<PAGE>

                                                                   EXHIBIT 10.37


                         FOURTH AMENDMENT AND ADDENDUM
                           TO COLLABORATION AGREEMENT

     THIS FOURTH AMENDMENT AND ADDENDUM TO COLLABORATION AGREEMENT (the "Fourth
Amendment") is made and entered into as of the 25th day of October, 1996 (the
"Effective Date"), by and between Energy BioSystems Corporation, a Delaware
corporation ("EBC"), and Petrolite Corporation, a Delaware corporation ("PLIT").

                                   WITNESSETH

     WHEREAS, EBC and PLIT are parties to that certain Collaboration Agreement
dated March 5, 1992, as amended July 1, 1992 (the "First Amendment"), October
18, 1993 (the "Second Amendment") and August 24, 1995 (the "Third Amendment")
(collectively, the "Collaboration Agreement");

     WHEREAS, EBC is engaged in discussions with an investment banking firm
regarding a possible equity financing scheduled to be completed in 1996 (the
"Financing") and in connection therewith has agreed with PLIT to amend and grant
to EBC the right to amend the Collaboration Agreement pursuant to the terms of
this Fourth Amendment to the Collaboration Agreement;

     NOW, THEREFORE, in consideration of the mutual covenants and promises
contained herein, One Dollar ($1.00) and other good and valuable consideration,
the receipt and sufficiency of which hereby are acknowledged, the parties hereby
agree to the following:

     1.  (a)  If the Financing is completed during 1996, EBC shall pay to PLIT
One Million Dollars ($1,000,000) (the "First Cash Payment") by corporate check
or wire transfer within ten business days of the closing of the Financing and
the Collaboration Agreement shall be amended as provided in Section 1(b) hereof.

     (b) Upon delivery of the First Cash Payment, without any further action by
the parties:

     (i)  Until the first to occur of the Election Date and the Expiration Date,
          as hereinafter defined, except as provided in this Section 1(b) PLIT
          shall be under no obligation to provide any research and development,
          technical support or consulting services pursuant to the Collaboration
          Agreement including, but not limited to, any obligations contained in
          Section 2.4 of the Collaboration Agreement.

     (ii) The Collaboration Agreement shall be automatically amended by deleting
          the second and third sentence of Section 4 of the Third Amendment and
          substituting in place thereof the following sentences:
<PAGE>

               "Until December 31, 1998, or some other date as to which the
               parties agree in writing, PLIT will assign not less than three
               (3) employees full-time to provide operational and engineering
               staff support for the Working Pilot Plant.  The costs of these
               employees and the reasonable costs of maintaining the Working
               Pilot Plant and providing analytical lab support for the Working
               Pilot Plant, will be the sole responsibility of PLIT until
               December 31, 1998, unless the parties agree in writing to some
               other date; provided that during the period commencing January 1,
               1997 and ending on the date of the Second Cash Payment (as
               defined in the Fourth Amendment and Addendum to Collaboration
               Agreement dated October 25, 1996), EBC will reimburse PLIT
               quarterly for the direct out-of-pocket cash costs and expenses
               incurred by PLIT relating to these employees, maintaining the
               Working Pilot Plant and providing analytical lab support for the
               Working Pilot Plant (the "Reimbursable Expenses")."

     2.  (a)  EBC may, at any time during the period commencing with the payment
of the First Cash Payment and ending at 5:00 p.m. (Central time) on the
"Expiration Date," as hereinafter defined, elect to amend the Collaboration
Agreement as provided in Section 2(b) hereof.  If EBC shall elect to amend the
Collaboration Agreement as provided in Section 2(b) hereof, on the date of such
election (the "Election Date") EBC shall deliver to PLIT: (i) written notice
(the "Notice") of the exercise of its right to amend the Collaboration Agreement
as provided in Section 2(b) hereof; (ii) Nine Million Dollars ($9,000,000) less
the amount of Reimbursable Expenses previously paid by EBC to PLIT (the "Second
Cash Payment") by corporate check or wire transfer; and (iii) a warrant (the
"Warrant"), in the form attached hereto as Exhibit A, granting PLIT the right to
purchase upon the terms and subject to the conditions set forth in the Warrant
at an aggregate exercise price of One Million Dollars ($1,000,000) that number
of shares of EBC common stock, par value $0.01 per share, (the "Common Stock"),
equal to One Million dollars ($1,000,000) divided by the "Conversion Price,") as
hereinafter defined.

     The "Expiration date" shall mean (x) if the Financing raises at least
Twenty-Five Million Dollars ($25,000,000) in gross cash proceeds, December 31,
1996 or (y) if the Financing raises less than Twenty-Five Million Dollars
($25,000,000) in gross cash proceeds, the earlier to occur of (i) ten business
days following the closing of any subsequent equity financing by EBC in which
the gross cash proceeds raised in such equity financing together with the gross
cash proceeds raised in the Financing equal or exceed Twenty-Five Million
Dollars ($25,000,000) and (ii) the date that is 24 months following the payment
of the First Cash Payment.

     The "Conversion Price" shall mean the initial per share price at which the
EBC securities issued in the Financing may be converted into one share of Common
Stock.

     (b) Upon delivery of the Notice, the Second Cash Payment and the Warrant,
the Collaboration Agreement shall be automatically amended, without any further
action by the parties, as follows:

                                      -2-
<PAGE>

     (i) Section 1.24 of the Collaboration Agreement, as amended by the Second
Amendment, is hereby deleted in its entirety, and the following new Section 1.24
is substituted therefor:

          "1.24   EBC Ninety and One-Half Percent Royalty - shall be equal to
          ninety and one-half percent (90.5%) of the Throughput Base for PLIT
          for each barrel of liquid hydrocarbons throughput by Site Licensees of
          PLIT during a calendar month plus ninety and one-half percent (90.5%)
          of the site Fee base for PLIT for such calendar month."

     (ii) Section 5.1 of the Collaboration Agreement, as amended by the Second
Amendment, is hereby deleted in its entirety, and the following new Section 5.1
is substituted therefor:

          "5.1   Site License Fees.   During the Collaboration Period, EBC shall
          be entitled to retain ninety and one-half percent (90.5%) of all Site
          License Fees and shall pay the remaining nine and one-half percent
          (9.5%) of such Site License Fees to PLIT."

     (iii) Section 5.2 of the Collaboration Agreement, as amended by the Second
Amendment, is hereby deleted in its entirety, and the following new Section 5.2
is substituted therefor:

          "5.2   Site Throughput Fees.  During the Collaboration Period, EBC
          shall be entitled to keep ninety and one-half percent (90.5%) of the
          Adjusted Gross Profit of EBC and EBC shall pay nine and one-half
          percent (9.5%) of the Adjusted Gross Profit of EBC to PLIT.  The
          Catalyst Charge shall be paid by the Site Licensor to the Third Party
          Catalyst Supplier unless the Site Licensee has purchased the Catalyst
          directly from the Third Party Catalyst Supplier.  EBC shall not
          collect any Equipment Amortization Charge from the Site Licensee if
          the Site Licensee purchases the Equipment itself."

     (iv) Section 6.2 of the Collaboration Agreement is hereby deleted in its
entirety, and the following new Section 6.2 is substituted therefor:

          "6.2   Termination.  Either party may terminate the Collaboration for
          Cause, effective on one hundred twenty (120) days' notice, unless the
          party in breach makes all payments under or cures the breach within
          said one hundred twenty (120) days.  PLIT may terminate the
          Collaboration without Cause upon one (1) year's notice.  If not
          earlier terminated, the Collaboration shall terminate on March 5,
          2016."

     (v) Subsections 7.1(2)(e) and 7.1(3)(e) of the Collaboration Agreement, as
amended by the Second Amendment, are hereby deleted in their entirety and the
following new Subsections 7.1(2)(e) and 7.1(3)(e) are substituted therefor:

                                      -3-
<PAGE>

          "7.1(2)(e)   If the termination is with Cause, PLIT shall pay EBC the
          EBC Fifty Percent Royalty and the Five Percent Customer Products
          Royalty.  If the termination is without Cause, PLIT shall pay EBC the
          EBC Ninety and One-Half Percent Royalty and the Five Percent Customer
          Products Royalty."

          "7.1(3)(e)   PLIT shall pay EBC the EBC Ninety and One-Half Percent
          Royalty and the Five Percent Customer Products Royalty."

     (vi) Section 7.2(1) of the Collaboration Agreement is hereby deleted in its
entirety.

     (vii)   Section 7.2(2) of the Collaboration Agreement is hereby deleted in
its entirety.

     (viii)  Section 7.2(4) of the Collaboration Agreement is hereby deleted in
its entirety.

     (ix) The percentage "22%," "18%," "11%," and "3%" in subsections i), ii),
iii) and iv) of the Section a) of Schedule A of the Collaboration Agreement, as
amended by the Second Amendment, are hereby deleted and "9.5%," "7.8%," "4.7%"
and "1.3%" are hereby substituted, respectively, therefor.

     (x) The percentages "18%," "15%," "11%" and "3%" in subsections i), ii),
iii) and iv) of Section b) of Schedule A of the Collaboration Agreement, as
amended by the Second Amendment, are hereby deleted and "7.8%," "6.5%," "4.7%"
and "1.3%" are hereby substituted, respectively, therefor.

     (xi) The percentages "15%," "11%," "7%" and "3%" in subsections i), ii),
iii) and iv) of Section c) of Schedule A of the Collaboration Agreement, as
amended by the Second Amendment, are hereby deleted and "6.5%," "4.7%," "3.0%"
and "1.3%" are hereby substituted, respectively, therefor.

     (xii) The percentages "11%," "7%," "3%" and "3%" in subsections i), ii),
iii) and iv) of Section d) of Schedule A of the Collaboration Agreement, as
amended by the Second Amendment, are hereby deleted and "4.7%," "3.0%," "1.3%"
and "1.3%" are hereby substituted respectively, therefor.

     (xiii) All of PLIT's obligations to provide research and development,
technical support or consulting services in the Collaboration Agreement
including, but not limited to, those set out in Section 2.4 of the Collaboration
Agreement, are hereby deleted and the following shall remain the sole obligation
of PLIT to provide research and development, technical support or consulting
services pursuant to the Collaboration Agreement:

                                      -4-
<PAGE>

          "Until December 31, 1998, or some other date as to which the parties
          agree in writing, PLIT will assign not less than three (3) employees
          full-time to provide operational and engineering staff support for the
          Working Pilot Plant.  The costs of these employees and the reasonable
          costs of maintaining the Working Pilot Plant and providing analytical
          lab support for the Working Pilot Plant, will be the sole
          responsibility of PLIT until December 31, 1998, unless the parties
          agree in writing to some other date.  In addition to the foregoing
          support, during the Collaboration Period PLIT shall make the
          appropriate employees available upon reasonable request, to consult
          with EBC employees or consultants regarding the operation of the
          Working Pilot Plant and the commercialization of MDS."

     3.  Except as expressly amended herein, the Collaboration Agreement shall
remain in full force and effect.

     IN WITNESS WHEREOF, the parties have caused this Fourth Amendment to be
executed by their duly authorized representatives as of the Effective Date.

ENERGY BIOSYSTEMS CORPORATION                  PETROLITE CORPORATION



By:  /s/ John H. Webb                          By:    /s/ David Winslette
     ----------------                             ------------------------------
Title:  President and Chief Executive Officer  Title: Vice President, Technology
        -------------------------------------        ---------------------------

                                      -5-
<PAGE>

                                   EXHIBIT A


NEITHER THIS WARRANT NOR THE SECURITIES ISSUABLE UPON EXERCISE HEREOF HAVE BEEN
REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE "SECURITIES ACT"),
OR THE SECURITIES LAWS OF ANY STATE.  SUCH SECURITIES MAY NOT BE SOLD OR
OTHERWISE DISPOSED OF UNLESS PURSUANT TO A REGISTERED OFFERING OR BY TRANSFER
EXEMPT FROM REGISTRATION OR UNLESS SOLD PURSUANT TO RULE 144 UNDER THE
SECURITIES ACT.

THIS WARRANT SHALL BE VOID AFTER 5:00 P.M., CENTRAL TIME, ON ____________ /(1)/,
2001 OR, IF SUCH DAY IS NOT A BUSINESS DAY, AT 5:00 P.M., CENTRAL TIME, ON THE
NEXT FOLLOWING BUSINESS DAY.  THE TRANSFER OF THIS WARRANT IS RESTRICTED.  SEE
SECTION 6.02 - "RESTRICTIONS ON TRANSFER."  THE COMPANY HAS THE RIGHT TO
ACCELERATE THE EXPIRATION DATE OF THIS WARRANT UNDER CERTAIN CIRCUMSTANCES.  SEE
SECTION 4.04 - "COMPANY'S RIGHT TO ACCELERATE EXPIRATION DATE."



                        COMMON  STOCK  PURCHASE  WARRANT

                                       OF

                         ENERGY BIOSYSTEMS CORPORATION


NO. ___                                                     ____________, 1996


This certifies that Petrolite Corporation, a Delaware corporation, any successor
in interest thereto, or any assignee or transferee thereof in whose name this
Warrant is registered upon the books to be maintained by the Company for that
purpose (the "Warrantholder"), is entitled to purchase from Energy BioSystems
Corporation, a Delaware corporation (the "Company"), at any time on or prior to
5:00 p.m., Central time, on the Expiration Date (as hereinafter defined) and
subject to the terms and conditions hereof _________/2/, fully paid and
nonassessable shares of the Company's Common Stock at a price per share equal to
the Exercise Price.  The Exercise Price and the number of shares which may be
purchased pursuant to this Warrant are subject to adjustment under certain
conditions as provided in Article III hereof.

---------------

        /1/ Five years after EBC issues this Warrant.

        /2/ A number of shares equal to One Million Dollars ($1,000,000) divided
        by the Conversion Price (as such term is defined in the Fourth Amendment
        and Addendum to Collaboration Agreement).


                                      -1-
<PAGE>

Stock at a price per share equal to the Exercise Price. The Exercise Price and
the number of shares which may be purchased pursuant to this Warrant are subject
to adjustment under certain conditions as provided in Article III hereof.


                                   ARTICLE I

                                  DEFINITIONS

As used in this Warrant, the following capitalized terms shall have the
following respective meanings:

     (a) Business Day:  A day other than a Saturday, Sunday or other day on
     which banks in the States of New York or Texas are authorized by law to
     remain closed.

     (b) Common Stock:  Common Stock, par value $0.01 per share, of the Company.

     (c) Exercise Price:  The per share price for which the Warrantholder may
     purchase shares of Common Stock pursuant to this Warrant.  The initial
     Exercise Price is $____/3/. The Exercise Price may be adjusted from time to
     time pursuant to Article III hereof.

     (d) Expiration Date:  _____________/4/, 2001 or, if such day is not a
     Business Day, on the next following Business Day.

     (e) Net Consideration Per Share:  The Total Consideration attributable to
     purchase rights, options or warrants exercisable for Common Stock, divided
     by the aggregate number of shares of Common Stock that would be issued if
     all such purchase rights, options or warrants were exercised.

     (f) Person:  An individual, partnership, joint venture, corporation, trust,
     unincorporated organization or government or any department or agency
     thereof.

     (g) Registrable Securities:  (i) The Warrant Shares, and (ii) any Common
     Stock issued as a dividend or other distribution with respect to or in
     exchange for or in replacement of such Warrant Shares, provided, however,
     that Registrable Securities shall not include any shares of Common Stock
     which have previously been registered under the Securities Act or which may
     be sold pursuant to Rule 144 (or any successor to such Rule).

-------------------

        /3/ A number equal to $1,000,000 divided by the number of shares
        calculated pursuant to footnote (2).

        /4/ Five years after EBC issues this Warrant.


                                      -2-
<PAGE>

     (h) Securities Act:  The Securities Act of 1933, as amended.

     (i) Total Consideration: The  amount equal to the total amount of
     consideration received by the Company for the issuance of purchase rights,
     options or warrants exercisable for Common Stock, plus the minimum amount
     of consideration, if any, payable to the Company upon exercise thereof.

     (j) Warrant:  This Warrant and all other warrants that may be issued in its
     place.

     (k) Warrant Shares:  Shares of Common Stock purchasable upon exercise of
     the Warrant.


                                  ARTICLE II

                        DURATION AND EXERCISE OF WARRANT

Section 2.01  Duration of Warrant.  Subject to the terms contained herein, this
Warrant may be exercised at any time on or after the date of issuance of this
Warrant and before 5:00 p.m., Central time, on the Expiration Date.  If this
Warrant is not exercised at or before 5:00 p.m., Central time, on the Expiration
Date, it shall become void and all rights hereunder shall thereupon cease.

Section 2.02  Exercise of Warrant.

(a)  The Warrantholder may exercise this Warrant, in whole or in part, upon
surrender of this Warrant with the Subscription Form attached hereto duly
executed, to the Company at its corporate office, together with payment in full
of the Exercise Price for the Warrant Shares to be purchased in lawful money of
the United States or by certified check or bank draft payable in currency of the
United States to the order of the Company.

(b)  Upon receipt of this Warrant with the Subscription Form duly executed and
accompanied by payment of the Exercise Price for the Warrant Shares for which
this Warrant is then being exercised, the Company will cause to be issued
certificates for the total number of whole shares of Common Stock for which this
Warrant is being exercised in such denominations as are required for delivery to
the Warrantholder and the Company shall thereupon deliver such certificates to
the Warrantholder.

(c)  In case the Warrantholder shall exercise this Warrant with respect to less
than all of the Warrant Shares that may then be purchased under this Warrant,
the Company will execute a new warrant in the form of this Warrant for the
balance of such Warrant Shares and deliver such new warrant to the
Warrantholder.

(d)  The Company covenants and agrees that (i) it will pay, when due and
payable, any and all stock transfer and similar taxes that may be payable in
respect of the issuance of this Warrant or of

                                      -3-
<PAGE>

any Warrant Shares; and (ii) the Warrant Shares shall be deemed to be issued to
the Warrantholder as the record owner of such Warrant Shares as of the close of
business on the date on which this Warrant shall have been surrendered and
payment has been tendered for the purchase of such Warrant Shares.


                                  ARTICLE III

                      ADJUSTMENT OF SHARES OF COMMON STOCK
                       PURCHASABLE AND OF EXERCISE PRICE

The Exercise Price and the number and type of Warrant Shares shall be subject to
adjustment from time to time upon the occurrence of certain events as provided
in this Article III.

Section 3.01  Mechanical Adjustments.

(a)  If at any time prior to the full exercise of this Warrant, the Company
shall: (i) pay a dividend or make a distribution on its shares of Common Stock
in shares of Common Stock; (ii) subdivide, reclassify or recapitalize its
outstanding shares of Common Stock into a greater number of shares; or (iii)
combine, reclassify or recapitalize its outstanding shares of Common Stock into
a smaller number of shares, the number of Warrant Shares in effect at the time
of the record date of such dividend, subdivision, combination, reclassification
or recapitalization shall be proportionately adjusted so that the Warrantholder
shall be entitled to receive the aggregate number and type of shares that, if
this Warrant had been exercised in full immediately prior to such time, it would
have owned upon such exercise and been entitled to receive upon such dividend,
distribution, subdivision, combination, reclassification or recapitalization.
Such adjustment shall be made successively whenever any event listed in this
Section 3.01 (a) shall occur.

(b)  In case the Company shall issue after the date hereof purchase rights,
options or warrants exercisable for Common Stock to Persons other than
employees, directors, consultants or advisors of the Company entitling the
holders thereof to subscribe for or purchase shares of Common Stock at a Net
Consideration Per Share which is less than the Exercise Price at the time of
such issuance, the Exercise Price shall be adjusted so that the same shall equal
the price determined by multiplying the Exercise Price in effect immediately
prior thereto by a fraction, of which the numerator shall be the number of
shares of Common Stock outstanding on the date of such issuance, plus the number
of additional shares of Common Stock which the Total Consideration could
purchase at the Exercise Price, and of which the denominator shall be the number
of shares of Common Stock outstanding on such record date plus the number of
shares of Common Stock issuable upon the exercise of such purchase rights,
options or warrants. Such adjustment shall be made whenever such purchase
rights, options or warrants are issued and shall become effective immediately
(or if a record date has been established by the Company for the determination
of stockholders entitled to receive such purchase rights, options or warrants,
shall become effective retroactively immediately after the record date for the
determination of stockholders entitled to receive such purchase rights, options
or warrants). In

                                      -4-
<PAGE>

the event the Company shall subsequently cancel or terminate any of such
purchase rights, options or warrants, or any of such purchase rights, options or
warrants shall expire unexercised, the Exercise Price shall be readjusted to be
the same as if the Company had not issued such purchase rights, options or
warrants so cancelled, terminated or expired.

(c) Whenever the number of Warrant Shares issuable upon exercise of this Warrant
is adjusted pursuant to Section 3.01(a), the Exercise Price payable for such
Warrant Shares shall simultaneously be adjusted by multiplying the number of
Warrant Shares initially issuable upon exercise of each Warrant by the Exercise
Price in effect on the date thereof and dividing the product so obtained by the
number of Warrant Shares, as adjusted.

(d) No adjustment in the Exercise Price shall be required unless such adjustment
would require an increase or decrease of at least five cents ($.05) in such
price; provided, however, that any adjustments which by reason of this Section
3.01(d) are not required to be made shall be carried forward and taken into
account in any subsequent adjustment. All calculations under this Section 3.01
shall be made to the nearest cent or to the nearest one-hundredth of a share, as
the case may be.

(e) In the event that at any time, as a result of any adjustment made pursuant
to this Section 3.01(a), the Warrantholder thereafter shall become entitled to
receive any securities of the Company other than shares of Common Stock,
thereafter the number of such other securities so receivable upon exercise of
any warrant shall be subject to adjustment from time to time in a manner and on
terms as nearly equivalent as practicable to the provisions with respect to the
Common Stock contained in this Section 3.01.

Section 3.02  No Adjustment for Cash Dividends.  No adjustment in respect of any
cash dividends shall be made during the term of this Warrant or upon the
exercise of this Warrant.

Section 3.03  Adjustment for Merger, Consolidation, etc.  In case of any
consolidation of the Company with or merger of the Company into another
corporation or any sale or other disposition to another corporation of all or
substantially all the property of the Company, the corporation resulting from
such consolidation or surviving such merger or to which such sale or transfer
shall be made, as the case may be, shall make suitable provision and shall
assume the obligations of the Company hereunder (by written instrument executed
and mailed to the Warrantholder) pursuant to which, upon exercise of this
Warrant, at any time during the duration of this Warrant after such
consolidation, merger, sale or other disposition the Warrantholder shall be
entitled to receive the stock or other securities or property that the
Warrantholder would have been entitled to receive upon consummation if the
Warrantholder had executed this Warrant immediately prior thereto, all subject
to further adjustment as provided in this Article III.

Section 3.04  Notice of Adjustment.  Whenever the number of Warrant Shares or
the Exercise Price is adjusted as herein provided, the Company shall prepare and
deliver to the Warrantholder a certificate signed by its President, or any Vice
President, Treasurer or Secretary, setting forth the adjusted number of shares
purchasable upon the exercise of this Warrant and the Exercise Price of


                                      -5-
<PAGE>

such shares after such adjustment, setting forth a brief statement of the facts
requiring such adjustment and setting forth the computation by which such
adjustment was made.

Section 3.05  Form of Warrant After Adjustments. The form of this Warrant need
not be changed because of any adjustments in the Exercise Price or the number or
kind of the Warrant Shares, and Warrants theretofore and thereafter issued may
continue to express the same price and number and kind of shares as are stated
in this Warrant as initially issued.

Section 3.06 Action by the Company.  The Company will not, by amendment of its
certificate of incorporation or through any reorganization, transfer of assets,
consolidation, merger, dissolution, issue or sale of securities or any other
voluntary action, avoid or seek to avoid the observance or performance of any of
the terms of the Warrant but will at all times in good faith assist in the
carrying out of all such terms and in the taking of all such action as may be
necessary or appropriate in order to protect the rights of the Warrantholder
against dilution or other impairment; provided, that the provisions of this
Section 3.06 shall not preclude the Company from taking any action that the
Company determines is in the best interests of the Company and its stockholders,
independent of its effect on the Warrant and the Warrantholder.


                                  ARTICLE IV

              OTHER PROVISIONS RELATING TO RIGHTS OF WARRANTHOLDER

Section 4.01  Lost, Stolen, Mutilated or Destroyed Warrants.  If this Warrant is
lost, stolen, mutilated or destroyed, the Company shall, on such reasonable
terms as it may in its discretion impose (which shall, in the case of a
mutilated Warrant, include the surrender thereof), issue a new Warrant of like
denomination and tenor as, and in substitution for, this Warrant.

Section 4.02  Reservation of Shares.  The Company covenants and agrees that at
all times it shall reserve and keep available for the exercise of this Warrant
such number of authorized shares of Common Stock as are sufficient to permit the
exercise in full of this Warrant, and that it will take such action as may be
required from time to time to assure that the par value per share of the Warrant
Shares is at all times equal to or less than the per share Exercise Price.

Section 4.03  No Fractional Shares.  Anything contained herein to the contrary
notwithstanding, the Company shall not be required to issue any fraction of a
share in connection with the exercise of this Warrant, and in any case where the
Warrantholder would, except for the provisions of this Section 4.03, be entitled
under the terms of this Warrant to receive a fraction of a share upon the
exercise of this Warrant, the Company shall, upon the exercise of this Warrant
and receipt of the Exercise Price, issue the larger number of whole shares
purchasable upon exercise of this Warrant.


                                      -6-
<PAGE>

Section 4.04  Company's Right to Accelerate Expiration Date.  If at any time
after _________/5/, 1998, the Common Stock trades at a price per share that is
greater than two times the Exercise Price for a period of 20 trading days, the
Company shall thereafter have the right, exercisable at any time in its sole
discretion, to accelerate the Expiration Date of this Warrant by providing
written notice of such acceleration to Warrantholder.  The Warrantholder shall
have the right to exercise this Warrant, in whole or in part, at any time during
the period of 60 days after the date such notice is given.  The Company's
provision of written notice of acceleration hereunder shall have the effect of
causing the last day of such 60 day period to be the Expiration Date of this
Warrant for all purposes thereof.

Section 4.05  Notice of Record Date. In case of:

(a) any setting of a record date by the Company for the purpose of determining
the holders of any class of securities who are entitled to receive any dividend
or other distribution, or any right to subscribe for, purchase or otherwise
acquire any shares of stock of any class or any other securities or property, or
to receive any other right, that, in any such case, will result in an adjustment
in the number of Warrant Shares or the Exercise Price pursuant to Article III,
or

(b) any capital reorganization of the Company, any reclassification or
recapitalization of the Common Stock of the Company or any transfer of all or
substantially all the assets of the Company to or consolidation or merger of the
Company with or into any other person, or

(c)  any voluntary or involuntary dissolution, liquidation or winding up of the
Company, or

(d) any proposed issue or grant by the Company of any purchase right, option or
warrant to subscribe for, purchase or otherwise acquire any shares of Common
Stock that will result in an adjustment to the Exercise Price pursuant to
Article III,

then and in each such event the Company will mail or cause to be mailed to the
Warrantholder a notice specifying (i) the date on which any such record is to be
taken for the purpose of such dividend, distribution or right, and stating the
amount and character of such dividend, distribution or right, (ii) the date on
which any such reorganization, reclassification, recapitalization, transfer,
consolidation, merger, dissolution, liquidation or winding up is to take place,
and the time, if any is to be fixed, as of which the holders of record of Common
Stock shall be entitled to exchange their shares of Common Stock for securities
or other property deliverable on such reorganization, reclassification,
recapitalization, transfer, consolidation, merger, dissolution, liquidation or
winding up, and (iii) the amount and character of any purchase rights, options
or warrants with respect to Common Stock that will result in an adjustment to
the Exercise Price pursuant to Article III, proposed to be issued or granted,
the date of such proposed issue or grant and the persons or class of persons to
whom such proposed issue or grant is to be offered or made.  Such notice shall
be
--------------
/5/ Two years after EBC issues this Warrant.

                                      -7-
<PAGE>

mailed at least 30 days prior to the date specified in such notice on which
any such action is to be taken.

Section 4.06 Incidental Registration Rights

(a)  Notice of Registration. If the Company shall determine to register any of
its Common Stock either for its own account or the account of a stockholder,
other than a registration relating solely to employee benefit plans, a
registration on Form S-4 or S-8 or any successor or similar forms, or a
registration on any registration form that does not permit secondary sales, the
Company will:

     (i) promptly give to Petrolite Corporation ("Petrolite") written notice
     thereof; and

     (ii) use reasonable efforts to include in such registration (and any
     related qualification under blue sky laws or other compliance), except as
     set forth in Sections 4.06(b) and (c), and in any underwriting involved
     therein, all the Registrable Securities specified in a written request or
     requests, made by Petrolite within 20 days after the written notice from
     the Company described in clause (i) above is given.  Such written request
     may specify all or a part of Petrolite's Registrable Securities.

(b)  Right to Terminate Registration. The Company shall have the right to
terminate or withdraw any registration prior to the effectiveness of such
registration whether or not Petrolite has elected to include Registrable
Securities in such registration.

(c)  Underwriting. (i) If the registration of which the Company gives notice is
     for a registered public offering involving an underwriting, the Company
     shall so advise Petrolite as a part of the written notice given pursuant to
     subsection Section 4.06(a). In such event, the right of Petrolite to
     registration pursuant to this Section 4.06 shall be conditioned upon
     Petrolite's participation in such underwriting and the inclusion of
     Petrolite's Registrable Securities in the underwriting to the extent
     provided herein. Petrolite (together with the Company and such other
     stockholders of the Company exercising registration rights with respect to
     such registration) shall enter into an underwriting agreement in customary
     form with the representative of the underwriter or underwriters selected by
     the Company or the stockholders initiating such registration, as the case
     may be.

     (ii) Notwithstanding any other provision of this Section 4.06, if the
     representative of the underwriters advises the Company in writing that
     marketing factors require a limitation on the number of shares to be
     underwritten, the representative may (subject to the limitations set forth
     below) exclude all Registrable Securities from, or limit the number of
     Registrable Securities to be included in, the registration and
     underwriting.  The Company shall so advise all holders of securities
     requesting registration, and the amount of securities that are entitled to
     be included in the registration and underwriting shall be allocated as
     follows: (a) first, to the Company up to the full number of securities
     proposed to be sold for its own account) (b) second, to the stockholders on
     behalf of whom registration may have been initially requested


                                      -8-
<PAGE>

     up to the full number of securities proposed to be sold for the account of
     such stockholders, and (c) third, to Petrolite and other stockholders
     entitled to participate in the registration, drawn from them pro rata based
     on the number of securities each has requested to be included in such
     registration. If Petrolite does not agree to the terms of any such
     underwriting, Petrolite shall be excluded therefrom by written notice from
     the Company or the underwriter. Any Registrable Securities or other
     securities excluded or withdrawn from such underwriting shall be withdrawn
     from such registration.

(d)  Delay of Registration. Petrolite shall not have any right to take any
action to restrain, enjoin, or otherwise delay any registration as the result of
any controversy that might arise with respect to the interpretation or
implementation of this Section 4.06.

(e)  Termination of Registration Rights. The right of Petrolite to request
registration or inclusion in any registration pursuant to this Section 4.06
shall terminate on the earlier of (i) the second anniversary of the earlier of
(A) the Expiration Date and (B) the date on which the Warrant has been exercised
in full and (ii) such date as all shares of Registrable Securities held or
entitled to be held upon conversion by such Holder may immediately be sold under
Rule 144 (or any successor to such Rule).

(f)  Number of Incidental Registrations. Petrolite may exercise its right to
incidental registration under this Section 4.06 two times; provided, however,
that if Petrolite has exercised its incidental registration rights during the
term of this Agreement but was prevented from registering all Registrable
Securities due to Section 4.06(c)(ii), Petrolite may exercise its right to
incidental registration one additional time for each such occurrence.


                                   ARTICLE V

                           TREATMENT OF WARRANTHOLDER

Prior to due presentment for registration of transfer of this Warrant, the
Company may deem and treat the Warrantholder as the absolute owner of this
Warrant (notwithstanding any notation of ownership or other writing hereon) for
the purpose of any exercise hereof and for all other purposes and the Company
shall not be affected by any notice to the contrary.  This Warrant does not
entitle the Warrantholder to any rights of a stockholder of the Company.


                                      -9-
<PAGE>

                                   ARTICLE VI

            SPLIT-UP, COMBINATION EXCHANGE AND TRANSFER OF WARRANTS

Section 6.01  Split-Up, Combination, Exchange and Transfer of Warrants.  Subject
to and limited by the provisions of Section 6.02 hereof, this Warrant may be
split up, combined or exchanged for another Warrant or Warrants containing the
same terms and entitling the Warrantholder to purchase a like aggregate number
of Warrant Shares.  If the Warrantholder desires to split up, combine or
exchange this Warrant, it shall make such request in writing delivered to the
Company and shall surrender to the Company this Warrant and any other Warrants
to be so split up, combined or exchanged.  Upon any such surrender for a split-
up, combination or exchange, the Company shall execute and deliver to the Person
entitled thereto a Warrant or Warrants, as the case may be, as so requested.
The Company shall not be required to effect any split-up, combination or
exchange which will result in the issuance of a Warrant entitling the
Warrantholder to purchase upon exercise a fraction of a share of Common Stock or
a fractional Warrant. The Company may require such Warrantholder to pay a sum
sufficient to cover any tax or governmental charge that may be imposed in
connection with any split-up, combination or exchange of Warrants.

Section 6.02   Restrictions on Transfer.

(a)  This Warrant and the Warrant Shares shall be restricted from sale,
transfer, assignment, exercise or hypothecation, except in compliance with the
Securities Act and the provisions of this Section 6.02.

(b)  The Company may require the Person to whom the Warrantholder or holder of
such Warrant Shares proposes to transfer such Warrant or Warrant Shares to make
such investment intent representations, and may place such legends on
certificates representing this Warrant or the Warrant Shares, as may reasonably
be required in the opinion of counsel to the Company to permit the Warrant or
Warrant Shares, as the case may be, to be transferred without registration under
the Securities Act.


                                  ARTICLE VII

                         REPRESENTATIONS AND WARRANTIES

Section 7.01  Representations and Warranties of the Company.  The Company
represents and warrants to and agrees with the Warrantholder that:

     (a) The Company has all requisite power and authority, corporate or
     otherwise, and has taken all necessary action, to execute, deliver and
     perform its obligations under this Warrant.  This Warrant has been duly and
     validly authorized, executed and delivered by the Company and constitutes a
     valid and binding agreement of the Company enforceable against the


                                     -10-
<PAGE>

     Company in accordance with its terms. No authorization, approval, consent,
     order, license, franchise, certificate or permit of or from any Person or
     regulatory authority is required to be obtained by the Company in
     connection with the execution, delivery or performance of this Warrant.

     (b) None of the execution, delivery or performance of the Company's
     obligations under this Warrant will conflict with, or result in a breach of
     any of the terms or provisions of, or constitute a default under or violate
     any term of (i) the certificate of incorporation, as amended, or the by-
     laws of the Company; (ii) any indenture, mortgage, joint venture agreement,
     lease, sublease, sales agreement or other agreement or instrument to which
     the Company is a party or by  which it or any of its properties is bound;
     or (iii) any law, rule, regulation, judgment, order or decree of any
     government, governmental or regulatory body or court, foreign or domestic,
     having jurisdiction over the Company or any of its properties or assets.

     (c) The Warrant Shares have been duly reserved for issuance upon exercise
     of this Warrant and, when issued upon such exercise in accordance with the
     terms of this Warrant, will be duly and validly issued, fully paid and
     nonassessable, and the issuance of the Warrant Shares is not subject to any
     preemptive or similar rights granted by the Company, any other Person or
     any statute.

Section 7.02  Representations and Warranties of the Warrantholder.  The
Warrantholder represents and warrants to the Company that it is acquiring this
Warrant for its own account, for investment purposes and not with a view to, or
for resale in connection with, any distribution or public offering thereof.  The
Warrantholder understands that this Warrant has not been registered under the
Securities Act or any applicable state securities laws; that it was issued in
reliance upon an exemption therefrom; that it may not be transferred unless
registered under the Securities Act and such state securities laws or pursuant
to an exemption therefrom; and that it will bear a restrictive legend to such
effect.


                                 ARTICLE VIII

                                 MISCELLANEOUS

Section 8.01  Expenses of Transfer.  The Company will from time to time promptly
pay all taxes and charges that may be imposed upon the Company with respect to
the issuance or delivery of Warrant Shares upon the exercise of this Warrant by
the Warrantholder.

Section 8.02  Successors and Assigns.  All the covenants and provisions of this
Warrant shall bind and inure to the benefit of successors and assigns of the
Company and the Warrantholder; provided that the rights granted to Petrolite
pursuant to Section 4.06 are personal to Petrolite and may not be assigned by
Petrolite to any other Person.


                                     -11-
<PAGE>

Section 8.03  No Inconsistent Agreements.  The Company will not on or after the
date of this Warrant enter into any agreement with respect to its capital stock
which is inconsistent with the rights granted to the Warrantholder in this
Warrant or otherwise conflicts with the provisions hereof.

Section 8.04  Governing Law.  THIS WARRANT SHALL BE GOVERNED BY AND CONSTRUED IN
ACCORDANCE WITH THE LAWS OF THE STATE OF DELAWARE, EXCEPT FOR THE CONFLICTS OF
LAWS PRINCIPLES THEREOF.

Section 8.05  Severability.  In the event that any one or more of the provisions
contained herein, or the application thereof in any circumstances, is held
invalid, illegal or unenforceable, the validity, legality and enforceability of
any such provisions in every other respect and of the remaining provisions
contained herein shall not be affected or impaired thereby.

Section 8.06  Integration/Entire Agreement.  This Warrant is intended by the
parties as a final expression of their agreement and intended to be a complete
and exclusive statement of the agreement and understanding of the parties hereto
with respect to the subject matter contained herein. This Warrant supersedes all
prior agreements and understandings between the parties with respect to such
subject matter.

Section 8.07  Attorney's Fees.  In any action or proceeding brought to enforce
any provisions of this Warrant, or where any provisions hereof or thereof is
validly asserted as a defense, the successful party shall be entitled to recover
attorneys' fees and disbursements in addition to its costs and expenses and any
other available remedy.

Section 8.08  Notices.  Notice or demand pursuant to this Warrant to be given or
made by the Warrantholder to or on the Company shall be sufficiently given or
made if sent by first class mail, postage prepaid, addressed (until another
address is designated in writing by the Company) as follows:

     Energy BioSystems Corporation
     4200 Research Forest Drive
     The Woodlands, Texas 77381
     Attention:  President

Any notice or demand authorized by this Warrant to be given or made by the
Company to or on the Warrantholder shall be sufficiently given or made if sent
by first class mail, postage prepaid, to the Warrantholder at its last known
address as it shall appear on the books of the Company.

Section 8.09  Headings.  The article and section headings in this Warrant are
for convenience only and are not part of this Warrant and shall not affect the
interpretation thereof.

IN WITNESS WHEREOF, this Warrant has been duly executed by the Company as of the
____ day of __________, 1996.

                                     -12-
<PAGE>

                                     ENERGY BIOSYSTEMS CORPORATION



                                     By:
                                         --------------------------
                                         John H. Webb
                                         President and Chief Executive Officer


                                     -13-
<PAGE>

                                  ASSIGNMENT

                (TO BE EXECUTED ONLY UPON ASSIGNMENT OF WARRANT)

For value received, _________________________ hereby sells, assigns and
transfers unto _________________________ the within Warrant, together with all
right, title and interest therein, and does hereby irrevocably constitute and
appoint _________________________ attorney, to transfer said Warrant on the
books of the within-named Company with respect to the number of Warrant Shares
set forth below, with full power of substitution in the premises:

              NAME(S) OF
              ASSIGNEE(S)            ADDRESS              NO. OF WARRANTS
--------------------------------------------------------------------------------







If said number of Warrant Shares shall not be all the Warrant Shares represented
by the Warrant, a new Warrant is to be issued in the name of said undersigned
for the balance remaining of the Warrant Shares represented by said Warrant.



                              Signature: __________________________________

                              Note:  The above signature should correspond
                              exactly with the name on the first page of said
                              Warrant.

Dated:____________


                                     -14-
<PAGE>

                               SUBSCRIPTION FORM
                   (TO BE EXECUTED UPON EXERCISE OF WARRANT)


Energy BioSystems Corporation:

The undersigned hereby irrevocably elects to exercise the right of purchase
represented by the within Warrant for, and to purchase thereunder, _______
shares of Common Stock, as provided for therein, and tenders herewith payment of
the purchase price in full in the form of cash or a certified or official bank
check in the amount of $__________________.

Please issue a certificate or certificates for such shares of Common Stock in
the name of:

                              Name:_______________________
                              Address:


                              Social Security Number:
                              (Please Print)


If said number of shares shall not be all the shares purchasable under the
within Warrant, a new Warrant is to be issued in the name of said undersigned
for the balance remaining of the shares purchasable thereunder.



                              Signature:__________________

                              NOTE:  The above signature should correspond
                                     exactly with the name on the first page of
                                     said Warrant or with the name of the
                                     assignee appearing in the assignment form
                                     above.

Dated: _________________


                                     -15-
<PAGE>


[LOGO OF ENERGY BIOSYSTEMS APPEARS HERE]

               PAUL G. BROWN, III
               Vice President, Finance

December 27, 1996

Mr. Charles Miller
Petrolite Corporation
369 Marshall Ave
St. Louis, MO 63119

Dear Mr. Miller:

        At this time it appears that the Financing referred to in the Fourth
Amendment and Addendum to Collaboration Agreement (the "Fourth Amendment")
between Energy Biosystems Corporation and Petrolite Corporation will close
sometime early in 1997. We would like, however, to proceed with the payment of
the First Cash Payment under the Fourth Amendment of One Million Dollars
($1,000,000). By acceptance of the First Cash Payment of One Million Dollars
($1,000,000) you also agree that the definitions of Expiration Date and
Conversion Price as set forth in the Fourth Amendment shall be amended and
restated in their entirety as set forth on Exhibit A hereto.

        If you are in agreement with the foregoing, please execute a copy of
this letter in the space provided below. Upon receipt of a copy of this letter
signed by Petrolite Corporation we will wire transfer to your account the First
Cash Payment of One Million Dollars ($1,000,000).

                                                Sincerely,

                                                ENERGY BIOSYSTEMS CORPORATION

                                                By: /s/ PAUL G. BROWN III
                                                   ---------------------------

                                                Name:  Paul  G. Brown
                                                     -------------------------

                                                Title: Vice President Finance
                                                      ------------------------

Agreed to this 30th day of December, 1996:

PETROLITE CORPORATION

By: /s/ DAVID WINSLETT
   -------------------------

Name:  David Winslett
     -----------------------

Title: Vice President
      ----------------------

ENERGY BIOSYSTEMS CORPORATION
4200 Research Forest Drive,  The Woodlands, Texas 77381
TEL 281.364.6100 FAX 281.364.6110


<PAGE>



                                   EXHIBIT A

        The "Expiration Date" shall mean the earlier to occur of (x) ten
business days following the closing of any equity financing by EBC after the
date hereof in which the gross cash proceeds raised in such equity financing
together with the gross cash proceeds raised in any other equity financings by
EBC after the date hereof equal or exceed Twenty-Five Million Dollars
($25,000,000) and (y) the date that is 24 months following the payment of the
First Cash Payment.

        The "Conversion Price" shall mean (x) if the Financing is completed by
January 31, 1997, and the securities issued in the Financing are convertible
into shares of  Common Stock, the initial conversion price per share of Common
Stock at which the EBC securities issued in the Financing may be converted into
Common Stock or (y) if the Financing is not completed by January 31, 1997, or if
the securities issued in the Financing are not convertible into shares of Common
Stock, 120% of the closing sale price of the shares of EBC Common Stock as
reported on the Nasdaq Stock Market on the date of the First Cash Payment.