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                                                                     Exhibit 4.3


                                                                  EXECUTION COPY


                       AMENDMENT NO. 2 TO RIGHTS AGREEMENT


      THIS AMENDMENT NO. 2 (this "Amendment"), dated as of November 21, 2003, to
the Rights Agreement, dated as of May 10, 2001, as amended by Amendment No. 1,
dated as of November 4, 2002 (the "Rights Agreement"), between APPLIED MOLECULAR
EVOLUTION, INC., a Delaware corporation (the "Company"), and EQUISERVE TRUST
COMPANY, N.A., as Rights Agent (the "Rights Agent"), is made with reference to
the following facts:

      A. The Company and the Rights Agent have heretofore entered into the
Rights Agreement. Pursuant to Section 27 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 such Section.

      B. The Board of Directors of the Company has determined that it is in the
best interests of the Company to enter into that certain Agreement and Plan of
Merger (the "Merger Agreement") by and among Eli Lilly and Company, an Indiana
corporation ("Lilly"), Genesis Merger Sub, Inc., a Delaware corporation ("Merger
Sub"), and the Company.

      C. Pursuant to the Merger Agreement, Merger Sub will merge with and into
the Company, which shall be the surviving corporation, in accordance with
Delaware General Corporation Law (the "DGCL"), as well as all other applicable
Laws.

      D. In connection with the Merger Agreement, Lilly and certain stockholders
of the Company propose to enter into certain Voting and Support Agreements,
pursuant to which such stockholders of the Company will grant Lilly a proxy and
certain other rights (the "Voting and Support Agreements").

      E. There is not, and has not occurred, as of the date hereof any Acquiring
Person or Distribution Date (as such terms are defined in the Rights Agreement).

      F. The Company is obligated and the Company desires to amend the Rights
Agreement to (i) render the Rights Agreement inapplicable to the Merger
Agreement, the Voting and Support Agreements, the Merger (as defined in the
Merger Agreement) and the other transactions contemplated by the Merger
Agreement or the Voting and Support Agreements, (ii) ensure that (a) none of
Lilly, Merger Sub or any other affiliate of Lilly is an Acquiring Person (as
defined in the Rights Agreement) pursuant to the Rights Agreement and (b) a
Distribution Date or a Stock Acquisition Date (as such terms are defined in the
Rights Agreement) does not occur, in the case of clauses (a) and (b), by reason
of the execution of the Merger Agreement or the Voting and Support Agreements or
the consummation of the Merger or the other transactions contemplated by the
Merger Agreement or the Voting and Support Agreements, and (iii) provide that
the Expiration Date (as defined in the Rights Agreement) shall occur immediately
prior to the Effective Time (as defined in the Merger Agreement).


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

      1. Amendment of Section 1(a). Section 1(a) of the Rights Agreement is
amended to add the following sentence at the end thereof:

      "Notwithstanding anything in this Agreement to the contrary, none of Eli
      Lilly and Company, an Indiana corporation ("Lilly"), Genesis Merger Sub,
      Inc., a Delaware corporation ("Merger Sub"), or any of their respective
      Affiliates or Associates shall be deemed to be an "Acquiring Person" by
      virtue of (i) the approval, execution or delivery of the Agreement and
      Plan of Merger, dated as of November 21, 2003 by and among Lilly, Merger
      Sub and the Company, as amended from time to time (the "Merger
      Agreement"), (ii) the approval, execution and delivery of the Voting and
      Support Agreements dated as of November 21, 2003 by and between Lilly and
      certain stockholders of the Company signatory thereto, as amended from
      time to time (the "Voting and Support Agreements"), (iii) the consummation
      of the Merger (as defined in the Merger Agreement), (iv) the consummation
      of any of the other transactions contemplated in the Merger Agreement or
      the Voting and Support Agreements, or (v) the public announcement of any
      of the foregoing (each such event, an "Exempt Event")."

      2. The definition of "Acquiring Person" set forth in Section 1(a) of the
Rights Agreement is hereby amended in its entirety to read as follows:

            "(a) "Acquiring Person" shall mean any Person (as such term is
      hereinafter defined) who or which, together with all Affiliates (as such
      term is hereinafter defined) and Associates (as such term is hereinafter
      defined) of such Person, shall be the Beneficial Owner (as such term is
      hereinafter defined) of 15% or more of the shares of Common Stock then
      outstanding or who was such a Beneficial Owner at any time after the date
      hereof, whether or not such Person continues to be the Beneficial Owner of
      15% or more of the outstanding shares of Common Stock. Notwithstanding the
      foregoing,

                  (i) in no event shall a Person who or which, together with all
            Affiliates and Associates of such Person, is the Beneficial Owner of
            less than 15% of the Company's outstanding shares of Common Stock
            become an Acquiring Person solely as a result of a reduction of the
            number of shares of outstanding Common Stock, including repurchases
            of outstanding shares of Common Stock by the Company, which
            reduction increases the percentage of outstanding shares of Common
            Stock beneficially owned by such Person (provided that any
            subsequent increase in the amount of Common Stock beneficially owned
            by such Person, together with all Affiliates and Associates of such
            Person, without the prior approval of the Company shall cause such
            Person to be an Acquiring Person);


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                  (ii) the term Acquiring Person shall not mean (A) the Company,
            (B) any subsidiary of the Company (as such term is hereinafter
            defined), (C) any employee benefit plan of the Company or any of its
            subsidiaries, (D) any entity holding securities of the Company
            organized, appointed or established by the Company or any of its
            subsidiaries for or pursuant to the terms of any such plan, (E)
            William D. Huse, M.D., Ph.D. ("Huse"), or any Affiliate or Associate
            thereof, as a result of the acquisition by Huse of up to 17.5% of
            the shares of Common Stock of the Company due to the issuance of
            compensatory stock options, or the issuance of Common Stock on the
            exercise thereof, previously or subsequently granted under
            agreements approved by the Company's Board of Directors pursuant to
            stock option plans approved by the stockholders of the Company, (F)
            BVF Partners L.P. ("BVF"), or any Affiliate or Associate thereof, as
            a result of the acquisition by BVF and its Affiliates and Associates
            of up to an aggregate of 15.8% of the shares of Common Stock of the
            Company, or (G) Lilly or Merger Sub, or any Affiliate or Associate
            thereof as a result of the execution of the Merger Agreement, as
            result of the execution of the Voting and Support Agreements or as
            or as a result of the consummation of the Merger (as defined in the
            Merger Agreement) or any of the transactions contemplated by the
            Merger Agreement or the Voting and Support Agreements; and

                  (iii) no Person shall be deemed to be an Acquiring Person if
            (A) within five business days after such Person would otherwise have
            become an Acquiring Person (but for the operation of this clause
            (iii)), such Person notifies the Board of Directors that such Person
            did so inadvertently and, within two business days after such
            notification, such Person is the Beneficial Owner of less than 15%
            of the outstanding shares of Common Stock, (B) by reason of such
            Person's Beneficial Ownership of 15% or more of the outstanding
            shares of Common Stock on the date hereof if, prior to the Record
            Date, such Person notifies the Board of Directors that such Person
            is no longer the Beneficial Owner of 15% or more of the then
            outstanding shares of Common Stock or (C) if the Board of Directors
            determines in good faith that a person who would otherwise be an
            "Acquiring Person," as defined pursuant to the foregoing provisions
            of this paragraph (a), has become such inadvertently, and such
            Person divests Beneficial Ownership as promptly as practicable of a
            sufficient number of shares of Common Stock so that such Person
            would no longer be an "Acquiring Person" as defined pursuant to the
            foregoing provisions of this paragraph (a)."

      3. Amendment of Section 1(i). Section 1(i) of the Rights Agreement is
amended to add the following sentence at the end thereof:

      "Notwithstanding anything in this Agreement to the contrary, a Stock
      Acquisition Date shall not be deemed to have occurred as the result of an
      Exempt Event."


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      4. Amendment of Section 3(a). (i) The first sentence of Section 3(a) of
the Rights Agreement is hereby amended by adding the following to the end of
such sentence:

      "; and provided, further, that in no event shall a Distribution Date be
      deemed to occur as a result of the execution of the Merger Agreement or
      the Voting and Support Agreements or as a result of the consummation of
      the Merger or any of the transactions contemplated by the Merger Agreement
      or Voting and Support Agreements."

      (ii) Section 3(a) of the Rights Agreement is further amended to add the
following sentence at the end thereof:

      "Notwithstanding anything in this Agreement to the contrary, a
      Distribution Date shall not be deemed to have occurred as the result of an
      Exempt Event."

      5. Amendment of Section 11(a). Section 11(a) of the Rights Agreement is
amended to add the following clause (iv):

      "(iv) Notwithstanding the foregoing or anything in the Rights Agreement to
      the contrary, this Section 11(a) shall not apply to any Exempt Event."

      6. Amendment of Section 13(a). Section 13(a) of the Rights Agreement is
amended to add the following sentence at the end thereof:

      "Notwithstanding anything in this Rights Agreement to the contrary, no
      Exempt Event shall be deemed to be an event of the type described in the
      first sentence of this Section 13, and shall not cause the Rights to be
      adjusted or exercisable in accordance with, or any other action to be
      taken or obligation to arise pursuant to, this Section 13."

      7. The Rights Agreement is hereby amended by adding Section 36 which shall
read in its entirety as follows:

      "36. Termination. Notwithstanding anything to the contrary contained
      herein, this Rights Agreement shall terminate and the Rights shall expire
      and be of no further force and effect immediately prior to the Effective
      Time (as defined in the Merger Agreement)."

      8. No "Stock Acquisition Date" shall be deemed to occur under the Rights
Agreement as a result of the execution of the Merger Agreement or the Voting and
Support Agreements or as a result of the consummation of the Merger or any of
the transactions contemplated by the Merger Agreement or the Voting and Support
Agreements.

      9. Rights Agreement as Amended. The term "Agreement" as used in the Rights
Agreement shall be deemed to refer to the Rights Agreement as amended hereby.
Except as set forth herein, the Rights Agreement shall remain in full force and
effect and otherwise shall be unaffected hereby.


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      10. All amendments made to the Rights Agreement in this Amendment shall be
deemed to apply retroactively as well as prospectively.

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

      12. This Amendment may be executed in counterparts, each of which shall be
an original, but such counterparts shall together constitute one and the same
instrument.



                  [Remainder of page intentionally left blank.]


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


Attest:                                      APPLIED MOLECULAR EVOLUTION, INC.



By: /s/ WILLIAM D. HUSE                      By:  /s/ LAWRENCE E. BLOCH
    -----------------------------                 -----------------------------
    William D. Huse, M.D., Ph.D                   Lawrence E. Bloch, M.D., J.D.
    President and Chief Executive Officer         Chief Financial Officer and
                                                  Secretary


Attest:                                      EQUISERVE TRUST COMPANY, N.A.



By: /s/ GREG VELIOTIS                        By:  /s/ CAROL  MULVEY-EORI
    -----------------------------                 -----------------------------
    Greg Veliotis                                 Carol Mulvey-Eori
    Title: Account Manager                        Title: Managing Director



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