WARRANT TO PURCHASE COMMON STOCK

Exhibit 4.1

THIS WARRANT HAS BEEN, AND THE SHARES OF COMMON STOCK WHICH MAY BE RECEIVED PURSUANT TO THE EXERCISE OF THIS WARRANT WILL BE, ACQUIRED SOLELY FOR INVESTMENT AND NOT WITH A VIEW TO, OR FOR RESALE IN CONNECTION WITH, ANY DISTRIBUTION THEREOF. NEITHER THIS WARRANT NOR SUCH SHARES HAVE BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE “ACT”), OR QUALIFIED UNDER ANY STATE SECURITIES LAWS. SUCH SECURITIES MAY NOT BE SOLD OR OFFERED FOR SALE IN THE ABSENCE OF SUCH REGISTRATION OR QUALIFICATION OR AN OPINION OF COUNSEL IN FORM AND SUBSTANCE REASONABLY SATISFACTORY TO THE COMPANY THAT SUCH DISPOSITION IS EXEMPT FROM THE REGISTRATION REQUIREMENTS OF THE ACT AND ANY REGISTRATION OR QUALIFICATION REQUIREMENTS UNDER APPLICABLE STATE SECURITIES LAWS.

Dated as of May 4, 2016

WARRANT TO PURCHASE COMMON STOCK

This Warrant to Purchase Common Stock (the “Warrant”) certifies that, for good and valuable consideration, DANFORTH ADVISORS, LLC (along with its permitted assignees, the “Holder”) is entitled to, and GI DYNAMICS, INC., a Delaware corporation (the “Company”), hereby grants the Holder the right to, purchase, as of the date of issuance set forth above (the “Warrant Date”), Twenty-Eight Thousand Five Hundred Thirty-Two (28,532) fully paid and nonassessable shares of Common Stock, par value $0.01 (“Common Stock”), of the Company (as adjusted pursuant to Section 3 hereof) (the “Warrant Shares”) at a price per share equal to $0.64 (as adjusted pursuant to Section 3) (the “Exercise Price”). This Warrant is issued pursuant to the Consulting Agreement (the “Consulting Agreement”) dated as of May 4, 2016 by and between the Company and Holder.

(a) Vesting of Warrant Shares. The Warrant Shares subject to this Warrant shall vest in equal installments of 1/24th of the Warrant Shares on the last day of each successive month during the term of the Consulting Agreement beginning May 31, 2016 and ending April 30, 2018; provided however, that all unvested Warrant Shares shall vest immediately upon a Change of Control. For purposes of this Warrant, the term “Change of Control” means the occurrence of any of the following events (which shall be interpreted, if applicable, in a manner, and limited to the extent necessary, so that it will not cause adverse tax consequences under Section 409A):

(i) Ownership. Any “Person” (as such term is used in Sections 13(d) and 14(d) of the Securities Exchange Act of 1934, as amended (the “Exchange Act”)) becomes the “Beneficial Owner” (as defined in Rule 13d-3 under the Exchange Act), directly or indirectly, of securities of the Company representing 50% or more of the total voting power represented by the Company’s then outstanding voting securities (excluding for this purpose any such voting securities held by the Company or its Affiliates or by any employee benefit plan of the Company) pursuant to a transaction or a series of related transactions which the Board of Directors does not approve; or

(ii) Merger/Sale of Assets. (A) A merger or consolidation of the Company whether or not approved by the Company’s Board of Directors, other than a merger or consolidation which would result in the voting securities of the Company outstanding immediately prior thereto continuing to represent (either by remaining outstanding or by being converted into voting securities of the surviving entity or the parent of such corporation) more than 50% of the total voting power represented by the voting securities of the Company or such surviving entity or parent of such corporation, as the case may be, outstanding immediately after such merger or consolidation; or (B) the sale or disposition by the Company of all or substantially all of the Company’s assets in a transaction requiring stockholder approval; or

(iii) Change in Board Composition. A change in the composition of the Company’s Board of Directors, as a result of which fewer than a majority of the directors are Incumbent Directors. “Incumbent Directors” shall mean directors who either (A) are directors of the Company as of the date of this Warrant, or (B) are elected, or nominated for election, to the Company’s Board of Directors with the affirmative votes of at least a majority of the Incumbent Directors at the time of such election or nomination (but shall not include an individual whose election or nomination is in connection with an actual or threatened proxy contest relating to the election of directors to the Company).

(b) Exercise Period. This Warrant may be exercised in whole or part by the Holder during the term (as set forth in Section 8) and in compliance with the provisions of this Warrant at any time after the Warrant Date for all or any part of the Warrant Shares that have vested pursuant to Section 1(a) above, by the surrender of this Warrant (with the notice of exercise form attached hereto as Exhibit A (the “Notice of Exercise”) duly executed) at the principal office of the Company. If this Warrant shall have been exercised in part, the Company shall, at the time of delivery of the notice of book entry or certificate or certificates representing Warrant Shares, deliver to the Holder a new Warrant evidencing the rights of the Holder to purchase the then unpurchased Warrant Shares, which new Warrant shall in all other respects be identical with this Warrant, or at the request of the Holder, appropriate notation may be made on this Warrant and the same returned to the Holder.

(c) Cash Exercise. Upon exercise of this Warrant, the Holder shall pay the Company an amount (“Exercise Payment”) equal to the product of the Exercise Price multiplied by the total number of vested Warrant Shares purchased pursuant to such exercise of this Warrant, by wire transfer of immediately available funds or check payable to the order of the Company. The Holder shall be deemed to have become the holder of record of, and shall be treated for all purposes as the record holder of, the Warrant Shares represented by such exercise (and such Warrant Shares shall be deemed to have been issued) immediately prior to the close of business on the date upon which the Exercise Payment is paid to the Company.

(d) Net Exercise. The Exercise Payment also may be paid at the Holder’s election by surrender of all or a portion of the Warrant for the vested Warrant Shares to be exercised under this Warrant (“Net Exercise”). If the Holder elects the Net Exercise method, the Company will issue Warrant Shares in accordance with the following formula:

X = Y(A-B)

           A

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Where:

For purposes of the above calculation, fair market value of Common Stock shall mean the following (“Fair Market Value”):

(i) if CHESS Depository Interests representing interests in shares of the Company’s Common Stock (“CDIs”) are then quoted on the Australian Securities Exchange (“ASX”), then the fair market value per share of Common Stock shall be equal to the result obtained by multiplying (A) the volume weighted average price of one CDI in Australian dollars over five (5) consecutive trading days ending three days before the day the Fair Market Value is being determined by (B) the number of CDIs (or fraction thereof) which equal an interest in exactly one share of Common Stock on such dates;

(ii) if CDIs are not then quoted on the ASX, then if the Common Stock is traded on another securities exchange, the Fair Market Value shall be deemed to be the average of the closing prices over the five (5) consecutive trading days ending three days before the day the Fair Market Value is being determined;

(iii) if CDIs are not then quoted on the ASX and the Common Stock is not then traded on another securities exchange, then if the Common Stock is traded over-the-counter, the Fair Market Value shall be deemed to be the average of the closing bid and asked prices quoted on the principal market on which or through which the Common Stock is traded over the five (5) consecutive trading days ending three days before the day the Fair Market Value is being determined;

(iv) if CDIs are not then quoted on the ASX and the Common Stock is not then listed on any securities exchange or traded in the over-the-counter market, the Fair Market Value of the Common Stock shall be the highest price per share which the Company could reasonably obtain from a willing buyer (other than an employee, director or “Affiliate” of the Company, as such term is defined in Rule 405 under the Securities Act of 1933, as amended (the “Securities Act”)) for Common Stock sold by the Company, as determined in good faith by its Board of Directors (which determination shall take into consideration any available appraisals);

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If any of the amounts used to calculate the Fair Market Value are expressed in Australian dollars and not the United States dollar, then each such amount shall be converted into United States dollars based on the closing exchange rate published by the Reserve Bank of Australia in their Official Bulletin at 4pm for the applicable date. The amounts used to calculate the Fair Market Value shall be equitably adjusted for the occurrence of any of the events for which an adjustment would be made pursuant Section 3 but which is not otherwise fully reflected in the Fair Market Value calculation.

(e) Election to receive CDIs. The Holder may include in their notice of exercise, the election to receive the corresponding number of CDIs for the vested Warrant Shares. In such case, the Holder may nominate a CHESS account or accounts for those CDIs to be issued into.

(f) Stock Certificates. In the event of the exercise of this Warrant, a notice of book entry for the vested Warrant Shares so purchased (or in the event that CDIs were elected, a Holding Statement to certify that CDIs were issued) shall be delivered to the Holder within a reasonable time (and in no event more than 5 Business Days) after the Exercise Payment is paid to the Company.

(a) Reclassification, Consolidation or Reorganization. In case of any reclassification of the Common Stock (other than a change in par value, or as a result of a subdivision or combination), or in case of any consolidation or merger of the Company with or into another corporation or sale of all or substantially all of the Company’s assets (any of which is a “Reorganization Transaction”), the Company, or such successor corporation as the case may be, shall execute a new warrant, providing that the Holder shall have the right to exercise such new warrant, and procure upon such exercise and payment of the same aggregate Exercise Price, in lieu of the Warrant Shares then issuable upon exercise of this Warrant, the kind and amount of shares of stock, other securities, money and property as would be received by the Holder for such Warrant Shares as if such Warrant Shares were outstanding immediately prior to the consummation of the Reorganization Transaction.

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(b) Stock Splits, Dividends and Combinations. In the event that the Company shall at any time subdivide the outstanding shares of Common Stock, or shall issue a stock dividend on its outstanding shares of Common Stock, the number of Warrant Shares issuable upon exercise of this Warrant immediately prior to such subdivision or to the issuance of such stock dividend shall be proportionately increased and the Exercise Price shall be proportionately decreased, and in the event that the Company shall at any time combine the outstanding shares of Common Stock, the number of Warrant Shares issuable upon exercise of this Warrant immediately prior to such combination shall be proportionately decreased and the Exercise Price shall be proportionately increased, effective at the close of business on the date of such subdivision, stock dividend or combination, as the case may be such that in each case, the result obtained by multiplying the Exercise Price by the number of Warrant Shares shall be the same immediately prior to, and immediately after, such event.

(c) Notice of Corporate Action. If at any time:

(i) the Company shall take a record of the holders of its Common Stock for the purpose of entitling them to receive a dividend (other than a cash dividend payable out of earnings or earned surplus legally available for the payment of dividends under the laws of the jurisdiction of incorporation of the Company) or other distribution, or any right to subscribe for or purchase any evidences of its indebtedness, any shares of stock of any class or any other securities or property, or to receive any other right; or

(ii) there shall be any Reorganization Transaction; or

(iii) there shall be a voluntary or involuntary dissolution, liquidation or winding up of the Company,

then, in any one or more of such cases, the Company shall give to the Holder (i) at least five-days’ prior written notice of the date on which a record date shall be selected for such dividend, distribution or right or for determining rights to vote in respect of any such Reorganization Transaction or such dissolution, liquidation or winding up, and (ii) in the case of any such Reorganization Transaction or such dissolution, liquidation or winding up, at least five-days’ prior written notice of the date when the same shall take place. Such notice in accordance with the foregoing clause also shall specify (i) the date on which any such record is to be taken for the purpose of such dividend, distribution or right, the date on which the holders of Common Stock shall be entitled to any such dividend, distribution or right, and the amount and character thereof, and (ii) the date on which any such Reorganization Transaction or such dissolution, liquidation or winding up is to take place and the time, if any such time is to be fixed, as of which the holders of Common Stock shall be entitled to exchange their shares of Common Stock for securities or other property deliverable upon such Reorganization Transaction or such dissolution, liquidation or winding up. Each such written notice shall be sufficiently given if addressed to the Holder at the last address of the Holder appearing on the books of the Company and delivered in accordance with Section 10(d).

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(a) Holder represents and warrants to the Company that:

(i) it has the ability to bear the economic risks of such Holder’s prospective investment, including a complete loss of Holder’s investment in the Warrants and the Warrant Shares; and

(ii) the Warrants and the Warrant Shares are purchased for the Holder’s own account, and not with view to distribution of either the Warrants or any securities purchasable upon exercise thereof; provided however that the Holder may transfer the Warrant and any Warrant Shares to any Affiliate of the Holder.

(b) This Warrant will be freely tradeable and only be subject to federal and state securities laws and any escrow imposed by the ASX.

(c) At the time of the surrender of this Warrant in connection with any transfer of this Warrant or the resale of the vested Warrant Shares (except to an Affiliate), the Company may require, as a condition of allowing such transfer (i) that the Holder or transferee of this Warrant or the Warrant Shares as the case may be, furnish to the Company a written opinion of counsel that is reasonably acceptable to the Company to the effect that such transfer may be made without registration under the Securities Act or qualification under any state securities laws and (ii) that the Holder or transferee execute and deliver to the Company an investment representation letter in form and substance acceptable to the Company and substantially in the form of Exhibit B hereto. Transfer of this Warrant and all rights hereunder, in whole or in part, in accordance with the foregoing provisions, shall be registered on the books of the Company to be maintained for such purpose, upon surrender of this Warrant at the principal office of the Company or the office or agency designated by the Company, together with a written assignment of this Warrant substantially in the form of Exhibit C hereto duly executed by the Holder or its attorney-in-fact. Upon such surrender and, if required, such payment, the Company shall execute and deliver a new Warrant or Warrants in the name of the assignee or assignees and in the denomination specified in such instrument of assignment, and shall issue to the Holder a new warrant evidencing the portion of this Warrant not so assigned, and this Warrant shall be deemed cancelled.

(a) Each certificate evidencing the vested Warrant Shares issued upon exercise of this Warrant shall be stamped or imprinted with a legend substantially in the following form:

THE SECURITIES REPRESENTED HEREBY HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933 (THE “SECURITIES ACT”) AND MAY NOT BE OFFERED, SOLD OR OTHERWISE TRANSFERRED, PLEDGED OR HYPOTHECATED UNLESS AND UNTIL REGISTERED UNDER THE ACT OR, IN THE OPINION OF COUNSEL IN FORM AND SUBSTANCE REASONABLY SATISFACTORY TO THE ISSUER OF THESE SECURITIES, SUCH OFFER, SALE OR TRANSFER, PLEDGE OR HYPOTHECATION IS IN COMPLIANCE THEREWITH.

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(b) Removal of Legend and Transfer Restrictions. Any legend endorsed on a certificate pursuant to this Section 5 shall be removed, and the Company shall issue a certificate without such legend to the holder of such vested Warrant Shares if (i) such Warrant Shares are resold pursuant to an effective registration statement under the Securities Act, (ii) if such holder satisfies the requirements of Rule 144(b)(i) under the Securities Act or (iii) if such holder provides the Company with an opinion of counsel for such holder of the Warrant Shares, in form and substance reasonably satisfactory to the Company, to the effect that a sale, transfer or assignment of such Warrant Shares may be made without registration and that upon such sale, transfer or assignment such Warrant Shares will not be deemed “restricted securities,” as such term is defined in Rule 144 under the Securities Act.

(a) This Warrant is being delivered in the Commonwealth of Massachusetts, United States and shall be construed and enforced in accordance with and governed by the laws of the Commonwealth of Massachusetts, without giving effect to principles of conflicts of laws.

(b) The headings in this Warrant are for purposes of reference only, and shall not limit or otherwise affect any of the terms hereof.

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(c) The terms of this Warrant shall be binding upon and shall inure to the benefit of any successors or assigns of the Company and of the Holder and of the Warrant Shares issued or issuable upon the exercise hereof.

(d) Any notice provided for or permitted under this Warrant shall be treated as having been given (i) upon receipt, when delivered personally, (ii) one day after sending, when sent by commercial overnight courier with written verification of receipt, (iii) upon confirmed transmission when sent via facsimile on a business day prior to 5:00 pm local time or, if sent after 5:00 pm local time, the next business day after confirmed transmission, or (iv) three business days after deposit with the United States Postal Service, when mailed postage prepaid by certified or registered mail, return receipt requested, in each case, addressed to the address or facsimile number set forth on the signature pages hereof or as otherwise furnished in writing.

(e) This Warrant and the Consulting Agreement constitute the full and entire understanding and agreement between the parties with regard to the matters contained herein.

(f) Upon receipt of evidence reasonably satisfactory to the Company of the loss, theft, destruction or mutilation of this Warrant and, in the case of any such loss, theft or destruction, upon delivery of an indemnity agreement reasonably satisfactory in form and amount to the Company or, in the case of any such mutilation, upon surrender and cancellation of such Warrant, the Company at the Holder’s expense will execute and deliver to the holder of record, in lieu thereof, a new Warrant of like date and tenor.

(g) This Warrant and any provision hereof may be amended, waived or terminated only by an instrument in writing signed by the Company and the Holder.

[continued and to be signed on following page]

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IN WITNESS WHEREOF, the Company has caused this Warrant to be signed by its duly authorized officer, all as of the day and year first above written.

COMPANY:

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EXHIBIT A

NOTICE OF EXERCISE

1. Cash Exercise. The undersigned hereby elects to purchase             shares of Common Stock, par value $0.01 per share (“Common Stock”), of GI DYNAMICS, INC., a Delaware corporation (the “Company”) pursuant to the terms of Section 1(c) of the Warrant to Purchase Common Stock dated             , (the “Warrant”), and tenders herewith payment of the Exercise Price (as such term is defined in the Warrant) therefor.

2. Net Exercise. The undersigned hereby elects to effect a Net Exercise for             shares of Common Stock pursuant to Section 1(d) of the Warrant.

Please issue a notice of book entry representing said             shares of Common Stock in the name of the undersigned or in such other name as is specified below:

3. CDI Election. By initialing here, the undersigned hereby elects to receive the number of CHESS Depository Interest corresponding to the shares of Common Stock noted above in lieu of the shares of Common Stock otherwise issuable:             

The undersigned hereby represents and warrants that the aforesaid shares of Common Stock or CDIs, as the case may be, 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.

EXHIBIT B

FORM OF INVESTMENT REPRESENTATION LETTER

In connection with the acquisition of             shares of Common Stock of GI DYNAMICS, INC. (the “Company”), par value $0.01 per share (or CHESS Depository Interests representing the same, the “Common Stock”), by             (the “Holder”) from             , the Holder hereby represents and warrants to the Company as follows:

The Holder has such knowledge and experience in financial and business matters that the Holder is capable of evaluating the merits and risks of an investment in the Common Stock (collectively, the “Securities”); and, has the ability to bear the economic risks of such Holder’s investment, including a complete loss of the Holder’s investment in Securities.

The Holder, by acceptance of the Securities, represents to the Company that the Securities are purchased for the Holder’s own account, and not with view to distribution of the Securities in violation of applicable securities laws.

The Holder acknowledges that (i) the Securities have not been registered under the Act, (ii) the certificate(s) representing the Securities shall bear a legend as set forth in the Warrant until such Securities shall have been registered for resale by the Holder under the Act that has been declared effective by the SEC; or (ii) in the opinion of counsel in form and substance reasonably satisfactory to the Company, such Securities may be sold without registration under the Act.

IN WITNESS WHEREOF, the Holder has caused this Investment Representation Letter to be executed in its corporate name by its duly authorized officer this             day of             20    .

EXHIBIT C

ASSIGNMENT FORM

FOR VALUE RECEIVED, the undersigned owner of this Warrant for the purchase of shares of Common Stock of GI DYNAMICS, INC., a Delaware corporation (the “Company”) hereby sells, assigns and transfers unto the assignee named below all of the rights of the undersigned under this Warrant, with respect to the number of shares of Common Stock set forth below:

and does hereby irrevocably constitute and appoint             attorney-in-fact to register such transfer on the books of the Company, maintained for the purpose, with full power of substitution in the premises.