<PAGE>

                                                                     EXHIBIT 4.4

                SECOND AMENDMENT TO STOCKHOLDER RIGHTS AGREEMENT

         THIS SECOND AMENDMENT TO STOCKHOLDER RIGHTS AGREEMENT (this
"Amendment"), is executed by and between Enchira Biotechnology Corporation
(f/k/a Energy BioSystems Corporation), a Delaware corporation (the "Company"),
and Harris Trust and Savings Bank (successor in interest to Society National
Bank) (the "Rights Agent"), at the direction of the Company.

                                    RECITALS

         WHEREAS, the Company and the Rights Agent are parties to a Stockholder
Rights Agreement dated as of March 8, 1995, as amended by that certain First
Amendment dated as of April 30, 1997 (the "Rights Agreement");

         WHEREAS, the Company, pursuant to Section 26 of the Rights Agreement,
desires to amend the Rights Agreement and on June 8, 2000, the Board of
Directors approved resolutions authorizing the amendment of the Rights Plan as
herein provided; and

         WHEREAS, pursuant to Section 26 of the Rights Agreement, the Company
and the Rights Agent, at the direction of the Company, hereby agree to amend the
Rights Agreement as set forth below.

         NOW, THEREFORE, the Rights Agreement is hereby amended as follows:

         1.       AMENDMENT OF SECTION 1.

         Section 1(a) of the Rights Agreement is 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 and Associates (as such terms are hereinafter
                  defined) of such Person, shall be the Beneficial Owner (as
                  such term is hereinafter defined) of 20% or more of the Common
                  Shares of the Company then outstanding, but shall not include
                  (i) the Company, (ii) any Subsidiary (as such term is
                  hereinafter defined) of the Company, (iii) any employee
                  benefit plan of the Company or of any Subsidiary of the
                  Company or any Person or entity holding shares of capital
                  stock of the Company for or pursuant to the terms of any such
                  plan, in its capacity as an agent or trustee for any such
                  plan, (iv) Ethyl Corporation, a Delaware corporation
                  ("Ethyl"), (v) Gryphon Ventures II, Limited Partnership, a
                  Massachusetts limited partnership ("Gryphon"), (vi) William M.
                  Haney, III ("Haney"), and (vii) any registered investment
                  company or registered investment adviser acquiring or holding
                  shares in the ordinary course of business for its clients and
                  not for its own benefit for so long as such registered
                  investment company or registered investment adviser is
                  permitted to report its Beneficial Ownership of Common Shares
                  on a Schedule 13G filed under the Exchange Act (as such term
                  is hereinafter defined) (such registered investment company
                  and registered investment adviser being hereinafter referred
                  to as a "Schedule 13G Filer"). 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 20% or more of the Common Shares of the Company then
                  outstanding; provided, however, that if a Person shall become
                  the Beneficial Owner of 20% or more of the Common Shares of
                  the Company then outstanding by reason of share purchases by
                  the Company and shall, after such share purchases by the
                  Company, become the Beneficial Owner of any additional Common
                  Shares of the Company, then such Person shall be deemed to be
                  an "Acquiring Person."

<PAGE>

         2.       AMENDMENT OF SECTION 3.

         Section 3(a) of the Rights Agreement is amended in its entirety to read
as follows:

                           (a)      Until the earlier of (i) the close of
                  business on the 30th day after the Shares Acquisition Date and
                  (ii) the close of business on the 30th day after the date that
                  a tender or exchange offer by any Person (other than the
                  Company, any Subsidiary of the Company, any employee benefit
                  plan of the Company or of any Subsidiary of the Company, or
                  any entity holding shares of capital stock of the Company for
                  or pursuant to the terms of any such plan, in its capacity as
                  an agent or trustee for any such plan, Ethyl, Gryphon, Haney
                  or a Schedule 13G Filer) is first published or sent or given
                  within the meaning of Rule 14d-2(a) (or any successor rule) of
                  the General Rules and Regulations under the Exchange Act, the
                  consummation of which would result in any Person becoming the
                  Beneficial Owner of Common Shares aggregating 20% or more of
                  the then outstanding Common Shares (including any such date
                  which is after the date of this Agreement and prior to the
                  issuance of the Rights; the earlier of such dates being herein
                  referred to as the "Distribution Date"), (x) the Rights will
                  be evidenced (subject to the provisions of paragraph (b) of
                  this Section 3) by the certificates for Common Shares
                  registered in the names of the holders thereof (which
                  certificates for Common Shares shall also be deemed to be
                  certificates for the Rights) and not by separate certificates,
                  and (y) the Rights and interests therein will be transferable
                  only in connection with the transfer of the associated Common
                  Shares. As soon as practicable after the Distribution Date,
                  the Company will prepare and execute, the Rights Agent will
                  countersign, and the Company will send or cause to be sent
                  (and the Rights Agent will, if requested, send) by
                  first-class, insured, postage-prepaid mail, to each record
                  holder of Common Shares as of the close of business on the
                  Distribution Date, at the address of such holder shown on the
                  records of the Company, one or more Rights certificates, in
                  substantially the form of Exhibit B hereto (a "Rights
                  Certificate"), evidencing one Right for each Common Share so
                  held, subject to adjustment as provided herein. In the event
                  that an adjustment in the number of Rights per Common Share
                  has been made pursuant to Section 11(n) hereof, then at the
                  time of distribution of the Rights Certificates, the Company
                  shall make the necessary and appropriate rounding adjustments
                  (in accordance with Section 14(a) hereof) so that Rights
                  Certificates representing only whole numbers of Rights are
                  distributed and cash is paid in lieu of any fractional Rights.
                  As of and after the Distribution Date, the Rights will be
                  evidenced solely by such Rights Certificate.

         3.       AMENDMENT OF SECTION 11.

         Section 11(a)(ii) of the Rights Agreement is amended in its entirety to
read as follows:

                                    (ii)     In the event that any Person (other
                  than (i) the Company, (ii) any Subsidiary of the Company,
                  (iii) any employee benefit plan of the Company or of any
                  Subsidiary of the Company or any Person or entity holding
                  shares of capital stock of the Company for or pursuant to the
                  terms of any such plan, in its capacity as an agent or trustee
                  for any such plan, (iv) Ethyl, (v) Gryphon, (vi) Haney or
                  (vii) a Schedule 13G Filer), alone or together with its
                  Affiliates and Associates, shall, at any time after the Rights
                  Dividend Declaration Date, become an Acquiring Person then,
                  promptly following the first occurrence of such event, proper
                  provision shall be made so that each holder of a Right (except
                  as provided in Section 7(e) hereof) shall thereafter have the
                  right to receive, upon exercise thereof at the then current
                  Purchase Price in accordance with the terms of this Agreement
                  and in lieu of Preferred Share Fractions, such number of
                  Common Shares of the Company as shall equal the result
                  obtained by (x) multiplying the then current Purchase Price by
                  the then

<PAGE>

                  number of Preferred Share Fractions for which a Right is then
                  exercisable and (y) dividing that product (which shall
                  thereafter be referred to as the "Purchase Price" for each
                  Right and for all purposes of this Agreement) by 50% of the
                  then current market price (determined pursuant to Section
                  11(d) hereof) per Common Share on the fifth day after the date
                  on which a Person has become an Acquiring Person, or the fifth
                  day after the Shares Acquisition Date, whichever market price
                  shall be less (such number of shares being hereinafter
                  referred to as the "Adjustment Shares"). In the event that any
                  Person shall become an Acquiring Person and the Rights shall
                  then be outstanding, the Company shall not take any action
                  that would eliminate or diminish the benefits intended to be
                  afforded by the Rights.

         4.       EFFECTIVENESS.

         This Amendment shall be deemed effective as of June 3, 1999. Except as
amended hereby, the Rights Agreement shall remain in full force and effect and
shall be otherwise unaffected hereby.

         5.       MISCELLANEOUS.

         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. This Amendment may be executed in any
number of counterparts, 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. If any term, provision, covenant or restriction
of this Amendment is held by a court of competent jurisdiction or other
authority to be invalid, illegal, 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.

                  [Remainder of Page Intentionally Left Blank]

<PAGE>





         IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be
duly executed on June 23, 2000.

                                   ENCHIRA BIOTECHNOLOGY CORPORATION


                                   By:   /s/ Peter P. Policastro
                                      ------------------------------------------
                                         Peter P. Policastro, Ph.D.
                                         President and Chief Executive Officer


                                   HARRIS TRUST AND SAVINGS BANK,
                                   AS RIGHTS AGENT


                                   By:   /s/ Lorraine Rodewald
                                      ------------------------------------------
                                         Lorraine Rodewald
                                         Vice President