<PAGE>

                                                                    Exhibit 10.7

                      NOTE AND WARRANT PURCHASE AGREEMENT

     This Note and Warrant Purchase Agreement is made as of October 9, 1998 by
and between Genomica Corporation, a Delaware corporation (the "Company"), and
the persons or entities named on the signature page attached hereto
(individually, a "Purchaser" and collectively, the "Purchasers").

     The Parties hereby agree as follows:

1.   Amount and Terms of the Loan; Purchase and Sale of the Warrants

     1.1  The Loan. Subject to the terms of this Agreement, the Company shall
borrow from the Purchaser and the Purchaser, severally and not jointly, shall
lend to the Company up to the amount set forth opposite the Purchaser's name on
the attached Schedule of Purchasers (each, a "Loan Amount") pursuant to
convertible promissory notes in the form attached hereto as Exhibit A (the
"Notes"). The Loan Amounts are hereinafter referred to collectively as the
"Loan." The Company will borrow fifty percent (50%) of the Loan initially and
thereafter may, but shall not be required to, borrow an additional amount up to
the remaining fifty percent (50%) of the Loan.

     1.2  Purchase and Sale of Warrants. The Company will issue and sell to the
Purchaser and the Purchaser will purchase, severally and not jointly, warrants
in the form attached hereto as Exhibit B (the "Warrants") to purchase up to that
number of shares of the Company's Applicable Series Preferred Stock (as defined
below) as set forth opposite the Purchaser's name on the Schedule of Purchasers
(each, a "Warrant Amount") on the following terms: (i) the per share exercise
price will be the price per share (the "Applicable Series Preferred Stock
Price") at which the next round of Preferred Stock issued and sold by the
Company in which the gross proceeds to the Borrower are at least $3,000,000, not
including any conversion of the Notes (a "Qualified Financing"). The "Applicable
Series Preferred Stock" shall be the series of Preferred Stock next issued and
sold by the Company in a Qualified Financing. The Company will issue and sell
Warrants to purchase fifty percent (50%) of the Warrant Amount initially and
thereafter, will issue and sell an additional number of Warrants if and only if
the Company has a Second Closing (as defined below) with respect to the Loan. In
the case of a Second Closing, the number of additional Warrants to be issued in
the Second Closing will be in proportion to the additional amount of the Loan
that is borrowed by the Company in the Second Closing.

2.   The Closing

     2.1  Closing Dates. The first closing as to the purchase and sale of the
Notes and the Warrants (the "First Closing") shall be held no later than October
9, 1998, at the offices of Cooley Godward llp, 2595 Canyon Blvd., Suite 250,
Boulder, Colorado 80302, or at such other time as the Company and the Purchasers
of a majority of the Notes shall agree (the

<PAGE>

"First Closing Date"). Any second closing (the "Second Closing") as to the
purchase and sale of the Notes and Warrants may be held at the place and time
determined by the Company, provided that the Company shall provide the
Purchasers with seven (7) days advance written notice of the Second Closing. The
First Closing and the Second Closing are referred to collectively hereinafter as
the "Closings."

     2.2  Delivery. At the First Closing (i) the Purchaser will deliver to the
Company a check or wire transfer of funds in the amount of fifty percent (50%)
of such Purchaser's Loan Amount; and (ii) the Company shall deliver to the
Purchaser a Note representing fifty percent (50%) of such Purchaser's Loan
Amount, an executed Warrant and an amendment to the Registration Rights
Agreement dated as of March 22, 1996, as amended, by and among the Company and
certain investors, to the effect that the shares of Common Stock underlying the
shares of Preferred Stock issuable upon conversion of the Notes and exercise of
the Warrants will have the registration rights provided for in that agreement.
At the Second Closing, if any, (i) each Purchaser will deliver to the Company a
check or wire transfer of funds in the amount of the portion of the remaining
amount of such Purchaser's Loan Amount that the Company is borrowing; and (ii)
the Company shall deliver to the Purchaser a Note representing the remaining
amount of such Purchaser's Loan Amount that the Company is borrowing and an
executed Warrant.

3.   Representations and Warranties of the Company

     The Company hereby represents and warrants to each Purchaser as follows:

     3.1  Operations. As of the date hereof there is no action, suit, claim,
proceeding or investigation pending or threatened against or affecting the
Company and the Company is not subject to any order, writ, injunction or decree
entered in any lawsuit or proceeding.

     3.2  Organization, Qualifications Corporate Power

          (a) The Company is a corporation duly incorporated, validly existing
and in good standing under the laws of the State of Delaware and is duly
licensed or qualified to transact business as a foreign corporation and is in
good standing in each other jurisdiction in which the nature of the business
transacted by it or the character of the properties owned or leased by it
requires such licensing or qualification, except where failure to so qualify
would not have a material adverse effect on the business, affairs or prospects
of the Company. The Company has the corporate power and authority to own and
hold its properties and to carry on its business as now conducted and as
proposed to be conducted, to execute, deliver and perform this Agreement.

     3.3  Authorization of Agreements, Etc.

          (a) The execution and delivery by the Company of this Agreement, the
Notes and the Warrants (the "Transaction Documents") the performance by the
Company of its obligations hereunder and thereunder, have been duly authorized
by all requisite corporate action and will not violate any provision of law, any
order of any court or other agency of

                                      2.
<PAGE>

government, the Certificate of Incorporation of the Company, as amended (the
"Charter") or the Bylaws of the Company (the "Bylaws"), as amended, or any
provision of any indenture, agreement or other instrument to which the Company
or its properties or assets are bound, or conflict with, result in a breach of
or constitute (with due notice or lapse of time or both) a default under any
such indenture, agreement or other instrument, or result in the creation or
imposition of any lien, charge, restriction, claim or encumbrance of any nature
whatsoever upon any of the properties or assets of the Company. To the best of
the Company's knowledge, the execution, delivery and performance of the
Transaction Agreements does not violate, conflict with, result in a breach of or
constitute (with due notice or lapse of time or both) a default by any other
party under any other indenture, agreement or instrument.

     3.4  Third Party Approvals. No registration or filing with, or consent or
approval of or other action by any third party, is or will be necessary for the
valid execution, delivery and performance by the Company of the Transaction
Agreements, the issuance, any eventual sale and delivery of the preferred stock
or upon conversion thereof, the issuance and delivery of any shares issuable
upon conversion of the preferred stock, other than filings pursuant to state
securities laws (all of which filings have been made by the Company, other than
those which are required to be made after the Closing and which will be duly
made on a timely basis).

     3.5  Proprietary Information of Third Parties. To the best knowledge of the
Company, no third party has claimed or has reason to claim that any person
employed by or affiliated with (or currently proposed to be employed by or
affiliated with) the Company has (a) violated or may be violating any of the
terms and conditions of his employment, non-competition or non-disclosure
agreement with such third party, (b) disclosed or may be disclosing or utilized
or may be utilizing any trade secret or proprietary information or documentation
of such third party or (c) interfered or may be interfering in the employment
relationship between such third party and any of its present or former
employees. No third party has requested information from the Company which
suggests that such a claim might be contemplated. To the best knowledge of the
Company, no person employed by or affiliated with (or currently proposed to be
employed by or affiliated with) the Company has employed or proposes to employ
any trade secret or any information or documentation proprietary to any former
employer, and to the best knowledge of the Company, no person employed by or
affiliated with (or currently proposed to be employed by or affiliated with) the
Company has violated any confidential relationship with such person may have had
with any third party, in connection with the development, manufacture or sale of
any product or proposed product or the development or sale of any service or
proposed service of the Company, and the Company has no reason to believe there
will be any such employment or violation. To the best knowledge of the Company,
none of the execution or delivery of the Transaction Agreements, or the carrying
on of the business of the Company as officers, employees or agents by any
officer, director or key employee of the Company (or currently proposed to be
such an officer, director or key employee), or the conduct or proposed conduct
of the business of the Company, will conflict with or result in a breach of the
terms, conditions or provisions of or constitute a default under any contract,
covenant or instrument under which any such person is obligated.

                                      3.
<PAGE>

     3.6  Patents, Trademarks, Etc. The Company owns or possesses adequate
licenses or other rights to use all patents, patent applications, trademarks,
trademark applications, service marks, service mark applications, trade names,
copyrights, manufacturing processes, formulae, trade secrets, customer lists and
know how (collective, "Intellectual Property") necessary or desirable to the
conduct of its business as conducted and as proposed to be conducted, and no
claim is pending or, to the best of the Company's knowledge, threatened to the
effect that the operations of the Company as conducted and as proposed to be
conducted infringe upon or conflict with the asserted rights of any other person
under any Intellectual Property, and to the best of the Company's knowledge,
there is no basis for any such claim (whether or not pending or threatened). No
claim is pending or, to the best of the Company's knowledge, threatened to the
effect that any such Intellectual Property owned or licensed by the Company, or
which the Company otherwise has the right to use, is invalid or unenforceable by
the Company, and there is no basis for any such claim (whether or not pending or
threatened). To the best of the Company's knowledge, all technical information
developed by and belonging to the Company which has not been patented has been
kept confidential.

     3.7  Authorized Capital Stock. The authorized capital stock of the Company
consists of (i) 18,000,000 shares of Preferred Stock, $.001 par value (the
"Preferred Stock"), of which 12,688,178 shares have been designated Series A
Convertible Preferred Stock, and (ii) 22,000,000 shares of Common Stock.
Immediately prior to the Closing, 12,533,676 shares of Series A Convertible
Preferred Stock and 2,747,308 shares of Common Stock will be validly issued and
outstanding, fully paid and nonassessable with no personal liability attaching
to the ownership thereof, and 12,533,676 shares of Common Stock reserved for
issuance upon conversion of the Series A Preferred Stock.

     3.8  Litigation. There are no (nor to the Company's knowledge is there any
reasonable basis for any) (a) actions, suits, proceedings or investigations at
law or in equity or by or before any governmental instrumentality or other
agency now pending or to the Company's knowledge, threatened against or
affecting the Company, or (b) judgments, decrees, injunctions or orders of any
court, governmental department, commission, agency, instrumentality or
arbitrator against or affecting the Company.

     3.9  Title to Properties. The Company has good and marketable title to all
of its owned properties and assets, free and clear of all mortgages, pledges,
security interests, liens, charges and other encumbrances, except for Permitted
Encumbrances (as defined below). As of the Closing and after giving effect to
the transactions contemplated hereby, the Company will have good and marketable
title to all its properties and assets free and clear of mortgages, pledges,
security interests, liens, charges and other encumbrances, except under for
Permitted Encumbrances. As used herein, "Permitted Encumbrances" means any
mortgages, pledges, security interests, liens, charges and other encumbrances
(i) as described in Schedule II hereto, (ii) liens for current taxes,
assessments and other governmental charges not overdue, (iii) mechanic's,
materialmen's and similar liens which may have arisen in the ordinary course of
business and which, in the aggregate, would not be material to the financial
condition of the Company, (iv) security interests securing indebtedness not in
default for the purchase price of

                                      4.
<PAGE>

or lease rental payments on property purchased or leased under capital lease
arrangements in the ordinary course of business, and (v) minor imperfections of
title, if any, not material in amount and not materially detracting from the
value or impairing the use of the property subject thereto or impairing the
operations or proposed operations of the Company. The Company is in compliance
with all of its leases and, to its knowledge, holds a valid leasehold interest
in all of its properties free and clear of all liens, charges and other
encumbrances.

     3.10 Taxes. The Company has timely filed all tax returns (federal, state
and local) required to be filed by it. All taxes shown to be due and payable on
such returns, any assessments imposed, and to the Company's knowledge all other
taxes due and payable by the Company on or before the Closing have been paid or
will be paid prior to the time they become delinquent. The Company has not been
advised (i) that any of its returns, federal, state or other, have been or are
being audited as of the date hereof, or (ii) of any deficiency in assessment or
proposed judgment to its federal, state or other taxes. The Company has no
knowledge of any liability of any tax to be imposed upon its properties or
assets as of the date of this Agreement that is not adequately provided for.

     3.11 Compliance with Other Instruments. The Company is not in violation or
default of any provision of the Charter or By-laws or of any instrument,
judgment, order, writ, decree, or contract to which it is a party or by which it
is bound or, to its knowledge, of any provision of federal or state statute,
rule or regulation, license, or permit applicable to the Company which would
have a material adverse effect on the Company. The Company does not have any
knowledge of any termination or material breach or anticipated termination or
material breach by the other parties to any material contract or commitment to
which it is a party or to which any of its assets is subject. To the Company's
knowledge, there are no warranty claims or other uninsured claims against the
Company under completed contracts which might involve a material monetary
liability which is not reserved against in the Financial Statements.

4.   Representations and Warranties of the Purchaser

     4.1  Purchase for Own Account. The Purchaser represents that it is
acquiring the Notes, the equity securities issuable upon conversion of the
Notes, the Warrants and the equity securities issuable upon exercise of the
Warrants (collectively, the "Securities") solely for its own account and
beneficial interest for investment and not for sale or with a view to
distribution of the Securities or any part thereof, has no present intention of
selling (in connection with a distribution or otherwise), granting any
participation in, or otherwise distributing the same, and does not presently
have reason to anticipate a change in such intention.

     4.2  Information and Sophistication. The Purchaser acknowledges that it has
received all the information it has requested from the Company and considers
necessary or appropriate for deciding whether to acquire the Notes and Warrants.
The Purchaser represents that it has had an opportunity to ask questions and
receive answers from the Company regarding the terms and conditions of the
offering of the Notes and Warrants and to obtain any

                                      5.
<PAGE>

additional information necessary to verify the accuracy of the information given
the Purchaser. The Purchaser further represents that it has such knowledge and
experience in financial and business matters that it is capable of evaluating
the merits and risk of this investment.

     4.3  Ability to Bear Economic Risk. The Purchaser acknowledges that
investment in the Notes and Warrants involves a high degree of risk, and
represents that it is able, without materially impairing its financial
condition, to hold the Securities for an indefinite period of time and to suffer
a complete loss of its investment.

     4.4  Further Limitations on Disposition. Without in any way limiting the
representations set forth above, the Purchaser further agrees not to make any
disposition of all or any portion of the Securities unless and until:

          (a) There is then in effect a registration statement under the 1933
Act covering such proposed disposition and such disposition is made in
accordance with such registration statement; or

          (b) (i) The Purchaser shall have notified the Company of the proposed
disposition and shall have furnished the Company with a detailed statement of
the circumstances surrounding the proposed disposition, and (ii) if reasonably
requested by the Company, such Purchaser shall have furnished the Company with
an opinion of counsel, reasonably satisfactory to the Company, that such
disposition will not require registration under the 1933 Act.

          (c) Notwithstanding the provisions of paragraphs (a) and (b) above, no
such registration statement or opinion of counsel shall be necessary for a
transfer by such Purchaser to a stockholder or partner (or retired partner) of
such Purchaser, or a registered investment company with a common investment
advisor, or transfers by gift, will or intestate succession to any spouse or
lineal descendants or ancestors (or to a custodian or trustee for the benefit of
the Purchaser or his or her spouse, lineal descendants or ancestors), if all
transferees agree in writing to be subject to the terms hereof to the same
extent as if they were Purchasers hereunder.

     4.5  Accredited Investor. The Purchaser is an "accredited investor" as such
term is defined in Rule 501 under the 1933 Act.

5.   Miscellaneous

     5.1  Binding Agreement. The terms and conditions of this Agreement shall
inure to the benefit of and be binding upon the respective successors and
assigns of the parties. Nothing in this Agreement, express or implied, is
intended to confer upon any third party any rights, remedies, obligations, or
liabilities under or by reason of this Agreement, except as expressly provided
in this Agreement.

                                      6.
<PAGE>

     5.2  Governing Law. This Agreement shall be governed by and construed under
the laws of the State of Colorado as applied to agreements among Colorado
residents, made and to be performed entirely within the State of Colorado.

     5.3  Counterparts. This Agreement may be executed in two or more
counterparts, each of which shall be deemed an original, but all of which
together shall constitute one and the same instrument.

     5.4  Titles and Subtitles. The titles and subtitles used in this Agreement
are used for convenience only and are not to be considered in construing or
interpreting this Agreement.

     5.5  Notices. Any notice required or permitted under this Agreement shall
be given in writing and shall be deemed effectively given upon personal
delivery, one business day after deposit with a reputable overnight courier, or
four business days after deposit with the United States Post Office, by
registered or certified mail, postage prepaid, addressed to the Company at 4001
Discovery Drive, Suite 130, Boulder, Colorado 80303, or to the Purchaser at its
address shown on the signature page, or at such other address as such party may
designate by ten (10) days advance written notice to the other party.

     5.6  Modification; Waiver. No modification or waiver of any provision of
this Agreement, the Notes or the Warrants or consent to departure therefrom
shall be effective unless in writing and approved by the Company and a majority
in interest of the Notes (determined by reference to the principal amount of the
Notes outstanding).

     5.7  Survival of Warranties. The warranties, representations, and covenants
of the Company and the Purchasers contained in or made pursuant to this
Agreement shall survive the execution and delivery of this Agreement and the
Closing and shall in no way be affected by any investigation of the subject
matter thereof made by or on behalf of the Purchasers or the Company.

     5.8  Finder's Fee. Each party represents that it neither is nor will be
obligated for any finder's fee or commission in connection with this
transaction. The Company agrees to indemnify and hold harmless the Purchasers
from any liability for any commission or compensation in the nature of a
finder's fee (and the costs and expenses of defending against such liability or
asserted liability) for which the Company or any of its officers, employees or
representatives is responsible.

     5.9  Invalidity. If any of the provisions of this Agreement are held
invalid or unenforceable, such invalidity or unenforceability shall not affect
in any way the validity or enforceability of any other provision of this
Agreement except those which the invalidated or unenforceable provision
comprises an integral part of or is otherwise clearly inseparable from. In the
event any provision is held invalid or unenforceable, the parties shall attempt
to agree on a valid or enforceable provision which shall be a reasonable
substitute for such invalid or unenforceable provision in light of the tenor of
this Agreement and, on so agreeing, shall incorporate such substitute provision
in this Agreement.

                                      7.
<PAGE>

     5.10  Expenses. The Company shall reimburse the reasonable fees and
expenses of counsel to the Purchasers, incurred in connection with this
Agreement and the transactions contemplated herein in an amount not to exceed
$25,000.

     In Witness Whereof, the parties have executed this Agreement as of the date
first written above.

                                  Company

                                  Genomica Corporation

                                  By:/s/ Thomas G. Marr
                                     __________________________
                                       Thomas G. Marr
                                       President

                                  Purchaser:

                                      /s/ William Galvin
                                  _______________________________________
                                      Assistant Secretary
                                  _______________________________________

                                  _______________________________________

                                  Address: Invesco Global Health Sciences
                                          _______________________________
                                  c/o Invesco Funds Group, Inc.
                                  _______________________________________
                                  7800 East Union Ave
                                  _______________________________________
                                  Denver, CO 80237
                                  _______________________________________
                                  Attn: Buck Phillips
                                  _______________________________________

                                  Purchaser:

                                  Falcon Technology Partners, L.P.
                                  _______________________________________
                                  /s/ James L. Rathmann
                                  _______________________________________
                                  General Partner
                                  _______________________________________

                                  Address: 600 Dorset Rd.
                                          _______________________________
                                  Devon, PA 19333
                                  _______________________________________

                                  _______________________________________

                                  _______________________________________

                                  Purchaser:

                                      /s/ Robert Nelson
                                  _______________________________________

                                  _______________________________________

                                  _______________________________________

                                  Purchaser:

                                      /s/ Kyle Lefkoff
                                  _______________________________________
                                       Kyle Lefkoff, Partner
                                  _______________________________________
                                       Boulder, Co 80302
                                  _______________________________________

                                  Address:
                                          _______________________________

                                  _______________________________________

                                  _______________________________________

                                  _______________________________________

                                  _______________________________________

                                  Purchaser:

                                  The Caruthers Family LLC
                                  _______________________________________
                                  by: Marvin H. Caruthers, Manager
                                  _______________________________________
                                      /s/ Marvin H. Caruthers
                                  _______________________________________

                                  Address: 2450 Cragmoor Rd.
                                          _______________________________
                                  Boulder, CO 80303
                                  _______________________________________

                                  _______________________________________

                                  _______________________________________

                                  _______________________________________

                                      8.
<PAGE>

                            Schedule of Purchasers
                            ----------------------

First Closing
-------------

<TABLE>
<CAPTION>
                                        Convertible                                   Total
            Purchaser                      Notes              Warrants             Investment
-----------------------------------     -----------     ---------------------    -------------
<S>                                     <C>             <C>                      <C>
Invesco Global Health Sciences Fund     $   362,500       Note Amount x 15%      $  362,500.00
                                                        ---------------------
                                                          Applicable Series
                                                        Preferred Stock Price
Falcon Technology Partners, L.P.        $   362,500                              $  362,500.00
Arch Venture Fund III, L.P.             $   237,500                              $  237,500.00
Boulder Ventures, L.P.                  $    25,000                              $   25,000.00
The Caruthers Family, L.L.C.            $    12,500                              $   12,500.00
                                        -----------     ---------------------    -------------
             TOTALS                     $ 1,000,000                              $1,000,000.00

Second Closing
--------------

                                        Convertible                                   Total
            Purchaser                      Notes              Warrants             Investment
-----------------------------------     -----------     ---------------------    -------------
Invesco Global Health Sciences Fund     $   362,500       Note Amount x 15%      $  362,500.00
                                                        ---------------------
                                                          Applicable Series
                                                        Preferred Stock Price

Falcon Technology Partners, L.P.        $   362,500                              $  362,500.00
Arch Venture Fund III, L.P.             $   237,500                              $  237,500.00
Boulder Ventures, L.P.                  $    25,000                              $   25,000.00
The Caruthers Family, L.L.C.            $    12,500                              $   12,500.00
                                        -----------     ---------------------    -------------
             TOTALS:                    $ 1,000,000                              $1,000,000.00
</TABLE>

                                      9.