<PAGE>   1
                                                                     EXHIBIT 4.1

THIS NOTE HAS NOT BEEN REGISTERED, AND THE SHARES OF STOCK WHICH MAY BE ISSUABLE
UPON CONVERSION OF THIS NOTE WILL NOT HAVE BEEN REGISTERED, UNDER THE SECURITIES
ACT OF 1933, AS AMENDED, OR ANY OTHER APPLICABLE SECURITIES LAW (COLLECTIVELY
THE "ACTS") AND MAY NOT BE OFFERED FOR SALE, SOLD, PLEDGED, OTHERWISE
HYPOTHECATED OR OTHERWISE TRANSFERRED WITHOUT AN EFFECTIVE REGISTRATION
STATEMENT RELATING THERETO UNDER SUCH ACTS OR PURSUANT TO AN EXEMPTION FROM
REGISTRATION UNDER THE ACTS, THE AVAILABILITY OF WHICH IS TO BE ESTABLISHED TO
THE REASONABLE SATISFACTION OF THE COMPANY.

                           CONVERTIBLE PROMISSORY NOTE

                                                                   June 30, 1997
US$755,000                                                  Radnor, Pennsylvania


        FOR VALUE RECEIVED, ARENA PHARMACEUTICALS INC. (the "Company") whose
address is 203 Garden Place, Radnor, Pennsylvania 19087, promises, subject to
the other terms and conditions herein contained, to pay to the order of Tripos,
Inc. (which, together with any permitted assignee of this Note, is referred to
herein as "Holder") at 1699 S. Hanley Road, St. Louis, Missouri 63144-2913, or
at such other address as may be designated in written notice by the Holder to
the Company, the principal amount of Seven Hundred Fifty-Five Thousand Dollars
($755,000) (the "Principal Amount"), together with interest on the outstanding
Principal Amount at the annual rate of nine and one-half percent (9_%), from the
date first set forth above, based on a 365 day year.

        1. DEFINITIONS.

        As used herein, the following terms, unless the context otherwise
required, shall have the following meanings:

            1.1 "Act" shall mean the Securities Act of 1933, as amended, or any
similar federal statute, and the rules and regulations thereunder, as shall be
in effect at the time.

            1.2 "Conversion Price" shall have the meaning ascribed in Section
3.3.

            1.3 "Effective Date" shall have the meaning ascribed in Section 3.2.

            1.4 "Holder" shall mean any person who shall at the time be the
holder of this Note, and any additional Holder as defined in Section 6.

            1.5 "Maturity Date" shall have the meaning ascribed in Section 2.1.

            1.6 "Note" shall mean this Convertible Note issued to the Holder and
any new note as defined in Section 6.

            1.7 "Principal Amount" shall have the meaning ascribed above.

<PAGE>   2

            1.8 "Series A Preferred Stock" shall mean the shares of preferred
stock of the Company which have those rights, preferences and privileges set
forth in the Company's Amended and Restated Certificate of Incorporation, as
filed with the Secretary of State of the State of Delaware,

            1.9 "Shares" shall mean the shares of Series A Preferred Stock that
the Holder is entitled to receive upon conversion of this Note.

            All other capitalized terms not otherwise defined herein shall have
the meanings given to them in that certain Purchase Agreement, of even date
herewith, by and between the Holder and the Company (the "Purchase Agreement").

        2. PRECONVERSION PAYMENT OF PRINCIPAL AND INTEREST.

            2.1 PAYMENT AT MATURITY. Unless the obligation of the Company to pay
principal and interest hereunder is previously discharged by conversion to
Shares pursuant to Section 3 hereof, the Principal Amount and all interest
accrued hereunder shall be paid in full on June 26, 2002 (the "Maturity Date")
in United States funds by wire transfer to the Holder per instructions from the
Holder. The Company shall not have the right to prepay this Note.

            2.2 DEFAULT.

                (a) An "Event of Default" occurs if, prior to the Effective Date
and while this Note is outstanding: (i) the Company fails to pay to the Holder
on the Maturity Date the Principal Amount and all accrued interest thereon; (ii)
the Company, pursuant to or within the meaning of any Bankruptcy Law: (A)
commences a voluntary case, (B) consents to the entry of an order for relief
against it in an involuntary case, (C) consents to the appointment of a
Custodian for it or for all or substantially all of its property, or (D) makes a
general assignment for the benefit of its creditors; (iii) a court of competent
jurisdiction enters an order or decree under any Bankruptcy Law that remains
unstayed and in effect for 60 days and that: (A) is for relief against the
Company in an involuntary case, (B) appoints a Custodian for the Company or for
all or substantially all of its property, (C) orders the liquidation of the
Company, or (D) requires all or substantially all of the Company's property to
be sold or otherwise transferred; (iv) all or substantially all of the Company's
property shall be sold or otherwise transferred in any foreclosure action; or
(v) the Company shall breach or be in default of any representation, warranty,
covenant or agreement made by it in the Purchase Agreement, the Investor Rights
Agreement or the Co-Sale Agreement, each of even date herewith.

            The term "Bankruptcy Law" means Title 11, U.S. Code or any similar
federal or state law for the relief of debtors. The term "Custodian" means any
receiver, trustee, assignee, liquidation or similar official under any
Bankruptcy Law. Nothing in this Section 2.2 shall limit the effect of Section
2.3.

                (b) If an Event of Default occurs and is continuing, the Holder
of this Note may declare the Principal Amount and all accrued interest to be due
and payable by sending notice to the Company. Upon such declaration, the
Principal Amount and all accrued interest thereon shall be due and payable
immediately.


                                      -2-
<PAGE>   3

            2.3 LIQUIDATION, ETC.

                (a) In the event of (i) any liquidation, dissolution, or winding
up of the Company, whether voluntary or involuntary, (ii) a merger of
consolidation of the Company with another corporation (other than a wholly owned
subsidiary of the Company) in which the Company shall not be the survivor, (iii)
the sale, transfer or lease (other than a transfer or lease to a bona fide
lender to secure an obligation of the Company) of all or substantially all of
the assets of the Company, or (iv) a sale of more than 51% of the outstanding
voting stock of the Company, there shall be deemed to be a liquidation of the
Company for purposes of this Note; provided that, if the stockholders of the
Company immediately prior to any transaction described in clauses (i) through
(iv) above are the holders of at least 51% of the outstanding voting securities
of the surviving or acquiring corporation or entity immediately after the
completion of the transaction (for purposes of this calculation, securities that
any stockholder of the Company owned prior to the transaction as a securities
holder of another party to the transaction shall be disregarded), then such
merger, consolidation, sale, transfer, or lease shall not be deemed to be a
liquidation of the Company.

                (b) If there is a liquidation or deemed liquidation of the
Company pursuant to Section 2.3(a), then, without demand or notice, the
Principal Amount and all accrued interest thereon shall be due and payable
immediately.

                (c) The Company shall provide written notice to the Holder at
least thirty (30) days prior to a voluntary liquidation or deemed liquidation of
the Company.

        3. CONVERSION AND DISCHARGE OF PRINCIPAL AND INTEREST OBLIGATION.

            3.1 OPTIONAL CONVERSION. The Holder, by notice to the Company, may
elect to convert all or a portion of the Principal Amount on the date of such
notice into that number of shares of the Company's Series A Preferred Stock as
provided in Section 3.2.

            3.2 NUMBER OF SHARES -- ISSUANCE OF SHARES. The conversion date
described in Section 3.1 shall be referred to herein as the "Effective Date". On
the Effective Date, this Note shall be converted into that number of shares of
Series A Preferred Stock equal to the quotient resulting from dividing the
number of dollars of the Principal Amount plus the accrued interest to be
converted by the Conversion Price. No fractional Shares will be issued. The
Company shall pay the Holder in cash the value of any fractional Share, using
the Conversion Price to determine the value.

            3.3 CONVERSION PRICE. The Conversion Price shall equal the quotient
resulting from dividing the sum of the Principal Amount plus the accrued
interest by the Principal Amount. The Conversion Price and the number of shares
issuable upon conversion of this Note are subject to adjustment as provided in
Section 4 of this Note.


                                      -3-
<PAGE>   4

        4. ADJUSTMENT OF NUMBER AND KIND OF SHARES AND ADJUSTMENT OF CONVERSION
PRICE.

            4.1 ADJUSTMENTS. The number and kind of securities of the Company
issuable upon the conversion of this Note and the Conversion Price shall be
subject to adjustment from time to time upon the occurrence of certain events,
as follows:

                (a) RECLASSIFICATION, REORGANIZATION, CONSOLIDATION OR MERGER.
In the case of any reclassification of the Series A Preferred Stock, or any
reorganization, consolidation or merger of the Company with or into another
corporation (other than a merger or reorganization with respect to which the
Company is the surviving corporation and which does not result in any
reclassification of the Series A Preferred Stock), the Company, or such
successor corporation, as the case may be, shall execute a new note. The Holder
shall have the right to convert such new note and upon such conversion the right
to receive, in lieu of each share of the Series A Preferred Stock, the number
and kind of securities receivable upon such reclassification, reorganization,
consolidation or merger by a holder of shares of the Series A Preferred Stock
for each share of the Series A Preferred Stock. The aggregate Conversion Price
under the new note shall be the aggregate Conversion Price in effect immediately
prior to the reclassification, reorganization, consolidation or merger. Such new
note shall provide for adjustments which shall be as nearly equivalent as may be
practicable to the adjustments provided for in this Section 4 including, without
limitation, adjustments to the Conversion Price and to the number of shares
issuable upon conversion of this Note. The provisions of this subsection (a)
shall similarly apply to successive reclassifications, reorganizations,
consolidations or mergers.

                (b) SPLIT, SUBDIVISION OR COMBINATION OF SHARES. If the Company
at any time while this Note remains outstanding shall split, subdivide or
combine the Series A Preferred Stock, the Conversion Price shall be
proportionately decreased in the case of a split or subdivision or
proportionately increased in the case of a combination. Any adjustment under
this subsection (b) shall become effective when the split, subdivision or
combination becomes effective.

                (c) STOCK DIVIDENDS. If the Company, at any time while this Note
remains outstanding and unexpired, shall pay a dividend with respect to the
Series A Preferred Stock, payable in shares of Series A Preferred Stock, the
Conversion Price shall be adjusted to that price determined by multiplying the
Conversion Price in effect immediately prior to such date of determination by a
fraction (i) the numerator of which shall be the total number of shares of
Series A Preferred Stock outstanding immediately prior to such dividend or
distribution, and (ii) the denominator of which shall be the total number of
shares of Series A Preferred Stock outstanding immediately after such dividend
or distribution (including shares of Series A Preferred Stock issuable upon
exercise, conversion or exchange of any options or convertible securities issued
as such dividend or distribution). Any adjustment under this subsection (c)
shall become effective on the record date.

                (d) EVENT OF DEFAULT. If an Event of Default occurs and is
continuing, the Conversion Price in effect shall be decreased by one-half (1/2).


                                      -4-
<PAGE>   5


            4.2 ADJUSTMENT OF NUMBER OF SHARES. Upon each adjustment in the
Conversion Price pursuant to this Section 4, the number of Shares issuable upon
conversion of this Note shall be adjusted to the product obtained by multiplying
the number of Shares issuable immediately prior to such adjustment in the
Conversion Price by a fraction (i) the numerator of which shall be the
Conversion Price immediately prior to such adjustment, and (ii) the denominator
of which shall be the Conversion Price immediately after such adjustment.

            4.3 NOTICE OF ADJUSTMENTS. So long as this Note remains outstanding,
whenever the Conversion Price shall be adjusted pursuant to this Section 4. the
Company shall issue a certificate signed by its chief financial officer setting
forth, in reasonable detail, the event requiring the adjustment, the amount of
the adjustment, the method by which such adjustment was calculated and the
Conversion Price after giving effect to such adjustment, and shall cause a copy
of such certificate to be mailed (by first class mail, postage prepaid) to the
Holder.

        5. COMPLIANCE WITH ACT; TRANSFERABILITY OF NOTE; DISPOSITION OF SHARES.

            5.1 LEGENDS. The Shares issued upon conversion of this Note shall be
imprinted with a legend in substantially the following form:

        "THE SECURITIES REPRESENTED BY THIS CERTIFICATE HAVE NOT BEEN REGISTERED
        UNDER THE SECURITIES ACT OF 1933, AS AMENDED, OR ANY OTHER APPLICABLE
        SECURITIES LAW (COLLECTIVELY THE "ACTS") AND MAY NOT BE OFFERED FOR
        SALE, SOLD, PLEDGED OR OTHERWISE TRANSFERRED OR HYPOTHECATED WITHOUT AN
        EFFECTIVE REGISTRATION STATEMENT RELATING THERETO UNDER SUCH ACTS OR
        PURSUANT TO AN EXEMPTION FROM REGISTRATION UNDER THE ACTS, THE
        AVAILABILITY OF WHICH IS TO BE ESTABLISHED TO THE REASONABLE
        SATISFACTION OF THE COMPANY."

            5.2 TRANSFERABILITY AND NON-NEGOTIABILITY OF NOTE AND SHARES. This
Note and the Shares issued upon conversion thereof shall not be sold,
transferred or assigned in whole or in part without compliance with applicable
federal and state securities, laws by the transferor and the transferee
(including, without limitation, the delivery of investment representation
letters and legal opinions reasonably satisfactory to the Company, if reasonably
requested by the Company). Subject to the provisions of this Section 5.2 and
Section 6 below, title to this Note may be transferred in the same manner as a
negotiable instrument transferable by endorsement and delivery, except to a
person or entity deemed by the Board of Directors of the Company, in its
reasonable judgment, to be a competitor of the Company.

        6. ASSIGNMENT; CHANGES. Subject to the provisions of Section 5.2, this
Note may be assigned in whole or in part, by the Holder. If this Note is ever
assigned in part, then (i) upon surrender of this Note, the Company shall issue
and deliver to the assignee a Note with the same terms as this Note and in the
aggregate principal amount assigned by the Holder, (ii) the Company either shall
issue and deliver to the assigning Holder a replacement Note with the same terms
as this Note and in the aggregate outstanding principal amount not assigned or
shall mark this Note so as to indicate an assignment of a portion thereof, (iii)
the term "Note" as used herein and in any such new Note shall include this Note
and any Notes for any part of the original


                                      -5-
<PAGE>   6

principal amount hereof, and (iv) the term of the "Holder" shall include any
assignees holding any Note for any part of the original principal amount of this
Note.

        7. PURCHASE AGREEMENT. If this Note is converted into shares of Series A
Preferred Stock as provided in Section 3 above, the Company and the Holder, at
the time of the delivery to the Holder of the Shares of Series A Preferred
Stock, shall enter into agreements substantially similar to the Investor Rights
Agreement and Co-Sale Agreement, of even date herewith.

        8. MISCELLANEOUS.

            (a) The Holder shall not, by virtue hereof, be entitled to any
rights of a stockholder in the Company, either at law or equity, and the rights
of the Holder are limited to those expressly in this Note and are not
enforceable against the Company, except to the extent set forth herein.

            (b) The terms and provisions of this Note shall inure to the benefit
of, and be binding upon, the Company and the Holders hereof and their respective
permitted successors and assigns.

            (c) THIS NOTE SHALL BE GOVERNED BY AND CONSTRUED FOR ALL PURPOSES
UNDER AND IN ACCORDANCE WITH THE LAWS OF THE STATE OF DELAWARE AS SUCH LAWS ARE
APPLIED TO AGREEMENTS BETWEEN DELAWARE RESIDENTS ENTERED INTO AND PERFORMED
ENTIRELY IN DELAWARE.

            (d) The titles of the sections and subsections of this Note are for
convenience only and are not to be considered in construing this Note.

            (e) All pronouns used herein shall be deemed to include masculine,
feminine and neuter forms.

            (f) The Company waives demand for payment, presentment for payment,
notice of nonpayment or dishonor, protest and notice of protest, except as
expressly provided in this Note. No renewal or extension of this Note, no delay
in the enforcement hereof, and no delay or omission in exercising any right or
power hereunder, shall affect the liability of Company. No delay or omission by
the Holder in exercising any power or right hereunder shall impair such right or
power or be construed to be a waiver of any default, nor shall any single or
partial exercise of any power or right hereunder preclude any or full exercise
thereof or the exercise of any other right or power.

            (g) Any notice or communication by the Company or by the Holder
required or permitted hereunder shall be in writing and shall be deemed
effectively given upon personal delivery, upon confirmed transmission by
telecopy, or upon delivery by air express service or courier as evidenced by a
receipt by a person normally accepting such deliveries for the party, addressed
(i) if to the Holder, at Holder's address set forth above, or at such other
address as the Holder shall have furnished to the Company in writing, or (ii) if
to the Company, at its address set forth above, or at such other address as the
Company shall have furnished to the Holder in writing.


                                      -6-
<PAGE>   7

            (h) It is the intention of the parties to conform strictly to the
usury laws, whether state or federal, that are applicable to this Note. All
agreements between the Company and Holder, whether now existing or hereafter
arising and whether oral or written, are hereby expressly limited so that in no
contingency or event whatsoever, shall the amount paid or agreed to be paid to
Holder, or collected by Holder, for the use, forbearance or detention of the
money loaned or to be loaned hereunder or otherwise, or for the payment or
performance of any covenant or obligation contained herein, or in any other
document evidencing, securing or pertaining to the indebtedness evidenced hereby
exceed the maximum amount permissible under applicable federal or state usury
laws. If under any circumstances whatsoever fulfillment of any provision hereof
or any other documents, at the time performance of such provision shall be due,
shall involve exceeding the limit of validity prescribed by law, then the
obligation to be fulfilled shall be reduced to the limit of such validity; and
if under any circumstances Holder shall ever receive an amount deemed interest
by applicable law, which would exceed the highest lawful rate, such amount that
would be excessive interest under applicable usury laws shall be applied to the
reduction of the principal amount owing hereunder and not to the payment of
interest, or if such excessive interest exceeds the unpaid balance of principal
and such other indebtedness, the excess shall be deemed to have been a payment
made by mistake and shall be refunded to the Company or to any other person
making such payment on the Company's behalf. All sums paid or agreed to be paid
to Holder for the use, forbearance or detention of the indebtedness of the
Company evidenced hereby outstanding from time to time shall, to the extent
permitted by applicable law, and to the extent necessary to preclude exceeding
the limit of validity prescribed by law, be amortized, prorated, allocated and
spread from the date of disbursement of the proceeds of this Note until payment
in full of the loan evidenced hereby so that the actual rate of interest on
account of such indebtedness is uniform throughout the term hereof. The terms
and provisions of this paragraph shall control and supersede every other
provision of all agreements between the Company and Holder.

                                                  ARENA PHARMACEUTICALS INC.




                                                  By:     /s/ Jack Lief
                                                          ----------------------
                                                          Jack Lief, President


                                      -7-