<PAGE>   1
                                                                   Exhibit 10.37





                               SECURITY AGREEMENT
                                      AMONG
                                BIO-PLEXUS, INC.,
                                   as Obligor

                                       and

             APPALOOSA INVESTMENT LIMITED PARTNERSHIP I, L.P.,
                                    as Holder



                          Dated as of October 21, 1999
<PAGE>   2
                                TABLE OF CONTENTS
                             -----------------



<TABLE>
<S>                                                                          <C>
Article I.  Definitions and Interpretation.............................        1

   1.01  Certain Defined Terms.........................................        1

   1.02  Interpretation................................................        3

Article II.  Collateral................................................        3

   2.01  Grant of First Priority Security Interest.....................        3

   2.02  Reserved......................................................        5

   2.03  Intellectual Property.........................................        5

   2.04  Perfection....................................................        6

   2.05  Preservation and Protection of Security Interests.............        6

   2.06  Reserved......................................................        7

   2.07  Special Provisions Relating to Securities Collateral..........        7

   2.08  Use of Intellectual Property..................................        8

   2.09  Instruments...................................................        8

   2.10  Use of Collateral.............................................        8

   2.11  Rights and Obligations........................................        8

   2.12  Release of Motor Vehicles.....................................        9
</TABLE>
<PAGE>   3

<TABLE>
<S>                                                                          <C>
   2.13  Termination..................................................         9

Article III.  Cash Proceeds of Collateral.............................         9

   3.01  Collateral Account...........................................         9

   3.02  Certain Proceeds.............................................        10

   3.03  Investment of Balance in Collateral Account..................        10

Article IV.  Representations and Warranties...........................        10

   4.01  Title........................................................        10

   4.02  Intellectual Property........................................        11

   4.03  Goods........................................................        11

Article V.  Covenants.................................................        11

   5.01  Books and Records............................................        11

   5.02  Removals, Etc................................................        11

   5.03  Stock Collateral.............................................        11

   5.04  Intellectual Property........................................        12

Article VI.  Remedies.................................................        13

   6.01  Events of Default, Etc.......................................        13

   6.02  Deficiency...................................................        14

   6.03  Private Sale.................................................        14

   6.04  Application of Proceeds......................................        15

Article VII.  Miscellaneous...........................................        15

   7.01  Waiver.......................................................        15

   7.02  Notices......................................................        16

   7.03  Expenses, Etc................................................        16

   7.04  Amendments...................................................        16

   7.05  Successors and Assigns.......................................        17

   7.06  Survival.....................................................        17

   7.07  Agreements Superseded........................................        17

   7.08  Severability.................................................        17

   7.09  Captions.....................................................        17

   7.10  Counterparts.................................................        17

   7.11  GOVERNING LAW................................................        17

   7.12  Submission to Jurisdiction...................................        17

   7.13. Service of Process...........................................        18
   7.14. WAIVER OF JURY TRIAL.........................................        18
</TABLE>
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Annex I -      Schedule of Pledged Debt
Annex II -     Jurisdictions for Filing of Financing Statements
Annex III -    Business Locations
<PAGE>   5
                               SECURITY AGREEMENT


     This SECURITY AGREEMENT (this "Agreement") dated as of October 21, 1999, is
made by and among BIO-PLEXUS, INC., a Connecticut corporation (the "Obligor"),
and APPALOOSA INVESTMENT LIMITED PARTNERSHIP I, L.P. (the "Holder").

     WHEREAS, pursuant to the 7.5% Secured Note, dated as of the date hereof (as
amended, supplemented, restated or otherwise modified from time to time, the
"Note"), the Company is borrowing $3.0 million from the Obligor;

     WHEREAS, as a condition, and material inducement, to the Holder's agreement
to loan the Obligor the money under the Note, the Holder required that the
Obligor deliver this Agreement to the Holder;

     NOW, THEREFORE, in consideration of the premises and mutual covenants
herein contained and for other good and valuable consideration, the receipt and
sufficiency of which are hereby acknowledged, the Obligor agrees with the Holder
as follows:

Article I.  Definitions and Interpretation.

     1.01 Certain Defined Terms. Unless otherwise defined, all capitalized terms
used in this Agreement that are defined in the Note (including those terms
incorporated therein by reference) shall have the respective meanings assigned
to them in the Note. In addition, the following terms shall have the following
meanings under this Agreement:

     "Accounts" shall have the meaning assigned to that term in Section
2.01(b).

     "Additional Debt" shall have the meaning assigned to that term in Section
2.01(a).

     "Additional Shares" shall have the meaning assigned to that term in Section
5.03.

     "Casualty Event" shall mean, with respect to any property of any Person,
any loss of or damage to, or any condemnation or other taking of, such property
for which such Person or any of its Subsidiaries receives insurance proceeds, or
proceeds of a condemnation award or other compensation.

     "Collateral" shall have the meaning assigned to that term in Section
<PAGE>   6
2.01.

     "Collateral Account" shall have the meaning assigned to that term in
Section 3.01.

     "Copyright Collateral" shall mean all Copyrights, whether now owned or
hereafter acquired by the Obligor.

     "Copyrights" shall mean, collectively, (a) all copyrightable works, all
copyrights, and all registrations, applications and renewals and extensions in
connection therewith and (b) all rights, now existing or hereafter coming into
existence, (i) to all income, royalties, damages and other payments (including
in respect of all past, present or future infringements) now or hereafter due or
payable under or with respect to any of the foregoing, (ii) to sue for all past,
present and future infringements with respect to any of the foregoing and (iii)
otherwise accruing under or pertaining to any of the foregoing throughout the
world.

     "Documents" shall have the meaning assigned to that term in Section
2.01(f).

     "Equipment" shall have the meaning assigned to that term in Section
2.01(e).

     "Equity Rights" shall mean, with respect to any Person, any outstanding
subscriptions, options, warrants, commitments, preemptive rights or agreements
of any kind (including any stockholders' or voting trust agreements) for the
issuance, sale, registration or voting of, or outstanding securities convertible
into, any additional shares of capital stock of any class, or partnership or
other ownership interests of any type in, such Person.

     "Holder" shall have the meaning assigned to that term in the preamble.

     "Instruments" shall have the meaning assigned to that term in Section
2.01(c).

     "Inventory" shall have the meaning assigned to that term in Section
2.01(d).

     "Issuers" shall mean, collectively, each Subsidiary, directly or
indirectly, of the Obligor that is the issuer (as defined in the Uniform
Commercial Code) of any shares of capital stock now owned or hereafter acquired
by the Obligor.

     "Loan Documents" shall mean the Note and this Agreement.

     "Motor Vehicles" shall mean motor vehicles, tractors, trailers and other
like property, whether or not the title to any such property is governed by a
certificate of title or ownership.

     "Patent Collateral" shall mean all Patents, whether now owned or hereafter
acquired by the Obligor.

     "Person" shall mean any individual, firm, corporation, limited liability
company, partnership, company or other entity, and shall
<PAGE>   7
include any successor (by merger or otherwise) of such entity.

     "Pledged Debt" shall have the meaning assigned to that term in Section
2.01(a).

     "Pledged Stock" shall have the meaning assigned to that term in Section
2.01(a).

     "Securities Collateral" means the Stock Collateral and the Pledged
Debt.

     "Signing Date" shall mean the date on which the Obligor shall sign and
deliver this Agreement.

     "Stock Collateral" shall have the meaning assigned to that term in Section
2.01(a).

     "Trademark Collateral" shall mean all Trademarks, whether now owned or
hereafter acquired by the Obligor. Notwithstanding the foregoing, the Trademark
Collateral shall not include any Trademark which would be rendered invalid,
abandoned, void or unenforceable by reason of its being included as part of the
Trademark Collateral.

     "Trademarks" shall mean, collectively, (a) all trade names, trademarks,
service marks, logos, trade dress, domain names, and corporate names, together
with all translations, adaptations, decorations, and combinations thereof and
including all goodwill associated therewith and all registrations and
applications in connection with any of the foregoing, (b) all renewals and
extensions of any of the foregoing and (c) all rights, now existing or hereafter
coming into existence, (i) to all income, royalties, damages and other payments
(including in respect of all past, present and future infringements) now or
hereafter due or payable under or with respect to any of the foregoing, (ii) to
sue for all past, present and future infringements with respect to any of the
foregoing and (iii) otherwise accruing under or pertaining to any of the
foregoing throughout the world, together, in each case, with the product lines
and goodwill of the business connected with the use of, or otherwise symbolized
by, each of the foregoing.

     "Uniform Commercial Code" shall mean the Uniform Commercial Code as in
effect in the State of New York from time to time or, by reason of mandatory
application, any other applicable jurisdiction.

     1.02 Interpretation. In this Agreement, unless otherwise indicated, the
singular includes the plural and plural the singular; words importing either
gender include the other gender; references to statutes or regulations are to be
construed as including all statutory or regulatory provisions consolidating,
amending or replacing the statute or regulation referred to; references to
"writing" include printing, typing,
<PAGE>   8
lithography and other means of reproducing words in a tangible visible form; the
words "including," "includes" and "include" shall be deemed to be followed by
the words "without limitation"; references to articles, sections (or
subdivisions of sections), exhibits, annexes or schedules are to this Agreement;
references to agreements and other contractual instruments shall be deemed to
include all subsequent amendments, extensions and other modifications to such
instruments (without, however, limiting any prohibition on any such amendments,
extensions and other modifications by the terms of any Loan Document); and
references to Persons include their respective permitted successors and assigns
and, in the case of governmental Persons, Persons succeeding to their respective
functions and capacities.

Article II.  Collateral.

     2.01 Grant of First Priority Security Interest. As collateral security for
the prompt payment in full when due (whether at stated maturity, by acceleration
or otherwise) and performance of the Secured Obligations and obligations of
every kind and nature of the Obligor now or hereafter incurred, existing or
created, to the Holder (including, without limitation, under the Convertible
Note Purchase Agreement), the Obligor hereby pledges and grants to the Holder a
first priority security interest in all of the Obligor's right, title and
interest in and to the following property, whether now owned or hereafter
acquired by the Obligor and whether now existing or hereafter coming into
existence including, without limitation, all real and personal property and
interests in real and personal property (collectively, the "Collateral"):

          (a)(i) all of the shares of capital stock of the Issuers now owned or
hereafter acquired by the Obligor together with in each case the certificates
representing the same (collectively, the "Pledged Stock"); (ii) all shares,
securities, moneys or property representing a dividend on, or a distribution or
return of capital in respect of, any of the Pledged Stock, resulting from a
split-up, revision, reclassification or other like change of any of the Pledged
Stock or otherwise received in exchange for any of the Pledged Stock and all
Equity Rights issued to the holders of, or otherwise in respect of, any of the
Pledged Stock; and (iii) without affecting the obligations of the Obligor under
any provision prohibiting such action under any Loan Document, in the event of
any consolidation or merger in which any Issuer is not the surviving
corporation, all shares of each class of the capital stock of the successor
corporation (unless such successor corporation is the Obligor itself) formed by
or resulting from such consolidation or merger (collectively, and together with
the property described in clauses (i) and (ii) above, the "Stock Collateral");
(iv) the Indebtedness described in Annex I and issued by the obligors named
<PAGE>   9
therein (the "Pledged Debt"); (v) all additional Indebtedness for money borrowed
or for the deferred purchase price of property from time to time owed to the
Obligor by any Person, "Additional Debt"); (vi) all notes or other instruments
evidencing the Indebtedness referred to in clauses (iv) and (v) above;

          (b) all accounts and general intangibles (each as defined in the
Uniform Commercial Code) of the Obligor constituting a right to the payment of
money, whether or not earned by performance, including, without limitation, (i)
in payments due and to become due to the Obligor under the Development and
License Agreement, dated as of January 28, 1997, between Johnson & Johnson
Medical, Inc. and the Company, as such agreement may be amended from time to
time (the "Development and License Agreement"), (ii) in payments due and to
become due to the Obligor under any existing or future licensing, supply,
development, or similar agreements, (iii) in repayment of any loans or advances
(including loans and advances to Subsidiaries of the Obligor), (iv) in payment
for goods (including Inventory and Equipment) sold or leased or for services
rendered and (v) in payment of tax refunds and in payment of any guarantee of
any of the foregoing (collectively, the "Accounts");

          (c) all instruments, chattel paper or letters of credit (each as
defined in the Uniform Commercial Code) of the Obligor evidencing, representing,
arising from or existing in respect of, relating to, securing or otherwise
supporting the payment of, any of the Accounts (collectively, the
"Instruments");

          (d) all inventory (as defined in the Uniform Commercial Code) and all
other goods (including Motor Vehicles) of the Obligor that are held by the
Obligor for sale, lease or furnishing under a contract of service (including to
its Subsidiaries or Affiliates), that are so leased or furnished or that
constitute raw materials, work in process or material used or consumed in its
business, including all spare parts and related supplies, all goods obtained by
the Obligor in exchange for any such goods, all products made or processed from
any such goods and all substances, if any, commingled with or added to any such
goods (collectively, the "Inventory");

          (e) all equipment (as defined in the Uniform Commercial Code) and all
other goods (including Motor Vehicles) of the Obligor that are used or bought
for use primarily in its business, including all spare parts and related
supplies, all goods obtained by the Obligor in exchange for any such goods, all
substances, if any, commingled with or added to such goods and all upgrades and
other improvements to such goods, in each case to the
<PAGE>   10
extent not constituting Inventory (collectively, the "Equipment");

          (f) all documents of title (as defined in the Uniform Commercial Code)
or other receipts of the Obligor covering, evidencing or representing Inventory
or Equipment (collectively, the "Documents");

          (g) all contracts and other agreements of the Obligor relating to the
sale or other disposition of all or any part of the Inventory, Equipment or
Documents and all rights, warranties, claims and benefits of the Obligor against
any Person arising out of, relating to or in connection with all or any part of
the Inventory, Equipment or Documents of the Obligor, including any such rights,
warranties, claims or benefits against any Person storing or transporting any
such Inventory or Equipment or issuing any such Documents;

          (h) all other accounts or general intangibles of the Obligor not
constituting Accounts, including, to the extent related to all or any part of
the other Collateral, all books, correspondence, credit files, records,
invoices, tapes, cards, computer runs and other papers and documents in the
possession or under the control of the Obligor or any computer bureau or service
company from time to time acting for the Obligor;

          (i) the balance from time to time in the Collateral Account;

          (j) all other tangible and intangible property of the Obligor,
including all Intellectual Property (provided, however, that with respect to
Patents jointly developed by the Obligor and Johnson & Johnson Medical, Inc.
under the Development and License Agreement, only to the extent consented to by
Johnson & Johnson Medical, Inc.); and

          (k) all proceeds and products in whatever form of all or any part of
the other Collateral, including all proceeds of insurance and all condemnation
awards and all other compensation for any Casualty Event with respect to all or
any part of the other Collateral (together with all rights to recover and
proceed with respect to the same), and all accessories to, substitutions for and
replacements of all or any part of the other Collateral.

     2.02 Reserved

     2.03 Intellectual Property. For the purpose of enabling the Holder to
exercise its rights, remedies, powers and privileges under Article VI at such
time or times as the Holder shall be lawfully entitled to exercise such rights,
remedies, powers and privileges, and for no other purpose, the Obligor hereby
grants to the Holder, the right to immediately, without demand of performance
and without additional notice, or demand whatsoever to the Obligor, sell at
public or private sale or otherwise realize
<PAGE>   11
upon, all right, title, and interest in all or any of the Intellectual Property
and any associated good will, as the case may be, or any interest that the
Obligor may have therein, and after deducting all expenses (including all
reasonable expenses for brokers' fees and legal services) from the proceeds of
such sale or other disposition of the Intellectual Property and any associated
good will, as the case may be, the Holder shall apply the residue of such
proceeds toward the payment of all liabilities.

     2.04 Perfection. Concurrently with the execution and delivery of this
Agreement, the Obligor shall (i) file such financing statements and other
documents in such offices as shall be necessary or as the Holder may request to
perfect and establish a first priority of the Liens granted by this Agreement
(including promptly filing the Trademark Collateral Security Agreement and
Patent Collateral Security Agreement, in the form executed on the date hereof by
the Obligor, in the United States Patent and Trademark Office) (subject only to
such Permitted Liens), (ii) deliver and pledge to the Holder any and all
Instruments, endorsed or accompanied by such instruments of assignment and
transfer in such form and substance as the Holder may request, (iii) cause the
Holder to be listed as the lienholder on all certificates of title or ownership
relating to Motor Vehicles owned by the Obligor and deliver to the Holder
originals of all such certificates of title or ownership for the Motor Vehicles
together with the odometer statements for each respective Motor Vehicle, (iv)
deliver and pledge to the Holder all certificates for the Pledged Stock and
notes, instruments or other documents evidencing the Pledged Debt, accompanied
by undated stock or bond powers, as the case may be, duly executed in blank and
(v) take all such other actions as shall be necessary or as the Holder may
request to perfect and establish a first priority of the Liens granted by this
Agreement (subject only to such Permitted Liens). The Holder shall have the
right, at any time in its discretion and with notice to the Obligor, to transfer
to or to register in its name or in the name of any of its nominees any or all
of the Pledged Stock or Pledged Debt.

     2.05 Preservation and Protection of Security Interests. The Obligor
shall:

          (a) upon the acquisition after the Signing Date by the Obligor of any
Securities Collateral, promptly either (x) transfer and deliver to the Holder
all such Securities Collateral (together with the certificates or instruments
representing such Securities Collateral securities duly endorsed in blank or
accompanied by undated powers duly executed in blank) or (y) take such other
action as the Holder shall deem necessary or appropriate to perfect, and
establish the priority of, the Liens granted
<PAGE>   12
by this Agreement in such Securities Collateral;

          (b) upon the acquisition after the Signing Date by the Obligor of any
Instrument, promptly deliver and pledge to the Holder all such Instruments,
endorsed or accompanied by such instruments of assignment and transfer in such
form and substance as the Holder may request;

          (c) upon the acquisition after the Signing Date by the Obligor of any
Equipment or Motor Vehicle covered by a certificate of title or ownership,
promptly cause the Holder to be listed as the lienholder on such certificate of
title and within 45 days of the acquisition of such property deliver evidence of
the same to the Holder;

          (d) upon the Obligor's acquiring, or otherwise becoming entitled to
the benefits of, any Copyright (or copyrightable material), Patent (or
patentable invention), Trademark (or associated goodwill) or other Intellectual
Property or upon or prior to the Obligor's filing, either directly or through
any agent, licensee or other designee, of any application with any governmental
Person for any Copyright, Patent, Trademark, or other Intellectual Property, in
each case after the Signing Date, execute and deliver such contracts, agreements
and other instruments as the Holder may request to evidence, validate, perfect
and establish the first priority (subject only to Liens permitted under Section
6.7 of the Note Purchase Agreement) of the Liens granted by this Agreement in
such and any related Intellectual Property; and

          (e) give, execute, deliver, file or record any and all financing
statements, notices, contracts, agreements or other instruments, obtain any and
all governmental approvals and take any and all steps that may be necessary or
as the Holder may request to create, perfect a first priority of the Liens
granted by this Agreement or to preserve the validity, perfection with regard to
such first priority or to enable the Holder to exercise and enforce its rights,
remedies, powers and privileges under this Agreement with respect to such Liens,
including causing any or all of the Securities Collateral to be transferred of
record into the name of the Holder or its nominee (and the Holder agrees that if
any Securities Collateral is transferred into its name or the name of its
nominee, the Holder will thereafter promptly give to the Obligor copies of any
notices and communications received by it with respect to the Stock Collateral
pledged by the Obligor), provided that notices to account debtors in respect of
any Accounts or Instruments shall be subject to the provisions of Section
3.02(b).

     2.06 Reserved
<PAGE>   13
     2.07 Special Provisions Relating to Securities Collateral. (a) So long as
no Event of Default shall have occurred and be continuing, the Obligor shall
have the right to exercise all voting, consensual and other powers of ownership
pertaining to the Securities Collateral for all purposes not inconsistent with
the terms of any Loan Document, provided that the Obligor agrees that it will
not vote the Securities Collateral in any manner that is inconsistent with the
terms of any Loan Document; and the Holder shall, at the Obligor' expense,
execute and deliver to the Obligor or cause to be executed and delivered to the
Obligor all such proxies, powers of attorney, dividends and other orders and
other instruments, without recourse, as the Obligor may reasonably request for
the purpose of enabling the Obligor to exercise the rights and powers which it
is entitled to exercise pursuant to this Section 2.07(a).

          (b) So long as no Event of Default shall have occurred and be
continuing, the Obligor shall be entitled to receive and retain any dividends or
distributions on the Securities Collateral paid in cash.

          (c) If any Event of Default shall have occurred and be continuing, and
whether or not the Holders or the Holder exercise any available right to declare
any Secured Obligation due and payable or seek or pursue any other right,
remedy, power or privilege available to them under applicable law, this
Agreement or any other Loan Document, all dividends and other distributions on
the Securities Collateral shall be paid directly to the Holder and retained by
it in the Collateral Account as part of the Securities Collateral, subject to
the terms of this Agreement, and, if the Holder shall so request, the Obligor
agrees to execute and deliver to the Holder appropriate additional dividend,
distribution and other orders and instruments to that end, provided that if such
Event of Default is cured, any such dividend or distribution paid to the Holder
prior to such cure shall, upon request of the Obligor (except to the extent
applied to the Secured Obligations), be returned by the Holder to the Obligor.

     2.08 Use of Intellectual Property. Subject to such action not otherwise
constituting a Default and so long as no Event of Default shall have occurred
and be continuing, the Obligor will be permitted to exploit, use, enjoy,
protect, license, sublicense, assign, sell, dispose of or take other actions
with respect to the Intellectual Property in the ordinary course of the business
of the Obligor subject to the rights of the Holder, whose rights shall not be
subordinated, impaired or diminished. In furtherance of the foregoing, so long
as no Event of Default shall have occurred and be continuing, the Holder shall
from time to time, upon the request of the Obligor, execute and deliver any
instruments, certificates or other documents, in the form so requested, which
the Obligor shall
<PAGE>   14
have certified are appropriate (in its reasonable judgment) to allow it to take
any action permitted above. The exercise of rights, remedies, powers and
privileges under Article VI by the Holder shall not terminate the rights of the
holders of any licenses or sublicenses theretofore granted by the Obligor in
accordance with the first sentence of this Section 2.08.

     2.09 Instruments. So long as no Default or Event of Default shall have
occurred and be continuing, the Obligor may retain for collection in the
ordinary course of business any Instruments obtained by it in the ordinary
course of business, and the Holder shall, promptly upon the request, and at the
expense of the Obligor, make appropriate arrangements for making any Instruments
pledged by the Obligor available to the Obligor for purposes of presentation,
collection or renewal. Any such arrangement shall be effected, to the extent
deemed appropriate by the Holder, against trust receipt or like document.

     2.10 Use of Collateral. So long as no Event of Default shall have occurred
and be continuing, the Obligor shall, in addition to its rights under Sections
2.07, 2.08 and 2.09 hereof and Section 6.18 of the Note Purchase Agreement, in
respect of the Collateral contemplated in those sections, be entitled to use and
possess the other Collateral and to exercise its rights, title and interest in
all contracts, agreements, licenses and governmental approvals, subject to the
rights, remedies, powers and privileges of the Holder under Articles III and VI
and to such use, possession or exercise not otherwise constituting a Default.

     2.11 Rights and Obligations. (a) The Obligor shall remain liable to perform
its duties and obligations under the contracts and agreements included in the
Collateral in accordance with their respective terms to the same extent as if
this Agreement had not been executed and delivered. The exercise by the Holder
of any right, remedy, power or privilege in respect of this Agreement shall not
release the Obligor from any of its duties and obligations under such contracts
and agreements and the Obligor shall save, indemnify and keep the Holder
harmless from and against all expense, loss or damage suffered by reason of such
exercise. The Holder shall have no duty, obligation or liability under such
contracts and agreements or with respect to any governmental approval included
in the Collateral by reason of this Agreement or any other Loan Document, nor
shall the Holder be obligated to perform any of the duties or obligations of the
Obligor under any such contract or agreement or any such governmental approval
or to take any action to collect or enforce any claim (for payment) under any
such contract or agreement or governmental approval.

          (b) No Lien granted by this Agreement in the Obligor's right, title
and interest in any contract, agreement or governmental approval shall be deemed
to be a consent by the Holder to any such contract, agreement or governmental
approval.
<PAGE>   15
          (c) No reference in this Agreement to proceeds or to the sale or other
disposition of Collateral shall authorize the Obligor to sell or otherwise
dispose of any Collateral except to the extent otherwise expressly permitted by
the terms of any Loan Document.

          (d) The Holder shall not be required to take steps necessary to
preserve any rights against prior parties to any part of the Collateral.

     2.12 Release of Motor Vehicles. So long as no Default shall have occurred
and be continuing, upon the request of, and at the expense of, the Obligor, the
Holder shall execute and deliver to the Obligor such instruments as the Obligor
shall reasonably request to remove the notation of the Holder as lienholder on
any certificate of title for any Motor Vehicle; provided that any such
instruments shall be delivered, and the release shall be effective, only upon
receipt by the Holder of a certificate from the Obligor stating that the Motor
Vehicle the Lien on which is to be released is to be sold or has suffered a
casualty loss (with title passing to the appropriate casualty insurance company
in settlement of the claim for such loss).

     2.13 Termination. When all Secured Obligations shall have been indefeasibly
paid in full, this Agreement shall terminate, and the Holder shall, at the
expense of the Obligor, forthwith cause to be assigned, transferred and
delivered, against receipt but without any recourse, warranty or representation
whatsoever, any remaining Collateral and money received in respect of the
Collateral, to or on the order of the Obligor and to be released, canceled and
granted back all licenses and rights referred to in Section 2.03. The Holder
shall also, at the expense of the Obligor, execute and deliver to the Obligor
upon such termination such Uniform Commercial Code termination statements,
certificates for terminating the Liens on the Motor Vehicles and such other
documentation as shall be reasonably requested by the Obligor to effect the
termination and release of the Liens granted by this Agreement on the
Collateral.

Article III.  Cash Proceeds of Collateral.

     3.01 Collateral Account. There is hereby established with the Holder a cash
collateral account (the "Collateral Account") in the name and under the
exclusive domain and control of the Holder into which there shall be deposited
from time to time the cash proceeds of any of the Collateral (including proceeds
resulting from insurance or condemnation) required to be delivered to the Holder
pursuant to this Agreement and into which the Obligor may from time to time
deposit any additional amounts which it wishes to pledge to the Holder as
additional collateral security under this Agreement. The balance from time to
time in the Collateral Account shall constitute part of the Collateral and shall
not constitute payment of the Secured Obligations until applied as provided in
this Agreement. If any Event of Default shall have occurred and be continuing,
the Holder may in
<PAGE>   16
its discretion apply (subject to collection) the balance from time to time
outstanding to the credit of the Collateral Account to the payment of the
Secured Obligations in the manner specified in Article VI. The balance from time
to time in the Collateral Account shall be subject to withdrawal only as
provided in this Agreement.

     3.02 Certain Proceeds. (a) If any Default or Event of Default shall have
occurred and be continuing, the Obligor shall, upon request of the Holder,
promptly notify (and the Obligor hereby authorizes the Holder so to notify) each
account debtor in respect of any Accounts or Instruments that such Collateral
has been assigned to the Holder under this Agreement and that any payments due
or to become due in respect of such Collateral are to be made directly to the
Holder. All such payments made to the Holder shall be immediately deposited in
the Collateral Account.

          (b) The Obligor agrees that if the proceeds of any Collateral
(including payments made in respect of Accounts and Instruments) shall be
received by it following the occurrence and during the continuation of a
Default, the Obligor shall as promptly as possible deposit such proceeds into
the Collateral Account. Until so deposited, all such proceeds shall be held in
trust by the Obligor for and as the property of the Holder and shall not be
commingled with any other funds or property of the Obligor.

     3.03 Investment of Balance in Collateral Account. Amounts on deposit in the
Collateral Account shall be invested from time to time in such Permitted
Investments as the Obligor (or, if any Default or Event of Default shall have
occurred and be continuing, the Holder) shall determine. All such investments
shall be held in the name and be under the control of the Holder. At any time
after the occurrence and during the continuance of an Event of Default, the
Holder may in its discretion at any time and from time to time elect to
liquidate any such investments and to apply or cause to be applied the proceeds
of such action to the payment of the Secured Obligations in the manner specified
in Article VI.

Article IV.  Representations and Warranties.

     The Obligor hereby represents and warrants to the Holder for the benefit of
the Holders as follows:

     4.01 Title. The Obligor is the sole beneficial owner of the Collateral in
which it purports to grant a Lien pursuant to this Agreement, and, except as set
forth in Schedule 4.01, such Collateral is free and clear of all Liens. The
first priority Liens granted by this Agreement in favor of the Holder for the
benefit of the Holder and the Holders have attached and, upon filing of the
respective financing statements in the jurisdictions
<PAGE>   17
listed on Annex II, and subject to the liens set forth on Schedule 4.01, this
Agreement is effective to create a perfected first priority security interest in
all of such Collateral, prior to all other Liens. With respect to the Pledged
Stock, the Pledged Debt and the cash in the Collateral Account, the pledge of
such Collateral pursuant to this Agreement creates a valid and perfected first
priority security interest in such Collateral in favor of the Holder for the
benefit of the Holders.

     4.02 Intellectual Property. (a) Except pursuant to licenses and other user
agreements entered into by the Obligor in the ordinary course of business, the
Obligor owns and possesses the right to use, and has done nothing to authorize
or enable any other Person to use, any Patent or Trademark constituting
Intellectual Property or any other Intellectual Property.

          (b) The Obligor owns any Trademarks registered in the United States of
America to which the last sentence of the definition of Trademark Collateral
applies.

     4.03 Goods. Any goods now or hereafter manufactured or otherwise produced
by the Obligor or any of its Subsidiaries included in the Collateral have been
and will be produced in compliance with the requirements of the Fair Labor
Standards Act.

Article V.  Covenants.

     5.01 Books and Records. The Obligor shall: (a) keep full and accurate books
and records relating to the Collateral and stamp or otherwise mark such books
and records in such manner as the Holder may reasonably require in order to
reflect the Liens granted by this Agreement; (b) furnish to the Holder from time
to time (but, unless a Default shall have occurred and be continuing, no more
frequently than quarterly) statements and schedules further identifying and
describing the Copyright Collateral, the Patent Collateral and the Trademark
Collateral and such other reports in connection with the Copyright Collateral,
the Patent Collateral and the Trademark Collateral, as the Holder may reasonably
request, all in reasonable detail; (c) prior to filing, either directly or
through an agent, licensee or other designee, any application for any Copyright,
Patent or Trademark, furnish to the Holder prompt notice of such proposed
filing; and (d) permit representatives of the Holder, upon reasonable notice, at
any time during normal business hours to inspect and make abstracts from its
books and records pertaining to the Collateral, permit representatives of the
Holder to be present at the Obligor's place of business to receive copies of all
communications and remittances relating to the Collateral and forward copies of
any notices or communications received by the Obligor with respect to the
Collateral, all in such manner as the Holder may reasonably request.

     5.02 Removals, Etc. Without at least 30 days' prior written notice to the
Holder, the Obligor shall (i) not maintain any of its books and
<PAGE>   18
records with respect to the Collateral at any office or maintain its principal
place of business at any place, or permit any Inventory or Equipment to be
located anywhere, other than (a) at the address initially indicated for notices
to it under Article VII, (b) at one of the other business locations presently
owned or operated by the Obligor or any of its Affiliates and identified in
Annex II or III or (c) in transit from one of such locations to another, or (ii)
change its corporate name, or the name under which it does business, from the
name shown on the signature pages to this Agreement.

     5.03 Stock Collateral. The Obligor will cause the Stock Collateral to
constitute at all times 100% of the total number of shares of each class of
capital stock of each Issuer then outstanding. The Obligor shall cause all such
shares to be duly authorized, validly issued, fully paid and nonassessable and
to be free of any contractual restriction or any restriction under the charter
or bylaws of the respective Issuer of such Stock Collateral, upon the transfer
of such Stock Collateral (except for any such restriction contained in any Loan
Document). The Obligor agrees that it will (i) cause each issuer of the Pledged
Stock not to issue any shares of stock or other securities in addition to or in
substitution for the Pledged Stock, (ii) pledge hereunder, immediately upon its
acquisition (directly or indirectly) thereof, any and all additional shares of
capital stock issued to the Obligor (the "Additional Shares") and any and all
Additional Debt, and (iii) promptly (and in any event within three business
days) deliver to the Holder an amendment to this Agreement, duly executed by the
Obligor, in respect of the Additional Shares or Additional Debt, together with
all certificates, notes or other instruments representing or evidencing the
same. The Obligor agrees that all Additional Shares and Additional Debt listed
on any such amendment delivered to the Holder shall for all purposes hereunder
constitute Pledged Stock and Pledged Debt, respectively, and (iii) is deemed to
have made, upon such delivery, the representations and warranties contained in
Article IV hereof with respect to such Collateral.

     5.04 Intellectual Property. (a) The Obligor (either itself or through
licensees) will, for each Trademark, (i) to the extent consistent with past
practice and good business judgment, continue to use such Trademark on each and
every trademark class of goods applicable to its current line as reflected in
its current catalogs, brochures and price lists in order to maintain such
Trademark in full force and effect free from any claim of abandonment for
nonuse, (ii) maintain as in the past the quality of products and services
offered under such Trademark, (iii) employ such Trademark with the appropriate
notice of registration and (iv) not (and not permit any licensee or sublicensee
to) do any act or knowingly omit to do
<PAGE>   19
any act whereby any Trademark material to the conduct of its business may become
invalidated.

          (b) The Obligor (either itself or through licensees) will not do any
act or knowingly omit to do any act whereby any Patent or Copyright material to
the conduct of its business may become abandoned or dedicated.

          (c) The Obligor shall notify the Holder immediately if it knows or has
reason to know that any Intellectual Property material to the conduct of its
business may become abandoned or dedicated, or of any adverse determination or
development (including the institution of, or any such determination or
development in, any proceeding before any governmental Person) regarding the
Obligor's ownership of any Intellectual Property material to its business, its
right to apply for registration or register the same (as the case may be), or
its right to keep, use and maintain the same.

          (d) The Obligor will take all necessary steps that are consistent with
good business practices in any proceeding before any appropriate governmental
Person to maintain and pursue each application relating to any Intellectual
Property (and to obtain the relevant registrations) and to maintain each
registration material to the conduct of its business, including but not limited
to payment of maintenance fees, filing of applications for renewal, affidavits
of use, affidavits of incontestability and opposition, interference and
cancellation proceedings.

          (e) In the event that any Intellectual Property material to the
conduct of its business is infringed, misappropriated or diluted by, or comes in
conflict with, a third party, the Obligor shall notify the Holder within ten
days after it learns of such event and shall, if consistent with good business
practice, promptly sue for infringement, misappropriation or dilution, seek
temporary restraints and preliminary injunctive relief to the extent
practicable, seek to recover any and all damages for such infringement,
misappropriation or dilution and take such other actions as are appropriate
under the circumstances to protect such Collateral.

          (f) The Obligor shall prosecute diligently any application for any
Intellectual Property pending as of the date of this Agreement or thereafter
made until the termination of this Agreement, make application on uncopyrighted
but copyrightable material, unpatented but patentable inventions and
unregistered but registerable Trademarks and preserve and maintain all rights in
applications for any Intellectual Property; provided, however, that the Obligor
shall have no obligation to make any such application if making such application
would be unnecessary or imprudent in the good faith business judgment of the
Obligor. Any expenses incurred in connection with such an application shall be
borne by the Obligor.
<PAGE>   20
          (g) The Holder shall have the right but shall in no way be obligated
to bring suit in its own name to enforce the Copyrights, Patents and Trademarks
or any other Intellectual Property and any license under such Intellectual
Property, in which event the Obligor shall, at the request of the Holder, do any
and all lawful acts and execute and deliver any and all proper documents
required by the Holder in aid of such enforcement action.

Article VI.  Remedies.

     6.01 Events of Default, Etc. If any Event of Default shall have occurred
and be continuing:

          (a) the Holder in its discretion may require the Obligor to, and the
Obligor shall, assemble the Collateral owned by it at such place or places,
reasonably convenient to both the Holder and the Obligor, designated in the
Holder's request;

          (b) the Holder in its discretion may make any reasonable compromise or
settlement it deems desirable with respect to any of the Collateral and may
extend the time of payment, arrange for payment in installments, or otherwise
modify the terms of, all or any part of the Collateral;

          (c) the Holder in its discretion may, in its name or in the name of
the Obligor or otherwise, demand, sue for, collect or receive any money or
property at any time payable or receivable on account of or in exchange for all
or any part of the Collateral, but shall be under no obligation to do so;

          (d) the Holder in its discretion may, upon five business days' prior
written notice to the Obligor of the time and place, with respect to all or any
part of the Collateral which shall then be or shall thereafter come into the
possession, custody or control of the Holder, or its agents, sell, lease or
otherwise dispose of all or any part of such Collateral, at such place or places
as the Holder deems best, for cash, for credit or for future delivery (without
thereby assuming any credit risk) and at public or private sale, without demand
of performance or notice of intention to effect any such disposition or of time
or place of any such sale (except such notice as is required above or by
applicable statute and cannot be waived), and the Holder or any other Person may
be the Holder, lessee or recipient of any or all of the Collateral so disposed
of at any public sale (or, to the extent permitted by law, at any private sale)
and thereafter hold the same absolutely, free from any claim or right of
whatsoever kind, including any right or equity of redemption (statutory or
otherwise), of the Obligor, any such demand, notice and right or equity being
hereby expressly waived and released. In the event of any sale, assignment,
license or other disposition of any of the Trademark Collateral, the goodwill
and business or portion thereof connected with and symbolized by
<PAGE>   21
the Trademark Collateral subject to such disposition shall be included, and the
Obligor shall supply to the Holder or its designee, for inclusion in such sale,
assignment, license or other disposition, all Intellectual Property relating to
such Trademark Collateral. The Holder may, without notice or publication,
adjourn any public or private sale or cause the same to be adjourned from time
to time by announcement at the time and place fixed for the sale, and such sale
may be made at any time or place to which the sale may be so adjourned; and

          (e) the Holder shall have, and in its discretion may exercise, all of
the rights, remedies, powers and privileges with respect to the Collateral of a
secured party under the Uniform Commercial Code (whether or not the Uniform
Commercial Code is in effect in the jurisdiction where such rights, remedies,
powers and privileges are asserted) and such additional rights, remedies, powers
and privileges to which a secured party is entitled under the laws in effect in
any jurisdiction where any rights, remedies, powers and privileges in respect of
this Agreement or the Collateral may be asserted, including the right, to the
maximum extent permitted by law, to exercise all voting, consensual and other
powers of ownership pertaining to the Collateral as if the Holder were the sole
and absolute owner of the Collateral (and the Obligor agrees to take all such
action as may be appropriate to give effect to such right).

          The proceeds of, and other realization upon, the Collateral by virtue
of the exercise of remedies under this Section 6.01 and of the exercise of the
license granted to the Holder in Section 2.03 shall be applied in accordance
with Section 6.04.

     6.02 Deficiency. If the proceeds of, or other realization upon, the
Collateral by virtue of the exercise of remedies under Section 6.01 and of the
exercise of the license granted to the Holder in Section 2.03 are insufficient
to cover the costs and expenses (including attorneys fees) of such exercise and
the payment in full of the other Secured Obligations, the Obligor shall remain
liable for any deficiency.

     6.03 Private Sale. (a) The Holder shall incur no liability as a result of
the sale, lease or other disposition of all or any part of the Collateral at any
private sale pursuant to Section 6.01 conducted in a commercially reasonable
manner. The Obligor hereby waives any claims against the Holder arising by
reason of the fact that the price at which the Collateral may have been sold at
such a private sale was less than the price which might have been obtained at a
public sale or was less than the aggregate amount of the Secured Obligations,
even if the Holder accepts the first offer received and does not offer the
Collateral to more than one offeree.

          (b) The Obligor recognizes that, by reason of certain prohibitions
contained in the Securities Act and applicable state securities laws, the Holder
may be compelled, with respect to any sale of
<PAGE>   22
all or any part of the Collateral, to limit the Holder to those who will agree,
among other things, to acquire the Collateral for their own account, for
investment and not with a view to distribution or resale. The Obligor
acknowledges that any such private sales may be at prices and on terms less
favorable to the Holder than those obtainable through a public sale without such
restrictions, and, notwithstanding such circumstances, agrees that any such
private sale shall be deemed to have been made in a commercially reasonable
manner and that the Holder shall have no obligation to engage in public sales
and no obligation to delay the sale of any Collateral for the period of time
necessary to permit the respective Issuer of such Collateral to register it for
public sale.

     6.04 Application of Proceeds. Except as otherwise expressly provided in
this Agreement and except as provided below in this Section 6.04, the proceeds
of, or other realization upon, all or any part of the Collateral by virtue of
the exercise of remedies under Section 6.01 or of the exercise of the license
granted in Section 2.03, and any other cash at the time held by the Holder under
Article III or this Article VI, shall be applied by the Holder:

     First, to the payment of the costs and expenses of such exercise of
remedies, including reasonable out-of-pocket costs and expenses of the Holder,
the fees and expenses of its agents and counsel and all other expenses incurred
and advances made by the Holder in that connection;

     Second, to the Holder for amounts due and unpaid on the Notes for principal
and interest and all other amounts due and unpaid under the Loan Documents.

     Third, to the Obligor or any other obligor on the Notes, as their interests
may appear, or as a court of competent jurisdiction may direct.

     As used in this Article VI, "proceeds" of Collateral shall mean cash,
securities and other property realized in respect of, and distributions in kind
of, Collateral, including any property received under any bankruptcy,
reorganization or other similar proceeding as to the Obligor or any issuer of,
or account debtor or other obligor on, any of the Collateral.

Article VII.  Miscellaneous.

     7.01 Waiver. No failure on the part of the Holder or any Holder to exercise
and no delay in exercising, and no course of dealing with respect to, any right,
remedy, power or privilege under this Agreement shall operate as a waiver of
such right, remedy, power or privilege, nor shall any single or partial exercise
of any right, remedy, power or privilege under this Agreement preclude any other
or further exercise of any such
<PAGE>   23
right, remedy, power or privilege or the exercise of any other right, remedy,
power or privilege. The rights, remedies, powers and privileges provided in this
Agreement are cumulative and not exclusive of any rights, remedies, powers and
privileges provided by law.

     7.02 Notices. All notices and, consents, requests, instructions, approvals,
financial statements, reports and other communications to be given under this
Agreement shall be deemed given, if in writing and delivered personally, by
telecopy or sent by registered mail, postage prepaid to:

          if to the Obligor:         Bio-Plexus, Inc.
                                     129 Reservoir Road
                                     Vernon, CT  06066
                                     Attention: Carl Sahi
                                     Fax: (860) 870-6118

          with a copy to:            Pepe & Hazard LLP
                                     Goodwin Square
                                     Hartford, CT  06103
                                     Attention: Walter W. Simmers, Esq.
                                     Fax: (860) 522-2796

          if to the Holder:          c/o Appaloosa Management, L.P.
                                     26 Main St., 1st Floor
                                     Chatham, NJ  07928
                                     Attention: Mr. James Bolin
                                     Fax: (973) 701-7055

          with a copy to:            Fried, Frank, Harris, Shriver & Jacobson
                                     One New York Plaza
                                     New York, NY  10004
                                     Attention: Robert C. Schwenkel, Esq.
                                     Fax: (212) 859-4000


     7.03 Expenses, Etc. The Obligor agrees to pay or to reimburse the Holder
for all costs and expenses (including reasonable attorney's fees and expenses)
that may be incurred by the Holder in any effort to enforce any of the
provisions of Article VI, or any of the obligations of the Obligor in respect of
the Collateral or in connection with (a) the preservation of the Lien of, or the
rights of the Holder under this Agreement or (b) any actual or attempted sale,
lease, disposition, exchange, collection, compromise, settlement or other
realization in respect of, or care of, the Collateral, including all such costs
and expenses (and reasonable attorney's fees and expenses) incurred in any
bankruptcy, reorganization, workout or other similar proceeding.

     7.04 Amendments. This Agreement may be amended as to the Holder and its
respective successors and assigns, and the Obligor may take any action herein
prohibited, or omit to perform any act required to be performed by it, if the
Obligor shall obtain the written consent of the Holder. This Agreement may not
be waived, changed, modified, or discharged orally, but
<PAGE>   24
only by an agreement in writing signed by the party or parties against whom
enforcement of any waiver, change, modification or discharge is sought or by
parties with the right to consent to such waiver, change, modification or
discharge on behalf of such party.

     7.05 Successors and Assigns. All covenants and agreements contained herein
shall bind and inure to the benefit of the parties hereto and their respective
successors and assigns.

     7.06 Survival. All covenants, agreements, representations and warranties
contained herein and in any certificates delivered pursuant hereto in connection
with the transactions contemplated hereby shall survive the Closing and the
delivery of the Loan Documents, regardless of any investigation made by or on
behalf of any party.

     7.07 Agreements Superseded. Except with respect to express references to
other Loan Documents, this Agreement supersedes all prior agreements and
understandings, written or oral, among the parties with respect to the subject
matter of this Agreement.

     7.08 Severability. If any term, provision, covenant or restriction of this
Agreement or any exhibit hereto is held by a court of competent jurisdiction to
be invalid, void or unenforceable, the remainder of the terms, provisions,
covenants and restrictions of this Agreement and such exhibits shall remain in
full force and effect and shall in no way be affected, impaired or invalidated.
It is hereby stipulated and declared to be the intention of the parties that
they would have executed the remaining terms, provisions, covenants and
restrictions without including any of such which may be hereafter declared
invalid, void or unenforceable.

     7.09 Captions. The table of contents and captions and section headings
appearing in this Agreement are included solely for convenience of reference and
are not intended to affect the interpretation of any provision of this
Agreement.

     7.10 Counterparts. This Agreement may be executed in one or more
counterparts, all of which shall be considered one and the same agreement, and
shall become effective when one or more of the counterparts have been signed by
each party and delivered to the other parties, it being understood that all
parties need not sign the same counterpart.

     7.11 GOVERNING LAW. THIS AGREEMENT SHALL BE CONSTRUED AND ENFORCED IN
ACCORDANCE WITH, AND THE RIGHTS OF THE PARTIES SHALL BE GOVERNED BY, THE LAW OF
THE STATE OF NEW YORK EXCLUDING CHOICE-OF-LAW PRINCIPLES OF THE LAW OF SUCH
STATE THAT WOULD REQUIRE THE APPLICATION OF THE LAWS OF A JURISDICTION OTHER
THAN SUCH STATE.

     7.12 Submission to Jurisdiction. If any action, proceeding or litigation
shall be brought by the Holder in order to enforce any right
<PAGE>   25
or remedy under this Agreement, the Obligor hereby consents and will submit, and
will cause each of its Subsidiaries to submit, to the jurisdiction of any state
or federal court of competent jurisdiction sitting within the area comprising
the Southern District of New York on the date of this Agreement. The Obligor
hereby irrevocably waives any objection, including, but not limited to, any
objection to the laying of venue or based on the grounds of forum non
conveniens, which it may now or hereafter have to the bringing of any such
action, proceeding or litigation in such jurisdiction.

     7.13. Service of Process. Nothing herein shall affect the right of the
Holder to serve process in any other manner permitted by law or to commence
legal proceedings or otherwise proceed against the Obligor in any other
jurisdiction.

     7.14. WAIVER OF JURY TRIAL. THE OBLIGOR HEREBY WAIVES ANY RIGHT IT MAY HAVE
TO A TRIAL BY JURY IN RESPECT OF ANY ACTION, PROCEEDING OR LITIGATION DIRECTLY
OR INDIRECTLY ARISING OUT OF, UNDER OR IN CONNECTION WITH, THIS AGREEMENT.

     IN WITNESS WHEREOF, the parties have caused this Agreement to be duly
executed and delivered as of the day and year first above written.



                                   BIO-PLEXUS, INC.


                                   By: /s/ Carl Sahi
                                      --------------------------------------
                                      Name:  Carl Sahi
                                      Title: President & CEO


                                   APPALOOSA INVESTMENT LIMITED
                                       PARTNERSHIP I, L.P.

                                   By:  Appaloosa Management, L.P., its
                                          General Partner
                                   By:  Appaloosa Partners Inc., its General
                                          Partner


                                   By: /s/ James E. Bolin
                                      --------------------------------------
                                      Name:  James E. Bolin
                                      Title: Vice President