<PAGE>
                                                                   EXHIBIT 10.31


                              [/\#/\] CERTAIN CONFIDENTIAL INFORMATION CONTAINED
                                  IN THIS DOCUMENT, MARKED BY BRACKETS, HAS BEEN
                                OMITTED AND FILED SEPARATELY WITH THE SECURITIES
                                  AND EXCHANGE COMMISSION PURSUANT TO RULE 24B-2
                             OF THE SECURITIES EXCHANGE ACT OF 1934, AS AMENDED.


           AMENDMENT NO. 1 TO PATENT AND TECHNOLOGY LICENSE AGREEMENT

         This Amendment No. 1 to Patent and Technology License Agreement (FIRST
AMENDMENT) is made and entered into as of February 10, 2004 by and between
Myogen, Inc. (LICENSEE) and the Board of Regents (BOARD) of the University of
Texas System (SYSTEM).

                                    RECITALS

A. LICENSEE and BOARD entered into a Patent and Technology License Agreement
effective as of January 1, 2002 (LICENSE AGREEMENT).

B. LICENSEE and BOARD wish to further amend the terms of the LICENSE AGREEMENT
as set forth below.

NOW, THEREFORE, it is hereby agreed as follows:

1. Section 5.1c of the LICENSE AGREEMENT shall be revised to read in its
entirety as follows:

         "milestone fees according to the table below, due and payable within 30
days of each milestone event for the first LICENSED PRODUCT or IDENTIFIED
PRODUCT to achieve such milestone event, [/\#/\], provided however, if LICENSEE
pays a milestone fee under the 1999 AGREEMENT for a milestone event listed
below, such payment is creditable toward the milestone fee due for the same
milestone event for the same LICENSED PRODUCT or IDENTIFIED PRODUCT pursuant to
this Section 5.1c:

<Table>
<Caption>
      MILESTONE EVENT                                        MILESTONE FEE
      ------------------------------------------------       -------------------
<S>                                                          <C>
      The date the first patient is dosed in the first       [/\#/\]
      Phase III clinical trial

      NDA approval in the U.S. for a LICENSED                [/\#/\]
      PRODUCT or IDENTIFIED PRODUCT
</Table>


2. Section 5.1d of the LICENSE AGREEMENT shall be revised to read in its
entirety as follows:

         "a running royalty equal to [/\#/\] of NET SALES [/\#/\], subject to
adjustment under Sections 5.1e and 5.1f below; provided, however, that if the
total earned royalty due to LICENSEE by a NON-SUBLICENSEE CORPORATE PARTNER or
sublicensee with respect to a LICENSED PRODUCT and/or IDENTIFIED PRODUCT is
reduced upon the expiration of applicable PATENT RIGHTS or introduction of a
generic product, the earned royalty due to BOARD by LICENSEE will be [/\#/\],
but in no event shall the earned royalty owed by LICENSEE in such instance be
greater than [/\#/\] of the total earned royalty due to LICENSEE from a
NON-SUBLICENSEE CORPORATE PARTNER or sublicensee;"

3. Section 5.1h of the LICENSE AGREEMENT shall be revised to read in its
entirety as follows:

         "a sublicense fee of [/\#/\] of SUBLICENSEE REVENUES and/or
NON-SUBLICENSEE CORPORATE PARTNERSHIP REVENUES, subject to adjustment under
Section 5.1i below, payable within 30 days of LICENSEE'S receipt of any such
consideration; provided, however, if LICENSEE receives SUBLICENSE REVENUES in
consideration for the grant of a sublicense under the licenses granted to
LICENSEE hereunder


                                        [/\#/\] CONFIDENTIAL TREATMENT REQUESTED

                                   Page 1 of 2
<PAGE>



and such sublicense also includes the grant of a license or sublicense to other
technology controlled by LICENSEE but not acquired from BOARD, then the
foregoing amount shall be adjusted by a percentage that fairly represents, as
reasonably determined by the parties, the contribution of the relevant LICENSED
SUBJECT MATTER to the total revenue received by LICENSEE; and"

4. Except as expressly provided in this FIRST AMENDMENT, all other terms,
conditions and provisions of the LICENSE AGREEMENT shall continue in full force
and effect as provided therein.

         IN WITNESS WHEREOF, LICENSEE and BOARD have entered into this FIRST
AMENDMENT effective as of the date first set forth above.


BOARD OF REGENTS OF THE                            MYOGEN, INC.
UNIVERSITY OF TEXAS SYSTEM


By    /s/ John A. Roan                             By    /s/ J. William Freytag
  ---------------------------------------------      ---------------------------
  John A. Roan                                       J. William Freytag
  Executive Vice President for Business Affairs      President and CEO
  UT Southwestern Medical Center at Dallas

Date 2/25/04                                       Date 2/10/04
     -------                                            -------


Approved as to Content:


By    /s/ Dennis K. Stone
  -----------------------------------------
  Dennis K. Stone, M.D.
  Vice President for Technology Development
  UT Southwestern Medical Center at Dallas

Date 2/25/04



                                        [/\#/\] CONFIDENTIAL TREATMENT REQUESTED

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