<PAGE>

                                                                    EXHIBIT 4.11


     THE SECURITIES REPRESENTED BY THIS CERTIFICATE HAVE NOT BEEN REGISTERED
UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE "ACT"), OR ANY STATE
SECURITIES LAW AND MAY NOT BE TRANSFERRED EXCEPT (i) PURSUANT TO AN EFFECTIVE
REGISTRATION STATEMENT UNDER THE ACT OR (ii) UPON FIRST FURNISHING TO THE
COMPANY AN OPINION OF COUNSEL SATISFACTORY TO IT THAT SUCH TRANSFER IS NOT IN
VIOLATION OF THE REGISTRATION REQUIREMENTS OF THE ACT OR ANY STATE SECURITIES
LAW.


                         GENZYME TRANSGENICS CORPORATION
                        WARRANT TO PURCHASE COMMON STOCK


         This certifies that, for value received, Genzyme Corporation
("GENZYME") is entitled to subscribe for and purchase up to 288,000 shares
(subject to adjustment from time to time pursuant to the provisions of Section 5
hereof) of fully paid and nonassessable Common Stock of GENZYME TRANSGENICS
CORPORATION, a Massachusetts corporation (the "Company"), at the Warrant Price
(as defined in Section 2 hereof), subject to the provisions and upon the terms
and conditions hereinafter set forth. The shares of Common Stock issuable upon
exercise or conversion of this Warrant are referred to herein as "WARRANT
SHARES".

         As used herein, the term "COMMON STOCK" shall mean the Company's
presently authorized Common Stock, $0.01 par value per share, and any stock into
or for which such Common Stock may hereafter be converted or exchanged.

         This Warrant to purchase Common Stock (this "WARRANT") is issued in
consideration for that certain Guaranty, dated as of December 28, 1998, issued
by Genzyme to Fleet National Bank (the "BANK") with respect to the obligations
of the Company under a Credit Agreement of even date herewith between the Bank
and the Company (the "CREDIT AGREEMENT") and a Guaranty of even date herewith
between the Bank and Genzyme (the "GUARANTY"). 

    1.   TERM OF WARRANT; VESTING SCHEDULE.

         (a) TERM. Subject to the vesting schedule set forth in the following
paragraph, the purchase or conversion right represented by this Warrant may be
exercised, in whole or in part, at any time during the period beginning on the
date hereof (the "ISSUE DATE") and ending on December 28, 2008 (the "EXPIRATION
DATE").

         (b) VESTING SCHEDULE. This Warrant shall be exercisable at any time
following the Issue Date as to 96,000 shares of Common Stock and shall become
exercisable at any time following each of the first and second anniversaries of
the Issue Date as to such additional number of shares of Common Stock equal to
the product obtained by multiplying: (i) 96,000 by (ii) a fraction, the
numerator of which shall be the sum of the Revolving Credit Commitment and the
Term Loan Commitment (each as defined in the Credit Agreement) on such
anniversary date, and the denominator of which shall be $24,600,000.
Notwithstanding the foregoing, all unvested 

<PAGE>

Warrant Shares shall become exercisable immediately upon the payment by Genzyme
to the Bank of any amounts due under the Guaranty.

    2.   WARRANT PRICE. The initial exercise price of this Warrant is $4.875,
subject to adjustment from time to time pursuant to the provisions of Section 5
hereof (the "WARRANT PRICE").

    3.   METHOD OF EXERCISE OR CONVERSION; PAYMENT; ISSUANCE OF NEW WARRANT.

         (a) EXERCISE. Subject to Section 1 hereof, the purchase right
represented by this Warrant may be exercised by the holder hereof, in whole or
in part, by the surrender of this Warrant (with the notice of exercise form
attached hereto as EXHIBIT 1 duly executed) at the principal office of the
Company and by the payment to the Company, by check or wire transfer, of an
amount equal to the then applicable Warrant Price per share multiplied by the
number of shares then being purchased. The Company agrees that the shares so
purchased shall be deemed to be issued to the holder hereof as the record owner
of such shares as of the close of business on the date on which this Warrant
shall have been surrendered and payment made for such shares as aforesaid. In
the event of any exercise of this Warrant, certificates for the shares of stock
so purchased shall be delivered to the holder hereof within 15 days thereafter
and, unless this Warrant has been fully exercised or expired, a new warrant
representing the portion of the shares, if any, with respect to which this
Warrant shall not then have been exercised shall also be issued to the holder
hereof within such 15-day period.

         (b) CONVERSION. Pursuant to the following formula and subject to
Section 1 hereof, the holder has a right to convert its purchase rights under
this Warrant (the "CONVERSION RIGHT"), in whole or in part, into a number of
shares of Common Stock of the Company by surrendering this Warrant (with the
notice of exercise form attached hereto as EXHIBIT 1 duly executed) at the
principal office of the Company, specifying the number of shares of Common Stock
of the Company subject to this Warrant which the holder desires to convert.

                                  X = Y (A - B)
                                      --------- 
                                         A

    where     X  =   the number of shares of Common Stock to be issued to the 
                     holder;

              Y  =   the number of shares of Common Stock subject to this
                     Warrant for which the Conversion Right is being exercised;
                                    
              A  =   the fair market value of one share of Common Stock;

              B  =   the Warrant Price

    As used herein, the fair market value of a share of Common Stock shall mean,
with respect to each share of Common Stock, the closing price per share of the
Company's Common Stock on the principal national securities exchange on which
the Common Stock is then listed or admitted to trading or, if not then listed or
admitted to trading on any such exchange, on The 

                                       2
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Nasdaq National Market, or if not then listed or traded on any such exchange or
market, the bid price per share on the Nasdaq Small-Cap Market or, in the sole
discretion of the Board of Directors of the Company, any other over-the-counter
market, including the OTC Bulletin Board, which reports bid and asked or last
sale prices and volume of sales, averaged over the ten consecutive trading days
prior to the business day on which notice of exercise duly executed and this
Warrant are duly delivered to the Company. If at any time such quotations are
not available, the current fair market value of a share of Common Stock shall be
the highest price per share which the Company could obtain from a willing buyer
(not a current employee or director) for shares of Common Stock sold by the
Company, from authorized but unissued shares, as determined in good faith by the
Board of Directors of the Company. The Company agrees that the shares so
converted shall be deemed to be issued to the holder hereof as the record owner
of such shares as of the close of business on the date on which this Warrant
shall have been surrendered as aforesaid. In the event of any conversion of this
Warrant, certificates for the shares of stock so converted shall be delivered to
the holder hereof within 15 days thereafter and, unless this Warrant has been
fully converted or expired, a new Warrant representing the portion of the
shares, if any, with respect to which this Warrant shall not then have been
converted shall also be issued to the holder hereof within such 15-day period.

    4.   STOCK FULLY PAID; RESERVATION OF SHARES. All Common Stock which may be
issued upon the exercise or conversion of this Warrant will, upon issuance, be
fully paid and nonassessable, and free from all taxes, liens and charges with
respect to the issue thereof. During the period within which the rights
represented by this Warrant may be exercised, the Company will at all times have
authorized, and reserved for the purpose of the issuance upon exercise or
conversion of the purchase rights evidenced by this Warrant, a sufficient number
of shares of its Common Stock to provide for the complete exercise of the rights
represented by this Warrant.

    5.   ADJUSTMENTS.

         (a) STOCK DIVIDENDS AND STOCK SPLITS. If, at any time after the date
hereof and before the Expiration Date, (i) the Company shall fix a record date
for the issuance of any stock dividend payable in shares of Common Stock or (ii)
the number of shares of Common Stock outstanding shall have been increased by a
subdivision or split-up of shares of Common Stock, then, on the record date
fixed for the determination of holders of Common Stock entitled to receive such
dividend or immediately after the effective date of such subdivision or
split-up, as the case may be, the number of shares of Common Stock to be
delivered upon exercise of this Warrant will be appropriately increased so that
the holder thereafter will be entitled to receive the number of shares of Common
Stock that the holder would have owned immediately following such action had
this Warrant been fully exercised (without regard to vesting dates) immediately
prior thereto, and the Warrant Price will be appropriately adjusted.

         (b) COMBINATION OF STOCK. If, at any time after the date hereof and
before the Expiration Date, the number of shares of Common Stock outstanding
shall have been decreased by a reverse stock split or other combination of the
outstanding shares of Common Stock, then, immediately after the effective date
of such combination, the number of shares of Common Stock to be delivered upon
exercise of this Warrant will be appropriately decreased so that the 

                                       3
<PAGE>

holder thereafter will be entitled to receive the number of shares of Common
Stock that the holder would have owned immediately following such action had
such Warrant been fully exercised (without regard to vesting dates) immediately
prior thereto, and the Warrant Price will be appropriately adjusted.

         (c) REORGANIZATION, ETC. If any capital reorganization of the Company,
or any reclassification of the Common Stock, or any consolidation of the Company
with or merger of the Company with or into any other person or any sale, lease
or other transfer of all or substantially all of the assets of the Company to
any other person (including any individual, partnership, joint venture,
corporation, trust or group thereof) shall be effected in such a way that,
following consummation of such transaction, the holders of Common Stock shall be
entitled to receive stock, securities or assets with respect to or in exchange
for Common Stock, then, upon exercise or conversion of this Warrant in
accordance with Section 3 hereof, the holder shall have the right to receive the
kind and amount of stock, securities or assets receivable upon such
reorganization, reclassification, consolidation, merger or sale, lease or other
transfer by a holder of the number of shares of Common Stock that the holder
would have been entitled to receive upon exercise or conversion of this Warrant
pursuant to Section 3 hereof had such Warrant been exercised immediately before
such reorganization, reclassification, consolidation, merger or sale, lease or
other transfer, subject to adjustments that shall be as nearly equivalent as may
be practicable to the adjustments provided for in this Section 5.

         (d) RIGHTS OFFERING. If the Company, at any time after the date hereof
and before the Expiration Date, shall issue or sell or fix a record date for the
issuance of rights, options, warrants or convertible or exchangeable securities
to all holders of Common Stock entitling them to subscribe for or purchase
Common Stock (or securities convertible into Common Stock) at a price per share
(or having a conversion price per share) that, together with the value of any
consideration paid for any such rights, options, warrants or convertible or
exchangeable securities (as determined in good faith by the Board of Directors
of the Company) is less than the fair market value of a share of Common Stock as
of the date of such issuance or sale or on such record date: then, immediately
after the date of such issuance or sale or on such record date, the holder shall
have the right to receive, upon the same terms as the holders of Common Stock,
the kind and amount of rights, options, warrants or convertible or exchangeable
securities receivable in such offering by a holder of the number of shares of
Common Stock that the holder would have been entitled to receive upon exercise
of this Warrant pursuant to Section 1 hereof had such Warrant been exercised
immediately (without regard to vesting dates) before such issuance or the record
date for such instance.

         (e) SPECIAL DIVIDEND. If (other than in dissolution or liquidation)
securities of the Company (other than shares of Common Stock or securities
issued pursuant to a shareholder rights or similar plan) or assets (other than
cash dividends) are issued by way of a dividend on outstanding shares of Common
Stock, then the Warrant Price shall be adjusted so that it shall equal the price
determined by multiplying the Warrant Price in effect immediately prior to the
close of business on the record date for the determination of the stockholders
entitled to receive such dividend by a fraction, the numerator of which shall be
the last sale price of the Common Stock on such record date less the then fair
market value as determined by the Board of Directors of the Company, whose
determination shall be conclusive, of the portion of the securities or 

                                       4
<PAGE>

assets distributed applicable to one share of Common Stock, and the denominator
of which shall be such last sale price. Such adjustment shall become effective
immediately prior to the opening of business on the day following such record
date.

         (f) LIMITATIONS. Anything in this Section 5 to the contrary
notwithstanding, no adjustment in the Warrant Price in accordance with the
provisions of 5(a), 5(b), 5(c), 5(d) or 5(e), hereof need be made if such
adjustment would amount to a change in such Warrant Price of less than $0.01;
PROVIDED, HOWEVER, that the amount by which any adjustment is not made by reason
of the provisions of this Section 5(f) shall be carried forward and taken into
account at the time of any subsequent adjustment in the Warrant Price.

         (g) READJUSTMENTS. If an adjustment is made under Sections 5(a), 5(b),
5(c), 5(d) or 5(e), and the event to which the adjustment relates does not
occur, then any adjustments in the Warrant Price or the number of Warrant Shares
that were made in accordance with such sections shall be adjusted back to the
Warrant Price and the number of Warrant Shares that were in effect immediately
prior to the date of or record date for such event.

         (h) NOTICE OF ADJUSTMENT UNDER THIS WARRANT. Upon any adjustment of the
Warrant Price or the number of Warrant Shares, then, and in each such case, the
Company shall give written notice thereof, in the form of an officer's
certificate, to the holder hereof which notice shall state the Warrant Price
resulting from such adjustment and the increase or decrease, if any, in the
number of Warrant Shares at such price upon the exercise of this Warrant,
setting forth in reasonable detail the method of calculation and the facts upon
which such calculation is based. However, failure to give such notice, or any
defect therein, shall not affect the legality or validity of the subject
adjustments.

         (i) CERTIFICATE OF INDEPENDENT PUBLIC ACCOUNTANTS. The Company may
retain a firm of independent public accountants of recognized standing (who may
be any such firm regularly employed by the Company) to make any computation
required under this Section 5, and a certificate signed by such firm shall be
conclusive evidence of the correctness of the computation made under this
Section 5.

    6.   FRACTIONAL SHARES. No fractional shares of Common Stock will be issued 
in connection with any exercise hereunder, but in lieu of such fractional shares
the Company shall make a cash payment therefor upon the basis of the fair market
value of a share of Common Stock as of the date of exercise.

    7.   COMPLIANCE WITH THE ACT; REGISTRATION RIGHTS.

         (a) COMPLIANCE WITH THE ACT. The holder of this Warrant, by acceptance
hereof, agrees that this Warrant and the shares of Common Stock to be issued
upon exercise hereof are being acquired for investment for such holder's own
account and not with a view toward distribution hereof or thereof, and that it
will not offer, sell or otherwise dispose of this Warrant or any shares of
Common Stock to be issued upon exercise hereof unless this Warrant has been
registered under the Act and applicable state securities laws or (i) such
registration is 

                                       5
<PAGE>

not required and (ii) an opinion of counsel satisfactory to the Company is
furnished to the Company to that effect.

         (b) REGISTRATION RIGHTS. The holder shall be entitled, with respect to
the shares of Common Stock issuable upon the exercise or conversion hereof, to
the same registration rights as are applicable to the shares of Common Stock
already held by Genzyme, which registration rights are set forth in Section 8 of
the Series A Convertible Preferred Stock Purchase Agreement dated May 1, 1993
between the Company and Genzyme.

    8.   TRANSFER AND EXCHANGE OF WARRANT.

         (a) TRANSFER. This Warrant may be transferred or succeeded to by any
person; PROVIDED, HOWEVER, that the Company is given written notice by such
transferee at the time of such transfer, stating the name and address of the
transferee and identifying the securities with respect to which the rights
hereunder are being assigned.

         (b) EXCHANGE. Subject to compliance with the terms hereof, this Warrant
and all rights hereunder are transferable, in whole or in part, at the office of
the Company by the holder hereof, in person or by duly authorized attorney, upon
surrender of this Warrant properly endorsed. Each taker and holder of this
Warrant, by taking or holding the same, consents and agrees that this Warrant,
when endorsed in blank, shall be deemed negotiable; provided that the last
holder of this Warrant as registered on the books of the Company may be treated
by the Company and all persons dealing with this Warrant as the absolute owner
hereof for any purposes and as the person entitled to exercise the rights
represented by this Warrant or to transfer hereof on the books of the Company,
any notice to the contrary notwithstanding, unless and until such holder seeks
to transfer registered ownership of this Warrant on the books of the Company and
such transfer is effected.

    9.   MISCELLANEOUS.

         (a) NO RIGHTS AS SHAREHOLDER. No holder of this Warrant, as such, shall
be entitled to vote or receive dividends or be deemed the holder of Common Stock
or any other securities of the Company which may at any time be issuable on the
exercise hereof for any purpose, nor shall anything contained herein be
construed to confer upon the holder of this Warrant, as such, any of the rights
of a shareholder of the Company or any right to vote for the election of
directors or upon any matter submitted to shareholders at any meeting thereof,
or to give or withhold consent to any corporate action (whether upon any
recapitalization, issuance of stock, reclassification of stock, change of par
value or change of stock to no par value, consolidation, merger, conveyance or
otherwise) or to receive notice of meetings, or to receive dividends or
subscription rights or otherwise until this Warrant shall have been exercised or
converted and the shares purchasable upon the exercise or conversion hereof
shall have become deliverable, as provided herein.

         (b) REPLACEMENT. On receipt of evidence reasonably satisfactory to the
Company of the loss, theft, destruction or mutilation of this Warrant and, in
the case of loss, theft or destruction, on delivery of an indemnity agreement,
or bond reasonably satisfactory in form 

                                       6
<PAGE>

and amount to the Company or, in the case of mutilation, on surrender and
cancellation of this Warrant, the Company, at its expense, will execute and
deliver, in lieu of this Warrant, a new warrant of like tenor.

         (c) NOTICE. Any notice given to either party under this Warrant shall
be in writing, and any notice hereunder shall be deemed to have been given upon
the earlier of (i) delivery thereof by hand delivery, by courier, or by standard
form of telecommunication, and (ii) three (3) business days after the mailing
thereof if sent registered mail with postage prepaid, addressed to the Company
at its principal executive offices and to the holder at its address set forth in
the Company's books and records or at such other address as the holder may have
provided to the Company in writing.

         (d) NO IMPAIRMENT. The Company will not, by amendment of its Restated
Articles of Organization of through any reorganization, transfer of assets,
consolidation, merger, dissolution, issue or sale of securities or any other
voluntary action, avoid or seek to avoid the observance or performance of any of
the terms to be observed or performed hereunder by the Company, but will at all
times in good faith assist in the carrying out of all the provisions in the
Warrant.

         (e) GOVERNING LAW. This Warrant shall be governed by and construed
under the laws of the Commonwealth of Massachusetts.

    IN WITNESS WHEREOF, this Warrant is executed as of this 28th day of
December, 1998.

                         GENZYME TRANSGENICS CORPORATION



                         By:   /s/ John B. Green                           
                            --------------------------------------------------
                            Name:  John B. Green
                            Title: Vice President and Chief Financial Officer






                                       7
<PAGE>

                                                                       EXHIBIT 1


                               NOTICE OF EXERCISE


TO:   GENZYME TRANSGENICS CORPORATION

      1. Check Box that Applies:

      / / The undersigned hereby elects to purchase ______ shares of Common
Stock of GENZYME TRANSGENICS CORPORATION pursuant to the terms of the attached
Warrant, and tenders herewith cash payment of the purchase price of such shares
in full.

      / / The undersigned hereby elects to convert ______ shares subject to the
attached Warrant into shares of Common Stock of GENZYME TRANSGENICS CORPORATION
pursuant to the terms of the attached Warrant.

      2. Please issue a certificate or certificates representing said shares of
Common Stock in the name of the undersigned or in such other name as is
specified below:


                      -------------------------------------
                                     (Name)


                      -------------------------------------


                      -------------------------------------
                                    (Address)


                                          -------------------------------------
                                          Signature




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