<PAGE>
                                                                   Exhibit 10.13


THE SECURITIES REPRESENTED HEREBY HAVE NOT BEEN REGISTERED UNDER THE SECURITIES
ACT OF 1933, AS AMENDED (THE "ACT"), OR UNDER THE SECURITIES LAWS OF ANY STATE.
THESE SECURITIES ARE SUBJECT TO RESTRICTIONS ON TRANSFERABILITY AND RESALE AND
MAY NOT BE TRANSFERRED OR RESOLD EXCEPT AS PERMITTED UNDER THE ACT AND THE
APPLICABLE STATE SECURITIES LAWS, PURSUANT TO REGISTRATION OR EXEMPTION
THEREFROM.  THE ISSUER OF THESE SECURITIES MAY REQUIRE AN OPINION OF COUNSEL
(WHICH MAY BE COMPANY COUNSEL) IN FORM AND SUBSTANCE SATISFACTORY TO THE ISSUER
TO THE EFFECT THAT ANY PROPOSED TRANSFER OR RESALE IS IN COMPLIANCE WITH THE ACT
AND ANY APPLICABLE STATE SECURITIES LAWS.

                           Warrant to Purchase Stock

Corporation:  Genomica Corporation
Number of Shares:  See Below
Class of Stock:  Series A Preferred
Initial Exercise Price:  See Below
Issue Date:  September 10, 1997
Expiration Date:  September 9, 2004

     THIS WARRANT CERTIFIES THAT, for the agreed upon value of $1.00 and for
other good and valuable consideration, SILICON VALLEY BANK ("Holder") is
entitled to purchase the number of fully paid and nonassessable shares of the
class of securities (the "Shares") of the corporation (the "Company") at the
initial exercise price per Share (the "Warrant Price") all as set forth herein
and as adjusted pursuant to Article 2 of this Warrant, subject to the provisions
and upon the terms and conditions set forth of this Warrant.  The Warrant Price
shall be equal to the price at which the Company sold its Series A Preferred
Stock pursuant to the Stock Purchase Agreement between the Company and the
Purchasers named therein; provided that the Warrant Price shall be equal to the
price per share at which the Company after the date hereof first sells its
shares of capital stock in an offering (the "Equity Event") in which the Company
receives not less than Two Million Dollars ($2,000,000) if the Company receives
the proceeds from such sale by November 30, 1997.  The number of Shares that
Holder may purchase under this Warrant is equal to Twelve Thousand Dollars
($12,000) divided by the Warrant Price; provided that, beginning September 15,
1997, and continuing on the fifteenth calendar day of each month thereafter
until Borrower receives the proceeds from the Equity Event, Holder may purchase
an additional number of Shares equal to Six Thousand Dollars ($6,000) divided by
the Warrant Price for each such month; provided the maximum number of Shares
that Holder may purchase pursuant to the terms of this sentence shall be equal
to Forty Thousand Dollars ($40,000) divided by the Warrant Price.

ARTICLE 1.  EXERCISE

            1.1  Method of Exercise.  Holder may exercise this Warrant by
delivering a duly executed Notice of Exercise in substantially the form attached
as Appendix 1 to the principal office of the Company. Unless Holder is
exercising the conversion right set forth in Section 1.2, Holder shall also
deliver to the Company a check for the aggregate Warrant Price for the Shares
being purchased.

            1.2  Conversion Right.  In lieu of exercising this Warrant as
specified in Section 1.1, Holder may from time to time convert this Warrant, in
whole or in part, into a number of Shares

                                       1.
<PAGE>

determined by dividing (a) the aggregate fair market value of the Shares or
other securities otherwise issuable upon exercise of this Warrant minus the
aggregate Warrant Price of such Shares by (b) the fair market value of one
Share. The fair market value of the Shares shall be determined pursuant Section
1.4.

            1.3  [Intentionally omitted.]

            1.4  Fair Market Value.  If the Shares are traded in a public
market, the fair market value of the Shares shall be the closing price of the
Shares (or the closing price of the Company's stock into which the Shares are
convertible) reported for the business day immediately before Holder delivers
its Notice of Exercise to the Company. If the Shares are not traded in a public
market, the Board of Directors of the Company shall determine fair market value
in its reasonable good faith judgment. The foregoing notwithstanding, if Holder
advises the Board of Directors in writing that Holder disagrees with such
determination, then the Company and Holder shall promptly agree upon a reputable
investment banking firm to undertake such valuation. If the valuation of such
investment banking firm is more than 5% greater than that determined by the
Board of Directors, then all fees and expenses of such investment banking firm
shall be paid by the Company. In all other circumstances, such fees and expenses
shall be paid by Holder.

            1.5  Delivery of Certificate and New Warrant.  Promptly after Holder
exercises or converts this Warrant, the Company shall deliver to Holder
certificates for the Shares acquired and, if this Warrant has not been fully
exercised or converted and has not expired, a new Warrant representing the
Shares not so acquired.

            1.6  Replacement of Warrants.  On receipt of evidence reasonably
satisfactory to the Company of the loss, theft, destruction or mutilation of
this Warrant and, in the case of loss, theft or destruction, on delivery of an
indemnity agreement reasonably satisfactory in form and amount to the Company
or, in the case of mutilation, or surrender and cancellation of this Warrant,
the Company at its expense shall execute and deliver, in lieu of this warrant, a
new warrant of like tenor.

            1.7  Repurchase on Sale, Merger, or Consolidation of the Company.

                 1.7.1  "Acquisition".  For the purpose of this Warrant,
"Acquisition" means any sale, license, or other disposition of all or
substantially all of the assets of the Company, or any reorganization,
consolidation, or merger of the Company where the holders of the Company's
securities before the transaction beneficially own less than 50% of the
outstanding voting securities of the surviving entity after the transaction.

                 1.7.2  Assumption of Warrant.  Upon the closing of any
Acquisition the successor entity shall assume the obligations of this Warrant,
and this Warrant shall be exercisable for the same securities, cash, and
property as would be payable for the Shares issuable upon exercise of the
unexercised portion of this warrant as if such Shares were outstanding on the
record date for the Acquisition and subsequent closing. The Warrant Price shall
be adjusted accordingly.

                 1.7.3  Purchase Rights.  Notwithstanding the foregoing, at the
election of Holder, the Company shall purchase the unexercised portion of this
Warrant for cash upon the closing of any Acquisition for an amount equal to (a)
the fair market value of any consideration that would have been received by
Holder in consideration of the Shares had Holder exercised the unexercised
portion of this Warrant immediately before the record date for determining the
shareholders entitled to participate in the proceeds of the Acquisition, less
(b) the aggregate Warrant Price of the Shares, but in no event less than zero.

                                       2
<PAGE>

ARTICLE 2.  ADJUSTMENTS TO THE SHARES.

            2.1  Stock Dividends, Splits, Etc.  If the Company declares or pays
a dividend on its common stock (or the Share if the Shares are securities other
than common stock) payable in common stock, or other securities, subdivides the
outstanding common stock into a greater amount of common stock, or, if the
Shares are securities other than common stock, subdivides the Shares in a
transaction that increases the amount of common stock into which the Shares are
convertible, then upon exercise of this Warrant, for each Share acquired, Holder
shall receive, without cost to Holder, the total number and kind of securities
to which Holder would have been entitled had Holder owned the Shares of record
as of the date the dividend or subdivision occurred.

            2.2  Reclassification, Exchange or Substitution.  Upon any
reclassification, exchange, substitution, or other event that results in a
change of the number and/or class of the securities issuable upon exercise or
conversion of this Warrant, Holder shall be entitled to receive, upon exercise
or conversion of this Warrant, the number and kind of securities and property
that Holder would have received for the Shares if this Warrant had been
exercised immediately before such reclassification, exchange, substitution, or
other event. Such an event shall include any automatic conversion of the
outstanding or issuable securities of the Company of the same class or series as
the Shares to common stock pursuant to the terms of the Company's Certificate of
Incorporation upon the closing of a registered public offering of the Company's
common stock. The Company or its successor shall promptly issue to Holder a new
Warrant for such new securities or other property. The new Warrant shall provide
for adjustments which shall be as nearly equivalent as may be practicable to the
adjustments provided for in this Article 2 including, without limitation,
adjustments to the Warrant Price and to the number of securities or property
issuable upon exercise of the new Warrant. The provisions of this Section 2.2
shall similarly apply to successive reclassifications, exchanges, substitutions,
or other events.

            2.3  Adjustments for Combination, Etc.  If the outstanding Shares
are combined or consolidated, by reclassification or otherwise, into a lesser
number of shares, the Warrant Price shall be proportionately increased.

            2.4  Adjustments for Diluting Issuances.  The Warrant Price and the
number of Shares issuable upon exercise of this Warrant or, if the Shares are
Preferred Stock, the number of shares of common stock issuable upon conversion
of the Shares, shall be subject to adjustment, from time to time in accordance
with the Company's Certificate of Incorporation, as amended. In the event of the
issuance (a "Diluting Issuance") by the Company, after the Issue Date of the
Warrant, of securities at a price per share less than the Warrant Price, then
the number of shares of common stock issuable upon conversion of the Shares
shall be adjusted in accordance with those provisions (the "Provisions") of the
Company's Certificate of Incorporation which apply to Diluting Issuances. The
Company agrees that the Provisions, as in effect on the Issue Date, shall be
deemed to remain in full force and effect during the term of the Warrant at all
times prior to the sale by the Company of its equity securities in an initial
public offering, notwithstanding any subsequent amendment, waiver or termination
thereof by the Company's shareholders. Under no circumstances shall the
aggregate Warrant Price payable by the Holder upon exercise of the Warrant
increase as a result of any adjustment arising from a Diluting Issuance.

            2.5  No Impairment.  The Company shall not, by amendment of its
Certificate of Incorporation or through a 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 to be observed or performed under this Warrant by the Company, but
shall at all times in good faith assist in carrying out of all the provisions of
this Article 2 and in taking all such action as may be necessary or appropriate
to protect Holder's rights under this Article against impairment. If the

                                       3
<PAGE>

Company takes any action affecting the Shares or its common stock other than as
described above that adversely affects Holder's rights under this Warrant, the
Warrant Price shall be adjusted downward and the number of Shares issuable upon
exercise of this Warrant shall be adjusted upward in such a manner that the
aggregate Warrant Price of this Warrant is unchanged.

            2.6  Fractional Shares.  No fractional Shares shall be issuable upon
exercise or conversion of the Warrant and the number of Shares to be issued
shall be rounded down to the nearest whole Share. If a fractional share interest
arises upon any exercise or conversion of the Warrant, the Company shall
eliminate such fractional share interest by paying Holder amount computed by
multiplying the fractional interest by the fair market value of a full Share.

            2.7  Certificate as to Adjustments.  Upon each adjustment of the
Warrant Price, the Company at its expense shall promptly compute such
adjustment, and furnish Holder with a certificate of its Chief Financial Officer
setting forth such adjustment and the facts upon which such adjustment is based.
The Company shall, upon written request, furnish Holder a certificate setting
forth the Warrant Price in effect upon the date thereof and the series of
adjustments leading to such Warrant Price.

            2.8  No Rights As Shareholders.  This Warrant does not entitle
Holder to any voting rights or other rights as a stockholder of the Company
prior to the exercise of the Holder's rights to purchase Preferred Stock as
provided for herein.

            2.9  Minimum Adjustment.  No adjustment in the Warrant Price under
this Section 2 shall be required unless such adjustment would require an
increase or decrease of at least [twenty-five cents] in such Warrant Price;
provided, however, that any adjustments which by reason of this subsection are
not required to be made, shall be carried forward and taken into account in any
subsequent adjustment. All calculations under this Section 2 shall be made to
the nearest cent or the nearest share, as the case may be.

ARTICLE 3.  REPRESENTATIONS AND COVENANTS OF THE COMPANY.

            3.1  Representations and Warranties.  The Company hereby represents
and warrants to the Holder that all Shares which may be issued upon the exercise
of the purchase right represented by this Warrant, and all securities, if any,
issuable upon conversion of the Shares, shall, upon issuance, be duly
authorized, validly issued, fully paid and nonassessable, and free of any liens
and encumbrances except for restrictions on transfer provided for herein or
under applicable federal and state securities laws.

            3.2  Notice of Certain Events.  If the Company proposes at any time
(a) to declare any dividend or distribution upon its common stock, whether in
cash, property, stock, or other securities and whether or not a regular cash
dividend; (b) to offer for subscription pro rata to the holders of any class or
series of its stock any additional shares of stock of any class of series or
other rights; (c) to effect any reclassification or recapitalization of common
stock; (d) to merge or consolidate with or into any other corporation, or sell,
lease, license, or convey all or substantially all of its assets, or to
liquidate, dissolve or wind up; or (e) offer holders of registration rights the
opportunity to participate in an underwritten public offering of the company's
securities for cash, then, in connection with each such event, the Company shall
give Holder (1) at least 20 days prior written notice of the date on which a
record will be taken for such dividend, distribution, or subscription rights
(and specifying the date on which the holders of common stock will be entitled
thereto) or for determining rights to vote, if any, in respect of the matters
referred to in (c) and (d) above; (2) in the case of the matters referred to in
(c) and (d) above at least 20 days prior written notice of the date when the
same will take place (and specifying the date on which the holders of common
stock will be entitled to exchange their common stock for securities or other
property

                                       4
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deliverable upon the occurrence of such event); and (3) in the case of the
matter referred to in (e) above, the same notice as is given to the holders of
such registration rights.]

            3.3  Information Rights.  So long as the Holder holds this Warrant
and/or any of the Shares, the Company shall deliver to the Holder promptly after
mailing copies of all notices or other written communications to the
shareholders of the Company, generally.

            3.4  Registration Under Securities Act of 1933, as amended.  The
Company agrees that the Shares or, if the Shares are convertible into common
stock of the Company, such common stock, shall be subject to the registration
rights set forth on Exhibit A, if attached.

ARTICLE 4.  REPRESENTATIONS AND COVENANTS OF HOLDER.

     This Warrant has been entered into the Company in reliance upon the
following representations and covenants of Holder, which by its acceptance
hereof the Holder (including any permitted transferee of Holder on behalf of
such transferee) hereby confirms:

            4.1  Investment Purpose.  The right to acquire Preferred Stock or
the Preferred Stock issuable upon exercise of Holder's rights contained herein
will be acquired for investment and not with a view to the sale or distribution
of any part thereof, and the Holder has no present intention of selling or
engaging in any public distribution of the same except pursuant to a
registration or exemption.

            4.2  Private Issue.  Holder understands (i) that the Preferred
Stock, issuable upon exercise of the Holder's rights contained herein is not
registered under the 1933 Act or qualified under applicable state securities
laws on the ground that the issuance contemplated by this Warrant Agreement will
be exempt from the registration and qualifications requirements thereof, and
(ii) that the Company's reliance on such exemption is predicated on the
representations set forth in this Section 4.

            4.3  Financial Risk.  Holder has such knowledge and experience in
financial and business matters as to be capable of evaluating the merits and
risks of its investment and has the ability to bear the economic risks of its
investments.

            4.4  Risk of No Registration.  Holder understands that if the
Company does not register with the Securities and Exchange commission pursuant
to Section 12 of the 1933 Act, or file reports pursuant to Section 15(d) of the
Securities Exchange Act of 1934 (the "1934 Act"), or if a registration statement
covering the securities under the 1933 Act is not in effect when it desires to
sell (i) the rights to purchase Preferred Stock pursuant to this Warrant
Agreement, or (ii) the Preferred Stock issuable upon exercise of the right to
purchase, it may be required to hold such securities for an indefinite period.
The Holder also understands that any sale of the rights of the Holder to
purchase Preferred Stock which might be made by it in reliance upon Rule 144
under the 1933 Act may be made only in accordance with the terms and conditions
of that Rule.

            4.5  Accredited Investor.  Holder is an "accredited investor" within
the meaning of Rule 501 of Regulation D under the Act, as presently in effect.

ARTICLE 5.  MISCELLANEOUS.

            5.1  Term:  Notice of Expiration.  This Warrant is exercisable, in
whole or in part, at any time and from time to time on or before the Expiration
Date set forth above. To the extent this Warrant is not previously exercised,
and if the fair market value of one Share is greater than the Warrant

                                       5
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Price then in effect, this Warrant shall be deemed automatically exercised
pursuant to Section 1.2 above immediately before its expiration. For purposes of
such automatic exercise, the fair market value of one Share upon expiration
shall be determined pursuant to Section 1.3 above.

            5.2  Legends.  This Warrant and the Shares (and the securities
issuable, directly or indirectly, upon conversion of the Shares, if any) shall
be imprinted with a legend in substantially the following form:

     THE SECURITIES REPRESENTED HEREBY HAVE NOT BEEN REGISTERED UNDER THE
     SECURITIES ACT OF 1933, AS AMENDED (THE "ACT"), OR UNDER THE SECURITIES
     LAWS OF ANY STATE.  THESE SECURITIES ARE SUBJECT TO RESTRICTIONS ON
     TRANSFERABILITY AND RESALE AND MAY NOT BE TRANSFERRED OR RESOLD EXCEPT AS
     PERMITTED UNDER THE ACT AND THE APPLICABLE STATE SECURITIES LAWS, PURSUANT
     TO REGISTRATION OR EXEMPTION THEREFROM.  THE ISSUER OF THESE SECURITIES MAY
     REQUIRE AN OPINION OF COUNSEL (WHICH MAY BE COMPANY COUNSEL) IN FORM AND
     SUBSTANCE SATISFACTORY TO THE ISSUER TO THE EFFECT THAT ANY PROPOSED
     TRANSFER OR RESALE IS IN COMPLIANCE WITH THE ACT AND ANY APPLICABLE STATE
     SECURITIES LAWS.

            5.3  Compliance with Securities Laws on Transfer.  This Warrant and
the Shares issuable upon exercise this Warrant (and the securities issuable,
directly or indirectly, upon conversion of the Shares, if any) may not be
transferred or assigned in whole or in part without compliance with applicable
federal and state securities laws by the transferor and the transferee
(including, without limitation, the delivery of investment representation
letters and legal opinions reasonably satisfactory to the Company, as reasonably
requested by the Company). The Company shall not require Holder to provide an
opinion of counsel if the transfer is to an affiliate of Holder or if there is
no material questions as to the availability of current information as
referenced in Rule 144(c), Holder represents that it has complied with Rule
144(d) and (e) in reasonable detail, the selling broker represents that it has
complied with Rule 144(f), and the Company is provided with a copy of Holder's
notice of proposed sale.

            5.4  Transfer Procedure.  Subject to the provisions of Section 5.3,
Holder may transfer all or part of this Warrant or the Shares issuable upon
exercise of this Warrant (or the securities issuable, directly or indirectly,
upon conversion of the Shares, if any) by giving the Company notice of the
portion of the Warrant being transferred setting forth the name, address and
taxpayer identification number of the transferee and surrendering this Warrant
to the Company for reissuance to the transferee(s) (and Holder if applicable).
Unless the Company is filing financial information with the SEC pursuant to the
Securities Exchange Act of 1934, the Company shall have the right to refuse to
transfer any portion of this Warrant to any person who directly competes with
the Company.

            5.5  Notices.  All notices and other communications from the Company
to the Holder, or vice versa, shall be deemed delivered and effective when given
personally or mailed by first-class registered or certified mail, postage
prepaid, at such address as may have been furnished to the Company or the
Holder, as the case may be, in writing by the Company or such holder from time
to time.

            5.6  Waiver.  This Warrant and any term hereof may be changed,
waived, discharged or terminated only by an instrument in writing signed by the
party against which enforcement of such change, waiver, discharge or termination
is sought.

                                       6
<PAGE>

            5.7  Attorneys Fees.  In the event of any dispute between the
parties concerning the terms and provisions of this Warrant, the party
prevailing in such dispute shall be entitled to collect from the other party all
costs incurred in such dispute, including reasonable attorneys' fees.

            5.8  Governing Law.  This Warrant shall be governed by and
constructed in accordance with the laws of the State of California, without
giving effect to its principles regarding conflicts of law.

                                       GENOMICA CORPORATION,
                                       a Delaware corporation


                                       By: /s/ Thomas G. Marr
                                           -------------------------------------

                                       Name:   Thomas G. Marr
                                             -----------------------------------
                                                            (Print)

                                       Title:  Chairman of the Board, President,
                                               or Vice President



                                       By: /s/ Kenneth J. Collins
                                           -------------------------------------

                                       Name:   Kenneth J. Collins, CFO
                                             -----------------------------------
                                                            (Print)

                                       Title:  Chief Financial Officer,
                                               Secretary Assistant Treasurer, or
                                               Assistant Secretary

                                       7
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                                   EXHIBIT A
                                   ---------

                           Investor Rights Agreement
                           -------------------------

     The Company agrees that no amendments will be made to the Agreement which
would treat the Holder in a manner differently than the other holders of like
securities of the Company without the consent of Holder.

     The Company agrees, and by acceptance of the Warrant to which this Exhibit
A is attached Holder agrees, that at such time this Warrant is exercised, Holder
shall become a party to the Registration Rights Agreement dated as of March 22,
1996 by and among the Company and certain of the Company's stockholders (as
amended, modified, supplemented or restated, the "Registration Rights
Agreement"), shall be treated as a "Purchaser" of "Preferred Shares" thereunder,
shall have the rights, privileges and responsibilities of a party thereto, and
agrees to execute counterpart signature pages thereto at the request of the
Company.

                                       8.
<PAGE>

                                  APPENDIX 1

                              NOTICE OF EXERCISE
                              ------------------

     1.  The undersigned hereby elects to purchase ________ shares of the Series
__ Preferred Stock of Genomica Corporation pursuant to the terms of the attached
Warrant, and tenders herewith payment of the purchase price of such shares in
full.

     1.  The undersigned hereby elects to convert the attached Warrant into
Shares/cash [strike one] in the manner specified in the Warrant. This conversion
is exercised with respect to __________________ of the Shares covered by the
Warrants.

     [Strike paragraph that does not apply.]

     2.  Please issue a certificate or certificates representing said shares in
the name of the undersigned or in such other name as is specified below:

                           _________________________
                                    (Name)

                           _________________________

                           _________________________
                                   (Address)

     3.  The undersigned represents it is acquiring the shares solely for its
own account and not as a nominee for any other party and not with a view toward
the resale or distribution thereof except in compliance with applicable
securities laws.



                                       _________________________________________
                                       (Signature)


_________________________
         (Date)

                                       9.