<PAGE>

                                                                   EXHIBIT 10.37
                              S. R. ONE, LIMITED


                                      and


                                CARESIDE, INC.



                 ============================================

                        SECURITIES CONVERSION AGREEMENT

                 ============================================



                              Dated June 14, 1999
<PAGE>

     THIS SECURITIES CONVERSION AGREEMENT (the "Agreement") is made this 14th
                                                ---------
day of June, 1999, by and between S.R. One, Limited, a Pennsylvania business
trust with its principal office located at 4 Towers Bridge, 200 Bar Harbor
Drive, West Conshohocken, PA 19428 ( "Investor"), and CARESIDE, INC., a Delaware
                                      --------
corporation with its principal offices located at 6100 Bristol Parkway, Culver
City, California  90230 (the "Company").
                              -------

                             W I T N E S S E T H:
                             -------------------

     WHEREAS, in connection with the Company's bridge financing pursuant to a
certain Securities Purchase Agreement, dated December 17, 1998 by and between
Investor and the Company (the "Securities Purchase Agreement"), Investor
purchased promissory notes of the Company in the aggregate principal amount of
$3,000,000 (the "Existing Notes").  As partial consideration for its
                 --------------
obligations under the Securities Purchase Agreement, S.R. One received a
detachable warrant to purchase shares of Common Stock of the Company  (the
"Warrant Certificate SR-1").  In connection therewith, Investor was granted
-------------------------
certain rights regarding the registration of the Common Stock under a
Registration Rights Agreement, dated December 17, 1998 by and between the
Company and Investor (the "Registration Rights Agreement").
                           -----------------------------

     WHEREAS, the Company and Investor desire, simultaneously with the Closing
to exchange one-third of principal and interest under the Existing Notes for
shares of Series A Convertible Preferred Stock of the Company.

     WHEREAS, in connection with the conversion of a portion of the Existing
Notes to Series A Convertible Preferred Stock, the Company and Investor desire
to exchange the Warrant Certificate SR-1 for an amended warrant (the "Warrant
                                                                      -------
Certificate SR-2") and to  amend and restate the Registration Rights Agreement.
----------------

     NOW THEREFORE, in consideration of the premises and the mutual covenants
and agreements herein contained, and for other good and valuable consideration,
the receipt and sufficiency of which is hereby acknowledged, the parties hereto,
intending to be legally bound hereby, do hereby agree as follows:

                                   ARTICLE 1.
                                  Definitions
                                  -----------

     Section 1.1.    "Definitions.  Capitalized terms used but not defined
                      -----------
herein shall have the meaning set forth in this Section 1.1.

             1.1.1.  "Closing" shall mean the date of consummation of the
                      -------
Company's Initial Public Offering.

             1.1.2.  "Common Stock" shall mean the common capital stock of the
                      ------------
Company, $0.1 par value per share.

             1.1.3.  "Existing Notes" means the promissory notes originally
                      --------------
issued to Investor referenced in the recitals hereto.

             1.1.4.  "Governmental Entity" means any federal, state, local or
                      -------------------
foreign government or governmental body, or any political subdivision thereof,
including any Person exercising executive, legislative, judicial, regulatory or
administrative functions of or pertaining to government.
<PAGE>

          1.1.5.  "Initial Public Offering" means the first offering of the
                  -----------------------
Company's securities registered with the SEC under the Securities Act.

          1.1.6.  "Law" or "Regulation" means any applicable law, statute,
                   ---      ----------
rule, ordinance, regulation, order, decree, edict or other requirement of any
Governmental Entity.

          1.1.7.  "Lien" means any mortgage, lien, security interest, pledge,
                   ----
negative pledge, encumbrance, assessment, title retention agreement, restriction
or restraint on transfer, defect of title, charge in the nature of a lien or
security interest, or option (whether consensual, statutory or otherwise).

          1.1.8.  "New Note" means the promissory note delivered to Investor
                   --------
pursuant to Section 2.1.2 hereof and in the form of Exhibit B hereof.
                                                    ---------

          1.1.9.  "Person" means an individual, a sole proprietorship, a
                   ------
corporation, a partnership, a limited liability company or partnership, a joint
venture, an association, a trust, or any other entity or organization, including
a Governmental Entity.

          1.1.10.  "Registration Statement" means the Company's registration
                    ----------------------
statement on Form S-1 which the Company has filed with the SEC, as amended, the
most recent draft copy of which is attached hereto as Exhibit E.
                                                      ---------

          1.1.11.  "Regulation D" means Regulation D promulgated by the SEC
                    ------------
under the Securities Act, as amended from time to time.

          1.1.12.   "SEC" means the United States Securities and Exchange
                     ---
Commission or any successor Governmental Entity.

          1.1.13.   "Series A Convertible Preferred Stock" means the series of
                     ------------------------------------
preferred stock of the Company, the terms and conditions of which are set forth
in the Certificate of Designations attached hereto as Exhibit A.
                                                      ---------

          1.1.14.   "Securities Act" means the Securities Act of 1933, as
                     --------------
amended, and the Regulations promulgated thereunder or with respect thereto, or
any successor or substitute Laws.

          1.1.15.   "Shares" means shares of Common Stock of the Company issued
                     ------
by the Company upon exercise of Warrant Certificate SR-2.

          1.1.16.   "Transaction" means the conversion of a portion of the
                     -----------
Existing Notes pursuant to Article 2 hereof, and the matters related thereto, as
                           ---------
set forth herein.

          1.1.17.   "Unit" means a unit comprised of one share of Common Stock
                     ----
of the Company and  a warrant to purchase one share of Common Stock of the
Company.

          1.1.18.   "Warrant Certificate SR-1" means the detachable warrant
                     ------------------------
originally issued with the SR-1 Notes to Investor referenced in the recitals
hereto.

                                      -2-
<PAGE>

          1.1.19.   "Warrant Certificate SR-2" means the detachable warrant
                     ------------------------
delivered to Investor pursuant to Section 2.2 hereof and in the form of
Exhibit C hereto.
--------


                                  ARTICLE 2.
                          Conversion of the SR-1 Note
                          ---------------------------

     Section 2.1.

             2.1.1.   Conversion. Simultaneously with the Closing, the Company
                      ----------
shall convert one-third of the outstanding principal and accrued interest under
the Existing Notes into shares of Series A Convertible Preferred Stock. The
number of shares of Series A Convertible Preferred Stock received on conversion
shall be equal to the aggregate dollar amount of principal and interest being
converted, divided by 85% of the Initial Public Offering price per Unit. The
stated value of each share of Series A Convertible Preferred Stock shall be
equal to the Initial Public Offer price per Unit.

             2.1.2.   Issuance of New Note. Upon conversion, Investor shall
                      --------------------
deliver to the Company on or before Closing, one or more of the Existing Notes
and the Company shall deliver to Investor a new promissory note in the principal
amount equal to the remaining outstanding portion of the Existing Notes not
converted hereunder which shall be in the form of Exhibit B attached hereto.
                                                  ---------

     Section 2.2.     Issuance of Warrant Certificate SR-2. In consideration of
                      ------------------------------------
the conversion of a portion of the Existing Notes, Investor shall deliver to the
Company at the Closing the Warrant Certificate SR-1 in exchange for the Warrant
Certificate SR-2, which shall be is substantially in the form attached hereto as
Exhibit C.
---------

     Section 2.3.     Amended and Restated Registration Rights Agreement.
                      --------------------------------------------------
Simultaneously with the conversion of the aforementioned portion of the Existing
Notes, the Registration Rights Agreement shall be amended and restated,
substantially on the form attached hereto as Exhibit D (as modified by any
                                             ---------
amendment thereto herein after made).

                                  ARTICLE 3.
                        Representations and Warranties
                        ------------------------------

     Section 3.1.     Representations and Warranties of the Company. As a
                      ---------------------------------------------
material inducement to the Investor to enter into this Agreement and to
consummate the Transaction, the Company hereby represents and warrants to the
Investor as follows, which representations and warranties shall survive the
Closing and the issuance and delivery of the New Note:

             3.1.1.   Organization and Standing.  The Company is a corporation
                      -------------------------
duly organized, validly existing and in good standing under the laws of the
State of Delaware.

             3.1.2.   Corporate Power and Authority; Enforceability. The
                      ---------------------------------------------
Company has the requisite power and authority (corporate and otherwise) to
execute, deliver and perform this Agreement and to consummate the Transaction.
The execution, delivery and performance by the Company of this Agreement and the
consummation by the Company of the Transaction, have been duly authorized by all
necessary action (corporate or otherwise) on its part. This Agreement
constitutes a legal, valid and binding obligation of the

                                      -3-
<PAGE>

Company, enforceable in accordance with its terms, except insofar as
enforceability is limited by bankruptcy, insolvency, moratorium and similar laws
affecting creditors' rights generally, and by general principles of equity.

      3.1.3.   Validity of Contemplated Transactions.  The execution, delivery
               -------------------------------------
and performance by the Company of this Agreement, and the consummation by it of
the Transaction, do not violate or contravene any provision of the Company's
charter or bylaws, or of any material contract to which the Company is a party.

      3.1.4.   Issuance of Shares.  The shares of Series A Convertible Preferred
               ------------------
Stock issued upon conversion of Existing Notes, and any Shares issued and
delivered to, and paid for by the Investor pursuant to and in accordance with
exercise of Warrant Certificate SR-2 or conversion of Series A Convertible
Preferred Stock, (a) will have been validly issued, fully paid and non-
assessable, (b) will be free and clear of any Liens (other than Liens imposed by
the Securities Act), and (c) will have been issued without violation of any
preemptive or other right to purchase or restrict the transfer of Common Stock.

      3.1.5.   Accuracy and Completeness of the Financial Information.  The
               ------------------------------------------------------
Company's financial information that has been provided to the Investor is
accurate and complete in all materials respects, except that the Company makes
no representations or warranties with respect to any projections of the
Company's future results of operations, financial condition or otherwise.

      3.1.6.   Compliance with all Laws.  To the best of its knowledge, the
               ------------------------
Company is  in compliance in all material respects with all Laws.

      3.1.7.   Registration Statement.  The Registration Statement is
               ----------------------
true and correct in all material respects and does not contain any statement
that is misleading or omit any statement necessary to make the statements made
therein not misleading.

  Section 3.2. Representations, Warranties and Covenants of the Investor.  As a
               ---------------------------------------------------------
material inducement to the Company to enter into this Agreement and to
consummate the Transaction, the Investor hereby represents and warrants to the
Company as follows, which representations and warranties shall survive the
Closing and the issuance and delivery of the New Note:

      3.2.1.   Corporate Power and Authority; Enforceability.  The Investor has
               ---------------------------------------------
the requisite power and authority (corporate and otherwise) to execute, deliver
and perform this Agreement and to consummate the Transaction.  The execution,
delivery and performance by the Investor of this Agreement and the consummation
by the Investor of the Transaction, have been duly authorized by all necessary
action (corporate or otherwise) on its part.  This Agreement constitutes a
legal, valid and binding obligation of the Investor, enforceable in accordance
with its terms, except insofar as enforceability is limited by bankruptcy,
insolvency, moratorium and similar laws affecting creditors' rights generally
and by general principles of equity.

      3.2.2.   Securities Act Representations.  The Investor hereby represents
               ------------------------------
and warrants to the Company that:

                    (a)  the Investor is an "accredited investor" within the
meaning of Regulation D;

                                      -4-
<PAGE>

                    (b)  the Investor (i) has such experience in financial and
business matters such that it is capable of evaluating the merits and risks of
purchasing the securities acquired hereunder, (ii) has been furnished any and
all materials which it has requested relating to the Company or the offering of
these securities and the Investor has been afforded the opportunity to ask
questions of the senior management and directors of the Company concerning the
terms and conditions of the offering and to obtain any additional information
necessary to verify the accuracy of the information provided to the Investor,
and (iii) is satisfied that the Investor has received adequate information with
respect to all matters that the Investor considers material to the Investor's
decision to make this investment;

                    (c)  the Investor has purchased the securities to be
acquired hereunder for its own account and has not transferred, distributed or
resold such securities, or any part thereof;

                    (d)  the Investor understands that the securities to be
acquired under this Agreement have not been registered under the Securities Act
or under the Laws of any jurisdiction, and that the Company does not contemplate
and, except as set forth herein, is under no obligation to so register such
securities;

                    (e)  the Investor is aware that: (i) investment in the
Company involves a high degree of risk, lack of liquidity and substantial
restrictions on transferability of interest; (ii) no Governmental Entity has
made any finding or determination as to the fairness for investment by the
public, nor has it made any recommendation or endorsement of the securities to
be acquired hereunder; and (iii) such securities must be held indefinitely
unless they are subsequently registered under the Securities Act or an exemption
from registration under the Securities Act covering the sale of the Shares is
available;

                    (f)  the Investor has sufficient financial resources
available to support the loss of all or a portion of the Investor's investment
in the Company, has no need for liquidity in the investment in the Company and
is able to bear the economic risk of the investment; and

                    (g)  the Investor has received, reviewed and understands the
section entitled "Risk Factors" contained in the Registration Statement, and the
Investor further acknowledges that (i) prior to the execution of a definitive
underwriting agreement neither the Company nor any other Person has made any
commitment or agreement that said Registration Statement will become effective
or that the initial public offering described therein will occur at a particular
price or within a particular range of prices or occur at all; (ii) there can be
no assurance that the initial public offering described therein will occur at a
particular price or within a particular range of prices or occur at all; and
(iii) the securities to be acquired hereunder are not being offered pursuant to
such Registration Statement.

                                  ARTICLE 4.
                                Related Matters
                                ---------------

     Section 4.1. Board Visitation Rights.  Prior to consummation of the Initial
                  ------------------------
Public Offering, but only for so long as the New Note  remains outstanding or
Investor owns Warrant Certificate SR-2 or any Shares (i) the Company shall
provide the same advance written notice to Investor as it supplies to its
directors in advance of or at such meeting, at the same time and by the

                                      -5-
<PAGE>

same means as they are provided to the Company's directors, and (ii) Investor
shall be entitled to have one representative attend all meetings of the
Company's Board of Directors.

                                  ARTICLE 5.
                                 Miscellaneous
                                 -------------

  Section 5.1.  Entire Agreement.  The Securities Purchase Agreement, the
                ----------------
Securities Conversion Agreement, the Amended and Restated Registration Rights
Agreement, and Warrant Certificate SR-2 and the New Note issued pursuant hereto
contain the entire understanding between the parties hereto and supersede all
prior agreements and understandings, written or oral, with respect to the
subject matter hereof.

  Section 5.2.  Expenses.  All costs and expenses incurred in connection with
                --------
this Agreement shall be paid by the Person incurring such expenses.

  Section 5.3.  Jurisdiction.  The Company and the Investor hereby agree that
                ------------
any action, proceeding or claim against it arising out of, or relating in any
way to, this Agreement, the New Note or Warrant Certificate SR-2 shall be
brought and enforced in the courts of the State of California, and any Federal
court located in any county in the State of California in which the Company has
an office and irrevocably submits to such jurisdiction, which jurisdiction shall
be exclusive.  The Company and the Investor hereby irrevocably waive any
objection to such exclusivity based on the doctrine of inconvenient forum or
otherwise.  Any such process or summons to be served upon either the Company or
the Investor (at the option of the party bringing such action, proceeding or
claim) may be served by transmitting a copy thereof, by registered or certified
mail, return receipt requested, postage prepaid, addressed to it at the address
as set forth in Section 5.8 hereof.  Such mailing shall be deemed personal
service and shall be legal and binding upon the party so served in any action,
proceeding or claim.  The Company and the Investor, by its execution of this
Agreement and acceptance of the New Note and Warrant Certificate SR-2, agree
that the prevailing party(ies) in any such action or proceeding shall be
entitled to recover from the other party(ies) all of its/their reasonable legal
costs and expenses relating to such action or proceeding and/or incurred in
connection with the preparation therefor.

  Section 5.4. Binding Effect; Assignment; Benefit.  This Agreement shall
               -----------------------------------
inure to the benefit of and be binding upon the parties hereto and their
respective successors and permitted assigns, but neither this Agreement nor any
of the rights, interests or obligations hereunder shall be assigned by either of
the parties hereto without the prior written consent of the other party.
Nothing in this Agreement, expressed or implied, is intended to confer on any
person, other than the parties hereto or their respective successors and
permitted assigns, any rights, remedies, obligations or liabilities under or by
reason of this Agreement.

  Section 5.5. Amendment and Modification.  Subject to applicable law, this
               --------------------------
Agreement may be amended, modified and supplemented only by a writing duly
authorized and executed by the parties hereto.

  Section 5.6. Headings.  The descriptive headings of the several Articles and
               --------
Sections of this Agreement are inserted for convenience only, do not constitute
a part of this Agreement and shall not affect in any way the meaning or
interpretation of this Agreement.

  Section 5.7. Exhibits.  All exhibits attached hereto are a material part of
               --------
this Agreement and are hereby incorporated into this Agreement.

                                      -6-
<PAGE>

  Section 5.8. Notices.  All notices and other communications hereunder shall
               -------
be in writing and shall be given to a Person either personally or by sending a
copy thereof by first class United States express mail, postage prepaid and
return-receipt requested, or by a nationally-recognized courier service
guaranteeing next-day delivery, charges prepaid, or by telecopier (with the
original sent by either of the foregoing manners), to such Person's address (or
to such Person's telecopier number).  All notices shall be deemed to have been
given to the Person entitled thereto when received.

          If to the Investor, to:

               S.R. One, Limited
               4 Towers Bridge
                200 Barr Harbor Drive
                Suite 250
                West Conshohocken, Pennsylvania 19428
                Attention:  Ms. Brenda Gavin
                Facsimile No.: __________________

          If to the Company, to:

                CARESIDE, Inc.
                6100 Bristol Parkway
                Culver City, CA  90230
                Attention:  President and Chief Executive Officer
                Facsimile No.: 310.338.6789

          with a copy to:

                Pepper Hamilton LLP
                3000 Two Logan Square
                18th & Arch Streets
                Philadelphia, PA  19103-2799
                Attention:  Julia D. Corelli, Esq.
                Facsimile No.: 215.981.4750

  Notice of any change in any such address shall also be given in the manner
set forth above.  Whenever the giving of notice is required, the giving of such
notice may be waived by the party entitled to receive such notice.

  Section 5.9.  Waiver.  No provision of this Agreement may be waived except by
                ------
a written instrument signed by the party hereto sought to be bound.  No failure
or delay by any party hereto in exercising any right or remedy hereunder or
under applicable Law will operate as a waiver thereof, and a waiver of a
particular right or remedy on one occasion will not be deemed a waiver of any
other right or remedy, or a waiver on any subsequent occasion (it being
understood that specific time frames for notice or actions to be taken shall be
binding on the parties).

                                      -7-
<PAGE>

  Section 5.10. Severability.  If any term, provision, covenant or restriction
                ------------
contained in this Agreement is held by a court of competent jurisdiction or
other authority to be invalid, void, unenforceable or against its regulatory
policy, the remainder of the terms, provisions, covenants and restrictions
contained in this Agreement shall remain in full force and effect and shall in
no way be affected, impaired or invalidated.

  Section 5.11. Governing Law.  This Agreement shall be construed and enforced
                -------------
in accordance with the Laws of the State of Delaware without regard to
principles of conflicts of law applicable in such jurisdiction.

  Section 5.12. Continuing Obligation.  Except as otherwise specifically
                ---------------------
provided herein, neither termination nor expiration of this Agreement shall
relieve any party hereto from any obligation under this Agreement which accrued,
or arose from facts and circumstances in existence, prior thereto.

  Section 5.13. Counterparts.  This Agreement and any amendment or supplement
                ------------
hereto may be executed by the parties in separate counterparts, whether
originally or by facsimile, each of which when so executed and delivered, shall
be an original, but all such counterparts shall together constitute one and the
same agreement.  The execution of this Agreement and any such amendment or
supplement by any party hereto will not become effective until counterparts
hereof have been executed by all the parties hereto.


  IN WITNESS WHEREOF, the parties have caused this Agreement to be duly
executed and delivered as of the date first above written by their duly
authorized representative.

                              S.R. ONE, LIMITED

                              By:    /s/ Donald F. Parman
                                     -----------------------
                              Name:  Donald F. Parman
                              Title: Vice President


                              CARESIDE, INC.


                              By:    /s/ James Koch
                                     -----------------------
                                     James Koch
                                     Chief Financial Officer

                                      -8-
<PAGE>

                               TABLE OF CONTENTS
                               -----------------
<TABLE>
<CAPTION>
                                                                                        Page
                                                                                        ----
<S>                                                                                     <C>
ARTICLE 1. - Definitions................................................................   1

              Section 1.1.       Definitions............................................   1

ARTICLE 2. - Conversion of the SR-1 Note................................................   3

              Section 2.1.       2.1.1.  Conversion.....................................   3
                                 2.1.2.  Issuance of New Note...........................   3
              Section 2.2.       Issuance of Warrant Certificate SR-2...................   3
              Section 2.3.       Amended and Restated Registration Rights Agreement.....   3

ARTICLE 3. - Representations and Warranties.............................................   3

              Section 3.1.       Representations and Warranties of the Company..........   3
                                 3.1.1.  Organization and Standing......................   3
                                 3.1.2.  Corporate Power and Authority; Enforceability..   3
                                 3.1.3.  Validity of Contemplated Transactions..........   4
                                 3.1.4.  Issuance of Shares.............................   4
                                 3.1.5.  Accuracy and Completeness of the Financial
                                         Information....................................   4
                                 3.1.6.  Compliance with all Laws.......................   4
                                 3.1.7.  Registration Statement.........................   4
              Section 3.2.       Representations, Warranties and Covenants of the
                                 Investor...............................................   4

                                 3.2.1.  Corporate Power and Authority; Enforceability..   4
                                 3.2.2.  Securities Act Representations.................   4

ARTICLE 4. - Related Matters............................................................   5

              Section 4.1.       Board Visitation Rights................................   5

ARTICLE 5. - Miscellaneous..............................................................   6

              Section 5.1.       Entire Agreement.......................................   6
              Section 5.2.       Expenses...............................................   6
              Section 5.3.       Jurisdiction...........................................   6
              Section 5.4.       Binding Effect; Assignment;............................   6
              Section 5.5.       Amendment and Modification.............................   6
              Section 5.6.       Headings...............................................   6
              Section 5.7.       Exhibits...............................................   6
              Section 5.8.       Notices................................................   6
              Section 5.9.       Waiver.................................................   7
              Section 5.10.      Severability...........................................   7
</TABLE>
                               -i-
<PAGE>

<TABLE>
                                                                                        Page
                                                                                        ----
<S>                                                                                     <C>
              Section 5.11.      Governing Law.......................................      8
              Section 5.12.      Continuing Obligation...............................      8
              Section 5.13.      Counterparts........................................      8
</TABLE>
                                     -ii-
<PAGE>

Exhibits
--------

A.   Form of Certificate of Designations
B.   Form of New Note
C.   Form of Warrant Certificate SR-2
D.   Amended and Restated Registration Rights Agreement
E.   Draft of Registration Statement (dated May 5, 1999)

                                     -iii-
<PAGE>

                                   EXHIBIT A

                      Form of Certificate of Designations
                      -----------------------------------

                 (See Exhibit 3.2 of the Company's Form 10Q.)
<PAGE>

                                   EXHIBIT B
                                   ---------

                               Form of New Note
                               ----------------

                 (See Exhibit 4.9 of the Company's Form 10Q.)
<PAGE>

                                   EXHIBIT C
                                   ---------

                       Form of Warrant Certificate SR-2
                       --------------------------------

                 (See Exhibit 4.8 of the Company's Form 10Q.)
<PAGE>

                                   EXHIBIT D
                                   ---------

              Amended and Restated Registration Rights Agreement
              --------------------------------------------------

                (See Exhibit 10.38 of the Company's Form 10Q.)
<PAGE>

                                   EXHIBIT E
                                   ---------

              Draft of Registration Statement (dated May 5, 1999)
              ---------------------------------------------------

                      (Exhibit E Intentionally Omitted.)