AMENDMENT TO THE RIGHTS AGREEMENT

Exhibit 4.1

AMENDMENT

TO THE

RIGHTS AGREEMENT

This Amendment, dated as of May 28, 2004 (this “Amendment”), amends the Rights Agreement, dated as of March 16, 2001, by and between ACLARA BioSciences, Inc., a Delaware corporation (the “Company”), and Mellon Investor Services LLC, a New Jersey limited liability company, as rights agent (the “Rights Agent”) (the “Rights Agreement”).

WITNESSETH

WHEREAS, the Company and the Rights Agent have heretofore executed and entered into the Rights Agreement;

WHEREAS, pursuant to Section 26 of the Rights Agreement, the Company and the Rights Agent may from time to time supplement or amend the Rights Agreement in accordance with the provisions of Section 26 thereof; and

WHEREAS, the Board of Directors of the Company has determined that it is in the best interests of the Company and the holders of the Rights to amend the Rights Agreement as provided herein.

NOW THEREFORE, in consideration of the foregoing and the mutual agreements set forth herein, the Company and the Rights Agent agree as follows:

1. Any term not defined herein shall have the meaning ascribed to it in the Rights Agreement.

2. Section 1.1 shall be amended and restated in its entirety as follows:

“1.1 “Acquiring Person” shall mean any Person (as such term is hereinafter defined) who or which, together with all Affiliates and Associates (as such terms are hereinafter defined) of such Person, shall be the Beneficial Owner (as such term is hereinafter defined) of 15% or more of the Common Shares of the Company then outstanding but shall not include (i) an Exempt Person (as such term is hereinafter defined), (ii) if, as of the date hereof, any Person is the Beneficial Owner of 15% or more of the Common Shares outstanding (an “Existing Holder”), such Existing Holder shall not be or become an “Acquiring Person” unless and until such time as such Existing Holder shall become the Beneficial Owner of one or more additional Common Shares of the Company (other than pursuant to a dividend or distribution paid or made by the Company on the outstanding Common Shares in Common Shares or pursuant to a split or subdivision of the outstanding Common Shares), unless, upon becoming the Beneficial Owner of such additional Common Shares, such Existing Holder is not then the Beneficial Owner of 15% or more of the Common Shares then outstanding, or (iii) Virologic, Inc., a Delaware corporation (“Parent”), Apollo Acquisition Sub, Inc., a Delaware corporation (“Merger Sub I”), Apollo Merger Subsidiary, LLC, a Delaware limited

liability company (“Merger Sub II,” and together with Merger Sub I, the “Merger Subs”), or any Affiliate or Associate of Parent or the Mergers Subs; provided, however, that Parent, the Merger Subs or any Affiliate or Associate of Parent or Merger Subs will become an “Acquiring Person” in the event that Parent, Merger Subs, or any Affiliate or Associate of Parent or Merger Subs becomes the Beneficial Owner, individually or in the aggregate, of an aggregate of 15% or more of the Common Shares of the Company then outstanding other than pursuant to the terms of the Agreement and Plan of Merger and Reorganization dated as of May 28, 2004 (the “Merger Agreement”), among the Company, Parent and the Merger Subs. Notwithstanding the foregoing, no Person shall become an “Acquiring Person” as the result of an acquisition of Common Shares by the Company which, by reducing the number of shares outstanding, increases the proportionate number of shares beneficially owned by such Person to 15% or more of the Common Shares of the Company then outstanding; provided, however, that if a Person shall become the Beneficial Owner of 15% or more of the Common Shares of the Company then outstanding solely by reason of share purchases by the Company and shall, after such share purchases by the Company, become the Beneficial Owner of one or more additional Common Shares of the Company (other than pursuant to a dividend or distribution paid or made by the Company on the outstanding Common Shares in Common Shares or pursuant to a split or subdivision of the outstanding Common Shares), then such Person shall be deemed to be an “Acquiring Person” unless upon becoming the Beneficial Owner of such additional shares of Common Stock such Person does not beneficially own 15% or more of the shares of Common Stock then outstanding. Notwithstanding the foregoing, if the Board of Directors of the Company determines in good faith that a Person who would otherwise be an “Acquiring Person,” as defined pursuant to the foregoing provisions of this Section 1.1, has become such inadvertently (including, without limitation, because (A) such Person was unaware that it beneficially owned a percentage of Common Stock that would otherwise cause such Person to be an “Acquiring Person” or (B) such Person was aware of the extent of its Beneficial Ownership of Common Stock but had no actual knowledge of the consequences of such Beneficial Ownership under this Agreement), and without any intention of changing or influencing control of the Company, and such Person divests as promptly as practicable a sufficient number of Common Shares so that such Person would no longer be an Acquiring Person, as defined pursuant to the foregoing provisions of this Section 1.1, then such Person shall not be deemed to be or have become an “Acquiring Person” at any time for any purposes of this Agreement. For all purposes of this Agreement, any calculation of the number of Common Shares outstanding at any particular time, including for purposes of determining the particular percentage of such outstanding Common Shares of which any Person is the Beneficial Owner, shall be made in accordance with the last sentence of Rule 13d-3(d)(1)(i) of the General Rules and Regulations under the Securities Exchange Act of 1934, as amended (the “Exchange Act”), as in effect on the date of this Agreement.”

3. Section 1.9 of the Rights Agreement is hereby amended by adding as the final sentence thereto the following:

“Notwithstanding anything in this Agreement to the contrary, no Shares Acquisition Date shall be deemed to have occurred solely

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as a result of (i) the approval, execution or delivery of the Merger Agreement and the agreements entered into by the Company and Parent with certain of the other’s stockholders (the “Voting Agreements”); (ii) the announcement or consummation of the merger of Merger Sub I with and into the Company in accordance with the Delaware General Corporation Law (“Merger I”), immediately followed by the merger of the Company with and into Merger Sub II in accordance with the Delaware Limited Liability Company Act (“Merger II,” and together with Merger I, the “Transaction”) or the consummation of any of the other transactions contemplated by the Merger Agreement or the Voting Agreements or (iii) the acquisition of Common Shares of the Company by Parent or the Merger Subs pursuant to the Transaction.”

4. Section 3.1 of the Rights Agreement is hereby amended by adding as the final sentence thereto the following:

“Notwithstanding anything in this Agreement to the contrary, no Distribution Date shall be deemed to have occurred solely as a result of (i) the approval, execution or delivery of the Merger Agreement and the Voting Agreements; (ii) the announcement or consummation of the Transaction or the consummation of any of the other transactions contemplated by the Merger Agreement or the Voting Agreements or (iii) the acquisition of Common Shares of the Company by Parent or the Merger Subs pursuant to the Transaction.”

5. Section 7.1 shall be amended and restated in its entirety as follows:

“7.1 Exercise of Rights. Subject to Section 11.1.2 and except as otherwise provided herein, the registered holder of any Right Certificate may exercise the Rights evidenced thereby in whole or in part at any time after the Distribution Date upon surrender of the Right Certificate, with the form of election to purchase and certification on the reverse side thereof duly executed, to the Rights Agent at the office of the Rights Agent designated for such purpose, together with payment of the aggregate Purchase Price for the total number of one one-hundredths of a Preferred Share (or other securities, cash or other assets) as to which the Rights are exercised, at or prior to the time (the “Expiration Date”) that is the earliest of (i) the close of business on April 6, 2011 (the “Final Expiration Date”), (ii) the time at which the Rights are redeemed as provided in Section 23 (the “Redemption Date”), (iii) the closing of any merger or other acquisition transaction involving the Company pursuant to an agreement of the type described in Section 13.3 at which time the Rights are deemed terminated,

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(iv) the time at which the Rights are exchanged as provided in Section 27 or (v) upon written notice thereof from the Company to the Rights Agent, immediately prior to the filing of a Certificate of Merger for Merger I (the “Certificate of Merger”) by the Company with the Secretary of State of the State of Delaware (or such later time as may be agreed in writing by the parties and specified in the Certificate of Merger) and the filing of a Certificate of Merger for Merger II (the “Second Certificate of Merger”) by Merger Sub II with the Secretary of State of the State of Delaware (or such later time as may be agreed in writing by the parties and specified in the Second Certificate of Merger).”

6. Section 11.1.2 of the Rights Agreement is hereby amended by adding as the final paragraph thereto the following:

“Notwithstanding anything in this Agreement to the contrary, no Trigger Event shall be deemed to have occurred solely as a result of (i) the approval, execution or delivery of the Merger Agreement and the Voting Agreements; (ii) the announcement or consummation of the Transaction or the consummation of any of the other transactions contemplated by the Merger Agreement or the Voting Agreements or (iii) the acquisition of Common Shares of the Company by Parent or the Merger Subs pursuant to the Transaction.”

7. Section 13.1 of the Rights Agreement is hereby amended by adding as the final sentence thereto the following:

“Notwithstanding anything in this Agreement to the contrary, none of the events described in clauses (A) through (C) of Section 13.1 shall be deemed to have occurred solely as a result of (i) the approval, execution or delivery of the Merger Agreement and the Voting Agreements; (ii) the announcement or consummation of the Transaction or the consummation of any of the other transactions contemplated by the Merger Agreement or the Voting Agreements or (iii) the acquisition of Common Shares of the Company by Parent or the Merger Subs pursuant to the Transaction.”

8. A new Section 20.13 is hereby added to the Rights Agreement as follows:

“20.13 Compliance with Merger Agreement. The Rights Agent shall not be subject to, nor be required to comply with, or determine if any Person has complied with, the Merger Agreement or any agreements or documents related to or referred to in the Merger Agreement or any other agreement between or among the parties thereto, even though reference thereto may be made in this Agreement, or to determine any calculation set forth in the Merger

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Agreement or to determine whether any condition set forth in the Merger Agreement has been met, or to comply with any notice, instruction, direction, request or other communication, paper or document other than as expressly set forth in this Agreement.”

9. 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 such State applicable to contracts to be made and performed entirely within such State; provided, however, that all provisions regarding the rights, duties and obligations of the Rights Agent shall be governed by and construed in accordance with the laws of the State of New York applicable to contracts made and to be performed entirely within such State.

10. 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.

11. Except as expressly amended hereby, the Rights Agreement shall remain in full force and effect.

12. The undersigned officer of the Company, does hereby certify to the Rights Agent that this Amendment (i) complies with the terms of Section 26 of the Rights Agreement and (ii) will not change or increase the rights, duties, liabilities or obligations of the Rights Agent under the Rights Agreement.

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