Second Supplemental Indenture, dated May 10, 2016, by and between Horizon Pharma Rheumatology LLC and U.S. Bank National Association

Exhibit 4.10

Execution Version

SECOND SUPPLEMENTAL INDENTURE

SECOND SUPPLEMENTAL INDENTURE (this “Second Supplemental Indenture”), dated as of May 10, 2016, between Horizon Pharma Rheumatology LLC (the “Guaranteeing Entity”), a parent or subsidiary of Horizon Pharma, Inc. (or its permitted successor), a Delaware corporation (the “Company”), and U.S. Bank National Association, as trustee under the Indenture referred to below (the “Trustee”).

W I T N E S S E T H

WHEREAS, Horizon Pharma Financing, Inc., a Delaware corporation (the “Escrow Issuer”) has heretofore executed and delivered to the Trustee an indenture (the “Initial Indenture”), dated as of April 29, 2015, providing for the issuance of 6.625% Senior Notes due 2023 (the “Notes”);

WHEREAS, on May 7, 2015, the Escrow Issuer merged with and into the Company, with the Company being the surviving entity of such merger and the Escrow Issuer ceasing to exist (the “Merger”);

WHEREAS, in connection with the Merger, the Company, the Escrow Issuer and the Guarantors party thereto executed and delivered to the Trustee a first supplemental indenture to the Initial Indenture (the “First Supplemental Indenture” and the Initial Indenture as supplemented by the First Supplemental Indenture, the “Indenture”);

WHEREAS, Section 4.18 and Section 10.03 of the Indenture provides that under certain circumstances the Guaranteeing Entity shall execute and deliver to the Trustee a supplemental indenture pursuant to which the Guaranteeing Entity shall unconditionally guarantee all of the Company’s Obligations under the Notes and the Indenture on the terms and conditions set forth herein (the “Note Guarantee”); and

WHEREAS, pursuant to Section 9.01(j) of the Indenture, the Trustee and the Guarantor are authorized to execute and deliver 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 to this Second Supplemental Indenture mutually covenant and agree for the equal and ratable benefit of the Holders of the Notes as follows:

1. CAPITALIZED TERMS. Capitalized terms used herein without definition shall have the meanings assigned to them in the Indenture.

2. AGREEMENT TO GUARANTEE. The Guaranteeing Entity hereby agrees to provide an unconditional Guarantee on the terms and subject to the conditions set forth in the Note Guarantee and in the Indenture including but not limited to Article 10 thereof.

4. NO RECOURSE AGAINST OTHERS. No director, officer, employee, incorporator or stockholder of the Company or any Guarantor, as such, will have any liability for any obligations of the Company or the Guarantors under the Notes, this Indenture, the Note Guarantees or for any claim based on, in respect of, or by reason of, such obligations or their creation. Each Holder of Notes by accepting a Note waives and releases all such liability. The waiver and release are part of the consideration for issuance of the Notes. The waiver may not be effective to waive liabilities under the federal securities laws.

5. NEW YORK LAW TO GOVERN; WAIVER OF JURY TRIAL. THIS SECOND SUPPLEMENTAL INDENTURE SHALL BE GOVERNED BY, AND CONSTRUED IN ACCORDANCE WITH THE LAWS OF THE STATE OF NEW YORK. EACH OF THE COMPANY AND THE GUARANTORS CONSENTS AND IRREVOCABLY SUBMITS TO THE JURISDICTION OF ANY NEW YORK STATE OR U.S. FEDERAL COURT LOCATED IN THE BOROUGH OF MANHATTAN, CITY OF NEW YORK, COUNTY OF NEW YORK, STATE OF NEW YORK IN RELATION TO ANY LEGAL ACTION OR PROCEEDING (I) ARISING OUT OF, RELATING TO OR IN CONNECTION WITH THIS INDENTURE, AS SUPPLEMENTED, THE NOTES, THE GUARANTEES AND ANY RELATED DOCUMENTS AND/OR (II) ARISING UNDER ANY U.S. FEDERAL OR U.S. STATE SECURITIES LAWS IN RESPECT OF THE NOTES, THE GUARANTEES AND ANY SECURITIES ISSUED PURSUANT TO THE TERMS OF THE INDENTURE, AS SUPPLEMENTED. EACH OF THE COMPANY AND THE GUARANTORS WAIVES ANY OBJECTION TO PROCEEDINGS IN ANY SUCH COURTS, WHETHER ON THE GROUND OF VENUE OR ON THE GROUND THAT THE PROCEEDINGS HAVE BEEN BROUGHT IN AN INCONVENIENT FORUM. EACH OF THE COMPANY AND THE GUARANTORS, TO THE EXTENT ORGANIZED OUTSIDE OF THE UNITED STATES, SHALL APPOINT HORIZON PHARMA, INC. (HORIZON PHARMA, INC., 520 LAKE COOK ROAD, SUITE 520, DEERFIELD, IL 60015), AS ITS AGENT FOR SERVICE OF PROCESS IN ANY SUCH SUIT, ACTION OR PROCEEDING AND AGREES THAT SERVICE OF PROCESS UPON SAID AUTHORIZED AGENT SHALL BE DEEMED IN EVERY RESPECT EFFECTIVE SERVICE OF PROCESS UPON IT IN ANY SUCH SUIT, ACTION OR PROCEEDING. EACH OF THE COMPANY AND THE GUARANTORS AGREES TO DELIVER, UPON THE EXECUTION AND DELIVERY OF THIS SECOND SUPPLEMENTAL INDENTURE, A WRITTEN ACCEPTANCE BY SUCH AGENT OF ITS APPOINTMENT AS SUCH AGENT. EACH OF THE COMPANY AND THE GUARANTORS, TO THE EXTENT ORGANIZED OUTSIDE OF THE UNITED STATES, FURTHER AGREES TO TAKE ANY AND ALL ACTION, INCLUDING THE FILING OF ANY AND ALL SUCH DOCUMENTS AND INSTRUMENTS, AS MAY BE REASONABLY NECESSARY TO CONTINUE SUCH DESIGNATION AND APPOINTMENT OF CT CORPORATION SYSTEM IN FULL FORCE AND EFFECT FOR SO LONG AS THE INDENTURE, AS SUPPLEMENTED, REMAINS IN FORCE. THE COMPANY, THE TRUSTEE AND EACH OF THE GUARANTORS HEREBY IRREVOCABLY WAIVES, TO THE FULLEST EXTENT PERMITTED BY APPLICABLE LAW, ANY AND ALL RIGHT TO TRIAL BY JURY IN ANY LEGAL PROCEEDING ARISING OUT OF OR RELATING TO THIS SECOND SUPPLEMENTAL INDENTURE OR THE TRANSACTIONS CONTEMPLATED HEREBY.

6. COUNTERPARTS. The parties may sign any number of copies of this Second Supplemental Indenture. Each signed copy (which may be provided via facsimile or other electronic transmission) shall be an original, but all of them together represent the same agreement.

7. EFFECT OF HEADINGS. The Section headings herein are for convenience only and shall not affect the construction hereof.

8. THE TRUSTEE. The Trustee shall not be responsible in any manner whatsoever for or in respect of the validity or sufficiency of this Second Supplemental Indenture or for or in respect of the recitals contained herein, all of which recitals are made solely by the Guaranteeing Entity.

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

Dated: May 10, 2016    ,

[Signature Page to Second Supplemental Indenture]

[Signature Page to Second Supplemental Indenture]