<PAGE>

                                                                     Exhibit 4.3

                           ESPERION THERAPEUTCS, INC.

               AMENDMENT NO. 2 TO THE INVESTORS' RIGHTS AGREEMENT


     This AMENDMENT NO. 2 TO THE INVESTORS' RIGHTS AGREEMENT (this "Agreement")
is made and entered into as of January 7, 2000, by and among ESPERION
THERAPEUTICS, INC., a Delaware corporation (the "Company"), the Purchasers (as
such term is defined in the Original Agreement defined below), and the
Additional Purchasers set forth on Exhibit 1 attached hereto under the heading
"Additional Purchasers."

     WHEREAS, the Company and the Purchasers are parties to an Investors' Rights
Agreement made and entered into as of July 6, 1998 (the "Original Agreement");
and

     WHEREAS, the Original Agreement was amended as of August 11, 1998 pursuant
to Amendment No. 1 to the Investors' Rights Agreement ("Amendment No. 1"), to
provide for the addition of the Additional Purchasers as Purchasers thereunder
with respect to the issuance of the Series B Shares; and

     WHEREAS, the parties to the Original Agreement, as amended, desire to amend
further such agreement, to provide for the addition of the Additional Purchasers
as Purchasers thereunder with respect to the issuance of the Series C Shares,
among other things, on the terms and conditions stated herein and in the
Original Agreement as amended;

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

     1. Defined Terms.

       (a) Capitalized terms used and not otherwise defined in this Agreement
shall have the meanings given to such terms in the Original Agreement.

       (b) The following definitions set forth in Section 1 of the Original
Agreement are hereby amended and restated as follows:

       "Preferred Shares" shall mean the Series A Shares, the Series B Shares,
       the Series C Shares and shares of any additional series of preferred
       stock of the Company, the issuance of which is approved by the holders of
       at least 51 % of the Preferred Shares as required by the Restated
       Certificate.

       "Restated Certificate" shall mean the Company's Amended and Restated
       Certificate of Incorporation, as amended from time to time.

       "Transaction Documents" shall mean, collectively, the Series A Agreement,
       the Securities Purchase Agreement dated as of August 11, 1998 (the
       "Series B Agreement"), the Securities Purchase Agreement dated as of
       January , 2000
<PAGE>

       (the "Series C Agreement"), the Restated Certificate, this Agreement and
       the other Ancillary Agreements (as defined in the Series A Agreement, the
       Series B Agreement and the Series C Agreement).

       (c) The definition of the term "New Securities" set forth in Section 1 of
the Original Agreement is hereby amended to delete the number "380,000" in
subsection (vi) thereof and substitute therefor the number "680,000."

       (d) A new definition is hereby added to Section 1 of the Original
Agreement, to read in its entirety as follows:

       "Series C Shares" shall mean the Company's Series C Convertible Preferred
       Stock, par value $0.01 per share.

     2. Exhibit A. Exhibit A to the Original Agreement is amended and restated
in the form of Exhibit A hereto.

     3. Request for Registration. Section 1.5(a) of the Original Agreement is
hereby amended (i) to delete the date "July 6, 2002" in subsection (A) thereof
and substitute therefor the date "January , 2003," (ii) to delete the defined
term "("Initiating Holders")" and add after the words "then outstanding
Registrable Securities" in subsection (B) thereof the words "other than the
Series C Shares (or any Common Stock issued or issuable upon conversion thereof,
with respect thereto or in exchange therefor) (the "Non-Series C Initiating
Holders") or 30% of the then outstanding Registrable Securities consisting of
Series C Shares (and any Common Stock issued or issuable upon conversion
thereof, with respect thereto or in exchange therefor) (the "Series C Initiating
Holders"), and with reference to either or both the Series C Initiating Holders
and/or the Non-Series C Initiating Holders, the "Initiating Holders")" and (iii)
to amend and restate subsection (C) thereof to read in its entirety as follows:

         (C) After the Company has effected two such registrations pursuant to
         this Section 1.5, one such registration at the request of the
         Non-Series C Initiating Holders and one such registration at the
         request of the Series C Initiating Holders, which registrations have
         been declared or ordered effective and pursuant to which the securities
         have been sold; or

     4. Additional Information and Rights. Section 2.2(a) of the Original
Agreement is hereby amended to add the words "to such Holder" after the word
"issued" therein.

     5. Termination of Financial Information Rights. Section 2.3 of the Original
Agreement is hereby amended to delete the term "Series B" and the number
"$15,000,000" therein and substitute therefor the term "Series C" and the number
"$30,000,000," respectively.

     6. Employee and Other Stock Agreements. Section 2.5(a)(ii) of the Original
Agreement is hereby amended to delete the number "380,000" and substitute
therefor the number "680,000."
<PAGE>

     7. Section 2.16 of the Original Agreement is hereby amended to add the
words "to such Holder" after the word "issued" therein.

     8. Waiver of Antidilution Adjustment. Section 3.6 of the Original Agreement
is hereby amended to delete the words "Series B Shares" in subsection (a)(3),
(b), (c) and (d) thereof and substitute therefor the words "Series A Shares,
Series B Shares or Series C Shares."

     9. Successors and Assigns; Assignment of Rights. Section 4.2 of the
Original Agreement is hereby amended to add at the end of the first sentence
thereof the following:

         ;provided that the registration rights of a Holder of any Registrable
         Securities, as described in Sections 1.5 through 1.15 hereof, may be
         transferred or assigned only to a transferee or assignee who (i)
         acquires at least 500,000 shares of Registrable Securities, (ii) is
         already a Holder of Registrable Securities and already possesses such
         registration rights, (iii) acquires ten percent (10%) or more of the
         outstanding capital stock of the Company and the Company is given prior
         written notice thereof or (iv) is a transferee described in Section
         1.4(A), (B), (C), (D) or (E) hereof.

     10. Entire Agreement; Amendment; Waiver. Section 4.3 is hereby amended to
add at the end of the second sentence thereof the following:

         provided that no such amendment, waiver, discharge or termination may
         amend or modify the provisions of this Section 4.3, amend, modify or
         terminate the amount of the Series C Liquidation Value (as such term is
         defined in the Restated Certificate) or the respective rights of the
         holders of the Series C Shares relating thereto, or subordinate the
         rights of the holders of the Series C Shares to the holders of any
         other class or series of capital stock of the Company in existence on
         the date hereof, in any such case without the prior written consent of
         each holder of the Series C Shares.

     11. Joinder. The Additional Purchasers hereby agree to be bound by and
subject to the terms and conditions of the Original Agreement and the parties
hereto agree that the Additional Purchasers shall be entitled to all of the
rights and benefits of the Purchasers under the Original Agreement.

     12. Governing Law. This Agreement shall be governed in all respects by the
laws of the State of Delaware, as applied to agreements among Delaware residents
entered into and to be performed entirely within Delaware.

     13. Effective Date. In accordance with the terms of the Original Agreement,
this Agreement will become effective upon execution by the Company and the
holders of at least fifty one percent (51 %) of the Preferred Shares.

     14. Counterparts. This Agreement may be executed in any number of
counterparts, each of which shall be an original, but all of which together
shall constitute one instrument.
<PAGE>

        IN WITNESS WHEREOF, the parties hereto have executed this Investors'
Rights Agreement effective as of the day and year first above written.

THE COMPANY:                            ESPERION THERAPEUTICS, INC.


                                        By: /s/ Roger Newton
                                           -----------------------------------
                                           Name:  Roger Newton
                                           Title: President and CEO

THE PURCHASERS:                         CANAAN EQUITY II L.P.


                                        By:     Canaan Equity Partners II LLC,
                                                Its Member/Manager


                                        By:
                                           -----------------------------------
                                           Name:
                                           Title:


                                        TL VENTURES III L.P.



                                        By:     TL VENTURES III Management L.P.,
                                                its general partner



                                        By:     TL VENTURES III LLC,
                                                its general partner



                                        By:
                                                ------------------------------
                                                Name:
                                                Title: Managing Director



                                        TL VENTURES III OFFSHORE L.P.


                                        By:     TL VENTURES III Offshore
                                                Partners L.P.,
                                                its general partner



                                        By:     TL VENTURES III Offshore Ltd.,
                                                its general partner



                                        By:
                                                ------------------------------
                                                Name:
                                                Title:  Vice President
<PAGE>

                                        TL VENTURES III INTERFUND L.P.



                                        By:     TL VENTURES III LLC,
                                                its general partner



                                        By:
                                                ------------------------------
                                                Name:
                                                Title:


                                        TL VENTURES IV L.P.


                                        By:     TL VENTURES IV Management L.P.,
                                                its general partner




                                        By:
                                                ------------------------------
                                                Name:
                                                Title:



                                        TL VENTURES IV INTERFUND L.P.

                                        By:     TL VENTURES IV LLC,
                                                its general partner



                                        By:
                                                ------------------------------
                                                Name:
                                                Title:



                                        OAK INVESTMENT PARTNERS VII, LIMITED
                                        PARTNERSHIP

                                        By:     OAK ASSOCIATES VII, LLC
                                                Its General Partner



                                        By:
                                                ------------------------------
                                                A Member
<PAGE>

                                        OAK AFFILIATES FUND, LIMITED

                                        By:     OAK VII AFFILIATES, LLC
                                                Its General Partner



                                        By:
                                                ------------------------------
                                                A Member


                                        TECNO VENTURE MANAGEMENT




                                        By:
                                                ------------------------------
                                                A Member


                                        AVALAON INVESTMENTS




                                        By:
                                                ------------------------------
                                                A Member


                                        HEALTHCAP KB


                                        By:     HealthCap AB
                                                its general partner


                                        By:     /s/ Bjorn Odlander
                                                ------------------------------
                                                Bjorn Odlander
                                                Director



                                        By:     /s/ Peder Fredrikson
                                                ------------------------------
                                                Peder Fredrikson
                                                Director
<PAGE>

                                        HEALTHCAP COINVEST KB


                                        By:     HealthCap AB
                                                its general partner


                                        By:     /s/ Bjorn Odlander
                                                ------------------------------
                                                Bjorn Odlander
                                                Director



                                        By:     /s/ Peder Fredrikson
                                                ------------------------------
                                                Peder Fredrikson
                                                Director


                                                /s/ Cesare Sirtori
                                                ------------------------------
                                                Cesare Sirtori, M.D.


                                                /s/ Lennart Philipsson
                                                ------------------------------
                                                Lennart Philipsson

                                                /s/ Roger Newton
                                                ------------------------------
                                                Roger Newton, Ph.D.



                                        SCHEER INVESTMENT HOLDINGS II, L.L.C.


                                        By:     /s/ David I. Scheer
                                                ------------------------------
                                                David I. Scheer
                                                Managing Member


                                                /s/ Anders Wiklund
                                                ------------------------------
                                                Anders Wiklund


                                                /s/ Sandip Mukherjee
                                                ------------------------------
                                                Sandip Mukherjee, M.D.

                                                /s/ Seth A. Rudnick
                                                ------------------------------
                                                Seth A. Rudnick
<PAGE>

                            SCHEDULE OF PURCHASERS

--------------------------------------------------------------------------------
   Purchaser's Name                      No. of              Cash Consideration
   ----------------                      ------              ------------------
     and Address                     Series C Shares
--------------------------------------------------------------------------------
Canaan Equity II, L.P.                  2,280,093               $4,925,000.88
105 Rowayton Avenue
Rowayton, Connecticut 06853
--------------------------------------------------------------------------------
Seth A. Rudnick                            34,722                   74,999.52
6330 Quadrangle Drive, Suite 200
Chapel Hill, North Carolina 27514
--------------------------------------------------------------------------------
TL Ventures III, L.P.                   1,491,055                3,220,678.80
800 Safeguard Building
435 Devon Park Drive
Wayne, Pennsylvania 19087-1945
--------------------------------------------------------------------------------
TL Ventures III Offshore L.P.             312,110                  674,157.80
800 Safeguard Building
435 Devon Park Drive
Wayne, Pennsylvania 19087-1945
--------------------------------------------------------------------------------
TL Ventures III Interfund L.P.             48,687                  105,163.92
800 Safeguard Building
435 Devon Park Drive
Wayne, Pennsylvania 19087-1945
--------------------------------------------------------------------------------
TL Ventures IV L.P.                       902,088                1,948,510.08
800 Safeguard Building
435 Devon Park Drive
Wayne, Pennsylvania 19087-1945
--------------------------------------------------------------------------------
TL Ventures IV Interfund L.P.              23,838                   51,490.08
800 Safeguard Building
435 Devon Park Drive
Wayne, Pennsylvania 19087-1945
--------------------------------------------------------------------------------
Oak Investment Partners VII, LP         1,806,481                3,901,998.96
1 Gorham Island
Westport, Connecticut 06880
--------------------------------------------------------------------------------
Oak VII Affiliates Fund, LP                45,371                   98,001.36
1 Gorham Island
Westport, Connecticut 06880
--------------------------------------------------------------------------------
Tecno Venture Management                1,851,852                4,000,000.32
101 Arch Street, Suite 1950
Boston, Massachusetts 02110
--------------------------------------------------------------------------------
Avalon Investments                      1,157,408                2,500,001.28
201 West Main Street
Ann Arbor, Michigan 48104
--------------------------------------------------------------------------------
HealthCap KB                              583,335                1,260,003.60
c/o Odlander, Fredrikson & Co. AB
--------------------------------------------------------------------------------

<PAGE>

--------------------------------------------------------------------------------
Sturegatan 34
S-O 114 36 Stockholm, Sweden
--------------------------------------------------------------------------------
HealthCap CoInvest KB                     805,554                1,739,996.64
c/o Odlander, Fredrikson & Co. AB
Sturegatan 34
S-O 114 36 Stockholm, Sweden
--------------------------------------------------------------------------------
Cesare Sirtori                            462,963                1,000,000.08
Institute of Pharmacological Sciences
Via Balzaretti 9
20133 Milano
Italy
--------------------------------------------------------------------------------
Lennart Philipsson                        102,315                  221,000.40
Karolinska Institute
Department of Cell and Molecular
Biology
von Eulers vag 3
SE-17177 Stockholm
--------------------------------------------------------------------------------
Roger Newton                               95,741                        0
c/o Esperion Therapeutics Inc.
3621 South State Street
695 KMS Place
Ann Arbor, Michigan 48108
--------------------------------------------------------------------------------
Scheer Investment Holdings II, LLC         46,296                   99,999.36
250 West Main Street
Branford, Connecticut 06405
--------------------------------------------------------------------------------
Anders Wiklund                             31,673                        0
928 Sunset Ridge
Bridgewater, New Jersey
--------------------------------------------------------------------------------
Sandip Mukherjee                           23,149                   50,001.84
71 Quail Run
Madison, Connecticut 06433
--------------------------------------------------------------------------------
TOTALS                                 12,104,731               25,871,004.72
--------------------------------------------------------------------------------