Exhibit 4.1

AMENDMENT NO. 1 TO RIGHTS AGREEMENT

This AMENDMENT NO. 1 (this “Amendment”) to the Rights Agreement dated as of May 16, 2012 (the “Rights Agreement”) between Human Genome Sciences, Inc., a Delaware corporation (the “Company”), and American Stock Transfer & Trust Company, LLC, as rights agent (the “Rights Agent”), is entered into as of July 16, 2012. Capitalized terms used in this Amendment and not otherwise defined herein shall have the meanings given to them in the Rights Agreement.

WITNESSETH:

WHEREAS, the Board of Directors of the Company (the “Board”) has determined that it is in the best interests of the Company and its stockholders to amend the Rights Agreement as set forth herein immediately prior to and in connection with the execution of the Agreement and Plan of Merger, dated as of July 16, 2012 (as amended, modified or supplemented, from time to time, the “Merger Agreement”), by and among GlaxoSmithKline plc, a public limited company organized under the laws of England and Wales (“Parent“), H. Acquisition Corp., a Delaware corporation and a wholly-owned subsidiary of Parent (“Merger Sub“), and the Company, pursuant to which Merger Sub will be merged with and into the Company (the “Merger”), with the Company surviving the Merger as a wholly-owned subsidiary of Parent;

WHEREAS, the Company desires to amend the Rights Agreement pursuant to Section 5.4 of the Rights Agreement, immediately prior to entering into the Merger Agreement, to facilitate the transactions contemplated by the Merger Agreement;

WHEREAS, pursuant to Section 5.4 of the Rights Agreement, the Company has delivered to the Rights Agent a certificate signed by an appropriate officer of the Company which states that this Amendment is in compliance with the terms of Section 5.4(a) of the Rights Agreement; and

WHEREAS, pursuant to resolutions adopted at a duly convened special meeting of the Board held on July 16, 2012, the Board has determined that it is in the best interests of the Company and its stockholders, and consistent with the objectives of the Board in adopting the Rights Agreement, to amend the Rights Agreement in the manner set forth herein immediately prior to entering into the Merger Agreement to except from the operation of the Rights Agreement the Merger Agreement, the Offer, Merger and Top-Up Option (as such terms are defined in the Merger Agreement), and any and all other transactions contemplated by the Merger Agreement and to provide that the Rights Agreement shall expire immediately prior to the effective time of the Merger.

NOW, THEREFORE, in consideration of the foregoing and the mutual agreements herein set forth, the parties hereby agree as follows:

“Notwithstanding anything in this Agreement to the contrary, none of Parent, Merger Sub or any of their respective Affiliates or Associates shall be or become an Acquiring Person, and the term “Acquiring Person” shall not include any of Parent, Merger Sub or any of their respective Affiliates or Associates, solely by reason of (i) the approval, execution, delivery, performance or public announcement of the Merger Agreement (including any amendments or supplements thereto), (ii) the consummation or public announcement of the Offer, Merger or Top-Up Option or (iii) the consummation of any of the other transactions contemplated by the Merger Agreement.”

““Expiration Time” shall mean the earliest of (i) the Exchange Time, (ii) the Redemption Time, (iii) the close of business on the twelve-month anniversary of the Record Time, and (iv) the Effective Time of the Merger in accordance with the terms of the Merger Agreement.”

“Notwithstanding anything in this Agreement to the contrary, no Flip-in Date shall be deemed to have occurred solely as a result of (i) the approval, execution, delivery, performance or public announcement of the Merger Agreement (including any amendments or supplements thereto), (ii) the consummation or public announcement of the Offer, Merger or Top-Up Option or (iii) the consummation of any of the other transactions contemplated by the Merger Agreement.”

“Notwithstanding anything in this Agreement to the contrary, a Flip-over Transaction or Event shall be deemed not to have occurred, and the provisions of such section shall not be made or given effect, solely as a result of (i) the approval, execution, delivery, performance or public announcement of the Merger Agreement (including any amendments or supplements thereto), (ii) the consummation or public announcement of the Offer, Merger or Top-Up Option or (iii) the consummation of any of the other transactions contemplated by the Merger Agreement.”

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“Notwithstanding anything in this Agreement to the contrary, no Separation Time shall be deemed to have occurred solely as a result of (i) the approval, execution, delivery, performance or public announcement of the Merger Agreement (including any amendments or supplements thereto), (ii) the consummation or public announcement of the Offer, Merger or Top-Up Option or (iii) the consummation of any of the other transactions contemplated by the Merger Agreement.”

“Notwithstanding anything in this Agreement to the contrary, no Stock Acquisition Date shall be deemed to have occurred solely as a result of (i) the approval, execution, delivery, performance or public announcement of the Merger Agreement (including any amendments or supplements thereto), (ii) the consummation or public announcement of the Offer, Merger or Top-Up Option or (iii) the consummation of any of the other transactions contemplated by the Merger Agreement.”

“Effective Time” shall mean the time at which the Merger becomes effective pursuant to the terms and conditions of the Merger Agreement.

“Merger” shall have the meaning ascribed to such term in the Merger Agreement.

“Merger Agreement” shall mean that certain Agreement and Plan of Merger by and among Parent, Merger Sub and the Company, dated as of July 16, 2012 (as such agreement may be amended from time to time).

“Merger Sub” means H. Acquisition Corp., a Delaware corporation and wholly-owned subsidiary of Parent.

“Offer” shall have the meaning ascribed to such term in the Merger Agreement.

“Parent” means GlaxoSmithKline plc, a public limited company organized under the laws of England and Wales.

“Top-Up Option” shall have the meaning ascribed to such term in the Merger Agreement.”

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Section 3.1 of the Rights Agreement is hereby amended by adding the following sentence to the end of Section 3.1(a):

“Notwithstanding anything in this Agreement to the contrary, none of (i) the approval, execution, delivery, performance or public announcement of the Merger Agreement (including any amendments or supplements thereto), (ii) the consummation or public announcement of the Offer, Merger or Top-Up Option or (iii) the consummation of any of the other transactions contemplated by the Merger Agreement shall cause the Rights to be adjusted or become exercisable in accordance with this Section 3.1(a).”

Section 3.2 of the Rights Agreement is hereby amended by adding the following sentence to the end of Section 3.2(a):

“Notwithstanding anything in this Agreement to the contrary, the provisions of Section 3.2(a) shall not be applicable to the Offer, Merger or Top-Up Option.”

Section 5.2 of the Rights Agreement is hereby amended by adding the following sentence to the end of Section 5.2:

“For the avoidance of doubt, this Agreement shall expire immediately prior to the Effective Time of the Merger in accordance with the terms of the Merger Agreement.”

All of the covenants and provisions of this Amendment by or for the benefit of the Company or the Rights Agent shall bind and inure to the benefit of their respective successors and assigns hereunder.

If any term, provision, covenant or restriction of this Amendment is held by a court of competent jurisdiction or other authority to be invalid, void or unenforceable, the remainder of the terms, provisions, covenants and restrictions of this Amendment shall remain in full force and effect and shall in no way be affected, impaired or invalidated.

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This Amendment shall be deemed to be a contract made under the laws of the State of Delaware and for all purposes shall be governed by and construed in accordance with the laws of the State of Delaware applicable to contracts made and to be performed entirely within State of Delaware.

Descriptive headings of the several sections of this Amendment are inserted for convenience only and shall not control or affect the meaning or construction of any of the provisions hereof.

This Amendment may be executed in any number of counterparts and each of such counterparts shall for all purposes be deemed to be an original, and all such counterparts shall together constitute but one and the same instrument. A signature to this Amendment transmitted electronically shall have the same authority, effect, and enforceability as an original signature.

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IN WITNESS WHEREOF, the parties have executed this Amendment as of the date set forth in the first paragraph hereof.

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