Second Supplemental Indenture, by and among the Registrant, Xeris Biopharma Holdings, Inc. and U.S. Bank National Association, dated October 5, 2021

Exhibit 4.1

Execution Version

SECOND SUPPLEMENTAL INDENTURE

This SECOND SUPPLEMENTAL INDENTURE, dated as of October 5, 2021 (the “Second Supplemental Indenture”), is entered into among Xeris Pharmaceuticals, Inc., a Delaware corporation (the “Company”), Xeris Biopharma Holdings, Inc., a Delaware corporation (“Parent”), and U.S. Bank National Association, as trustee (the “Trustee”).

WHEREAS, the Company has heretofore executed and delivered to the Trustee an indenture, dated as of June 30, 2020 (the “Base Indenture”), between the Company and the Trustee, and a First Supplemental Indenture, dated as of June 30, 2020, between the Company and the Trustee (the “First Supplemental Indenture”; the Base Indenture as supplemented by the First Supplemental Indenture, the “Indenture”), providing for the issuance of the 5.00% Convertible Senior Notes due 2025 (the “Notes”);

WHEREAS, on May 24, 2020, the Company entered into a Transaction Agreement (the “Transaction Agreement”) with Parent, the Company, Strongbridge Biopharma plc, a public limited company incorporated in Ireland with registered number 562659 having its registered office at Suite 206, Fitzwilliam Hall, Fitzwilliam Place, Dublin 2, Ireland, and Wells MergerSub, Inc., a Delaware corporation and a direct wholly-owned subsidiary of Parent (“Merger Sub”);

WHEREAS, pursuant to the Transaction Agreement, and subject to the terms and conditions thereof, Merger Sub will merge with and into the Company, with the Company continuing as the surviving corporation and a direct wholly-owned subsidiary of Parent (the “Merger”);

WHEREAS, pursuant to the Transaction Agreement, at the effective time of the Merger (the “Effective Time”), each share of common stock, $0.0001 par value per share, of the Company (the “Common Stock”) issued and outstanding immediately prior to the Effective Time (other than any shares held by the Company) will be assumed by Parent, cancelled and automatically converted into and become the right to receive one fully paid and nonassessable share of Parent’s common stock, par value $0.0001 per share (“Parent Common Stock”), and cash in lieu of fractional entitlements as set forth in the Transaction Agreement;

WHEREAS, the Merger does not constitute a Fundamental Change or a Make-Whole Fundamental Change;

WHEREAS, the Merger constitutes a Common Stock Change Event;

WHEREAS, Section 5.08 of the First Supplemental Indenture provides, among other things, that from and after the effective time of a Common Stock Change Event (i) the consideration due upon conversion of any Note will be determined in the same manner as if each reference to any number of shares of Company Common Stock in the provisions described in Article 5 of the First Supplemental Indenture (or in any related definitions) were instead a reference to the same number of Reference Property Units, and (ii) in certain circumstances, a supplemental indenture pursuant to Section 5.08 of the First Supplemental Indenture shall be executed by an entity whose securities compose the Reference Property and shall contain such additional provisions to protect the interests of the Holders as the Company shall in good faith reasonably consider necessary in accordance with the Indenture;

WHEREAS, pursuant to Section 5.08 of the First Supplemental Indenture, at or before the effective time of a Common Stock Change Event, the Company and Parent are required to execute and deliver to the Trustee a supplemental indenture that will (i) provide for subsequent conversions of Notes in the manner set forth in Section 5.08 of the First Supplemental Indenture, (ii) provide for subsequent adjustments to the Conversion Rate pursuant to Section 5.05(A) of the First Supplemental Indenture in a manner consistent with Section 5.08 of the First Supplemental Indenture and (iii) contain such other provisions, if any, that the Company reasonably determines are appropriate to preserve the economic interests of the Holders and to give effect to the provisions of Section 5.08(A) of the First Supplemental Indenture;

WHEREAS, Parent wishes to fully and unconditionally guarantee all of the obligations of the Company under the Notes and the Indenture (the “Guarantee”);

WHEREAS, Section 8.01(F) of the First Supplemental Indenture provides that the Company and the Trustee may amend or supplement the First Supplemental Indenture or the Notes without the consent of any Holder by entering into supplemental indentures pursuant to, and in accordance with, Section 5.08 of the First Supplemental Indenture in connection with a Common Stock Change Event; and

WHEREAS, the Company has complied with all conditions precedent provided for in the Indenture relating to this Second Supplemental Indenture.

NOW THEREFORE, in consideration of the foregoing and for other good and valuable consideration, the receipt of which is hereby acknowledged, the parties hereto mutually covenant and agree for the equal and ratable benefit of the Holders as follows:

ARTICLE I

DEFINITIONS

Section 1.01 Definitions. All capitalized terms used but not defined in this Second Supplemental Indenture shall have the meanings ascribed to such terms in the Indenture.

ARTICLE II

MODIFICATIONS EFFECT OF MERGER

SECTION 2.01. Conversion Right. Pursuant to Section 5.08 of the First Supplemental Indenture, as a result of the Merger:

(a) from and after the Effective Time, (I) the Conversion Consideration due upon the conversion of any Note, and the conditions to any such conversion, will be determined in the same manner as if each reference to any number of shares of Common Stock in Article 5 of the First Supplemental Indenture (or in any related definitions) were instead a reference to the same number of Reference Property Units, with each such Reference Property Unit consisting of one share of Parent Common Stock; (II) for purposes of Section 4.03 of the First Supplemental Indenture, each reference to any number of shares of Common Stock in such Section (or in any related definitions) will instead be deemed to be a reference to the same number of Reference Property Units; and (III) for purposes of the definition of “Fundamental Change” and “Make-Whole Fundamental Change,” the terms “Common Stock” and “common equity” will be deemed to mean the Parent Common Stock;

(b) the definition of “Common Stock” means Parent Common Stock, subject to Section 5.08 of the First Supplemental Indenture, as supplemented by this Second Supplemental Indenture; and

(c) the provisions of the Indenture, as modified herein, including without limitation, (i) all references and provisions respecting the terms “Conversion Price,” “Conversion Rate,” “Last Reported Sale Price,” “Market Disruption Event,” “Trading Day” and “Scheduled Trading Day” and (ii) the provisions of Article 5 of the First Supplemental Indenture shall continue to apply, mutatis mutandis, to the Holders’ right to convert each Note into the Reference Property.

SECTION 2.02. Anti-Dilution Adjustments. As and to the extent required by Section 5.08(a) of the Indenture, the Conversion Rate shall be subject to anti-dilution and other adjustments with respect to the portion of Reference Property constituting Parent Common Stock that shall be as nearly equivalent as is possible to the adjustments provided for in Section 5.05(A) of the First Supplemental Indenture.

SECTION 2.03. Repurchase of Notes at Option of Holders. References to the “Company” in the definition of “Fundamental Change” in Section 1.01 of the Indenture shall instead be references to “Parent”. Except as amended hereby, the purchase rights set forth in Section 4.02 of the First Supplemental Indenture shall continue to apply.

SECTION 2.04. Parent to Provide Parent Common Stock. Parent hereby irrevocably and unconditionally agrees to be bound by the terms of the Indenture applicable to it and to issue shares of Parent Common Stock as necessary to satisfy the Company’s obligations with respect to any Notes validly surrendered for conversion pursuant to Article 5 of the Indenture.

ARTICLE III

GUARANTEE

SECTION 3.01. Guarantee. (a) Parent hereby unconditionally guarantees to each Holder of Notes and to the Trustee and its successors and assigns, (i) the full and punctual payment when due of all monetary obligations of the Company under the Indenture and (ii) the full and punctual performance within applicable grace periods of all other obligations of the Company under the Indenture. Parent further agrees that its obligations hereunder shall be unconditional, irrespective of the absence or existence of any action to enforce the same, the recovery of any judgment against the Company (except to the extent such judgment is paid) or any waiver or amendment of the provisions of the Indenture or the Notes to the extent that any such action or any similar action would otherwise constitute a legal or equitable discharge or defense of Parent (except that such waiver or amendment shall be effective in accordance with its terms).

(b) Parent further agrees that its Guarantee constitutes a guarantee of payment, performance and compliance and not merely of collection.

(c) Parent further agrees to waive presentment to, demand of payment from and protest to the Company of its Guarantee, and also waives diligence, notice of acceptance of its Guarantee, presentment, demand for payment, notice of protest for nonpayment, the filing of claims with a court in the event of merger or bankruptcy of the Company, any right to require a proceeding first against the Company or any other Person, and all other defenses based on suretyship. The obligations of Parent shall not be affected by any failure or delay on the part of the Trustee to exercise any right or remedy under the Indenture or the Notes.

(d) The obligation of Parent to make any payment hereunder may be satisfied by causing the Company to make such payment. If any Holder of any Note or the Trustee is required by any court or otherwise to return to the Company or Parent or any custodian, trustee, liquidator or other similar official acting in relation to the Company or Parent any amount paid by either of them to the Trustee or such Holder, the Guarantee, to the extent theretofore discharged, shall be reinstated in full force and effect.

(e) Upon the satisfaction and discharge of the Indenture in accordance with Article 9 thereof, Parent will be released and relieved of any obligations under the Guarantee.

ARTICLE IV

ACCEPTANCE OF SECOND SUPPLEMENTAL INDENTURE

SECTION 4.01. Trustee’s Acceptance. The Trustee hereby accepts this Second Supplemental Indenture and agrees to perform the same under the terms and conditions set forth in the Indenture.

ARTICLE V

MISCELLANEOUS PROVISIONS

SECTION 5.01. Effectiveness of Second Supplemental Indenture. This Second Supplemental Indenture shall become effective as of the Effective Time.

SECTION 5.02. Effect of Second Supplemental Indenture. Upon the execution and delivery of this Second Supplemental Indenture by the Company, Parent and the Trustee, the Indenture shall be supplemented and amended in accordance herewith, and this Second Supplemental Indenture shall form a part of the Indenture for all purposes, and every Holder heretofore or hereafter authenticated and delivered under the Indenture shall be bound hereby. All the provisions of this Second Supplemental Indenture shall thereby be deemed to be incorporated in, and a part of, the Indenture; and the Indenture, as supplemented and amended by this Second Supplemental Indenture, shall be read, taken and construed as one and the same instrument.

SECTION 5.03. Indenture Remains in Full Force and Effect. This Second Supplemental Indenture shall form a part of the Indenture for all purposes and, except as supplemented or amended hereby, all other provisions in the Indenture and the Notes, to the extent not inconsistent with the terms and provisions of this Second Supplemental Indenture, shall remain in full force and effect and is in all respects confirmed and preserved.

SECTION 5.04. Headings. The titles and headings of the articles and sections of this Second Supplemental Indenture have been inserted for convenience of reference only, are not to be considered a part hereof, and shall in no way modify or restrict any of the terms or provisions of the Indenture.

SECTION 5.05. Counterparts. The parties may sign any number of copies of this Second Supplemental Indenture. Each signed copy will be an original, and all of them together represent the same agreement. Delivery of an executed counterpart of the Second Supplemental Indenture by facsimile, electronically in portable document format or in any other format will be effective as delivery of a manually executed counterpart. All notices, approvals, consents, requests and any communications hereunder must be in writing (provided that any communication sent to Trustee hereunder that is required to be signed must be in the form of a document that is signed manually or by way of a digital signature provided by DocuSign (or such other digital signature provider as specified in writing to Trustee by the Company)), in English. The Company agrees to assume all risks arising out of the use of using digital signatures and electronic methods to submit communications to Trustee, including without limitation the risk of Trustee acting on unauthorized instructions, and the risk of interception and misuse by third parties.

SECTION 5.06. Governing Law. THIS SECOND SUPPLEMENTAL INDENTURE, AND ANY CLAIM, CONTROVERSY OR DISPUTE ARISING UNDER OR RELATED TO THIS SECOND SUPPLEMENTAL INDENTURE, WILL BE GOVERNED BY AND CONSTRUED IN ACCORDANCE WITH THE LAWS OF THE STATE OF NEW YORK.

SECTION 5.07. Severability. In the event any provision of this Second Supplemental Indenture shall be invalid, illegal or unenforceable, then the validity, legality and enforceability of the remaining provisions of the Indenture or the Notes will not in any way be affected or impaired thereby.

SECTION 5.08. No Personal Liability of Directors, Officers, Employees and Stockholders. No past, present or future director, officer, employee, incorporator or stockholder of the Company or Parent, as such, will have any liability for any obligations of the Company or Parent under the Indenture or the Notes or for any claim based on, in respect of, or by reason of, such obligations or their creation. Each Holder waives and releases all such liability.

SECTION 5.09 Trustee Makes No Representation. The Trustee makes no representations as to the validity or sufficiency of this Second Supplemental Indenture. The recitals and statements contained in this Second Supplemental Indenture shall be taken as the statements of the Company and Parent, and the Trustee assumes no responsibility for the correctness of the same.

IN WITNESS WHEREOF, the parties hereto have caused this Second Supplemental Indenture to be duly executed as of the day and year first written above.

Signature Page to Second Supplemental Indenture