successor or surviving entity and that does not result in any reclassification or reorganization of the outstanding shares of the Class), or in the case of any sale or conveyance to another entity of the

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assets or other property of the Company as an entirety or substantially as an entirety in connection with which the Company is dissolved and liquidated, the holder of this Warrant shall thereafter have the right to purchase and receive, upon the basis and upon the terms and conditions specified in this Warrant and in lieu of the shares of the Class immediately theretofore purchasable and receivable upon the exercise of the rights represented thereby, the kind and amount of shares of stock or other securities or property (including cash) receivable upon such reclassification, reorganization, merger or consolidation, or upon a dissolution following any such sale or transfer, that the Warrant holder would have received if such Warrant holder had exercised this Warrant immediately prior to such event; and if any such event also results in a change in shares of the Class otherwise covered by Article 2.1, then such adjustment shall be made pursuant to Article 2.1 and this Article 2.2. The provisions of this Article 2.2 shall similarly apply to successive reclassifications, reorganizations, mergers or consolidations, sales or other transfers.

2.3 Merger, Consolidation. In case of any merger or consolidation of the Company into or with another entity (other than a consolidation or merger in which the Company is the successor or surviving entity and that does not result in any reclassification or reorganization of the outstanding shares of the Class), or in the case of any sale or conveyance to another entity of the assets or other property of the Company as an entirety or substantially as an entirety in connection with which the Company is dissolved and liquidated, this Warrant shall expire concurrently with the completion of such transaction unless otherwise provided in the definitive transaction documentation.

2.4 No Impairment. The Company shall not, by amendment of its Certificate of Incorporation or through a 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 under this Warrant by the Company, but shall at all times in good faith assist in carrying out of all the provisions of this Article 2 and in taking all such action as may be necessary or appropriate to protect Holder’s rights under this Article 2 against impairment; provided, however, that notwithstanding the foregoing, nothing in this Article 2.4 shall restrict or impair the Company’s right to effect changes to the rights, preferences, and privileges associated with the Shares with the requisite consent of the stockholders as may be required to amend the Certificate of Incorporation from time to time so long as such amendment affects the rights, preferences, and privileges granted to Holder associated with the Shares in the same manner as the other holders of outstanding shares of the Class.

2.5 Fractional Shares. No fractional Shares shall be issuable upon exercise or conversion of the Warrant and the number of Shares to be issued shall be rounded down to the nearest whole Share. If a fractional share interest arises upon any exercise or conversion of the Warrant, the Company shall eliminate such fractional share interest by paying Holder the amount computed by multiplying the fractional interest by the fair market value of a full Share.

2.6 Certificate as to Adjustments. Upon each adjustment of the Warrant Price, Class and/or number of Shares, the Company shall promptly notify Holder in writing, and, at the Company’s expense, promptly compute such adjustment, and furnish Holder with a certificate of its Chief Financial Officer setting forth such

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adjustment and the facts upon which such adjustment is based. The Company shall, upon written request, furnish Holder a certificate setting forth the Warrant Price, Class and number of Shares in effect upon the date thereof and the series of adjustments leading to such Warrant Price, Class and number of Shares.

ARTICLE 3. REPRESENTATIONS AND COVENANTS OF THE COMPANY.

3.1 Representations and Warranties. The Company represents and warrants to, and agrees with, the Holder as follows:

(a) All Shares which may be issued upon the exercise or conversion of this Warrant shall at all times during the term hereof and prior to exercise or conversion in full hereof be duly reserved out of the Company’s authorized and unissued capital stock for issuance upon exercise or conversion hereof and shall, upon issuance, be duly and validly issued, fully paid and non-assessable, and free of any liens and encumbrances except for restrictions on transfer provided for herein or under applicable federal and state securities laws.

3.2 Notice of Certain Events. If the Company proposes at any time (a) to declare any dividend or distribution upon the outstanding shares of the Class, whether in cash, property, stock, or other securities and whether or not a regular cash dividend; (b) to offer for subscription or sale pro rata to the holders of the outstanding shares of the Class any additional shares of any class or series of the Company’s stock; (c) to effect any reclassification, reorganization or recapitalization of the shares of the Class; or (d) to effect an Acquisition or to liquidate, dissolve or wind up; then in each such event the Company shall provide written notice thereof to Holder thereof at the same time and in the same manner as the Company gives notice thereof to the holders of the outstanding shares of the Class.

3.3 [Intentionally Omitted].

3.4 No Shareholder Rights. Without limitation of any provision of this Warrant, Holder agrees that it will not have any rights as a shareholder of the Company until the exercise of this Warrant.

ARTICLE 4. REPRESENTATIONS, WARRANTIES OF THE HOLDER. The Holder represents and warrants to the Company as follows:

4.1 Purchase for Own Account. This Warrant and the securities to be acquired upon exercise of this Warrant by Holder will be acquired for investment for Holder’s account, not as a nominee or agent, and not with a view to the public resale or distribution in violation of applicable securities laws. Holder also represents that it has not been formed for the specific purpose of acquiring this Warrant or the Shares.

4.2 Disclosure of Information. Holder has received or has had full access to all the information it considers necessary or appropriate to make an informed investment decision with respect to the acquisition of this Warrant and its underlying securities. Holder further has had an opportunity to ask questions and receive answers from the Company regarding the terms and conditions of the offering of this Warrant and its underlying securities and to obtain additional information (to the extent the Company possessed such information or could acquire it without unreasonable effort or expense) necessary to verify any information furnished to Holder or to which Holder has access.

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4.3 Investment Experience. Holder understands that the purchase of this Warrant and its underlying securities involves substantial risk. Holder has experience as an investor in securities of companies in the development stage and acknowledges that Holder can bear the economic risk of such Holder’s investment in this Warrant and its underlying securities and has such knowledge and experience in financial or business matters that Holder is capable of evaluating the merits and risks of its investment in this Warrant and its underlying securities and/or has a preexisting personal or business relationship with the Company and certain of its officers, directors or controlling persons of a nature and duration that enables Holder to be aware of the character, business acumen and financial circumstances of such persons.

4.4 Accredited Investor Status. Holder is an “accredited investor” within the meaning of Regulation D promulgated under the Act.

4.5 The Act. Holder understands that this Warrant and the Shares issuable upon exercise or conversion hereof have not been registered under the Act in reliance upon one or more exemptions therefrom, which exemptions depend upon, among other things, the bona fide nature of the Holder’s investment intent as expressed herein. Holder understands that this Warrant and the Shares issued upon any exercise or conversion hereof must be held indefinitely unless subsequently registered under the Act and qualified under applicable state securities laws, or unless an exemption from such registration and qualification requirements is otherwise available.

ARTICLE 5. MISCELLANEOUS.

5.1 Term: This Warrant is exercisable in whole or in part at any time and from time to time on or before the Expiration Date.

5.2 Legends. This Warrant and the Shares shall be imprinted with a legend in substantially the following form:

THIS WARRANT AND THE SHARES ISSUABLE HEREUNDER HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE “ACT”), OR THE SECURITIES LAWS OF ANY STATE AND, EXCEPT AND PURSUANT TO THE PROVISIONS OF ARTICLE 5 OF THAT CERTAIN WARRANT TO PURCHASE STOCK ISSUED BY THE COMPANY TO OXFORD FINANCE CORPORATION DATED AS OF MAY 10, 2010, MAY NOT BE OFFERED, SOLD OR OTHERWISE TRANSFERRED, PLEDGED OR HYPOTHECATED UNLESS AND UNTIL REGISTERED UNDER SAID ACT AND APPLICABLE STATE SECURITIES LAW OR, IN THE OPINION OF LEGAL COUNSEL IN FORM AND SUBSTANCE SATISFACTORY TO THE ISSUER OF THESE SECURITIES, SUCH OFFER, SALE OR TRANSFER, PLEDGE OR HYPOTHECATION IS EXEMPT FROM REGISTRATION.

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5.3 Compliance with Securities Laws on Transfer. This Warrant and/or the Shares issued upon exercise or conversion of this Warrant may not be transferred or assigned in whole or in part without compliance with applicable federal and state securities laws by the transferor and the transferee (including, without limitation, the delivery of investment representation letters and legal opinions reasonably satisfactory to the Company, as reasonably requested by the Company). The Company shall not require Holder to provide an opinion of counsel if the transfer is to any affiliate of Holder, provided that such affiliate is an “accredited investor” as defined in Regulation D promulgated under the Act.

5.4 Transfer Procedure. Subject to the provisions of Article 5.3 and upon providing the Company with written notice, Holder may transfer all or part of this Warrant or the Shares issuable upon exercise of this Warrant (or the securities issuable directly or indirectly, upon conversion of the Shares, if any) to any transferee, provided, however, in connection with any such transfer, Holder will give the Company notice of the portion of the Warrant being transferred with the name, address and taxpayer identification number of the transferee and Holder will surrender this Warrant to the Company for reissuance to the transferee(s) (and Holder if applicable). The foregoing provisions of this Article 5.4 shall not apply to a public sale of any Shares issued on exercise or conversion of this Warrant in reliance on the provisions of Rule 144 promulgated under the Act.

5.5 Notices. All notices and other communications from the Company to the Holder, or vice versa, shall be deemed delivered and effective when given personally or mailed by first-class registered or certified mail, postage prepaid (or on the first business day after transmission by facsimile), at such address as may have been furnished to the Company or Holder, as the case may be, in writing by the Company or such holder from time to time. All notices to Holder shall be addressed as follows until the Company receives notice of a change of address in connection with a transfer or otherwise:

Oxford Finance Corporation

Attn: Mr. John Henderson

133 North Fairfax Street

Alexandria, VA 22314

Facsimile: 703 ###-###-####

Notice to the Company shall be addressed as follows until Holder receives notice of a change in address:

MediciNova, Inc.

Attn: Chief Financial Officer

4350 La Jolla Village Drive, Suite 950

San Diego, CA 92122

Telephone: 858 ###-###-####

Facsimile: 858 ###-###-####

copy to:

David E. Schulman, Esq.

Dechert LLP

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1775 I Street, NW

Washington, DC 20006-2401

Telephone: 202 ###-###-####

Facsimile: 202 ###-###-####

5.6 Waiver. This Warrant and any term hereof may be changed, waived, discharged or terminated only by an instrument in writing signed by the party against which enforcement of such change, waiver, discharge or termination is sought.

5.7 Attorney’s Fees. In the event of any dispute between the parties concerning the terms and provisions of this Warrant, the party prevailing in such dispute shall be entitled to collect from the other party all costs incurred in such dispute, including reasonable attorneys’ fees.

5.8 Automatic Conversion upon Expiration. In the event that, upon the Expiration Date, the fair market value of one Share (or other security issuable upon the exercise hereof) as determined in accordance with Article 1.3 above is greater than the Warrant Price in effect on such date, then this Warrant shall automatically be deemed on and as of such date to be converted pursuant to Article 1.2 above as to all Shares (or such other securities) for which it shall not previously have been exercised or converted, and the Company shall, promptly following Holder’s written request therefor, deliver a certificate representing the Shares (or such other securities) issued upon such conversion to Holder.

5.9 Counterparts. This Warrant may be executed in counterparts, all of which together shall constitute one and the same agreement.

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5.10 Governing Law. This Warrant shall be governed by and construed in accordance with (i) to the extent applicable, the General Corporation Law of the State of Delaware, and (ii) otherwise, the laws of the State of New York, without giving effect to its principles regarding conflicts of law.

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APPENDIX 1

NOTICE OF EXERCISE

1. Holder elects to purchase              shares of the Common/Series              Preferred [strike one] Stock of                      pursuant to the terms of the attached Warrant, and tenders payment of the purchase price of the shares in full.

[or]

1. Holder elects to convert the attached Warrant into Shares/cash [strike one] in the manner specified in the Warrant. This conversion is exercised for                      of the Shares covered by the Warrant.

[Strike paragraph that does not apply.]

2. Please issue a certificate or certificates representing the Shares in the name specified below:

3. By its execution below and for the benefit of the Company, Holder hereby restates each of the representations and warranties in Article 4 of the Warrant as of the date hereof.

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