Document:

<PAGE>   1
                                                                    EXHIBIT 10.6

                                  AMENDMENT TO
                 AMENDED AND RESTATED INVESTOR RIGHTS AGREEMENT
                            OF XCYTE THERAPIES, INC.

        This Amendment to the Amended and Restated Investor Rights Agreement
dated as of May 25, 2000 of Xcyte Therapies, Inc. (the "Amendment") is entered
into as of October 18, 2000 by and between Xcyte Therapies, Inc., a Delaware
corporation (the "Company"), the holders of the Company's capital stock listed
on Schedule A attached to the Amended and Restated Investor Rights Agreement
(collectively, the "Investors"), Phoenix Leasing Incorporated and Robert
Kingsbook (each of whom is referred to as a "Warrantholder").

                                     RECITAL

        The Company, the Investors and the Warrantholders are parties to an
Amended and Restated Investor Rights Agreement dated as of May 25, 2000 and
amended by the Addendum to the Series D Preferred Stock Purchase Agreement and
Omnibus Amendment to Series D Financing Documents dated as of August 8, 2000
(the "Rights Agreement"). Capitalized terms used herein without definition shall
have the meaning ascribed to them in the Rights Agreement. The Company and
Landlord are entering into a Lease Agreement dated September 20, 2000 (the
"Lease Agreement") pursuant to which the Company will issue Landlord a warrant
to purchase shares of the Company's Series D Preferred Stock (the "Warrant").

                                    AGREEMENT

        1. Amendment to Section 2.2. Section 2.2 is hereby amended and restated
to read in its entirety as follows:

                2.2 Future Shares. "Future Shares" shall mean shares of any
capital stock of the Company, whether now authorized or not, and any rights,
options or warrants to purchase such capital stock, and securities of any type
that are, or may become, convertible into such capital stock; provided however,
that "Future Shares" do not include (i) the Shares purchased under the Series D
Stock Purchase Agreement (ii) the shares of Common Stock issued or issuable upon
the conversion of the Preferred Stock, (iii) securities offered pursuant to a
registration statement filed under the Act, (iv) securities issued pursuant to
the acquisition of another corporation by the Company by merger or, purchase of
substantially all of the assets or other reorganization, (v) securities issued
in connection with or as consideration for a collaborative partnership
arrangement, as approved by a majority of the Board of Directors of the Company,
or the acquisition, leasing or licensing of technology or other significant
assets to be used in the Company's business, as approved by a majority of the
Board of Directors of the Company, (vi) securities issued or issuable to
officers, directors, employees or consultants of the Company pursuant to any
employee or consultant stock offering, plan or arrangement approved by a
majority of the Board of Directors of the Company and (vii) all shares of Common
Stock or other securities, or options or warrants to purchase Common Stock or
any such other securities, issuable to landlords, financial institutions or
lessors in connection with office leases, commercial credit arrangements,
equipment financings or similar transactions."

<PAGE>   2

        2. No Other Amendments. Except as expressly amended as set forth above,
the Rights Agreement shall remain in full force and effect in accordance with
its terms.

        3. Counterparts. This Amendment may be executed in counterparts, each of
which shall be deemed an original and all of which together shall constitute one
document.

                            (signature page follows)

                                      -2-
<PAGE>   3
        The parties have executed this Amendment to Amended and Restated
Investor Rights Agreement of Xcyte Therapies, Inc. as of the date first written
above.

                                              COMPANY:

                                              XCYTE THERAPIES, INC.

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

                                              By:
                                                   ----------------------------

                                              Name:
                                                    ---------------------------

                                              Its:
                                                   ----------------------------

                                              WARRANTHOLDERS:

                                              PHOENIX LEASING INCORPORATED

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

                                              By:
                                                   ----------------------------

                                              Name:
                                                    ---------------------------

                                              Its:
                                                   ----------------------------

                                              ---------------------------------
                                              Robert Kingsbook

                                              INVESTORS:

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

                                              By:
                                                   ----------------------------

                                              Name:
                                                    ---------------------------

                                              Its:
                                                   ----------------------------

               [SIGNATURE PAGE TO XCYTE THERAPIES, INC. AMENDMENT
               TO AMENDED AND RESTATED INVESTOR RIGHTS AGREEMENT]

<PAGE>   4

                                              INVESTORS:

                                              ALTA CALIFORNIA PARTNERS, L.P.

                                              By:
                                                   ----------------------------

                                              Name:
                                                    ---------------------------

                                              Its:
                                                   ----------------------------

                                              Address: One Embarcadero Center
                                                       Suite 4050
                                                       San Francisco, CA  94111

               [SIGNATURE PAGE TO XCYTE THERAPIES, INC. AMENDMENT
               TO AMENDED AND RESTATED INVESTOR RIGHTS AGREEMENT]

<PAGE>   5

                                              INVESTORS:

                                              ARCH DEVELOPMENT CORPORATION

                                              By:
                                                   ----------------------------

                                              Name:
                                                    ---------------------------

                                              Its:
                                                   ----------------------------

                                              Address: 1000 Second Avenue
                                                       Suite 3700
                                                       Seattle, WA  98104-1053

                                              ARCH VENTURE FUND III, L.P.

                                              By:
                                                   ----------------------------

                                              Name:
                                                    ---------------------------

                                              Its:
                                                   ----------------------------

                                              Address: 1000 Second Avenue
                                                       Suite 3700
                                                       Seattle, WA  98104-1053

                                              ARCH VENTURE PARTNERS II, L.P.

                                              By:
                                                   ----------------------------

                                              Name:
                                                    ---------------------------

                                              Its:
                                                   ----------------------------
                                              Address: 1000 Second Avenue
                                                       Suite 3700
                                                       Seattle, WA  98104-1053

               [SIGNATURE PAGE TO XCYTE THERAPIES, INC. AMENDMENT
               TO AMENDED AND RESTATED INVESTOR RIGHTS AGREEMENT]

<PAGE>   6

                                              INVESTORS:

                                              RONALD J. BERENSON, M.D.

                                              By:
                                                   ----------------------------

                                              Name:
                                                    ---------------------------

                                              Its:
                                                   ----------------------------

                                              Address: 8836 S.E. 74th Place
                                                       Mercer Island, WA  98040

               [SIGNATURE PAGE TO XCYTE THERAPIES, INC. AMENDMENT
               TO AMENDED AND RESTATED INVESTOR RIGHTS AGREEMENT]

<PAGE>   7

                                              INVESTORS:

                                              DLJ CAPITAL CORP.

                                              By:
                                                   ----------------------------

                                              Name:
                                                    ---------------------------

                                              Its:
                                                   ----------------------------

                                              Address: 3000 Sand Hill Road
                                                       Building 3, Suite 170
                                                       Menlo Park, CA  94025

                                              DLJ FIRST ESC L.L.C.

                                              By:
                                                   ----------------------------

                                              Name:
                                                    ---------------------------

                                              Its:
                                                   ----------------------------

                                              Address: 3000 Sand Hill Road
                                                       Building 3, Suite 170
                                                       Menlo Park, CA  94025

                                              DLJ FIRST ESC. L.P.

                                              By:
                                                   ----------------------------

                                              Name:
                                                    ---------------------------

                                              Its:
                                                   ----------------------------

                                              Address: 3000 Sand Hill Road
                                                       Building 3, Suite 170
                                                       Menlo Park, CA  94025

               [SIGNATURE PAGE TO XCYTE THERAPIES, INC. AMENDMENT
               TO AMENDED AND RESTATED INVESTOR RIGHTS AGREEMENT]

<PAGE>   8

                                              INVESTORS:

                                              MPM ASSET MANAGEMENT INVESTORS

                                              By:
                                                   ----------------------------

                                              Name:
                                                    ---------------------------

                                              Its:
                                                   ----------------------------

                                              Address: One Cambridge Center
                                                       Cambridge, MA  02142

                                              MPM BIOVENTURES GMBH & CO.

                                              By:
                                                   ----------------------------

                                              Name:
                                                    ---------------------------

                                              Its:
                                                   ----------------------------

                                              Address: One Cambridge Center
                                                       Cambridge, MA  02142

                                              MPM BIOVENTURES II, LP

                                              By:
                                                   ----------------------------

                                              Name:
                                                    ---------------------------

                                              Its:
                                                   ----------------------------

                                              Address: One Cambridge Center
                                                       Cambridge, MA  02142

                                              MPM BIOVENTURES QP, LP

                                              By:
                                                   ----------------------------

                                              Name:
                                                    ---------------------------

                                              Its:
                                                   ----------------------------

                                              Address: One Cambridge Center
                                                       Cambridge, MA  02142

               [SIGNATURE PAGE TO XCYTE THERAPIES, INC. AMENDMENT
               TO AMENDED AND RESTATED INVESTOR RIGHTS AGREEMENT]

<PAGE>   9

                                              INVESTORS:

                                              SPROUT CAPITAL VII, L.P.

                                              By:
                                                   ----------------------------

                                              Name:
                                                    ---------------------------

                                              Its:
                                                   ----------------------------

                                              Address: 3000 Sand Hill Road
                                                       Building 3, Suite 170
                                                       Menlo Park, CA  94025

                                              SPROUT CEO FUND, L.P.

                                              By:
                                                   ----------------------------

                                              Name:
                                                    ---------------------------

                                              Its:
                                                   ----------------------------

                                              Address: 3000 Sand Hill Road
                                                       Building 3, Suite 170
                                                       Menlo Park, CA  94025

               [SIGNATURE PAGE TO XCYTE THERAPIES, INC. AMENDMENT
               TO AMENDED AND RESTATED INVESTOR RIGHTS AGREEMENT]

<PAGE>   10

                                              INVESTORS:

                                              TGI FUND II, LC

                                              By:
                                                   ----------------------------

                                              Name:
                                                    ---------------------------

                                              Its:
                                                   ----------------------------

                                              Address: 6501 Columbia Center
                                                       701 Fifth Ave.
                                                       Seattle, WA  98104

                                              VENGOTT LC
                                              C/O TREDEGAR INVESTMENTS

                                              By:
                                                   ----------------------------

                                              Name:
                                                    ---------------------------

                                              Its:
                                                   ----------------------------

                                              Address: 6501 Columbia Center
                                                       701 Fifth Ave.
                                                       Seattle, WA  98104

               [SIGNATURE PAGE TO XCYTE THERAPIES, INC. AMENDMENT
               TO AMENDED AND RESTATED INVESTOR RIGHTS AGREEMENT]<PAGE>   1
                                                                   EXHIBIT 10.7

         THE SECURITIES REPRESENTED BY THIS CERTIFICATE HAVE NOT BEEN REGISTERED
UNDER THE SECURITIES ACT OF 1933, AND HAVE BEEN ACQUIRED FOR INVESTMENT AND NOT
WITH A VIEW TO, OR IN CONNECTION WITH, THE SALE OR DISTRIBUTION THEREOF. NO SUCH
SALE OR DISTRIBUTION MAY BE EFFECTED WITHOUT AN EFFECTIVE REGISTRATION STATEMENT
RELATED THERETO OR AN OPINION OF COUNSEL IN A FORM SATISFACTORY TO THE COMPANY
THAT SUCH REGISTRATION IS NOT REQUIRED UNDER THE SECURITIES ACT OF 1933.
-------------------------------------------------------------------------------

Warrant No. <<WarrantNo>>                         Number of Shares: <<NoShares>>
ate of Issuance: <<Date>>                                (subject to adjustment)

                              XCYTE THERAPIES, INC.

                          COMMON STOCK PURCHASE WARRANT

        Xcyte Therapies, Inc., a Delaware corporation (the "Company"), for value
received, hereby certifies that <<Holder>>, or its registered assigns (the
"Registered Holder"), is entitled, subject to the terms set forth below, to
purchase from the Company, at any time after the date hereof and on or before
the Expiration Date (as defined in Section 5 below), up to <<NoShares>> shares
of Common Stock of the Company, at a purchase price of $0.30 per share. The
shares purchasable upon exercise of this Warrant and the purchase price per
share, as adjusted from time to time pursuant to the provisions of this Warrant,
are hereinafter referred to as the "Warrant Stock" and the "Purchase Price,"
respectively.

        This Warrant is issued pursuant to, and is subject to the terms and
conditions of, an Addendum to Series D Preferred Stock Purchase Agreement and
Omnibus Amendment to Series D Financing Agreements dated August 14, 2000 among
the Company and certain Investors (the "Purchase Agreement").

        1.     EXERCISE.

               (a) MANNER OF EXERCISE. This Warrant may be exercised by the
Registered Holder, in whole or in part, by surrendering this Warrant, with the
purchase/exercise form appended hereto as Exhibit A duly executed by such
Registered Holder or by such Registered Holder's duly authorized attorney, at
the principal office of the Company, or at such other office or agency as the
Company may designate, accompanied by payment in full of the Purchase Price
payable in respect of the number of shares of Warrant Stock purchased upon such
exercise. The Purchase Price may be paid by cash, check, wire transfer or by the
surrender of promissory notes or other instruments representing indebtedness of
the Company to the Registered Holder.

               (b) EFFECTIVE TIME OF EXERCISE. 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 in Section 1(a) above. At such

<PAGE>   2

time, the person or persons in whose name or names any certificates for Warrant
Stock shall be issuable upon such exercise as provided in Section 1(d) below
shall be deemed to have become the holder or holders of record of the Warrant
Stock represented by such certificates.

               (c)    NET ISSUE EXERCISE.

                      (i) In lieu of exercising this Warrant in the manner
provided above in Section 1(a), the Registered Holder may elect to receive
shares equal to the value of this Warrant (or the portion thereof being
canceled) by surrender of this Warrant at the principal office of the Company
together with notice of such election on the purchase/exercise form appended
hereto as Exhibit A duly executed by such Registered Holder or such Registered
Holder's duly authorized attorney, in which event the Company shall issue to
such Holder a number of shares of Warrant Stock computed using the following
formula:

                             X =    Y (A - B)
                                    ---------
                                       A
Where          X = The number of shares of Warrant Stock to be issued to the
                      Registered Holder.

               Y = The number of shares of Warrant Stock purchasable under
                      this Warrant (at the date of such calculation).

               A = The fair market value of one share of Warrant Stock (at
                      the date of such calculation).

               B = The Purchase Price (as adjusted to the date of such
                      calculation).

                      (ii) For purposes of this Section 1(c), the fair market
value of Warrant Stock on the date of calculation shall mean with respect to
each share of Warrant Stock:

                             (A) if the exercise is in connection with an
initial public offering of the Company's Common Stock, and if the Company's
Registration Statement relating to such public offering has been declared
effective by the Securities and Exchange Commission, then the fair market value
per share shall be the product of (x) the initial "Price to Public" specified in
the final prospectus with respect to the offering and (y) the number of shares
of Common Stock into which each share of Warrant Stock is convertible at the
date of calculation;

                             (B) if (A) is not applicable, the fair market value
of Warrant Stock shall be at the highest price per share which the Company could
obtain on the date of calculation from a willing buyer (not a current employee
or director) for shares of Warrant Stock sold by the Company, from authorized
but unissued shares, as determined in good faith by the Board of Directors,
unless the Company is at such time subject to an acquisition as described in
Section 5(b) below, in which case the fair market value of Warrant Stock shall
be deemed to be the value received by the holders of such stock pursuant to such
acquisition.

               (d) DELIVERY TO HOLDER. As soon as practicable after the exercise
of this Warrant in whole or in part, and in any event within ten (10) days
thereafter, the Company at its

                                      -2-
<PAGE>   3

expense will cause to be issued in the name of, and delivered to, the Registered
Holder, or as such Holder (upon payment by such Holder of any applicable
transfer taxes) may direct:

                      (i)  a certificate or certificates for the number of
shares of Warrant Stock to which such Registered Holder shall be entitled, and

                      (ii) in case such exercise is in part only, a new warrant
or warrants (dated the date hereof) of like tenor, calling in the aggregate on
the face or faces thereof for the number of shares of Warrant Stock equal
(without giving effect to any adjustment therein) to the number of such shares
called for on the face of this Warrant minus the number of such shares purchased
by the Registered Holder upon such exercise as provided in Section 1(a) or 1(c)
above.

        2.     ADJUSTMENTS.

               (a) STOCK SPLITS AND DIVIDENDS. If outstanding shares of the
Company's Common Stock shall be subdivided into a greater number of shares or a
dividend in Common Stock shall be paid in respect of Common Stock, the Purchase
Price in effect immediately prior to such subdivision or at the record date of
such dividend shall simultaneously with the effectiveness of such subdivision or
immediately after the record date of such dividend be proportionately reduced.
If outstanding shares of Common Stock shall be combined into a smaller number of
shares, the Purchase Price in effect immediately prior to such combination
shall, simultaneously with the effectiveness of such combination, be
proportionately increased. When any adjustment is required to be made in the
Purchase Price, the number of shares of Warrant Stock purchasable upon the
exercise of this Warrant shall be changed to the number determined by dividing
(i) an amount equal to the number of shares issuable upon the exercise of this
Warrant immediately prior to such adjustment, multiplied by the Purchase Price
in effect immediately prior to such adjustment, by (ii) the Purchase Price in
effect immediately after such adjustment.

               (b) RECLASSIFICATION, ETC. In case there occurs any
reclassification or change of the outstanding securities of the Company or of
any reorganization of the Company (or any other corporation the stock or
securities of which are at the time receivable upon the exercise of this
Warrant) or any similar corporate reorganization on or after the date hereof,
then and in each such case the Registered Holder, upon the exercise hereof at
any time after the consummation of such reclassification, change, or
reorganization shall be entitled to receive, in lieu of the stock or other
securities and property receivable upon the exercise hereof prior to such
consummation, the stock or other securities or property to which such Holder
would have been entitled upon such consummation if such Holder had exercised
this Warrant immediately prior thereto, all subject to further adjustment
pursuant to the provisions of this Section 2.

               (c) ADJUSTMENT CERTIFICATE. When any adjustment is required to be
made in the Warrant Stock or the Purchase Price pursuant to this Section 2, the
Company shall promptly mail to the Registered Holder a certificate setting forth
(i) a brief statement of the facts requiring such adjustment, (ii) the Purchase
Price after such adjustment and (iii) the kind and amount of stock or other
securities or property into which this Warrant shall be exercisable after such
adjustment.

                                      -3-
<PAGE>   4

               (d) ACKNOWLEDGEMENT. In order to avoid doubt, it is acknowledged
that the holder of this Warrant shall be entitled to the benefit of all
adjustments in the number of shares of Common Stock of the Company.

        3. TRANSFERS.

               (a) UNREGISTERED SECURITY. Each holder of this Warrant
acknowledges that this Warrant, the Warrant Stock and the Common Stock of the
Company have not been registered under the Securities Act of 1933, as amended
(the "Securities Act"), and agrees not to sell, pledge, distribute, offer for
sale, transfer or otherwise dispose of this Warrant, any Warrant Stock issued
upon its exercise in the absence of (i) an effective registration statement
under the Act as to this Warrant or such Warrant Stock and registration or
qualification of this Warrant or such Warrant Stock under any applicable U.S.
federal or state securities law then in effect, or (ii) an opinion of counsel,
satisfactory to the Company, that such registration and qualification are not
required. Each certificate or other instrument for Warrant Stock issued upon the
exercise of this Warrant shall bear a legend substantially to the foregoing
effect.

               (b) TRANSFERABILITY. Subject to the provisions of Section 3(a)
hereof and of Section 1.12 of the Investors' Rights Agreement dated May 25, 2000
among the Company and certain holders of the Company's securities, this Warrant
and all rights hereunder are transferable, in whole or in part, upon surrender
of the Warrant with a properly executed assignment (in the form of Exhibit B
hereto) at the principal office of the Company.

               (c) WARRANT REGISTER. The Company will maintain a register
containing the names and addresses of the Registered Holders of this Warrant.
Until any transfer of this Warrant is made in the warrant register, the Company
may treat the Registered Holder of this Warrant as the absolute owner hereof for
all purposes; provided, however, that if this Warrant is properly assigned in
blank, the Company may (but shall not be required to) treat the bearer hereof as
the absolute owner hereof for all purposes, notwithstanding any notice to the
contrary. Any Registered Holder may change such Registered Holder's address as
shown on the warrant register by written notice to the Company requesting such
change.

        4. NO IMPAIRMENT. The Company will not, by amendment of its charter or
through reorganization, consolidation, merger, dissolution, sale of assets or
any other voluntary action, avoid or seek to avoid the observance or performance
of any of the terms of this Warrant, but will (subject to Section 13 below) at
all times in good faith assist in the carrying out of all such terms and in the
taking of all such action as may be necessary or appropriate in order to protect
the rights of the holder of this Warrant against impairment.

        5. TERMINATION. This Warrant (and the right to purchase securities upon
exercise hereof) shall terminate upon the earliest to occur of the following
(the "Expiration Date"): (a) August 8, 2005, (b) the sale, conveyance or
disposal of all or substantially all of the Company's property or business or
the Company's merger into or consolidation with any other corporation (other
than a wholly-owned subsidiary of the Company) or any other transaction or
series of related transactions in which more than fifty percent (50%) of the
voting power of the Company is disposed of, provided that this Section 5(b)
shall not apply to a merger effected

                                      -4-
<PAGE>   5

exclusively for the purpose of changing the domicile of the Company, or (c) the
closing of a firm commitment underwritten public offering pursuant to a
registration statement on Form S-1 under the Securities Act, the public offering
price of which is not less than $4.00 per share (appropriately adjusted for any
stock split, dividend, combination or other recapitalization)] and which results
in aggregate cash proceeds to the Company of $20,000,000 (net of underwriting
discounts and commissions).

        6. NOTICES OF CERTAIN TRANSACTIONS.  In case:

               (a) the Company shall take a record of the holders of its Common
Stock (or other stock or securities at the time deliverable upon the exercise of
this Warrant) for the purpose of entitling or enabling them to receive any
dividend or other distribution, or to receive any right to subscribe for or
purchase any shares of stock of any class or any other securities, or to receive
any other right, to subscribe for or purchase any shares of stock of any class
or any other securities, or to receive any other right, or

               (b) of any capital reorganization of the Company, any
reclassification of the capital stock of the Company, any consolidation or
merger of the Company, any consolidation or merger of the Company with or into
another corporation (other than a consolidation or merger in which the Company
is the surviving entity), or any transfer of all or substantially all of the
assets of the Company, or

               (c) of the voluntary or involuntary dissolution, liquidation or
winding-up of the Company,

then, and in each such case, the Company will mail or cause to be mailed to the
Registered Holder of this Warrant a notice specifying, as the case may be, (i)
the date on which a record is to be taken for the purpose of such dividend,
distribution or right, and stating the amount and character of such dividend,
distribution or right, or (ii) the effective date on which such reorganization,
reclassification, consolidation, merger, transfer, dissolution, liquidation,
winding-up or redemption is to take place, and the time, if any is to be fixed,
as of which the holders of record of Common Stock (or such other stock or
securities at the time deliverable upon such reorganization, reclassification,
consolidation, merger, transfer, dissolution, liquidation, winding-up or
redemption) are to be determined. Such notice shall be mailed at least ten (10)
days prior to the record date or effective date for the event specified in such
notice.

        7. RESERVATION OF STOCK. The Company will at all times reserve and keep
available, solely for the issuance and delivery upon the exercise of this
Warrant, such shares of Warrant Stock and other stock, securities and property,
as from time to time shall be issuable upon the exercise of this Warrant.

        8. EXCHANGE OF WARRANTS. Upon the surrender by the Registered Holder of
any Warrant or Warrants, properly endorsed, to the Company at the principal
office of the Company, the Company will, subject to the provisions of Section 3
hereof, issue and deliver to or upon the order of such Holder, at the Company's
expense, a new Warrant or Warrants of like tenor, in the name of such Registered

                                      -5-
<PAGE>   6

Holder or as such Registered Holder (upon payment by such Registered Holder of
any applicable transfer taxes) may direct, calling in the aggregate on the face
or faces thereof for the number of shares of Common Stock called for on the face
or faces of the Warrant or Warrants so surrendered.

        9.  REPLACEMENT OF WARRANTS. Upon 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) upon delivery of an
indemnity agreement (with surety if reasonably required) in an amount reasonably
satisfactory to the Company, or (in the case of mutilation) upon surrender and
cancellation of this Warrant, the Company will issue, in lieu thereof, a new
Warrant of like tenor.

        10. MAILING OF NOTICES. Any notice required or permitted pursuant to
this Warrant shall be in writing and shall be deemed sufficient upon receipt,
when delivered personally or sent by courier, overnight delivery service or
confirmed facsimile, or forty-eight (48) hours after being deposited in the
regular mail, as certified or registered mail (airmail if sent internationally),
with postage prepaid, addressed (a) if to the Registered Holder, to the address
of the Registered Holder most recently furnished in writing to the Company and
(b) if to the Company, to the address set forth below or subsequently modified
by written notice to the Registered Holder.

        11. NO RIGHTS AS STOCKHOLDER. Until the exercise of this Warrant, the
Registered Holder of this Warrant shall not have or exercise any rights by
virtue hereof as a stockholder of the Company.

        12. NO FRACTIONAL SHARES. No fractional shares of Common Stock will be
issued in connection with any exercise hereunder. In lieu of any fractional
shares which would otherwise be issuable, the Company shall pay cash equal to
the product of such fraction multiplied by the fair market value of one share of
Common Stock on the date of exercise, as determined in good faith by the
Company's Board of Directors.

        13. AMENDMENT OR WAIVER. Any term of this Warrant may be amended or
waived upon written consent of the Company and the holders of at least a
majority of the Common Stock issuable upon exercise of outstanding warrants
purchased pursuant to the Purchase Agreement. By acceptance hereof, the
Registered Holder acknowledges that in the event the required consent is
obtained, any term of this Warrant may be amended or waived with or without the
consent of the Registered Holder; provided, however, that any amendment hereof
that would materially adversely affect the Registered Holder in a manner
different from the holders of the remaining warrants issued pursuant to the
Purchase Agreement shall also require the consent of Registered Holder.

        14. HEADINGS. The headings in this Warrant are for purposes of reference
only and shall not limit or otherwise affect the meaning of any provision of
this Warrant.

        15. GOVERNING LAW. This Warrant shall be governed, construed and
interpreted in accordance with the laws of the State of Washington, without
giving effect to principles of conflicts of law.

                                      -6-
<PAGE>   7

                                       XCYTE THERAPIES, INC.

                                       By
                                         ------------------------------------
                                         Address:      1124 Columbia Street
                                                       Suite 130
                                                       Seattle, Washington 98104

                                         Fax Number:   (206) 262-0900

                                      -7-
<PAGE>   8

                                    EXHIBIT A

                             PURCHASE/EXERCISE FORM

To:     XCYTE THERAPIES, INC.                                    Dated:

        The undersigned, pursuant to the provisions set forth in the attached
Warrant No. <<WarrantNo>>, hereby irrevocably elects to (a) purchase _____
shares of the Common Stock covered by such Warrant and herewith makes payment of
$ _________, representing the full purchase price for such shares at the price
per share provided for in such Warrant, or (b) exercise such Warrant for _______
shares purchasable under the Warrant pursuant to the Net Issue Exercise
provisions of Section 1(c) of such Warrant.

        The undersigned acknowledges that it has reviewed the representations
and warranties contained in Section 3 of the Purchase Agreement (as defined in
the Warrant) and by its signature below hereby makes such representations and
warranties to the Company. Defined terms contained in such representations and
warranties shall have the meanings assigned to them in the Purchase Agreement,
provided that the term "Purchaser" shall refer to the undersigned and the term
"Securities" shall refer to the Warrant Stock.

        The undersigned further acknowledges that it has reviewed the market
standoff provisions set forth in Section 1.14 of the Investors' Rights Agreement
dated May 25, 2000, as amended, among the Company and certain holders of the
Company's securities and agrees to be bound by such provisions.

                              Signature:
                                        -------------------------------------

                              Name (print):
                                           -----------------------------------

                              Title (if applic.)
                                                ------------------------------

                              Company (if applic.):
                                                   ---------------------------

<PAGE>   9

                                    EXHIBIT B

                                 ASSIGNMENT FORM

        FOR VALUE RECEIVED, _________________________________________ hereby
sells, assigns and transfers all of the rights of the undersigned under the
attached Warrant with respect to the number of shares of Common Stock covered
thereby set forth below, unto:

 NAME OF ASSIGNEE            ADDRESS/FAX NUMBER              NO. OF SHARES

Dated:                       Signature:
      ------------------               -----------------------------------

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

                              Witness:
                                       -----------------------------------

Source: [{"source": "alea-institute/alea-institute/kl3m-data-edgar-agreements/train-00018-of-00352.parquet"}, [{"source": "alea-institute/alea-institute/kl3m-data-edgar-agreements/train-00018-of-00352.parquet"}]]