<PAGE>   1
                                                                   EXHIBIT 10.20


                                 FORM OF WARRANT

        THIS WARRANT AND THE SECURITIES ISSUABLE UPON THE EXERCISE HEREOF HAVE
        NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE
        "ACT"), OR ANY STATE SECURITIES LAWS. THEY MAY NOT BE SOLD, OFFERED FOR
        SALE, PLEDGED, HYPOTHECATED OR OTHERWISE TRANSFERRED IN THE ABSENCE OF A
        REGISTRATION STATEMENT IN EFFECT WITH RESPECT TO THE SECURITIES UNDER
        SUCH ACT OR AN OPINION OF COUNSEL REASONABLY SATISFACTORY TO THE COMPANY
        THAT SUCH REGISTRATION IS NOT REQUIRED OR UNLESS SOLD PURSUANT TO AN
        EXEMPTION TO SUCH ACT.


PS-_______                                                            Void after
                                                              September 10, 2002


                      WARRANT TO PURCHASE __________ SHARES
                           OF SERIES A PREFERRED STOCK

                                       of

                                      IRORI


             INCORPORATED UNDER THE LAWS OF THE STATE OF CALIFORNIA

        THIS CERTIFIES THAT, for value received, _____________________________,
together with its successors and assigns (the "Holder") is entitled to subscribe
for and purchase, on the terms hereof, __________ shares of Series A Preferred
Stock (the "Series A Stock") of Irori, a California corporation (the "Company"),
subject to adjustment as provided herein.

        This Warrant is subject to the following terms and conditions:

        1. Convertible Demand Promissory Note and Warrant Purchase Agreement.
This Warrant is one of a series of warrants issued pursuant to that certain
Convertible Demand Promissory Note and Warrant Purchase Agreement dated
September 10, 1996 (the "Purchase Agreement") by and among the Company, the
Holder and the other holders of warrants and convertible demand promissory notes
issued in connection with the Purchase Agreement.

        2. Exercise of Warrant. The terms and conditions upon which this Warrant
may be exercised, and the Series A Stock covered hereby (the "Warrant Stock")
may be purchased, are as follows:

               2.1 Term. Subject to the terms hereof, this Warrant may be
exercised at any time after the date hereof, or from time to time, in whole or
in part; provided, however, that in no event may this Warrant be exercised (the
"Exercise Date") later than 5:00 p.m. (Pacific Time) on

<PAGE>   2

the earlier of (a) the close of business on September 10, 2002, (b)(i) the
closing of the acquisition of the Company by another entity by means of a
transaction or series of related transactions or (ii) the closing of the sale of
all or substantially all of the assets of the Company, unless the Company's
shareholders of record prior to such acquisition or sale shall hold at least
fifty percent (50%) of the voting power of the acquiring or surviving entity
immediately after such acquisition or sale, or (c) the initial underwritten
public offering of the Company's common stock (the "Common Stock") (the
"Exercise Period"). At least ten (10) days prior to the occurrence of an event
specified in (a), (b) or (c) of this Section 2.1, the Company shall send to the
Holder notice of such event and that the Holder's rights under this Warrant
shall terminate upon the occurrence of such event; provided, that if the Company
sends such notice less than ten (10) days prior to the occurrence of such event,
the Holder's right to exercise this Warrant shall be extended for a period of
ten (10) days after the date of the notice, after which time the Holder's rights
under this Warrant shall terminate.

               2.2 Purchase Price. The per share purchase price for the shares
of Series A Stock to be issued upon exercise of this Warrant shall be $2.00,
subject to adjustment as provided herein.

               2.3 Method of Exercise. The exercise of the purchase rights
evidenced by this Warrant shall be effected by (a) the surrender of the Warrant,
together with a duly executed copy of the form of a subscription attached
hereto, to the Company at its principal offices and (b) the delivery of the
purchase price by check or bank draft payable to the Company's order or by wire
transfer to the Company's account for the number of shares for which the
purchase rights hereunder are being exercised or any other form of consideration
approved by the Company's Board of Directors. Each exercise of this Warrant
shall be deemed to have been effected immediately prior to the close of business
on the day on which this Warrant shall have been surrendered to the Company as
provided herein or at such later date as may be specified in the executed form
of subscription, and at such time the person or persons in whose name or names
any certificate or certificates for shares of Preferred Stock shall be issuable
upon such exercise as provided herein shall be deemed to have become the holder
or holders of record thereof.

               2.4 Net Issuance.

                      2.4.1 Right to Convert. In addition to and without
limiting the rights of the Holder under the terms of this Warrant, the Holder
shall have the right to convert this Warrant or any portion thereof (the
"Conversion Right") into shares of Series A Stock as provided in this Section
2.4 at any time or from time to time during the Exercise Period. Upon exercise
of the Conversion Right with respect to a particular number of shares subject to
the Warrant (the "Converted Warrant Shares"), the Company shall deliver to the
Holder (without payment by the Holder of any exercise price or any cash or other
consideration) that number of shares of fully paid and nonassessable Series A
Stock computed using the following formula:

                      X = Y (Z - $2.00)
                          -------------
                                Z

               Where  X = the number of shares of Series A Stock to be delivered
                          to the Holder



                                       2.
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                      Y = the number of Converted Warrant Shares

                      Z = the per share fair market value of the Series A Stock
                          on the Conversion Date (as defined below)

The Conversion Right may only be exercised with respect to a whole number of
shares subject to the Warrant. No fractional shares shall be issuable upon
exercise of the Conversion Right, and if the number of shares to be issued
determined in accordance with the foregoing formula is other than a whole
number, the Company shall pay to the Holder an amount in cash equal to the fair
market value of the resulting fractional share on the Conversion Date (as
defined below). Shares issued pursuant to the Conversion Right shall be treated
as if they were issued upon the exercise of the Warrant.

                      2.4.2 Method of Exercise. The Conversion Right may be
exercised by the Holder by the surrender of the Warrant at the principal office
of the Company together with a written statement specifying that the Holder
thereby intends to exercise the Conversion Right and indicating the total number
of shares under the Warrant that the Holder is exercising through the Conversion
Right. Such conversion shall be effective upon receipt by the Company of the
Warrant together with the aforesaid written statement, or on such later date as
is specified therein (the "Conversion Date"). Certificates for the shares
issuable upon exercise of the Conversion Right and, if applicable, a new warrant
evidencing the balance of the shares remaining subject to the Warrant, shall be
issued as of the Conversion Date and shall be delivered to the Holder promptly
following the Conversion Date.

                      2.4.3 Determination of Fair Market Value. For purposes of
this Section 2.4, fair market value of a share of Series A Stock on the
Conversion Date shall mean the fair market value as determined by the Board of
Directors of the Company.

        3. Limit on Rights of the Holder upon Exercise. The Holder acknowledges
and agrees that upon the exercise of this Warrant in full or in part, the
following provisions shall apply to the rights of the Holder as a holder of
Series A Stock and of Common Stock that such Series A Stock is convertible into.

               3.1 Market Stand-Off Agreement. During the period of duration
(not to exceed 180 days) specified by the Company and an underwriter of Common
Stock or other securities of the Company, following the effective date of a
registration statement of the Company filed under the Act, the Holder shall not,
to the extent requested by the Company and such underwriter, directly or
indirectly sell, offer to sell, contract to sell (including, without limitation,
any short sale), grant any option to purchase or otherwise transfer or dispose
of (other than to transferees or donees who agree to be similarly bound) any
securities of the Company held by it at any time during such period except
Common Stock included in such registration; provided, however, that this Section
3.1 shall be applicable only to the first such registration statement of the
Company pursuant to which Common Stock (or other securities) of the Company are
to be sold on its behalf to the public in an underwritten offering, and (b) all
officers and directors of the Company and all other persons with registration
rights enter into similar agreements. In order to enforce the foregoing
covenant, the Company may impose stop-transfer



                                       3.
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instructions with respect to the Common Stock of the Holder (and the shares or
securities of every other person subject to the foregoing restriction) until the
end of such period.

        4. Adjustments to Conversion Price. The number and kind of shares of
Series A Stock (or any shares of stock or other securities which may be)
issuable upon the exercise of this Warrant and the exercise price hereunder
shall be subject to adjustment from time to time upon the happening of certain
events, as follows:

               4.1 Dividends, Distributions, Stock Splits or Combinations. If
the Company shall at any time or from time to time after the date hereof make or
issue, or fix a record date for the determination of holders of Series A Stock
entitled to receive, a dividend or other distribution payable in additional
shares of common or preferred stock (as the case may be), then and in each such
event the exercise price hereunder then in effect shall be decreased as of the
time of such issuance or, in the event such a record date shall have been fixed,
as of the close of business on such record date, by multiplying the exercise
price hereunder then in effect by a fraction: (a) the numerator of which shall
be the total number of shares of Common Stock (assuming the conversion of all
outstanding securities of the Company that are convertible into Common Stock and
the exercise of all options to purchase Common Stock or securities that are
convertible into Common Stock) issued and outstanding immediately prior to the
time of issuance or the close of business on such record date; and (b) the
denominator of which shall be the total number of shares of Common Stock
(assuming the conversion of all outstanding securities of the Company that are
convertible into Common Stock and the exercise of all options to purchase Common
Stock or securities that are convertible into Common Stock) issued and
outstanding immediately after the time of issuance or the close of business on
such record date. If the Company shall at any time subdivide the outstanding
shares of Series A Stock (or any securities into which such Series A Stock is
convertible), or if the Company shall at any time combine the outstanding shares
of Series A Stock (or any securities into which such Series A Stock is
convertible), then the exercise price hereunder immediately shall be decreased
proportionally (in the case of a subdivision) or increased proportionally (in
the case of a combination). Any such adjustment shall become effective at the
close of business on the date the subdivision or combination becomes effective.

               4.2 Reclassification or Reorganization. If the Series A Stock (or
any shares of stock or other securities which may be) issuable upon the exercise
of this Warrant shall be changed into the same or different number of shares of
any class or classes of stock, whether by capital reorganization,
reclassification or otherwise (other than a subdivision or combination of shares
or stock dividend provided for in Section 4.1 above, or a reorganization,
merger, consolidation or sale of assets provided for in Section 4.3 below), then
and in each such event the Holder shall be entitled to receive upon the exercise
of this Warrant the kind and amount of shares of stock and other securities and
property receivable upon such reorganization, reclassification or other change,
to which a holder of the number of shares of Series A Stock (or any shares of
stock or other securities which may be) issuable upon the exercise of this
Warrant would have received if this Warrant had been exercised immediately prior
to such reorganization, reclassification or other change, all subject to further
adjustment as provided herein.



                                       4.
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               4.3 Merger, Consolidation or Sale of Assets. If at any time or
from time to time there shall be a capital reorganization of the Series A Stock
(or any securities into which such Series A Stock is convertible) (other than a
subdivision, combination, reclassification or exchange of shares provided for
elsewhere in this Section 4) or a merger or consolidation of the Company with or
into another corporation, or the sale of all or substantially all of the
Company's assets and properties to any other person or entity, then as a part of
such reorganization, merger, consolidation or sale, provision shall be made so
that the Holder shall thereafter be entitled to receive upon the exercise of
this Warrant, the number of shares of stock or other securities or property of
the Company, or of the successor corporation resulting from such reorganization,
merger, consolidation or sale, to which a holder of the number of shares of
Series A Stock (or any shares of stock or other securities which may be)
issuable upon the exercise of this Warrant would have received if this Warrant
had been exercised immediately prior to such reorganization, merger,
consolidation or sale.

               4.4 Notice of Adjustments and Record Dates. The Company shall
promptly notify the Holder in writing of each adjustment or readjustment of the
exercise price hereunder and the number of shares of Series A Stock (or any
shares of stock or other securities which may be) issuable upon the exercise of
this Warrant. Such notice shall state the adjustment or readjustment and show in
reasonable detail the facts on which that adjustment or readjustment is based.
In the event of any taking by the Company of a record of the holders of Series A
Stock for the purpose of determining the holders thereof who are entitled to
receive any dividend or other distribution, the Company shall notify the Holder
in writing of such record date at least twenty (20) days prior to the date
specified therein.

               4.5 No Impairment. The Company shall not avoid or seek to avoid
the observance or performance of any of the terms to be observed or performed
hereunder by the Company, but shall at all times in good faith assist in the
carrying out of all the provisions of this Warrant. Without limiting the
generality of the foregoing, the Company (a) shall at all times reserve and keep
available a number of its authorized shares of Series A Stock (and Common Stock
into which such shares are convertible into such), free from all preemptive
rights therein, which shall be sufficient to permit the exercise of this Warrant
and (b)shall take all such action as may be necessary or appropriate in order
that all shares of Series A Stock (and Common Stock into which such shares are
convertible into) as may be issued pursuant to the exercise of this Warrant
shall, upon issuance, be duly and validly issued, fully paid and nonassessable
and free from all taxes, liens and charges with respect to the issue thereof.

        5. Replacement of Warrants. On receipt by the Company of evidence
reasonably satisfactory to the Company of the loss, theft, destruction or
mutilation of this Warrant and, in the case of any such loss, theft or
destruction of this Warrant, on delivery of an indemnity agreement reasonably
satisfactory in form and amount to the Company or, in the case of any such
mutilation, on surrender and cancellation of such Warrant, the Company at its
expense shall execute and deliver to the Holder, in lieu thereof, a new Warrant
of like tenor.

        6. Investment Intent. Unless a current registration statement under the
Securities Act of 1933, as amended, shall be in effect with respect to the
securities to be issued upon exercise of this Warrant, the Holder, by accepting
this Warrant, covenants and agrees that, at the time of exercise hereof, and at
the time of any proposed transfer of any securities acquired upon



                                       5.
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exercise hereof, the Holder shall deliver to the Company a written statement
that the securities acquired by the Holder upon exercise hereof are for the own
account of the Holder for investment and are not acquired with a view to, or for
sale in connection with, any distribution thereof (or any portion thereof) and
with no present intention (at any such time) of offering or distributing such
securities (or any portion thereof).

        7. No Rights or Liability as a Shareholder. This Warrant does not
entitle the Holder hereof to any voting rights or other rights as a shareholder
of the Company. No provisions hereof, in the absence of affirmative action by
the Holder to purchase Series A Stock, and no enumeration herein of the rights
or privileges of the Holder, shall give rise to any liability of the Holder as a
shareholder of the Company.

        8. Miscellaneous.

               8.1 Transfer of Warrant. This Warrant shall not be transferable
or assignable in any manner and no interest shall be pledged or otherwise
encumbered by Holder without the express written consent of the Company, and any
such attempted disposition of this Warrant or any portion hereof shall be of no
force or effect.

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

               8.3 Notices. Any notice required or permitted under this Warrant
shall be given in writing and in accordance with Section 6.3 of the Purchase
Agreement (for purposes of which, the term "Investor" shall mean Holder
hereunder), except as otherwise expressly provided in this Warrant.

               8.4 Attorneys' Fees. If any action at law or in equity is
necessary to enforce or interpret the terms of this Warrant, the prevailing
party shall be entitled to reasonable attorneys' fees, costs and disbursements
in addition to any other relief to which such party may be entitled.

               8.5 Amendments and Waivers. Any term of this Warrant may be
amended and the observance of any term of this Warrant may be waived (either
generally or in a particular instance and either retroactively or
prospectively), with the written consent of the Company and the holders of
Warrants representing together the right to purchase at least fifty-one percent
(51%) of all of the Series A Stock of the Company subject to purchase pursuant
to all of the Warrants and in accordance with the Purchase Agreement. Any
amendment or waiver effected in accordance with this Section 8.5 shall be
binding upon the Holder of this Warrant (and of any securities into which this
Warrant is convertible), each future holder of all such securities, and the
Company.

               8.6 Severability. If one or more provisions of this Warrant are
held to be unenforceable under applicable law, such provision shall be excluded
from this Warrant and the balance of the Warrant shall be interpreted as if such
provision were so excluded and shall be enforceable in accordance with its
terms.



                                       6.
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               8.7 Governing Law. This Warrant shall be governed by and
construed and enforced in accordance with the laws of the State of California,
without giving effect to its conflicts of laws principles.


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                                       7.
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               8.8 Counterparts. This Warrant may be executed in one or more
counterparts, each of which shall be deemed an original, but all of which
together shall constitute one and the same instrument.

Date: May 20, 1998                      IRORI, a California corporation



                                        By:____________________________________
                                             Riccardo Pigliucci
                                             Chief Executive Officer


ACKNOWLEDGED AND AGREED:

_________________________________

_________________________________

_________________________________

By:______________________________

Name:____________________________

Its:_____________________________


<PAGE>   9


                                   SCHEDULE 1


                              FORM OF SUBSCRIPTION

                   (To be signed only on exercise of Warrant)


To: IRORI


        The undersigned, the holder of the Warrant attached hereto, hereby
irrevocably elects to exercise the purchase rights represented by such Warrant
for, and to purchase thereunder, ________________* shares of Series A Preferred
Stock of IRORI, and herewith makes payment of $ ___________therefor, and
requests that the certificates for such shares be issued in the name of, and
delivered to ___________________________________________, whose address is

__________________________________________________________________________.


                                        ________________________________________
                                        (Signature must conform in all respects
                                        to name of the Holder as specified on
                                        the face of the Warrant)


                                        ________________________________________
                                                      (Print Name)

                                        ________________________________________
                                                       (Address)


Dated: ____________________


----------
* Insert here the number of shares as to which the Warrant is being exercised.


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                                   Schedule A


<TABLE>
<CAPTION>

<S>                                                     <C>
Number          Warrant holder                          Number of shares
------          --------------                          ----------------

5         Enterprise Partners III, L.P.                      81,865

6         Enterprise Partners III Associates, L.P.           7,118

7         Mayfield VIII                                      84,536

8         Mayfield Associates Fund II                        4,448

9         Crosspoint Venture Partners-1996                   14,388
</TABLE>