<PAGE>

                                                                    EXHIBIT 10.4

                               VOTING AGREEMENT

     AGREEMENT dated as of March 22, 1996, by and among Genomica Corporation, a
Delaware corporation (the "Company"), the persons listed as Purchasers in
Schedule I to a certain Series A Convertible Preferred Stock Purchase Agreement
of the Company dated as of the date hereof (the "Purchase Agreement")
(collectively, the "Purchasers" and individually a "Purchaser") and the persons
listed as Stockholders in the signature pages hereto (collectively, the
"Stockholders" and individually, a "Stockholder").

     WHEREAS, on the date hereof, the Purchasers are purchasing from the Company
shares of its Series A Preferred Stock (the "Series A Preferred") pursuant to
the terms of the Purchase Agreement, a copy of which is attached hereto as
Exhibit A; and

     WHEREAS, the Purchasers and the Stockholders wish to make certain
provisions for the voting of their Shares (as defined below); and

     WHEREAS, the purchases by the Purchasers will benefit the Company; and

     WHEREAS, it is a condition to the obligations of the Purchasers under the
Purchase Agreement that this Agreement be executed by the parties hereto, and
the parties are willing to execute this Agreement and to be bound by the
provisions hereof;

     NOW, THEREFORE, in consideration of the premises, the agreements set forth
below, and the parties' desire to further the interests of the Company and its
present and future stockholders, the parties agree as follows:

     1.  Definition. As used in this Agreement, the term "Shares" means all
shares of equity securities of the Company (i) now or hereafter owned (either
beneficially or of record) by a Stockholder or a Purchaser, and (ii) which a
Stockholder or a Purchaser does not own (either beneficially or of record) but
as to which it now or hereafter has the right to exercise voting control.

     2.  Designation of Nominees. (a) Each of Falcon Technology Partners, L.P.
("Falcon") and Harris & Harris Group, Inc. ("Harris") (together, the "Nominating
Purchasers" and individually, a "Nominating Purchaser") so long as they own any
shares shall have the right to designate a nominee (together, the "Nominees" and
individually, a "Nominee") for election as one of the directors of the Company
who shall be elected solely by the holders of the Series A Preferred, voting
separately as a series (the "Series A Directors") pursuant to the Company's
Certificate of Incorporation. Falcon and Harris together shall have the right to
designate a third Nominee who shall be elected as Series A Director. At least 10
days prior to any meeting (or written action in lieu of a meeting) of
stockholders of the Company at or by which directors are to be elected by the
holders of Series A Preferred, voting separately as a series, each Nominating
Purchaser shall
<PAGE>

notify the other Purchaser in writing of the Nominee designated by such
Nominating Purchaser for election as a director. In the absence of any such
notification, it shall be presumed that the Nominating Purchaser's then
incumbent Nominee has been redesignated as its Nominee. The initial Nominees of
Falcon and Harris are James L. Rathmann, Charles Hams and David C. Johnson, Jr.,
respectively.

         (b)  One of the directors of the Company (the "Common Director") is
elected solely by the holders of Common Stock pursuant to the Company's
Certificate of Incorporation. The holders of a majority in interest of the then
outstanding Common Stock, excluding for this purpose any shares of Common Stock
then owned, or as to which the power to vote is held, by any Purchaser and also
excluding Cold Spring Harbor Laboratory ("CSH") if CSH has the right to
designate a Nominee for election as a director pursuant to Section 2(c) below
(the "Designating Common Holders"), shall have the right to designate the
nominee for election as a director solely by the holders of Common Stock. At
least 10 days prior to any meeting (or written action in lieu of a meeting) of
stockholders of the Company at or by which the Common Directors are to be
elected, the Designating Common Holders shall notify all of the Purchasers and
Stockholders in writing of the person designated for election as the Common
Director. In the absence of any such notification, it shall be presumed that the
incumbent Common Director, if any, has been redesignated for election as the
Common Director. The initial person designated for election as the Common
Director is Dr. Thomas G. Marr.

         (c)  So long as CSH is the beneficial owner of at least 40% of the
Shares purchased by CSH on the date hereof, CSH shall have the right to
designate a Nominee for election as one of the directors of the Company who
shall be elected solely by the holders of Common Stock (the "CSH Director")
pursuant to the Company's Certificate of Incorporation. At least 10 days prior
to any meeting (or written action in lieu of a meeting) of stockholders of the
Company at or by which the CSH Director is to be elected, CSH shall notify all
of the Purchasers and Stockholders in writing of the person designated for
election as the CSH Director. In the absence of any such notification, it shall
be presumed that the incumbent CSH Director, if any, has been redesignated for
election as the CSH Director. The initial person designated for election as the
CSH Director is [_______]. If CSH shall not be entitled to designate a CSH
Director pursuant to the terms hereof, the Designating Common Holders shall have
the right to nominate two directors (including the Common Director) who shall be
elected soley by the holders of Common Stock. For purposes of Section 3 below,
the CSH Director shall constitute a Common Director.

     3.  Election of Directors. At each meeting (or written action in lieu of a
meeting) of stockholders of the Company at or by which directors are to be
elected by the holders of the Series A Preferred, voting separately as a series,
each Purchaser shall vote (or execute a written consent with respect to) all of
its Shares to elect, as directors of the Company, the Nominees designated in the
manner provided in Section 2. At each
<PAGE>

meeting (or written action in lieu of a meeting) of stockholders of the Company
at or by which the Common Directors are to be elected, each Purchaser and
Stockholder shall vote (or execute a written consent with respect to) all of its
Shares entitled to vote to elect, as directors of the Company, the Common
Directors designated in the manner provided in Section 2; provided, that, until
an initial public offering of Common Stock (an "IPO"), such Common Directors
shall be a "Founder" or an employee thereof, as such term is defined in a
certain Founders' Agreements with the Company dated as of even date herewith.

     4.  Successor Directors. (a) If a Nominee shall cease to serve as a
director for any reason, the Nominating Purchaser which designated such Nominee
shall have the right to designate a successor Nominee and each of the other
Purchasers and Stockholders shall use its best efforts (including by voting (or
executing a written consent with respect to) all Shares which it is entitled to
vote) to ensure that such successor Nominee is duly elected as a director. If
the Common Director shall cease to serve as a director for any reason, the
Designating Common Holders may designate a successor Common Director and each of
the Purchasers and Stockholders shall use its best efforts (including by voting
(or executing a written consent with respect to) all Shares which it is entitled
to vote) to ensure that such successor Common Director is duly elected as a
director. If the CSH Director shall cease to serve as a director for any reason
and CSH then has the right to designate a Nominee for elections as a director
pursuant to Section 2(c), then CSH may designate a successor CSH Director and
each of the Purchasers and Stockholders shall use its best efforts (including by
voting (or executing a written consent with respect to) all Shares which it is
entitled to vote) to ensure that such successor CSH Director is duly elected as
a director.

         (b)  If a Nominating Purchaser notifies the other Purchasers that it
desires to remove its Nominee as a director, each of the other Purchasers shall
use its best efforts (including by voting (or executing a written consent with
respect to) all Shares which it is entitled to vote) to ensure that such Nominee
is duly removed as a director. If the Designating Common Holders notify the
Purchasers and Stockholders that they desire to remove the Common Director as a
director, each of the Purchasers and Stockholders shall use its best efforts
(including by voting (or executing a written consent with respect to) all Shares
which it is entitled to vote) to ensure that such Common Director is duly
removed as a director. If CSH notifies the Purchasers and Stockholders that it
desires to remove the CSH Director as a director and CSH then has the right to
designate a Nominee for elections as a director pursuant to Section 2(c), each
of the Purchasers and Stockholders shall use its best efforts (including by
voting (or executing a written consent with respect to) all Shares which it is
entitled to vote) to ensure that such CSH Director is dub removed as a director.

         (c)  If (i) a Nominating Purchaser notifies the Company that it desires
to remove its Nominee as a director and/or designate a successor Nominee, (ii)
the
<PAGE>

Designating Common Holders notify the Company that they desire to remove the
Common Director as a director and/or designate a successor Common Director, or
(iii) CSH notifies the Company that it desires to remove the CSH Director as a
director and/or designate a successor CSH Director and CSH then has the right to
designate a Nominee for elections as a director pursuant to Section 2(c), then
the Company shall, at the request of such Nominating Purchaser, Designating
Common Holders or CSH, as the case may be, use its best efforts to ensure that a
meeting of stockholders of the Company is promptly called for such purpose.

     5.  Term. This Agreement shall continue until the earlier of, and shall
automatically terminate and be of no further force or effect at (i) such time as
no shares of Series A Preferred remain outstanding or (ii) the tenth anniversary
of the date of this Agreement; provided that no such termination shall relieve a
party from liability for prior breaches hereof.

     6.  Specific Enforcement. Each party hereto expressly agrees that the
Purchasers, Stockholders and the Company will be irreparably damaged if this
Agreement is not specifically enforced. Upon a breach or threatened breach of
the terms, covenants and/or conditions of this Agreement by a Stockholder, a
Purchaser or the Company, the Purchasers, Stockholders and the Company, as the
case may be, shall, in addition to all other remedies, be entitled to a
temporary or permanent injunction, without showing any actual damage, and/or a
decree for specific performance, in accordance with the provisions hereof.

     7.  Legend. Each certificate evidencing Shares shall bear a legend
substantially as follows:

         "The shares represented by this certificate are subject to the
         terms and conditions of a certain Voting Agreement dated as of
         March ____, 1996, a copy of which the Company will furnish to
         the holder of this certificate upon request and without charge."

     8.  Amendment of Charter. The Purchasers shall not without the consent of
the holders of 75% of the shares of outstanding Common Stock, take any action to
amend the Bylaws or the Certificate of Incorporation of the Corporation to
increase the stated dividend rate of the Series A Preferred, accelerate the date
upon which such dividends shall accrue or increase the liquidation preference of
the Series A Preferred.

     9.  Notices. All notices or other communications given hereunder shall be
in writing and shall be deemed effective upon delivery at the address of the
party to be notified and shall be mailed by certified or registered mail, return
receipt requested, delivered by courier, telecopied, or sent by other facsimile
method (notices by telecopy or facsimile must be confirmed by next day courier
delivery to be effective), addressed to
<PAGE>

the address specified below such party's signature hereto or such other address
as such party may subsequently notify the other parties of in writing.

     10.  Entire Agreement and Amendments. This Agreement constitutes the entire
agreement of the parties with respect to the subject matter hereof and neither
this Agreement nor any provision hereof may be waived, modified, amended or
terminated except by a written agreement signed by the Company, Stockholders
owning at least two-thirds of the Shares of Common Stock owned by all
Stockholders and Purchasers owning at least two thirds of the shares of Common
Stock (assuming for such purpose that all shares of Preferred Stock have been
converted into Common Stock at such time) owned by all Purchasers, provided
however that neither Section 2(c) nor any other Section hereof necessary to
effectuate the intent of or to enforce Section 2(c) may be amended without the
consent of CSH.

     11.  Governing Law Successors and Assigns. This Agreement shall be governed
by the internal laws of the State of Delaware (without giving effect to its
conflict of law principles) and shall bind and inure to the benefit of the
heirs, personal representatives, executors, administrators, successors, assigns
and transferees of the parties. Without limiting the generality of the
foregoing, all covenants and agreements of the Stockholders and Purchasers shall
bind any and all subsequent holders of their Shares, and the Company agrees that
it shall not transfer on its records any such Shares unless (i) the transferor
Stockholder or Purchaser, as the case may be, shall have first delivered to the
Company and the Purchasers the written agreement of the transferee to be bound
by this Agreement to the same extent as if such transferee had originally been a
Stockholder or Purchaser hereunder, as the case may be, and (ii) the certificate
or certificates evidencing the Shares so transferred bear the legend specified
in Section 7.

     12.  Captions. Captions are for convenience only and are not deemed to be
part of this Agreement.

     13.  Counterpart. This Agreement may be executed in two or more
counterpart, each of which shall be deemed an original, but all of which
together shall constitute one and the same instrument.
<PAGE>

     IN WITNESS WHEREOF, the parties hereto have executed this Agreement as of
the day and year first above written

                                COMPANY

                                GENOMICA CORPORATION


                                By:  /s/ James L. Rathmann
                                   ------------------------------------
                                   James L. Rathmann
                                   President
                                   Address:  c/o
                                             Falcon Technology Partners, L.P.
                                             James L. Rathmann
                                             General Partner
                                             600 Dorset Road
                                             Devon, PA  19333

                                PURCHASERS:

                                FALCON TECHNOLOGY PARTNERS, L.P.

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

                                Address:  600 Dorset Road
                                          Devon, PA  19333

                                HARRIS & HARRIS GROUP, INC.

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

                                Address:  One Rockefeller Plaza
                                          14 West 49th Street
                                          New York, New York 10020

                                  (Continued)
<PAGE>

                                STOCKHOLDERS:

                                COLD SPRING HARBOR LABORATORY


                                By:  /s/ John Maroney
                                   ------------------------------------
                                   John Maroney
                                   Assistant Administrative Director

                                HARRIS & HARRIS GROUP, INC.


                                By:  /s/
                                   ------------------------------------


                                /s/ Thomas Marr
                                ---------------------------------------
                                Dr. Thomas Marr



                                /s/ Donald Fisher
                                ---------------------------------------
                                Donald Fisher



                                /s/ Steven Cozza
                                ---------------------------------------
                                Steven Cozza



                                /s/ Jacqueline Salit
                                ---------------------------------------
                                Jacqueline Salit



                                /s/ John Maroney
                                ---------------------------------------
                                John Maroney



                                /s/ James L. Rathmann
                                ---------------------------------------
                                James L. Rathmann


                                  (Continued)
<PAGE>

                                /s/ Margaret C. Rathmann
                                ---------------------------------------
                                Margaret C. Rathmann



                                /s/ Laura Jean Rathmann
                                ---------------------------------------
                                Laura Jean Rathmann



                                /s/ Sally A. Rathmann
                                ---------------------------------------
                                Sally A. Rathmann



                                /s/ Richard G. Rathmann
                                ---------------------------------------
                                Richard G. Rathmann
<PAGE>

                         SUPPLEMENTAL VOTING AGREEMENT

     AGREEMENT dated as of February 28, 1997, by and among Genomica Corporation,
a Delaware corporation (the "Company"), the persons listed as Purchasers in
Schedule I to a certain Series A Convertible Preferred Stock Purchase Agreement
of the Company dated as of the date hereof (the "Purchase Agreement")
(collectively, the "Purchasers" and individually a "Purchaser") and the persons
listed as Prior Stockholders in the signature pages hereto (the Prior
Stockholders and the Purchasers are herein defined as the "Stockholders" and
individually, as a "Stockholder").

     WHEREAS, on the date hereof, the Purchasers are purchasing from the Company
shares of its Series A Preferred Stock (the "Series A Preferred") pursuant to
the terms of the Purchase Agreement, a copy of which is attached hereto as
Exhibit A; and

     WHEREAS, the Prior Stockholders are parties to that certain Voting
Agreement dated as of March 22, 1996 (the "Prior Voting Agreement"); and

     WHEREAS, the Purchasers and the Prior Stockholders wish to make certain
provisions for the voting of their Shares (as defined below); and

     WHEREAS, the Purchasers and the Prior Stockholders wish to make certain
provisions regarding the transfer of their Shares; and

     WHEREAS, the purchases by the Purchasers will benefit the Company; and

     WHEREAS, it is a condition to the obligations of the Purchasers under the
Purchase Agreement that this Agreement be executed by the parties hereto, and
the parties are willing to execute this Agreement and to be bound by the
provisions hereof;

     NOW, THEREFORE, in consideration of the premises, the agreements set forth
below, and the parties' desire to further the interests of the Company and its
present and future stockholders, the parties agree as follows:

     1.  Definition.  As used in this Agreement, the term "Shares" means all
shares of equity securities of the Company (i) now or hereafter owned (either
beneficially or of record) by a Prior Stockholder or a Purchaser, and (ii) which
a Prior Stockholder or a Purchaser does not own (either beneficially or of
record) but as to which it now or hereafter has the right to exercise voting
control.

     2.  Designation of Nominees.  Each of ARCH Venture Fund III, L.P. ("ARCH'')
and Boulder Ventures L.P. ("Boulder") (together, the "Nominating Purchasers" and
individually, a "Nominating Purchaser"), so long as they each own 400,000 shares
of Series A Preferred, shall have the right to designate a nominee (together,
the "Nominees" and individually, a "Nominee") for election as a director of the
Company. At least 10 days prior to any meeting (or written action

                                      -1-
<PAGE>

in lieu of a meeting) of stockholders of the Company at or by which directors
are to be elected by the holders of Series A Preferred voting separately as a
series, or by all stockholders of the Company, as applicable, each Nominating
Purchaser shall notify the other parties to this Agreement in writing of the
Nominee designated by such Nominating Purchaser for election as a director. In
the absence of any such notification, it shall be presumed that the Nominating
Purchaser's then incumbent Nominee has been redesignated as its Nominee. The
initial Nominees of ARCH and Boulder are Robert Nelson and Marvin Caruthers,
respectively. Each of the Prior Stockholders hereby agrees to designate one of
the Nominees as a "Nominee" pursuant to the Prior Voting Agreement so that the
Prior Stockholders shall together select two directors, one by Falcon Technology
Partners, L.P. and one by Harris and Harris Group, Inc., and the Nominating
Purchasers shall together select two directors, one by ARCH and one by Boulder.

     3.  Election of Directors.  At each meeting (or written action in lieu of a
meeting) of stockholders of the Company at or by which directors are to be
elected by the holders of the Series A Preferred voting separately as a series,
or by all stockholders of the Company, as applicable, each party hereto shall
vote (or execute a written consent with respect to) all of its Shares to elect,
as directors of the Company, the Nominees designated in the manner provided in
Section 2.

     4.  Successor Directors.  (a) If a Nominee shall cease to serve as a
director for any reason, the Nominating Purchaser which designated such Nominee
shall have the right to designate a successor Nominee and each of the other
parties hereto shall use its best efforts (including by voting (or executing a
written consent with respect to) all Shares which it is entitled to vote) to
ensure that such successor Nominee is duly elected as a director.

          (b) If a Nominating Purchaser notifies the other parties hereto that
it desires to remove its Nominee as a director, each of the other parties hereto
shall use its best efforts (including by voting (or executing a written consent
with respect to) all Shares which it is entitled to vote) to ensure that such
Nominee is duly removed as a director.

          (c) If a Nominating Purchaser notifies the Company that it desires to
remove its Nominee as a director and/or designate a successor Nominee, then the
Company shall, at the request of such Nominating Purchaser, use its best efforts
to ensure that a meeting of stockholders of the Company, or holders of the
Series A Preferred, as applicable, is promptly called for such purpose.

     5.  Right of First Refusal.

          (a) If at any time a Stockholder desires to sell all or any part of
its Shares pursuant to a bona fide offer from a third party other than an
affiliate of such Stockholder who agrees to be bound by the terms of this
Agreement (the "Proposed Buyer"), the Stockholder shall submit a written offer
(the "Offer") to sell such remaining Shares (the "Offered Shares") to the
remaining Stockholders (the "Other Stockholders") on terms and conditions,
including price, not less favorable to the Other Stockholders than those on
which the Stockholder proposes to sell the Offered Shares to the Proposed Buyer.
The Offer shall disclose the identity of the Proposed

                                      -2-
<PAGE>

Buyer, the Offered Shares proposed to be sold, the total number of Shares then
owned by the selling Stockholder, the terms and conditions, including price, of
the proposed sale, and any other material facts relating to the proposed sale.
The Offer shall further state that each Other Stockholders may acquire, in
accordance with the provisions of this Agreement, all or any portion of their
respective pro rata share (based upon the percentage of Shares held by such
Other Stockholder bears to the total of all Shares then held by all Other
Stockholders) of Offered Shares for the price and upon the other terms and
conditions, including deferred payment (if applicable), set forth therein.

          (b) If any Other Stockholder desires to purchase all or any part of
the Offered Shares, such Other Stockholder shall communicate in writing its
election to purchase to the selling Stockholder, which communication shall state
the number of Offered Shares such Other Stockholder desires to purchase and
shall be given to the selling Stockholder and each other Other Stockholder
within ten (10) business days of the date the Offer was made. Such communication
shall, when taken in conjunction with the Offer, be deemed to constitute a
valid, legally binding and enforceable agreement for the sale and purchase of
such Offered Shares. Sales of the Offered Shares to be sold to the Other
Stockholders pursuant to this Section 5 shall be made at the offices of the
Company on the 25th day following the date the Offer was made (or if such 25th
day is not a business day, then on the next succeeding business day). Such sales
shall be effected by the selling Stockholder's delivery to the Company of a
certificate or certificates evidencing the Offered Shares to be purchased by the
Other Stockholder, duly endorsed for transfer to the Other Stockholder, against
payment to the selling Stockholder of the purchase price therefor by the Other
Stockholder.

          (c) If less than all of the Offered shares are purchased by the Other
Stockholders, then no later than the second business day after the expiration of
the 10-day period referred to in Section 3(b) above, the Company shall offer in
writing (the "Second Notice") to each Other Stockholder which offered to
purchase Offered Shares, an option to purchase its Proportionate Share (as
defined below) of the Offered Securities which were not previously elected to be
purchased. Within five (5) days after the receipt by each of the Other
Stockholders of the Second Notice or attempted delivery during working hours to
his/her/its address shown on the books of the Company (such date is referred to
as the "Second Receipt Date"), each Other Stockholder who received a Second
Notice, by delivering a written notice to the Company (the "Second Reply"), may
elect to purchase, at the price and on the terms specified in the original
Offer, its Proportionate Share of the Offered Shares. As used herein,
"Proportionate Share" equals the total number of Offered Shares not previously
elected to be purchased multiplied by a fraction, the numerator of which is the
number of shares (on a fully-diluted basis) of Common Stock (assuming that all
shares of Series A Preferred had been converted) then held by such Other
Stockholders, and the denominator of which is the sum of all shares (on a fully-
diluted basis) of Common Stock (assuming that all shares of Series A Preferred
had been converted) then held by all Other Stockholders delivering a Second
Reply.

          (d) If the Other Stockholders do not purchase all of the Offered
Shares, the Offered Shares not so purchased may be sold by the selling
Stockholder at any time within six

                                      -3-
<PAGE>

months after the date the Offer was made, subject to the provisions of this
Agreement. Any such sale shall be to the Proposed Buyer, at not less than the
price and upon other terms and conditions, if any, not more favorable to the
Proposed Buyer than those specified in the Offer. Any Offered Shares not sold
within such six-month period shall continue to be subject to the requirements of
this Section 5.

     6.  Term.  This Agreement shall continue until the earlier of, and shall
automatically terminate and be of no further force or effect at (i) such time as
no Purchaser holds more than 400,000 shares of Series A Preferred or (ii) the
tenth anniversary of the date of this Agreement; provided that no such
termination shall relieve a party from liability for prior breaches hereof.

     7.  Specific Enforcement.  Each party hereto expressly agrees that the
Purchasers, the Prior Stockholders and the Company will be irreparably damaged
if this Agreement is not specifically enforced. Upon a breach or threatened
breach of the terms, covenants and/or conditions of this Agreement by a Prior
Stockholder, a Purchaser or the Company, the Purchasers, Prior Stockholders and
the Company, as the case may be, shall, in addition to all other remedies, be
entitled to a temporary or permanent injunction, without showing any actual
damage, and/or a decree for specific performance, in accordance with the
provisions hereof.

     8.  Legend. Each certificate evidencing Shares shall bear a legend
substantially as follows:

         "The shares represented by this certificate are subject to the terms
and conditions of a certain Supplemental Voting Agreement dated as of February
28, 1997, a copy of which the Company will furnish to the holder of this
certificate upon request and without charge."

     9.  Covenant of the Company.  The Company hereby agrees that it will not
issue any of its voting securities to any person, if after giving effect to such
issuance (a) the Stockholders would have insufficient voting power to effect the
transactions contemplated by Sections 3 and 4 hereof or (b) such purchasers do
not agree to the rights of the Stockholders herein contained.

     10.  Notices.  All notices or other communications given hereunder shall be
in writing and shall be deemed effective upon delivery at the address of the
party to be notified and shall be mailed by certified or registered mail, return
receipt requested, delivered by courier, telecopied, or sent by other facsimile
method (notices by telecopy or facsimile must be confirmed by next day courier
delivery to be effective), addressed to the address specified below such party's
signature hereto or such other address as such party may subsequently notify the
other parties of in writing.

     11.  Entire Agreement and Amendments.  This Agreement constitutes the
entire agreement of the parties with respect to the subject matter hereof and
neither this Agreement nor any provision hereof may be waived, modified, amended
or terminated except by a written agreement signed by the Company, Prior
Stockholders owning at least two-thirds of the Shares owned by all Prior
Stockholders and Purchasers owning at least two thirds of the Shares owned by
all Purchasers.

                                      -4-
<PAGE>

     12.  Governing Law; Successors and Assigns.  This Agreement shall be
governed by the internal laws of the State of Delaware (without giving effect to
its conflicts of law principles) and shall bind and inure to the benefit of the
heirs, personal representatives, executors, administrators, successors, assigns
and transferees of the parties. Without limiting the generality of the
foregoing, all covenants and agreements of the Prior Stockholders and Purchasers
shall bind any and all subsequent holders of their Shares, and the Company
agrees that it shall not transfer on its records any such Shares unless (i) the
transferor Prior Stockholder or Purchaser, as the case may be, shall have first
delivered to the Company the written agreement of the transferee to be bound by
this Agreement to the same extent as if such transferee had originally been a
Prior Stockholder or Purchaser hereunder, as the case may be, and (ii) the
certificate or certificates evidencing the Shares so transferred bear the legend
specified in Section 7.

     13.  Captions.  Captions are for convenience only and are not deemed to be
part of this Agreement.

     14.  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-
<PAGE>

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

                                COMPANY:

                                GENOMICA CORPORATION

                                By:  /s/ James L. Rathmann
                                   ------------------------------------
                                   James L. Rathmann
                                   President
                                   Address:  600 Dorset Road
                                             Devon, PA 19333

                                PURCHASERS:

                                        ARCH VENTURE FUND III, L.P.

                                        By:  ARCH VENTURE PARTNERS,
                                        L.L.C., general partner


                                        By:  /s/
                                           -------------------------------------
                                                     Managing Director

                                        BOULDER VENTURES, L.P.

                                        By:  BV PARTNERS, L.L.C.


                                        By:  /s/
                                           -------------------------------------
                                           Partner

                                        PEGASUS TECHNOLOGY VENTURES, L.L.C.


                                        By:  /s/ Kenneth Collins
                                           -------------------------------------
                                           Kenneth Collins, Manager

                                        THE CARUTHERS FAMILY, L.L.C.


                                        By:  /s/ Marvin H. Caruthers
                                           -------------------------------------
                                           Marvin H. Caruthers, Manager

                                      -6-
<PAGE>

                                        PRIOR STOCKHOLDERS:

                                        FALCON TECHNOLOGY PARTNERS, L.P.

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

                                        Address:  600 Dorset Road
                                                  Devon, PA 19333


                                        HARRIS & HARRIS GROUP, INC.

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

                                        Address:  One Rockefeller Plaza
                                                  14 West 49th Street
                                                  New York, New York 10020

                                      -7-
<PAGE>

                  AMENDMENT TO SUPPLEMENTAL VOTING AGREEMENT

     This Amendment to Supplemental Voting Agreement (the "Amendment"), dated as
of June ___ , 1997, is by and among Genomica Corporation, a Delaware corporation
(the "Company"), the persons listed as Purchasers in Schedule I to that certain
Series A Convertible Preferred Stock Purchase Agreement (as amended, the
"Purchase Agreement") (individually a "Purchaser" and collectively
"Purchasers"), and the persons listed as Prior Stockholders in the signature
pages hereto.

                                   RECITALS

     A.  The Company and Purchasers have entered into that certain Amendment to
Series A Convertible Preferred Stock Purchase Agreement (the "Purchase Agreement
Amendment"), of even date herewith, pursuant to which the Purchase Agreement is
amended to make Frank Bonsal ("Bonsal") a party to the Purchase Agreement and
permit him to purchase certain shares of the Company's Series A Convertible
Preferred Stock.

     B.  As a condition to the execution and delivery of the Purchase Agreement
Amendment, the Company, Purchasers and the Prior Stockholders wish to have
Bonsal execute this Amendment so that he is bound by the terms and conditions of
the Supplemental Voting Agreement.

                                   AGREEMENT

     NOW, THEREFORE, for good and valuable consideration, the receipt and
adequacy of which is hereby acknowledged, the parties hereby amend the
Supplemental Voting Agreement as follows:

     1.  The signature page of the Supplemental Voting Agreement shall be
amended to add the following Purchaser:

         Frank Bonsal

     By execution of this Amendment, the Purchasers and the Prior Stockholders
agree that Bonsal shall become a party to the Supplemental Voting Agreement.
Except as expressly modified by this Amendment, the Supplemental Voting
Agreement shall remain in full force and effect without change.

     This Amendment may be executed in any number of counterparts, each of which
when executed and delivered shall be an original, but all of which together
shall constitute one and the same instrument.
<PAGE>

     IN WITNESS WHEREOF, the parties have executed this Amendment to be
effective as of the date first above written.

                                       GENOMICA CORPORATION, a Delaware
                                       corporation


                                       By: /s/ James Rathmann
                                          --------------------------------------
                                          James Rathmann, President

                                       FALCON TECHNOLOGY II PARTNERS, L.P.

                                       By:  FALCON TECHNOLOGY MANAGEMENT
                                       CORPORATION, general partner


                                       By: /s/ James Rathmann
                                          --------------------------------------
                                          James Rathmann, President

                                       ARCH VENTURE FUND III, L.P.

                                       By:  ARCH VENTURE PARTNERS, L.L.C.,
                                       general partner


                                       By: /s/
                                          --------------------------------------
                                          Managing Director

                                       BOULDER VENTURES, L.P.

                                       By:  BV PARTNERS, L.L.C., general partner


                                       By:  /s/ Kyle Lefkoff
                                          --------------------------------------
                                          Kyle Lefkoff, Manager


                                       PEGASUS TECHNOLOGY VENTURES, L.L.C.


                                       By:  /s/ Kenneth Collins
                                          --------------------------------------
                                          Kenneth Collins, Manager

                                       2
<PAGE>

                                          --------------------------------------
                                          Frank Bonsal

                                       THE CARUTHERS FAMILY, L.L.C.


                                       By: /s/ Marvin H. Caruthers
                                          --------------------------------------
                                          Marvin H. Caruthers, Manager


                                       PRIOR STOCKHOLDERS:

                                       FALCON TECHNOLOGY PARTNERS, L.P.


                                       By: /s/ James Rathmann
                                          --------------------------------------
                                          James Rathmann, General Partner

                                       HARRIS & HARRIS GROUP, INC.


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

                                       3
<PAGE>

               SECOND AMENDMENT TO SUPPLEMENTAL VOTING AGREEMENT

     This Second Amendment (the "Amendment"), dated as of October 6, 1997, to
the Supplemental Voting Agreement, dated as of February 28, 1997, as amended
(the "Supplemental Voting Agreement"), by and among Genomica Corporation, a
Delaware corporation (the "Company"), the persons listed as Purchasers in
Schedule I to the Series A Convertible Preferred Stock Purchase Agreement, dated
as of February 28, 1997, as amended (the "Purchase Agreement") (individually, a
"Purchaser" and collectively, the "Purchasers") and the Prior Stockholders
listed in the signature pages thereto (the "Prior Stockholders," and together
with the Purchasers, the "Stockholders"), is by and among the Company and the
Stockholders.

                                   RECITALS

     A.   The Company and the Purchasers have entered into that certain Second
Amendment to Series A Convertible Preferred Stock Purchase Agreement (the
"Purchase Agreement Amendment") of even date herewith, pursuant to which the
Purchase Agreement is being amended to make those parties listed on the Addendum
to Schedule I thereof (the "Investors") that are not already parties to the
Purchase Agreement parties to the Purchase Agreement (the "New Investors") and
to permit the Investors to purchase shares of the Company's Series A Convertible
Preferred Stock.

     B.   As a condition to the execution and delivery of the Purchase Agreement
Amendment, the Company and the Stockholders wish to (i) amend the Supplemental
Voting Agreement and (ii) have the New Investors execute this Amendment so that
they will be bound by the terms and conditions of the Supplemental Voting
Agreement.

                                   AGREEMENT

     Now, Therefore, for good and valuable consideration, the receipt and
adequacy of which is hereby acknowledged, the parties hereby amend the
Supplemental Voting Agreement as follows:

     1.   Section 2 of the Supplemental Voting Agreement is hereby amended and
restated to read in its entirety as follows:

     "2.  Designation of Nominees.  Each of Invesco Global Health Sciences Fund
          -----------------------
("Invesco"), ARCH Venture Fund III, L.P. ("ARCH") and Boulder Ventures L.P.
("Boulder") (together, the "Nominating Purchasers" and individually, a
"Nominating Purchaser") shall have the right to designate a nominee (together,
the "Nominees" and individually, a "Nominee") for election as a director of the
Company so long as the Nominating Purchaser in question owns 400,000 shares of
Series A Preferred. At least 10 days prior to any meeting (or written action in
lieu of a meeting) of stockholders of the Company at or by which directors are
to be elected by the holders of Series A Preferred voting separately as a
series, each Nominating Purchaser shall notify the other parties to this
Agreement in writing of the Nominee designated by such Nominating Purchaser for
election as a director. In the absence of any such notification, it shall be
presumed that the Nominating Purchaser's then incumbent Nominee has been
redesignated as

                                       1.
<PAGE>

its Nominee. The initial Nominees of Invesco, ARCH and Boulder are Ralph E.
Christoffersen, Robert Nelsen and Marvin Caruthers, respectively. Each of the
Prior Stockholders hereby agrees to designate one of the Nominees as a "Nominee"
pursuant to the Prior Voting Agreement and Harris & Harris Group, Inc.
("Harris") agrees that it will not have a right to nominate a director
individually, so that the Prior Stockholders shall select only one director (by
Falcon Technology Partners, L.P.), and the Nominating Purchasers shall together
select three directors, one by Invesco, one by ARCH and one by Boulder. Harris
and Invesco shall have the right to attend all meetings of the Board of
Directors in a nonvoting observer capacity, to receive notice of such meetings
at the same time and in the same manner notice is given to the members of the
Board of Directors and to receive the information provided by the Company to the
Board of Directors; provided, however, that the Company may require as a
condition precedent that the representatives of Harris and Invesco proposing to
attend any meeting of the Board of Directors and the representatives of Harris
and Invesco who will have access to any of the information provided by the
Company to the Board of Directors shall agree to hold in confidence and trust
and to act in a fiduciary manner with respect to all information so received
during such meetings or otherwise, and provided further that the failure to give
notice or to provide information to Harris or Invesco shall not affect or
nullify the actions taken by the Board of Directors."

     2.   Section 5 of the Supplemental Voting Agreement is hereby amended and
restated to read in its entirety as follows:

     "5.  Right of First Refusal.
          ----------------------

          (a)  If at any time a Stockholder desires to sell all or any part of
its Shares pursuant to a bona fide offer from a third party other than an
affiliate (which shall include a mutual fund with a common investment advisor as
a Stockholder) of such Stockholder who agrees to be bound by the terms of this
Agreement (the "Proposed Buyer"), the Stockholder shall submit a written offer
(the "Offer") to sell such Shares (the "Offered Shares") to the remaining
Stockholders (the "Other Stockholders") on terms and conditions, including
price, not less favorable to the Other Stockholders than those on which the
Stockholder proposes to sell the Offered Shares to the Proposed Buyer. The Offer
shall disclose the identity of the Proposed Buyer, the number of Offered Shares
proposed to be sold, the total number of Shares then owned by the selling
Stockholder, the terms and conditions, including price, of the proposed sale,
and any other material facts relating to the proposed sale. The Offer shall
further state that each Other Stockholder may acquire, in accordance with the
provisions of this Agreement, all or any portion of its pro rata share (based
upon the percentage of Shares held by such Other Stockholder bears to the total
of all Shares then held by all Other Stockholders) of Offered Shares for the
price and upon the other terms and conditions, including deferred payment (if
applicable), set forth therein.

          (b)  If any Other Stockholder desires to purchase all or any part of
the Offered Shares, such Other Stockholder shall communicate in writing its
election to purchase to the selling Stockholder, which communication shall state
the number of Offered Shares such Other Stockholder desires to purchase and
shall be given to the selling Stockholder and each Other Stockholder within ten
(10) business days of the date the Offer was received by such Other

                                       2.
<PAGE>

Stockholder. Such communication shall, when taken in conjunction with the Offer,
be deemed to constitute a valid, legally binding and enforceable agreement for
the sale and purchase of such Offered Shares. Sales of the Offered Shares to be
sold to the Other Stockholders pursuant to this Section 5 shall be made at the
offices of the Company on the 45th day following the date the Offer was made (or
if such 45th day is not a business day, then on the next succeeding business
day). Such sales shall be effected by the selling Stockholder's delivery to the
Company of a certificate or certificates evidencing the Offered Shares to be
purchased by the Other Stockholder, duly endorsed for transfer to the Other
Stockholder, against payment to the selling Stockholder of the purchase price
therefor by the Other Stockholder.

          (c)  If less than all of the Offered Shares are purchased by the Other
Stockholders, then no later than the second business day after the expiration of
the 10 business day period referred to in Section 3(b) above, the Company shall
offer in writing (the "Second Notice") to each Other Stockholder which offered
to purchase Offered Shares, an option to purchase its Proportionate Share (as
defined below) of the Offered Securities which were not previously elected to be
purchased. Within five (5) days after the receipt by each of the Other
Stockholders of the Second Notice or attempted delivery during working hours to
his/her/its address shown on the books of the Company (such date is referred to
as the "Second Receipt Date"), each Other Stockholder who received a Second
Notice, by delivering a written notice to the Company (the "Second Reply"), may
elect to purchase, at the price and on the terms specified in the original
Offer, up to its Proportionate Share of the Offered Shares. As used herein,
"Proportionate Share" equals the total number of Offered Shares not previously
elected to be purchased multiplied by a fraction, the numerator of which is the
number of shares (on a fully-diluted basis) of Common Stock (assuming that all
shares of Series A Preferred had been converted) then held by such Other
Stockholder, and the denominator of which is the sum of all shares (on a fully-
diluted basis) of Common Stock (assuming that all shares of Series A Preferred
had been converted) then held by all Other Stockholders delivering a Second
Reply.

          (d)  If the Other Stockholders do not purchase all of the Offered
Shares, the Offered Shares not so purchased may be sold by the selling
Stockholder at any time within three months after the date the Offer was made,
subject to the provisions of this Agreement. Any such sale shall be to the
Proposed Buyer, at not less than the price and upon other terms and conditions,
if any, not more favorable to the Proposed Buyer than those specified in the
Offer. Any Offered Shares not sold within such three-month period shall continue
to be subject to the requirements of this Section 5."

     3.   Section 6 of the Supplemental Voting Agreement is hereby amended and
restated to read in its entirety as follows:

     "6.  Term. This Agreement shall continue until the earlier of, and shall
          ----
automatically terminate and be of no further force or effect at (i) such time as
no Purchaser holds more than 400,000 shares of Series A Preferred; (ii) the
tenth anniversary of the date of this Agreement; or (iii) the completion of a
firmly underwritten public offering of the Company's Common Stock at a price of
at least $2.50 per share and which raises at least $5,000,000 of gross proceeds
to the

                                       3.
<PAGE>

Company; provided that no such termination shall relieve a party from liability
for prior breaches hereof."

     4.   The signature pages to the Supplemental Voting Agreement shall be
amended to add the following New Investor:

               Invesco Global Health Sciences Fund

     By execution of this Amendment, the Stockholders and the New Investor agree
that the New Investor shall become a party to the Supplemental Voting Agreement.
Except as expressly modified by this Amendment, the Supplemental Voting
Agreement shall remain in full force and effect without change.

     This Amendment may be executed in any number of counterparts, each of which
when executed and delivered shall be an original, but all of which together
shall constitute one and same instrument.

                 [REMAINDER OF PAGE INTENTIONALLY LEFT BLANK]

                                       4.
<PAGE>

     In Witness Whereof, the parties have executed this Amendment to be
effective as of the date first above written.

                                   Genomica Corporation, a Delaware corporation


                                   By: /s/ Thomas G. Marr,
                                       ___________________________________
                                       Dr. Thomas G. Marr, President


                                   Stockholders:

                                   Falcon Technology II Partners, L.P.

                                   By: Falcon Technology Management Corporation,
                                       general partner


                                   By: /s/ James Rathmann
                                       ___________________________________
                                       James Rathmann, President


                                   Arch Venture Fund III, L.P.


                                   By: Arch Venture Partners, L.L.C., general
                                       partner


                                   By: /s/ Robert Nelsen
                                       ___________________________________
                                       Managing Director


                                   Boulder Ventures, L.P.


                                   By: BV Partners, L.L.C., general partner


                                   By: /s/ Kyle Lefkoff
                                       ___________________________________
                                       Kyle Lefkoff, Manager


                                   Pegasus Technology Ventures, L.L.C.


                                   By: /s/ Kenneth Collins
                                       ___________________________________
                                       Kenneth Collins, Manager

                  AMENDMENT TO SUPPLEMENTAL VOTING AGREEMENT
<PAGE>

                                        The Caruthers Family, L.L.C.


                                        By: /s/ Marvin H. Caruthers
                                            _________________________________
                                            Marvin H. Caruthers, Manager


                                        Frank Bonsal


                                        _____________________________________
                                        Frank Bonsal


                                        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.,
                                            Executive Vice President


                                        New Investor:


                                        Invesco Global Health Sciences Fund


                                        By: /s/ Ronald L. Grooms
                                            _________________________________

                                        Name:   Treasurer
                                              _______________________________

                                        Title:  Ronald L. Grooms
                                               ______________________________

                                        New Investor:


                                        Invesco Global Health Sciences Fund


                                        By: /s/ Glen A. Payne
                                            _________________________________

                                        Name:   Glen A. Payne
                                              _______________________________

                                        Title:  Secretary
                                               ______________________________

                  AMENDMENT TO SUPPLEMENTAL VOTING AGREEMENT
<PAGE>

               THIRD AMENDMENT TO SUPPLEMENTAL VOTING AGREEMENT

     This Third Amendment (the "Amendment"), dated as of October 20, 1997, to
the Supplemental Voting Agreement, dated as of February 28, 1997, as amended
(the "Supplemental Voting Agreement"), by and among Genomica Corporation, a
Delaware corporation (the "Company"), the persons listed as Purchasers in
Schedule I to the Series A Convertible Preferred Stock Purchase Agreement, dated
as of February 28, 1997, as amended (the "Purchase Agreement") (individually, a
"Purchaser" and collectively, the "Purchasers") and the Prior Stockholders
listed in the signature pages thereto (the "Prior Stockholders," and together
with the Purchasers, the "Stockholders"), is by and among the Company and the
Stockholders.

                                   RECITALS

     A.   The Purchase Agreement is being amended to make the party listed on
the Addendum to Schedule I thereof, which is attached hereto (the "New
Investor"), a party to the Purchase Agreement and to permit the New Investor to
purchase shares of the Company's Series A Convertible Preferred Stock.

     B.   In connection with the purchase of shares of the Company's Series A
Convertible Preferred Stock by the New Investor, the Company and the
Stockholders wish to have the New Investor execute this Amendment so that the
New Investor will be bound by the terms and conditions of the Supplemental
Voting Agreement.

                                   AGREEMENT

     Now, Therefore, for good and valuable consideration, the receipt and
adequacy of which is hereby acknowledged, the parties hereby amend the
Supplemental Voting Agreement as follows:

     The signature pages to the Supplemental Voting Agreement shall be amended
to add the following New Investor:

               David B. Musket SEP IRA

     By execution of this Amendment, the Stockholders and the New Investor agree
that the New Investor shall become a party to the Supplemental Voting Agreement.
Except as expressly modified by this Amendment, the Supplemental Voting
Agreement shall remain in full force and effect without change.

     This Amendment may be executed in any number of counterparts, each of which
when executed and delivered shall be an original, but all of which together
shall constitute one and same instrument.

                 [REMAINDER OF PAGE INTENTIONALLY LEFT BLANK]

                                      1.
<PAGE>

     In Witness Whereof, the parties have executed this Amendment to be
effective as of the date first above written.

                                   Genomica Corporation, a Delaware corporation


                                   By: /s/ Thomas G. Marr
                                       ----------------------------------------
                                       Dr. Thomas G. Marr, President


                                   Stockholders:

                                   Falcon Technology II Partners, L.P.


                                   By: Falcon Technology Management Corporation,
                                       general partner


                                   By: /s/ James Rathmann
                                       ----------------------------------------
                                       James Rathmann, President


                                   Arch Venture Fund III, L.P.


                                   By: Arch Venture Partners, L.L.C., general
                                       partner


                                   By: /s/ Robert Nelsen
                                       ----------------------------------------
                                       Managing Director


                                   Boulder Ventures, L.P.


                                   By: BV Partners, L.L.C., general partner


                                   By: ________________________________________
                                       Kyle Lefkoff, Manager


                                   Pegasus Technology Ventures, L.L.C.


                                   By: /s/ Kenneth Collins
                                       ----------------------------------------
                                       Kenneth Collins, Manager

               THIRD AMENDMENT TO SUPPLEMENTAL VOTING AGREEMENT

<PAGE>

                                   The Caruthers Family, L.L.C.


                                   By: ________________________________________
                                       Marvin H. Caruthers, Manager


                                   Frank Bonsal


                                   ____________________________________________
                                   Frank Bonsal


                                   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.,
                                       Executive Vice President


                                   Invesco Global Health Sciences Fund


                                   By: /s/ Glen A. Payne
                                       ----------------------------------------

                                   Name:   Glen A. Payne
                                         --------------------------------------

                                   Title:  Secretary
                                          -------------------------------------


                                   New Investor:

                                   David B. Musket SEP IRA


                                   By: /s/ David B. Musket
                                       ----------------------------------------

                                   Name:   David B. Musket
                                         --------------------------------------

                                   Title:
                                          -------------------------------------

                  AMENDMENT TO SUPPLEMENTAL VOTING AGREEMENT