<PAGE>

                                                                    Exhibit 10.5

     SERIES A CONVERTIBLE PREFERRED STOCK PURCHASE AGREEMENT dated as of March
22, 1996 between Genomica Corporation, a Delaware corporation (the "Company"),
and the several purchasers named in the attached Schedule I (individually a
                                                 ----------
"Purchaser" and collectively the "Purchasers").

     WHEREAS, the Company wishes to issue and sell an aggregate of up to
3,320,400 shares (the "Preferred Shares") of the authorized but unissued Series
A Convertible Preferred Stock, $.001 par value, of the Company (the "Series A
Convertible Preferred Stock"); and

     WHEREAS, the Purchasers, severally, wish to purchase some or all of the
Preferred Shares on the terms and subject to the conditions set forth in this
Agreement;

     NOW, THEREFORE, in consideration of the premises and the mutual covenants
contained in this Agreement, the parties agree as follows:

                                   ARTICLE I

                              THE PREFERRED SHARES

     SECTION 1.1  Issuance, Sale and Delivery of the Preferred Shares.  The
                  ---------------------------------------------------
Company agrees to issue and sell to each Purchaser, and each Purchaser hereby
agrees to purchase from the Company, the number of Preferred Shares set forth
opposite the name of such Purchaser under the heading "Number of Preferred
Shares to be Purchased" on Schedule I, at the aggregate purchase price set forth
                           ----------
opposite the name of such Purchaser under the heading "Aggregate Purchase Price
for Preferred Shares" on Schedule I.
                         ----------

     SECTION 1.2  Closing.  The closing of the purchase and sale of Preferred
                  -------
Shares hereunder shall take place at the offices of Dechert Price & Rhoads,
Philadelphia, at 10:00 a.m., New York time, on March 22, 1996, or at such other
location, date and time as may be agreed upon between the Purchasers and the
Company (such closing being called the "Closing" and such date and time being
called the "Closing Date").  At the Closing, the Company shall issue and deliver
to each Purchaser a stock certificate or certificates in definitive form,
registered in the name of such Purchaser, representing the Preferred Shares
being purchased by it at the Closing.  As payment in full for the Preferred
Shares being purchased by it under this Agreement, and against delivery of the
stock certificate or certificates therefor as aforesaid, on the Closing Date
each Purchaser shall transfer to the account of the Company by wire transfer the
amount set forth opposite the name of such Purchaser under the heading
"Aggregate Purchase Price for Preferred Shares" on Schedule I.
                                                   ----------

<PAGE>

                                   ARTICLE II

                 REPRESENTATIONS AND WARRANTIES OF THE COMPANY

The Company represents and warrants to the Purchasers that, except as set forth
in the Disclosure Schedule attached as Schedule II:
                                       -----------

     SECTION 2.1  Operations.  The Company has not commenced any material
                  ----------
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.  Schedule II contains a complete list of the Company's
                        -----------
material agreements, obligations and liabilities. The Company does not have an
Employee Benefit Plan as defined in the Employee Retirement Income Security Act
of 1974, as amended.

     SECTION 2.2  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 the Commonwealth of Pennsylvania and in the State of New York
and 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, the Registration Rights Agreement
with the Purchasers in the form attached as Exhibit A (the "Registration Rights
                                            ---------
Agreement"), the Founders Agreements with the Purchasers and Dr. Thomas G. Marr,
Donald Fisher, Steven Cozza and Jackie Salit (the "Founders"), in the form
attached as Exhibit B-1 (the "Founders Agreements"), the Stockholders Agreements
            -----------
with the Purchasers and JRathmann, MRathmann, LRathmann, SRathmann and
RRathmann, Cold Spring Harbor Laboratory and John Maroney (the "Stockholders")
in the form attached as Exhibit B-2 (the "Stockholders Agreements"), a Voting
                        -----------
Agreement among the Company, and the Purchasers and the other parties thereto in
the form attached as Exhibit C (the "Voting Agreement"), the license Agreement
                     ---------
by and between the Company and Cold Spring Harbor Laboratory in the form
attached as Exhibit D (the "License Agreement"), the Common Stock Acquisition
            ---------
Agreements with Harris & Harris Group, Inc., JRathmann, MRathmann, LRathmann,
SRathmann and RRathmann, Cold Spring Harbor Laboratory, John Maroney, Jacqueline
Salit, Steven Cozza, Donald Fisher and Thomas Marr in the form attached as
Exhibit E (the "Common Stock Acquisition Agreements"), and the Consulting
---------
Agreement by and between the Company and Thomas Marr in the form attached as
Exhibit F (the "Marr Consulting Agreement)
---------

                                      -2-
<PAGE>

to issue, sell and deliver the Preferred Shares and to issue and deliver the
shares of Common Stock issuable upon conversion of the Preferred Shares (the
"Conversion Shares").

          (b) The Company has no subsidiaries. The Company does not (i) own of
record or beneficially, directly or indirectly, (A) any shares of capital stock
or securities convertible into capital stock of any other corporation or (B) any
participating interest in any partnership, joint venture or other non-corporate
business enterprise or (ii) control, directly or indirectly, any other entity.

     SECTION 2.3  Authorization of Agreements, Etc.
                  --------------------------------

          (a) The execution and delivery by the Company of this Agreement, the
Registration Rights Agreement, the Voting Agreement, the License Agreement, the
Founders Agreements, the Stockholders Agreements, the Common Stock Acquisition
Agreements and the Marr Consulting Agreement (collectively, the "Transaction
Agreements"), the performance by the Company of its obligations hereunder and
thereunder, the issuance, sale and delivery of the Preferred Shares and the
issuance and delivery of the Conversion Shares 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 government, the Certificate of Incorporation of
the Company, as amended (the "Charter") or the By-laws of the Company (the "By-
Laws"), as amended, or any provision of any indenture, agreement or other
instrument to which the Company, any of its subsidiaries or any of their
respective properties or assets is 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 or any of its
subsidiaries. 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.

          (b) The Preferred Shares have been duly authorized and, when issued in
accordance with this Agreement, will be validly issued, fully paid and
nonassessable shares of Series A Convertible Preferred Stock with no personal
liability attaching to the ownership thereof and will be free and clear of all
liens, charges, restrictions, claims and encumbrances imposed by or through the
Company except as set forth in the Registration Rights Agreement and the Voting
Agreement. The Conversion Shares have been duly reserved for issuance upon
conversion of the Preferred Shares and, when so issued, will be duly authorized,
validly issued, fully paid and nonassessable shares of Common Stock with no
personal liability attaching to the ownership thereof and will be free and clear
of all liens, charges, restrictions, claims and encumbrances imposed by or
through the

                                      -3-
<PAGE>

Company except as set forth in the Registration Rights Agreement and the Voting
Agreement. Neither the issuance, sale or delivery of the Preferred Shares nor
the issuance or delivery of the Conversion Shares is subject to any preemptive
right of stockholders of the Company or to any right of first refusal or other
right in favor of any person.

     SECTION 2.4  Validity.  This Agreement has been duly executed and delivered
                  --------
by the Company and constitutes the legal, valid and binding obligation of the
Company, enforceable in accordance with its terms, and each other Transaction
Agreements, when executed and delivered by the Company, will constitute the
legal, valid and binding obligations of the Company, enforceable in accordance
with their respective terms (subject in each case, as to the enforcement of
remedies, to applicable bankruptcy, reorganization, insolvency, moratorium and
similar laws affecting the rights of creditors generally and general principles
of equity).

     SECTION 2.5  Authorized Capital Stock.  The authorized capital stock of the
                  ------------------------
Company consists of (i) 4,000,000 shares of Preferred Stock, $.001 par value
(the "Preferred Stock"), all of which have been designated Series A Convertible
Preferred Stock, and (ii) 12,000,000 shares of Common Stock. Immediately prior
to the Closing, 2,929,600 shares of Common Stock will be validly issued and
outstanding, fully paid and nonassessable with no personal liability attaching
to the ownership thereof and no shares of Preferred Stock shall have been
issued. Immediately after giving effect to the Closing, the stockholders of
record and holders of subscriptions, warrants, options, convertible securities,
and other rights (contingent or other) to purchase or otherwise acquire equity
securities of the Company, and the number of shares of Common Stock and the
number of such subscriptions, warrants, options, convertible securities, and
other such rights held by each, will be as set forth in the attached Schedule
                                                                     --------
III.  The designations, powers, preferences, rights, qualifications, limitations
---
and restrictions in respect of each class and series of authorized capital stock
of the Company are as set forth in the Charter, a copy of which is attached as
Exhibit G, and all such designations, powers, preferences, rights,
---------
qualifications, limitations and restrictions are valid, binding and enforceable
and in accordance with all applicable laws. Except as set forth in the attached
Schedule III, (i) no person owns of record or is known to the Company to own
------------
beneficially any share of Common Stock, (ii) no subscription, warrant, option,
convertible security, or other right (contingent or other) to purchase or
otherwise acquire equity securities of the Company is authorized or outstanding
and (iii) except as provided by this Agreement and the Charter, there is no
commitment by the Company to issue shares, subscriptions, warrants, options,
convertible securities, or other such rights or to distribute to holders of any
of its equity securities any evidence of indebtedness or asset. Except as
provided for in the Charter, the Company has no obligation (contingent or other)
to purchase, redeem or otherwise acquire any of its equity securities or any
interest therein or to pay any dividend or make any other distribution in
respect thereof. Except as provided for in

                                      -4-
<PAGE>

the Charter, the Founders Agreements, Stockholders Agreements and the Voting
Agreement, there are no voting trusts or agreements, pledge agreements, buy-sell
agreements, rights of first refusal, preemptive rights or proxies relating to
any securities of the Company or any of its subsidiaries to which the Company or
any of its subsidiaries or, to the Company's knowledge, any other person or
entity, is a party. All of the outstanding securities of the Company were issued
in compliance with all applicable Federal and state securities laws.

     SECTION 2.6  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, sale and delivery of the Preferred
Shares or upon conversion thereof, the issuance and delivery of the Conversion
Shares, other than (i) 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) in
connection with the sale of the Preferred Shares and (ii) with respect to the
Registration Rights Agreement, the registration of the shares covered thereby
with the Commission and filings pursuant to state securities laws.

     SECTION 2.7  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 or 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 which 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

                                      -5-
<PAGE>

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.

     SECTION 2.8  Patents, Trademarks, Etc.  (a) Set forth in Schedule II is a
                  ------------------------                    -----------
list and brief description of all domestic and foreign patents, patent rights,
patent applications, trademarks, trademark applications, service marks, service
mark applications, trade names and copyrights, and all applications for such
which are in the process of being prepared, owned by or registered in the name
of the Company, or of which the Company is a licensor or licensee or in which
the Company has any right, and in each case a brief description of the nature of
such right.  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 (collectively,
"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.

          (b) No person or entity has any right, title or interest of any kind
in or to any of the research and other work which has been performed prior to
the date hereof by or under the direction of the Founders with respect to the
matters described in the Company's summary of proposed business set forth on
Exhibit H hereto (the "Plan"), except for (i) the Founders, each of whom has
---------
executed either an Employee Nondisclosure and Developments Agreement or a
Nondisclosure Agreement (in the case of employees of Cold Spring Harbor
Laboratory) in substantially the form of Exhibit I-1 or Exhibit I-2,
                                         -----------    -----------
respectively, (ii) Cold Spring Harbor Laboratory, which has licensed its entire
right, title and interest in and to all such research and other work to the
Company pursuant to the License Agreement, and (iii) the rights of any
governmental agency as set forth on Schedule II.
                                    -----------

     SECTION 2.9  Disclosure.  There is no state of facts known to the Company
                  ----------
relating to the business, affairs, condition or prospects of the Company which
materially adversely affects the same, or which may in the future (so far as the
Company can now

                                      -6-
<PAGE>

reasonably foresee) materially adversely the same, which has not been disclosed
to the Purchasers by the Company.

     SECTION 2.10  Knowledge.  As used in this Article II, the phrase "known to
                   ---------
the Company" (or words to such effect) shall mean the knowledge, after due
inquiry, of Dr. Thomas G. Marr and Cold Spring Harbor Laboratory.

                                  ARTICLE III

                REPRESENTATIONS AND WARRANTIES OF THE PURCHASERS

Each Purchaser severally represents and warrants to the Company that:

     (a) it is an "accredited investor" within the meaning of Rule 501 under the
Securities Act of 1933, as amended (the "Securities Act") and was not organized
for the specific purpose of acquiring the Preferred Shares;

     (b) it has sufficient knowledge and experience in investing in companies
similar to the Company in terms of the Company's stage of development so as to
be able to evaluate the risks and merits of its investment in the Company and it
is able financially to bear the risks thereof;

     (c) it has had an opportunity to discuss the Company's business, management
and financial affairs with the Company's management;

     (d) the Preferred Shares being purchased by it are being acquired for its
own account for the purpose of investment and not with a view to or for sale in
connection with any distribution thereof in violation of the Securities Act;

     (e) it understands that (i) the Preferred Shares and the Conversion Shares
have not been registered under the Securities Act by reason of their issuance in
a transaction exempt from the registration requirements of the Securities Act
pursuant to Section 4(2) thereof or Rule 505 or 506 promulgated under the
Securities Act, (ii) the Preferred Shares (and, upon conversion thereof, the
Conversion Shares) must be held indefinitely unless a subsequent disposition
thereof is registered under the Securities Act or is exempt from such
registration, (iii) the Preferred Shares and Conversion Shares will bear a
legend to such effect and (iv) the Company will make a notation on its transfer
books to such effect; and

                                      -7-
<PAGE>

     (f) if it sells any Conversion Shares pursuant to Rule 144A promulgated
under the Securities Act, it will take all necessary steps in order to perfect
the exemption from registration provided thereby, including (i) obtaining
information to enable it to establish a reasonable belief that the purchaser is
a qualified institutional buyer and (ii) advising such purchaser that Rule 144A
is being relied upon with respect to such resale.

                                   ARTICLE IV

                CONDITIONS TO THE OBLIGATIONS OF THE PURCHASERS

The obligation of each Purchaser to purchase and pay for the Preferred Shares
being purchased by it on the Closing Date is, at its option, subject to the
satisfaction, on or before the Closing Date, of the following conditions:

     (a) Opinion of Company's Counsel. The Purchasers shall have received from
         ----------------------------
Dechert, Price, & Rhoads, counsel for the Company, an opinion dated the Closing
Date, in substantially the form attached as Exhibit J hereto.
                                            ---------

     (b) Representations and Warranties to be True and Correct.  The
         -----------------------------------------------------
representations and warranties contained in Article II shall be true, complete
and correct on and as of the Closing Date with the same effect as though such
representations and warranties had been made on and as of such date, and the
President and Treasurer of the Company shall have certified to such effect to
the Purchasers in writing.

     (c) Performance. The Company shall have performed and complied with all
         -----------
agreements contained herein required to be performed or complied with by it
prior to or at the Closing Date, and the President and Treasurer of the Company
shall have certified to the Purchasers in writing to such effect and to the
further effect that all of the conditions set forth in this Article IV have been
satisfied.

     (d) All Proceedings to be Satisfactory.  All corporate and other
         ----------------------------------
proceedings to be taken by the Company in connection with the transactions
contemplated hereby and all documents incident thereto shall be satisfactory in
form and substance to the Purchasers and their counsel, and the Purchasers and
their counsel shall have received all such counterpart originals or certified or
other copies of such documents as they reasonably may request.

     (e) Supporting Documents.  The Purchasers and their counsel shall have
         --------------------
received copies of the following documents:

                                      -8-
<PAGE>

          (i)   (A) the Charter, certified as of a recent date by the Secretary
of State of the State of Delaware, and (B) a certificate of said Secretary dated
as of a recent date as to the due incorporation and good standing of the
Company, the payment of all franchise taxes by the Company and listing all
documents of the Company on file with said Secretary.

          (ii)  a certificate of the Secretary or an Assistant Secretary of the
Company dated the Closing Date and certifying: (A) that attached thereto is a
true and complete copy of the By-laws of the Company as in effect on the date of
such certification; (B) that attached thereto is a true and complete copy of all
resolutions adopted by the Board of Directors or the stockholders of the Company
authorizing the execution, delivery and performance of the Transaction
Agreements, the issuance, sale and delivery of the Preferred Shares and the
reservation, issuance and delivery of the Conversion Shares, and that all such
resolutions are in full force and effect and are all the resolutions adopted in
connection with the transactions contemplated by the Transaction Agreements; (C)
that the Charter has not been amended since the date of the last amendment
referred to in the certificate delivered pursuant to clause (i)(B) above; and
(D) to the incumbency and specimen signature of each officer of the Company
executing the Transaction Agreements, the stock certificates representing the
Preferred Shares and any certificate or instrument furnished pursuant hereto,
and a certification by another officer of the Company as to the incumbency and
signature of the officer signing the certificate referred to in this clause
(ii); and

          (iii) such additional supporting documents and other information with
respect to the operations and affairs of the Company as the Purchasers or their
counsel reasonably may request.

     (f)  Transaction Agreements.  The Transaction Agreements (other than this
          ----------------------
Agreement) shall have been duly executed and delivered by the parties thereto.

     (g)  Charter. The Charter shall read in its entirety as set forth in
          -------
Exhibit G.
---------

     (h)  By-Laws.  The By-Laws shall read in their entirety as set forth in
          -------
Exhibit K.
---------

     (i)  Proprietary Information.  Each of the Founders and the persons listed
          -----------------------
on Exhibit L shall have executed and delivered either an Employee Nondisclosure
   ---------
and Developments Agreement or a Nondisclosure Agreement (in the case of
employees of Cold Spring Harbor Laboratory) substantially in the form of Exhibit
                                                                         -------
I-1 or Exhibit I-2, respectively.
---    -----------

                                   ARTICLE V

                                      -9-
<PAGE>

                            COVENANTS OF THE COMPANY

The Company covenants and agrees with each of the Purchasers that for so long as
any Series A Convertible Preferred Stock is outstanding:

     SECTION 5.1  Financial Statements, Reports, Etc.  The Company shall furnish
                  ----------------------------------
to each Purchaser who holds at least 1,000,000 Preferred Shares:

          (a) within ninety (90) days after the end of each fiscal year of the
Company, a consolidated balance sheet of the Company and its subsidiaries as of
the end of such fiscal year and the related consolidated statements of income,
stockholders' equity and cash flows for the fiscal year then ended, prepared in
accordance with generally accepted accounting principles and certified by a firm
of independent public accountants of recognized national standing selected by
the Board of Directors of the Company, provided that the Company's obligations
under this Section 5.1(a) shall terminate upon (i) the registration of the
Company's securities under Section 12(b) of the Securities Exchange Act of 1934,
as amended (the "Exchange Act") or (ii) the registration of the Company's
securities under Section 12(g) of the Exchange Act and the admission to listing
of such securities on the Nasdaq Stock Market;

          (b) within thirty days after the end of each month and each quarter in
each fiscal year (other than the last month in each fiscal year), a consolidated
balance sheet of the Company and its subsidiaries and the related consolidated
statements of income, stockholders' equity and cash flows, unaudited but
prepared in accordance with generally accepted accounting principles and
certified by the Chief Financial Officer of the Company, such consolidated
balance sheet to be as of the end of such month or quarter, as the case may be,
and such consolidated statements of income, stockholders' equity and cash flows
to be for such month or quarter, as the case may be, and for the period from the
beginning of the fiscal year to the end of such month or quarter, as the case
may be, in each case with comparative statements for the prior fiscal year,
provided that the Company's obligations under this Section 5.1(b) shall
terminate upon (i) the registration of the Company's securities under Section
12(b) of the Exchange Act or (ii) the registration of the Company's securities
under Section 12(g) of the Exchange Act and the admission to listing of such
securities on the Nasdaq Stock Market;

          (c) at the time of any delivery of each annual financial statement
pursuant to Section 5.1 (a), a certificate executed by the Chief Executive
Officer of the Company stating that such officer has caused this Agreement and
the Series A Convertible Preferred Stock to be reviewed and has no knowledge of
any default by the Company in the performance or observance of any of the
provisions of this Agreement or the Series A Convertible Preferred Stock or, if
such officer has such knowledge, specifying such default and the nature thereof,

                                      -10-
<PAGE>

          (d) at the time of any delivery of each monthly and quarterly
statement pursuant to Section 5.1(b), a management narrative report explaining
all material variances from forecasts and all material current developments in
staffing, marking, sales and operations;

          (e) no later than sixty (60) days prior to the start of each fiscal
year, consolidated capital and operating expense budgets, cash flow projections
and income and loss projections for the Company and its subsidiaries in respect
of such fiscal year, all itemized in reasonable detail and prepared on a monthly
basis, and, promptly after preparation, any revisions to any of the foregoing;

          (f) promptly following receipt by the Company, each audit response
letter, accountant's management letter and other written report submitted to the
Company by its independent public accountants in connection with an annual or
interim audit of the books of the Company or any of its subsidiaries;

          (g) promptly after the commencement thereof, notice of all actions,
suits, claims, proceedings, investigations and inquiries of the type described
in Sections 2.1, 2.7 or 2.8 that could materially adversely affect the Company
or any of its subsidiaries;

          (h) promptly upon sending, making available or filing the same, (i)
all press releases, and (ii) all reports and financial statements that the
Company sends or makes available to its stockholders or directors or files with
the Securities and Exchange Commission; and

          (i) promptly, from time to time, such other information regarding the
business, prospects, financial condition, operations, property or affairs of the
Company and its subsidiaries as such Purchaser reasonably may request.

     SECTION 5.2  Reserve for Conversion Shares.  The Company shall at all times
                  -----------------------------
reserve and keep available out of its authorized but unissued shares of Common
Stock, for the purpose of effecting the conversion of the Preferred Shares and
otherwise complying with the terms of this Agreement, such number of its duly
authorized shares of Common Stock as shall be sufficient to effect the
conversion of the Preferred Shares from time to time outstanding or otherwise to
comply with the terms of this Agreement.  If at any time the number of
authorized but unissued shares of Common Stock shall not be sufficient to effect
the conversion of the Preferred Shares or otherwise to comply with the terms of
this Agreement, the Company will forthwith take such corporate action as may be
necessary to increase its authorized but unissued shares of Common Stock to such
number of shares as shall be sufficient for such purposes. The Company will
obtain any authorization, consent, approval or other action by or make any
filing with any court or administrative body that may be required under
applicable state securities laws in

                                      -11-
<PAGE>

connection with the issuance of shares of Common Stock upon conversion of the
Preferred Shares.

     SECTION 5.3  Corporate Existence.  The Company shall maintain and, except
                  -------------------
as otherwise permitted by Section 5.14 cause each of its subsidiaries to
maintain, their respective corporate existence, rights and franchises in full
force and effect.

     SECTION 5.4  Properties, Business, Insurance.  The Company shall maintain
                  -------------------------------
and cause each of its subsidiaries to maintain as to their respective properties
and business, with financially sound and reputable insurers, insurance against
such casualties and contingencies and of such types and in such amounts as is
customary for companies similarly situated, which insurance shall be deemed by
the Company to be sufficient.

     SECTION 5.5  Inspection, Consultation and Advice.  The Company shall permit
                  -----------------------------------
and cause each of its subsidiaries to permit each Purchaser and such persons as
such Purchaser may designate, at such Purchaser's expense, to visit and inspect
any of the properties of the Company and its subsidiaries, examine their books
and take copies and extracts therefrom (subject to the prior execution and
delivery to the Company of a confidentiality agreement in a reasonable form
provided by the Company from time to time), discuss the affairs, finances and
accounts of the Company and its subsidiaries with their officers, employees and
public accountants (and the Company hereby authorizes said accountants to
discuss with such Purchaser and such designees such affairs, finances and
accounts), and consult with and advise the management of the Company and its
subsidiaries as to their affairs, finances and accounts, all at reasonable times
and upon reasonable notice.

     SECTION 5.6  Restrictive Agreements Prohibited.  Neither the Company nor
                  ---------------------------------
any of its subsidiaries shall become a party to any agreement which by its terms
restricts the Company's performance of any Transaction Agreement, the By-Laws or
the Charter.

     SECTION 5.7  Transactions with Affiliates.  Except for transactions
                  ----------------------------
contemplated by this Agreement or as otherwise approved by the Board of
Directors, neither the Company nor any of its subsidiaries shall enter into any
transaction with any director, officer, employee or holder of more than 5% of
the outstanding capital stock of any class or series of capital stock of the
Company or any of its subsidiaries, member of the family of any such person, or
any corporation, partnership, trust or other entity in which any such person, or
member of the family of any such person, is a director, officer, trustee,
partner or holder of more than 5% of the outstanding capital stock thereof,
except for transactions on customary terms related to such person's employment
with the Company.

                                      -12-
<PAGE>

     SECTION 5.8  Expenses of Directors.  The Company shall promptly reimburse
                  ---------------------
in full each director of the Company who is not an employee of the Company and
who was elected as a director solely or in part by the holders of Series A
Convertible Preferred Stock for all of his reasonable out-of-pocket expenses
incurred in attending each meeting of the Board of Directors of the Company or
any committee thereof.

     SECTION 5.9  Use of Proceeds.  The Company shall use the proceeds from the
                  ---------------
sale of the Preferred Shares solely for working capital.

     SECTION 5.10  Board of Directors Meetings.  The Company shall use its best
                   ---------------------------
efforts to ensure that meetings of its Board of Directors are held at least four
times each year and at least once each quarter.  The Company shall permit each
Purchaser owning at least 1,000,000 Preferred Shares to have one representative
attend each meeting of the Board of Directors of the Company and each meeting of
any committee thereof and to participate in all discussions during each such
meeting.  The Company shall send to each Purchaser and each such representative
the notice of the time and place of such meeting in the same manner and at the
same time as it shall send such notice to its directors or committee members, as
the case may be; provided, however, that the Company shall have no obligations
                 --------  -------
with respect to notice or permitted attendance of a non-director Purchaser's
representative under this Section 5.10 in the event of any meeting of the Board
of Directors, or portion thereof, as to which the Board shall reasonably
conclude (and shall have notified each Purchaser of such conclusion) that the
existence or potential existence of a significant conflict of interest or the
necessity of confidentiality in the best interests of the Company and the
stockholders precludes such notice or attendance.  As a condition to attendance
at any Board of Directors meeting, each Purchaser agrees that such Purchaser's
representative may be required to sign and deliver to the Company a
confidentiality agreement in a reasonable form provided by the Company from time
to time.  The Company shall also provide to each Purchaser and designee copies
of all notices, reports, minutes and consents at the time and in the manner as
they are provided to the Board of Directors or committee, except for information
reasonably designated as proprietary information by the Board of Directors.

     SECTION 5.11  By-Laws.  The Company shall at all times maintain provisions
                   -------
in its By-laws and/or Charter indemnifying all directors and officers against
liability (and providing for expense reimbursement thereof to the extent
contained therein on the date hereof) and absolving all directors from liability
to the Company and its stockholders to the maximum extent permitted under the
laws of the State of Delaware.

     SECTION 5.12  Performance of Contracts.  The Company shall not amend,
                   ------------------------
modify, terminate, waive or otherwise alter, in whole or in part, any of the
Transaction Agreements or any Nondisclosure and Developments Agreement or any
Nondisclosure Agreement with any person without the written consent of those
members of the Company's Board of Directors elected solely by the holders of
Series A Preferred Stock.

                                      -13-
<PAGE>

     SECTION 5.13  Vesting of Reserved Employee Shares.  The Company shall not
                   -----------------------------------
grant to any of its directors, employees or consultants options to purchase
Common Stock which will become exercisable at a rate in excess of 20% per annum
from the date of such grant without the unanimous written consent of those
members of the Company's Board of Directors elected solely by the holders of
Series A Convertible Preferred Stock.

     SECTION 5.14  Employee Nondisclosure and Developments Agreements.  The
                   --------------------------------------------------
Company shall obtain, and shall cause its subsidiaries to obtain, an Employee
Nondisclosure and Developments Agreement or a Nondisclosure Agreement (in the
case of employees of Cold Spring Harbor Laboratory) in substantially the form of
Exhibit I-2 or Exhibit I-2, respectively from all future officers, key employees
-----------    -----------
and all other employees who may have access to confidential information of the
Company or any of its subsidiaries, upon their employment by the Company or any
of its subsidiaries or by Cold Spring Harbor Laboratory pursuant to any
agreement between Cold Spring Harbor Laboratory and the Company.

     SECTION 5.15  Activities of Subsidiaries.  Without the unanimous consent of
                   --------------------------
the Company's Board of Directors (or unanimous consent of a special committee of
the Board of Directors appointed by unanimous consent of the whole Board of
Directors):  (i) the Company shall not permit any subsidiary to consolidate or
merge into or with or sell or transfer all or substantially all its assets,
except that any wholly-owned subsidiary may (A) consolidate or merge into or
with or sell or transfer assets to any other wholly-owned subsidiary, or (B)
merge into or sell or transfer assets to the Company; (ii) the Company shall not
sell or otherwise transfer any shares of capital stock of any subsidiary, except
to the Company or any wholly-owned subsidiary, or permit any subsidiary to
issue, sell or otherwise transfer any shares of its capital stock or the capital
stock of any subsidiary, except to the Company or any wholly-owned subsidiary;
or (iii) the Company shall not permit any subsidiary to purchase or set aside
any sums for the purchase of, or pay any dividend or make any distribution on,
any shares of its stock, except for dividends or other distributions payable to
the Company or any wholly-owned subsidiary.

     SECTION 5.16  Compliance with Laws.  The Company shall comply, and cause
                   --------------------
each subsidiary to comply, in all material respects with all applicable laws,
rules, regulations and orders.

     SECTION 5.17  Keeping of Records and Books of Account.  The Company shall
                   ---------------------------------------
keep, and cause each subsidiary to keep, adequate and accurate records and books
of account, in which complete entries will be made in accordance with generally
accepted accounting principles consistently applied, reflecting all financial
transactions of the Company and such subsidiary, and in which, for each fiscal
year, all proper reserves for depreciation, depletion, obsolescence,
amortization, taxes, bad debts and other purposes in connection with its
business shall be made.

                                      -14-
<PAGE>

     SECTION 5.18  Change in Nature of Business.  The Company shall not make, or
                   ----------------------------
permit any subsidiary to make, any material change in the nature of its business
as contemplated in the Plan.

     SECTION 5.19  U.S. Real Property Interest Statement.  The Company shall
                   -------------------------------------
provide prompt written notice to each Purchaser following any "determination
date" (as defined in Treasury Regulation Section 1.897-2(c)(i)) on which the
Company becomes a United States real property holding corporation.  In addition,
upon a written request by any Purchaser, the Company shall provide such
Purchaser with a written statement informing the Purchaser whether such
Purchaser's interest in the Company constitutes a U.S. real property interest.
The Company's determination shall comply with the requirements of Treasury
Regulation Section 1.897-2(h)(1) or any successor regulation, and the Company
shall provide timely notice to the Internal Revenue Service, in accordance with
and to the extent required by Treasury Regulation Section 1.897-2(h)(2) or any
successor regulation, that such statement has been made.  The Company's written
statement to any Purchaser shall be delivered to such Purchaser within ten (10)
days of such Purchaser's written request therefor.  The Company's obligation to
furnish a written statement pursuant to this Section 5.19 shall continue
notwithstanding the fact that a class of the Company's stock may be regularly
traded on an established securities market.

     SECTION 5.20  Rule 144A Information.  The Company shall, at all times
                   ---------------------
during which it is neither subject to the reporting requirements of Section 13
or 15(d) of the Exchange Act, nor exempt from reporting pursuant to Rule 12g3-
2(b) under the Exchange Act, provide in writing, upon the written request of any
Purchaser or a prospective buyer of Preferred Shares or Conversion Shares from
any Purchaser, all information required by Rule 144A(d)(4)(i) of the General
Regulations promulgated by the Commission under the Securities Act ("Rule 144A
Information").  The Company also shall, upon the written request of any
Purchaser, cooperate with and assist such Purchaser or any member of the
National Association of Securities Dealers, Inc. PORTAL system in applying to
designate and thereafter maintain the eligibility of the Preferred Shares or
Conversion Shares, as the case may be, for trading through PORTAL.  The
Company's obligations under this Section 5.20 shall at all times be contingent
upon the relevant Purchaser's obtaining from the prospective buyer of Preferred
Shares or Conversion Shares a written agreement to take all reasonable
precautions to safeguard the Rule 144A Information from disclosure to anyone
other than a person who will assist such buyer in evaluating the purchase of any
Preferred Shares or Conversion Shares.

     SECTION 5.21  Termination of Covenants.  The covenants set forth in
                   ------------------------
Sections 5.19 and 5.20 shall terminate and be of no further force or effect as
to each of the Purchasers when such Purchaser no longer holds any shares of
capital stock of the Company.  All of the other covenants set forth in this
Article V shall terminate and be of no further force or effect as to a Purchaser
when such Purchaser owns less than 50,000

                                      -15-
<PAGE>

Preferred Shares (appropriately adjusted to reflect stock splits, stock
dividends, combinations of shares and the like with respect to the Series A
Convertible Preferred Stock).

                                   ARTICLE VI

                                 MISCELLANEOUS

     SECTION 6.1  Expenses.  Each party hereto will pay its own expenses in
                  --------
connection with the transactions contemplated hereby, whether or not such
transactions shall be consummated, provided, however, that assuming a successful
completion of such transactions, the Company shall pay the reasonable fees and
disbursements of the Purchasers' special counsel Skadden, Arps, Slate, Meagher &
Flom and Dechert Price & Rhoads, in connection with such transactions and any
subsequent amendment, waiver, consent or enforcement thereof.

     SECTION 6.2  Survival of Agreements.  Except as otherwise specified herein,
                  ----------------------
all covenants, agreements, representations and warranties made herein or in the
Registration Rights Agreement, the Founders Agreements, the Stockholders
Agreements, the Voting Agreement or any certificate or instrument delivered to
the Purchasers pursuant to or in connection with this Agreement, the
Registration Rights Agreement, the Founders Agreements, the Stockholders
Agreements or the Voting Agreement, shall survive the execution and delivery of
this Agreement, the Registration Rights Agreement, the Founders Agreements, the
Stockholders Agreements and the Voting Agreement, the issuance, sale and
delivery of the Preferred Shares, and the issuance and delivery of the
Conversion Shares, and all statements contained in any certificate or other
instrument delivered by the Company hereunder or thereunder or in connection
herewith or therewith shall be deemed to constitute representations and
warranties made by the Company.

     SECTION 6.3  Brokerage.  Each party hereto will indemnify and hold harmless
                  ---------
the others against and in respect of any claim for brokerage or other
commissions relative to this Agreement or to the transactions contemplated
hereby, based in any way on agreements, arrangements or understandings made or
claimed to have been made by such party with any third party.

     SECTION 6.4  Parties in Interest.  All representations, covenants and
                  -------------------
agreements contained in this Agreement by or on behalf of any of the parties
hereto shall bind and inure to the benefit of the respective successors and
assigns of the parties hereto whether so expressed or not.  Without limiting the
generality of the foregoing, all representations, covenants and agreements
benefiting the Purchasers shall inure to the

                                      -16-
<PAGE>

benefit of any and all subsequent holders from time to time of Preferred Shares
or Conversion Shares.

     SECTION 6.5 Notices.  All notices, requests, consents and other
communications hereunder shall be in writing and shall be delivered in person,
mailed by certified or registered mail, return receipt requested, or sent by
telecopier or telex, addressed as follows:

          (a) if to the Company, c/o Falcon Technology Partners, L.P., 600
Dorset Road, Devon, PA 19333 Attention: President, with a copy to:  Henry
Nassau, Esq., Dechert, Price & Rhoads, 4000 Bell Atlantic Tower, 1717 Arch
Street, Philadelphia, PA 19103-2793 (Facsimile No. (215) 994-2222); and

          (b) if to any Purchaser, at the address of such Purchaser set forth in
Schedule I, with a copy to Kent Coit, Esq., Skadden, Arps, Slate, Meagher &
----------
Flom, One Beacon Street, Boston, Massachusetts 02108 (Facsimile No. (617) 573-
4822);

or, in any such case, at such other address or addresses as shall have been
furnished in writing by such party to the others.

     SECTION 6.6  Governing Law.  This Agreement shall be governed by and
                  -------------
construed in accordance with the laws of the State of New York.

     SECTION 6.7  Entire Agreement.  This Agreement, including the Schedules and
                  ----------------
Exhibits hereto, constitutes the sole and entire agreement of the parties with
respect to the subject matter hereof.  All Schedules and Exhibits hereto are
hereby incorporated herein by reference.

     SECTION 6.8  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.

     SECTION 6.9  Amendments.  This Agreement may not be amended or modified,
                  ----------
and no provisions hereof may be waived, except with the written consent of the
Company and the holders of Preferred Shares which are convertible into a number
of shares of Common Stock, and/or shares of Common Stock issued upon conversion
of Preferred Shares, constituting at least two-thirds of the outstanding shares
of Common Stock issued or issuable upon conversion of the Preferred Shares.

     SECTION 6.10 Severability.  If any provision of this Agreement shall be
                  ------------
declared void or unenforceable by any judicial or administrative authority, the
validity of any other provision and of the entire Agreement shall not be
affected thereby.

                                      -17-
<PAGE>

     SECTION 6.11  Titles and Subtitles.  The titles and subtitles used in this
                   --------------------
Agreement are for convenience only and are not to be considered in construing or
interpreting any term or provision of this Agreement.

     SECTION 6.12  Certain Defined Terms.  As used in this Agreement, the
                   ---------------------
following terms shall have the following meanings (such meanings to be equally
applicable to both the singular and plural forms of the terms defined):

          (a) "person" shall mean an individual, corporation, trust,
partnership, joint venture, unincorporated organization, government agency or
any agency or political subdivision thereof, or other entity.

          (b) "subsidiary" shall mean, as to the Company, (i) any corporation of
which more than 50% of the outstanding stock having ordinary voting power to
elect a majority of the board of directors of such corporation (irrespective of
whether or not at the time stock of any other class or classes of such
corporation shall have or might have voting power by reason of the happening of
any contingency) or (ii) any partnership, limited liability company or similar
entity of which more than 50% of the ownership interests, or any percentage of
general partner or managing member interest, is at the time directly or
indirectly owned by the Company, or by one or more of its subsidiaries, or by
the Company and one or more of its subsidiaries.


                  [REMAINDER OF PAGE INTENTIONALLY LEFT BLANK]

                                      -18-
<PAGE>

     IN WITNESS WHEREOF, the Company, and the Purchasers have executed this
Agreement as of the day and year first above written.

                                 GENOMICA CORPORATION

                                 By: /s/ James L. Rathmann
                                    -------------------------------
                                      James L. Rathmann
                                      President


[Corporate Seal]

                                 PURCHASERS:

                                 FALCON TECHNOLOGY PARTNERS, L.P.


                                 By: /s/ James L. Rathmann
                                    -------------------------------
                                      James L. Rathmann
                                      General Partner

                                 HARRIS & HARRIS GROUP, INC.

                                 By: /s/ David C. Johnson, Jr.
                                    -------------------------------
                                      David C. Johnson, Jr.
                                      Title: Executive Vice President

                                      -19-
<PAGE>

                                   SCHEDULE I

<TABLE>
<CAPTION>
                                    Number of Preferred           Aggregate Purchase Price
Purchaser                           Shares to be Purchased        for Preferred Shares
---------                           ----------------------        ------------------------
<S>                                 <C>                           <C>
Falcon Technology Partners, L.P.    1,660,200                     $1,000,104.48*

Harris & Harris Group, Inc.         1,660,200                     $1,000,104.48
</TABLE>


*    Partial payment for shares in the amount of $403,229.14 is being made
     Falcon Technology Partners as cancellation of certain indebtedness,
     described in the following chart, owed by the Company to Falcon Technology
     Partners, L.P.

         =================================================================
         Origination    Interest Rate     Principal      Interest Due as
         Date                                            of 3/22/96
         -----------------------------------------------------------------
         3/12/96         6%               $100,000       $  164.38
         -----------------------------------------------------------------
         2/16/96         6%               $200,000       $ 1150.68
         -----------------------------------------------------------------
         1/2/96          6%               $ 50,000       $  657.53
         -----------------------------------------------------------------
         10/18/95        5.88%            $ 50,000       $1,256.55
         =================================================================

                                      -20-
<PAGE>

                                  SCHEDULE II

Section 2.1 The Transaction Agreements, as such term is defined in the Series A
Convertible Preferred Stock Purchase Agreement to which this Schedule II is
attached (the "Agreement")

Section 2.8 (a)  Pursuant to the License Agreement, as such term is defined in
the Agreement and attached thereto as Exhibit D and incorporated by reference
                                      ---------
herein, the Company is the licensee of the Patent Rights, Licensed Copyrights
and Technical Information as such terms are defined in the License Agreement,
subject to the rights of Cold Spring Harbor Laboratory ("CSHL") and the federal
government as set forth therein.

            (b)  Pursuant to a certain Letter Agreement dated March 15, 1996
between CSHL and the Company, the Company is the licensee of future inventions
made by Marr and the Company prior to January 1, 2001.

                                      -21-
<PAGE>

                                  SCHEDULE III

                  Genomica Corporation Capitalization Table      March ___, 1996

<TABLE>
<CAPTION>
                                     Common Stock   % of Common   Series A Preferred  % Series A  Total Shares        $ of Total
<S>                                  <C>            <C>           <C>                 <C>         <C>                 <C>
Falcon Technology Partners L.P.                                           1,660,200       50.00%     1,660,200            26.06%
Rathmann Family                           600,000        19.67%                                        600,000             9.42%
Harris and Harris Group, Inc.             199,800         6.55%           1,660,200       50.00%     1,860,000            29.20%
Cold Spring Harbor Laboratories           679,679        22.29%                                        679,679            10.67%
John Maroney                               60,121         1.97%                                         60,121             0.94%
Thomas Marr                             1,080,000        35.41%                                      1,080,000            16.95%
Donald Fisher                             250,000         8.20%                                        250,000             3.92%
Jackie Salit                               30,000         0.98%                                         30,000             0.47%
Steve Cozza                                30,000         0.98%                                         30,000             0.47%
Pool for inventions                       120,000         3.93%                                        120,000             1.88%

Total                                   3,049,600       100.00%           3,320,400      100.00%     6,370,000           100.00%
</TABLE>