<PAGE>   1

EXHIBIT 10.11

               AMENDED AND RESTATED REGISTRATION RIGHTS AGREEMENT

     This Amended and Restated Registration Rights Agreement (the "Agreement")
is made as of September 3, 1998 among Genometrix Incorporated (the "Company")
and the Investors (as hereinafter defined).

     WHEREAS, the Company, the Investors listed on SCHEDULE A attached hereto
(the "Initial Investors") and the purchasers of the Series B Convertible
Preferred Stock of the Company (the "Series B Preferred Stock") listed on
SCHEDULE B attached hereto (the "Series B Purchasers" and, together with the
Initial Investors, the "Investors") entered into a Registration Rights Agreement
dated August 29, 1997, as amended by Amendment No. 1 to Registration Rights
Agreement dated as of March 26, 1998 (as amended, the "Prior Agreement"); and

     WHEREAS, the Company and each of Palmetto Partners, Ltd. and Donald and
Dianne Kendall entered into Note and Warrant Purchase Agreements dated July 6,
1994 (the "1994 Note Agreements") pursuant to which promissory notes (the "1994
Notes") and warrants (the "1994 Warrants") were issued, the 1994 Notes have been
converted into shares of the Series A Convertible Preferred Stock of the Company
(the "Series A Preferred Stock") and warrants to purchase shares of the common
stock of the Company (the "Common Stock") and the 1994 Warrants have become
exercisable to purchase shares of the Series A Preferred Stock and warrants to
purchase shares of the Common Stock (the "Palmetto 1997 Warrants"); and

     WHEREAS, the Company and Beckman Instruments, Inc. entered into a Note
Purchase Agreement (the "1995 Note Agreement") pursuant to which a promissory
note (the "1995 Note") was issued and the 1995 Note has been converted into
shares of the Series A Preferred Stock and warrants to purchase shares of the
Common Stock (the "Beckman 1997 Warrants"); and

     WHEREAS, the Company and each of Palmetto Partners, Ltd. and Donald and
Dianne Kendall have entered into Note and Purchase Agreements dated as of
January 24, 1996 (the "1996 Note Agreements") pursuant to which promissory notes
(the "1996 Notes") and warrants (the "1996 Warrants") were issued and the 1996
Notes are convertible into, and the 1996 Warrants are exercisable for, equity
securities of the Company upon the consummation of a Financing (as defined
therein); and

     WHEREAS, the Company and the Investors desire to amend and restate the
Prior Agreement to provide registration rights for holder of shares of
additional classes or series of the Preferred Stock of the Company; and

     WHEREAS, this Agreement amends and restates and replaces in its entirety
the Prior Agreement and the Company and holders of a majority of the Registrable
Shares (as defined in the Prior Agreement) hereby consent and agree to the
amendment and restatement of the Prior Agreement as set forth herein.


<PAGE>   2


     NOW, THEREFORE, in consideration of the foregoing and the mutual covenants
and agreements contained herein and for other good and valuable consideration,
the receipt and sufficiency of which are hereby acknowledged, the parties hereto
agree as follows:

     1.   CERTAIN DEFINITIONS. As used in this Agreement, the following terms
shall have the following respective meanings:

     "COMMISSION" shall mean the Securities and Exchange Commission and any
successor agency of the Federal government administering the Securities Act.

     "COMMON STOCK" shall mean (i) the common stock, $.0001 par value per share,
of the Company; or (ii) any other capital stock of the Company, however
designated, authorized on or after the date hereof, which shall neither be
limited to a fixed sum or percentage of par value in respect of the rights of
the holders thereof to participate in dividends nor entitled to a preference in
the distribution of assets upon the voluntary or involuntary liquidation,
dissolution or winding up of the Company.

     "PREFERRED SHARES" shall mean the shares of Series A Preferred Stock,
Series B Preferred Stock and any other class or series of the Preferred Stock of
the Company issued or sold after the date hereof.

     The terms "register", "registered" and "registration" shall refer to a
registration effected by preparing and filing a registration statement in
compliance with the Securities Act and applicable rules and regulations
thereunder, and the declaration or ordering of the effectiveness of such
registration statement.

     "REGISTRABLE SHARES" shall mean (i) the shares of Common Stock issued or
issuable pursuant to the conversion of the Preferred Shares, (ii) the shares of
Common Stock issued or issuable pursuant to the exercise of the Warrants, (iii)
the shares of Common Stock issued or issuable upon conversion of the 1996 Notes
or upon exercise of the 1996 Warrants or the shares of Common Stock issued or
issuable upon conversion or exercise of any security issued upon conversion of
the 1996 Notes or upon exercise of the 1996 Warrants and (iv) any shares of
Common Stock issued in respect of shares of Common Stock referred to in clauses
(i), (ii) or (iii) above upon any stock split, stock dividend, recapitalization
or similar event, excluding in any event shares which (a) have been registered
under the Securities Act pursuant to an effective registration statement filed
thereunder and disposed of in accordance with the registration statement
covering them, (b) have been publicly sold pursuant to Rule 144 under the
Securities Act or (c) may be sold without registration under the Securities Act.

     "REGISTRATION EXPENSES" shall mean the expenses so described in Section 3.

     "SECURITIES ACT" shall mean the Securities Act of 1933, as amended, and any
similar or successor Federal statute, and the rules and regulations of the
Commission thereunder, all as the same shall be in effect from time to time.


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<PAGE>   3


     "SELLING EXPENSES" shall mean the expenses so described in Section 3.

     "WARRANTS" shall mean the warrants dated August 29, 1997 to purchase shares
of the Common Stock issued to the purchasers of the Series A Preferred Stock
(the "Series A Warrants"), the Palmetto 1997 Warrants and the Beckman 1997
Warrants.

     2.   INCIDENTAL REGISTRATION.

     (a)  REGISTRATION RIGHT. If the Company at any time proposes to register
any of its securities under the Securities Act for sale to the public for its
own account (except with respect to registration statements on Forms S-4, S-8 or
any successor to such forms or another form not available for registering the
Registrable Shares for sale to the public), each such time it will promptly give
written notice to all holders of the Registrable Shares of its intention so to
do. Upon the written request of any such holder, received by the Company within
thirty (30) days after the giving of any such notice by the Company, to register
any or all of its Registrable Shares, the Company will use its best efforts to
cause the Registrable Shares as to which registration shall have been so
requested to be included in the securities to be covered by the registration
statement proposed to be filed by the Company, all to the extent requisite to
permit the sale or other disposition by the holder (in accordance with its
written request) of such Registrable Shares so registered.

     (b)  INITIAL PUBLIC OFFERING. The rights set forth in this Section 2 shall
not apply to the Company's initial public offering pursuant to a registration
statement filed under the Securities Act, unless any of the shares held by the
Principals (as defined below) shall be included in such offering for sale by the
Principals, in which event each Investor shall be entitled to include in such
registration, subject to the other provisions of this Section 2, that amount of
shares as equals the total number of Registrable Shares owned by it multiplied
by a fraction the numerator of which is the total number of shares registered
for sale in such offering by the Principals and the denominator of which is the
total number of shares owned by the Principals. For purposes of the calculation
of the denominator of such fraction, all options, rights and warrants shall be
included on an as exercised basis and all convertible or exchangeable securities
shall be included on an as converted or exercised basis. As used herein,
"Principals" shall mean (i) any director or officer of the Company, (ii)
Mitchell Eggers, (iii) Daniel Ehrlich, (iii) Kenneth Nill and (iv) Michael
Hogan.

     (c)  UNDERWRITTEN PUBLIC OFFERINGS. If the registration of which the
Company gives notice is for a registered public offering involving an
underwriting, the Company shall so advise the holders of Registrable Shares as a
part of the written notice given pursuant to this Section 2. In such event the
right of any holder of Registrable Shares to registration pursuant to this
Section 2 shall be conditioned upon such holder's participation in such
underwriting to the extent provided herein. All holders of Registrable Shares
proposing to distribute their securities through such underwriting shall
(together with the Company distributing their securities through such
underwriting) enter into an underwriting agreement in customary form with the
underwriter or underwriters selected for underwriting by the Company.
Notwithstanding any other provision of this Section 2, if the underwriter in its
discretion determines that because of marketing factors the


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<PAGE>   4


number of shares to be underwritten should be limited, the underwriter may
exclude from such registration and underwriting some or all of the Registrable
Shares which would otherwise be underwritten pursuant hereto. The Company shall
so advise all holders of Registrable Shares requesting registration of any
limitations on the number of shares to be underwritten, and the number of
Registrable Shares that are entitled to be included in the registration and
underwriting shall be allocated among all such holders in proportion, as nearly
as practicable, to the respective amounts of Registrable Shares owned by them.

     (d)  WITHDRAWAL OF REGISTRATION. Notwithstanding the foregoing provisions,
the Company may withdraw any registration statement referred to in this Section
2 without thereby incurring any liability to the holders of Registrable Shares.
If any holder of Registrable Shares disapproves of the terms of any such
underwriting, it may elect to withdraw therefrom by written notice to the
Company and the underwriter. Any Registrable Shares or other securities excluded
or withdrawn from such underwriting shall be withdrawn from such registration.

     (e)  PROVISION OF INFORMATION. In connection with each registration
hereunder, the sellers of Registrable Shares will furnish to the Company in
writing such information requested by the Company with respect to themselves and
the proposed distribution by them as shall be necessary in order to assure
compliance with Federal and applicable state securities laws; and such sellers
shall provide the Company with appropriate and customary representations and
indemnification with respect to the accuracy of such information.

     3.   EXPENSES.

     (a)  All expenses incurred by the Company in complying with Section 2,
including, without limitation, all registration and filing fees, printing
expenses, fees and disbursements of counsel and independent public accountants
for the Company, fees and expenses (including counsel fees) incurred in
connection with complying with state securities or "blue sky" laws, fees of the
National Association of Securities Dealers, Inc., transfer taxes, fees of
transfer agents and registrars and costs of any insurance which might be
obtained by the Company with respect to the offering by the Company, but
excluding any Selling Expenses, are called "Registration Expenses". All
underwriting discounts and selling commissions applicable to the sale of
Registrable Shares and fees and disbursements of counsel to the Investors are
called "Selling Expenses".

     (b)  The Company will pay all Registration Expenses in connection with each
registration statement under Section 2. All Selling Expenses in connection with
each registration statement under Section 2 shall be borne by the participating
Investors in proportion to the number of shares registered by each.

     4.   CHANGES IN COMMON STOCK OR PREFERRED SHARES. If, and as often as,
there is any change in the Common Stock and/or Preferred Shares by way of a
stock split, stock dividend, combination or reclassification, or through a
merger, consolidation, reorganization or recapitalization, or by any other
means, appropriate adjustment shall be made in the provisions hereof so that the
rights and privileges granted hereby shall continue with respect to the Common
Stock and/or Preferred Shares as so changed.


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<PAGE>   5


     5.   ADDITIONAL INVESTORS. Purchasers of additional Preferred Shares may
become parties to this Agreement as Investors upon purchasing such shares by
executing a counterpart signature page hereto in a form reasonably acceptable to
the Company. SCHEDULE C attached hereto, as amended from time to time, shall
list such additional Investor parties hereto.

     6.   MISCELLANEOUS.

     (a)  All covenants and agreements contained in this Agreement by or on
behalf of any of the parties hereto shall bind the respective heirs, successors
(including, without limitation, by sale or transfer of all or substantially all
assets, merger or consolidation) and assigns of the parties hereto, and shall
inure to the benefit of any transferee of all of the Registrable Shares of an
Investor.

     (b)  All notices, requests, consents and other communications hereunder
shall be in writing, shall be addressed to the receiving party's address set
forth below or to such other address as a party may designate by notice
hereunder, and shall be either (i) delivered by hand, (ii) made by telex,
telecopy or facsimile transmission, (iii) sent by overnight courier, or (iv)
sent by certified mail, return receipt requested, postage prepaid:

     If to the Company or any other party hereto, at the address of such party
set forth in the records of the Company; and

     If to any subsequent holder of Registrable Shares, to it at such address as
may have been furnished to the Company in writing by such holder;

     or, in any case, to such other address or addresses as shall have been
furnished in writing to the Company (in the case of a holder of Registrable
Shares) or to the holders of Registrable Shares (in the case of the Company) in
accordance with the provisions of this paragraph.

     All notices, requests, consents and other communications hereunder shall be
deemed to have been given (i) if by hand, at the time of the delivery thereof to
the receiving party at the address of such party set forth above, (ii) if made
by telex, telecopy or facsimile transmission, at the time that receipt thereof
has been acknowledged by electronic confirmation or otherwise, (iii) if sent by
overnight courier, on the next business day (or if sent overseas, on the second
business day) following the day such notice is delivered to the courier service,
or (iv) if sent by registered or certified mail, on the 5th business day (or if
sent overseas, on the 10th business day) following the day such mailing is made.

     (c)  This Agreement and the rights and obligations of the parties hereunder
shall be construed in accordance with and governed by the law of the State of
Delaware, without giving effect to the conflict of law principles thereof.

     (d)  This Agreement may not be amended or modified, and no provision hereof
may be waived, without the written consent of the Company and the holders of at
least a majority of the outstanding Registrable Shares. Any waiver or consent
hereunder shall be effective only in the


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<PAGE>   6


specific instance and for the purpose for which it was given, and shall not
constitute a continuing waiver or consent.

     (e)  This Agreement may be executed in one or more counterparts, and by
different parties hereto on separate counterparts, each of which shall be deemed
an original, but all of which together shall constitute one and the same
instrument.

     (f)  In the event that any court of competent jurisdiction shall determine
that any provision, or any portion thereof, contained in this Agreement shall be
unenforceable in any respect, then such provision shall be deemed limited to the
extent that such court deems it enforceable, and as so limited shall remain in
full force and effect. In the event that such court shall deem any such
provision, or portion thereof, wholly unenforceable, the remaining provisions of
this Agreement shall nevertheless remain in full force and effect.

     (g)  This Agreement embodies the entire agreement and understanding among
the parties hereto with respect to the subject matter hereof and supersedes all
prior oral or written agreements and understandings relating to the subject
matter hereof. No statement, representation, warranty, covenant or agreement of
any kind not expressly set forth in this Agreement shall affect, or be used to
interpret, change or restrict, the express terms and provisions of this
Agreement.

     (h)  The headings and captions of the various subdivisions of this
Agreement are for convenience of reference only and shall in no way modify or
affect the meaning or construction of any of the terms or provisions hereof.

     (i)  Wherever this Agreement refers to the neuter gender such reference
shall include the masculine and feminine genders as the context may require.

     IN WITNESS WHEREOF, the parties hereto have executed this Agreement as of
the date first written above.


                                     GENOMETRIX INCORPORATED


                                     By:  /s/  Mitchell D. Eggers
                                          -----------------------
                                          Mitchell Eggers, President and
                                          Chief Executive Officer


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<PAGE>   7


INITIAL INVESTORS:


_________________________________
Howard Salasin

/s/ Solomon Kal Rudman
---------------------------------
Solomon Kal Rudman

_________________________________
Joseph A. Leonetti


Henry M. Rambo, DDS and
  Joseph A. Leonetti, DMD
  Money Purchase Pension Plan


By:  /s/ Joseph A. Leonetti
   ------------------------------
      Joseph A. Leonetti


Henry M. Rambo, DDS and
  Joseph A. Leonetti, DMD
  Money Purchase Pension Plan, FBO
  Joseph A. Leonetti, DMD


By:  /s/ Joseph A. Leonetti
   ------------------------------
      Joseph A. Leonetti


Henry M. Rambo, DDS and
  Joseph A. Leonetti, DMD
  Profit Sharing Plan, FBO
  Joseph A. Leonetti, DMD


By:  /s/ Joseph A. Leonetti
   ------------------------------
      Joseph A. Leonetti


/s/ Brent Bailey
---------------------------------
Brent Bailey


                                       7
<PAGE>   8


/s/ Richard Toltzis
---------------------------------
Richard Toltzis


_________________________________
Lawrence Cherry


/s/ George Longo
---------------------------------
George Longo


/s/ Henry M. Rambo
---------------------------------
Henry M. Rambo


Palmetto Partners Ltd.

By:  Palmetto Capital Corporation,
     its General Partner


_________________________________


_________________________________
Donald R. Kendall, Jr., Joint Tenant
  with Right of Survivorship with
  Dianne S. Kendall


_________________________________
Dianne S. Kendall, Joint Tenant
  with Right of Survivorship with
  Donald R. Kendall, Jr.


Beckman Instruments, Inc.


By:  [J.H.]
   ------------------------------




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<PAGE>   9
SERIES B PURCHASERS


_________________________________
Brent Bailey

_________________________________
Scott A. Carr


/s/ Christopher J. Chambers
---------------------------------
Christopher J. Chambers


Jay R. Chiappa, D.D.S. P.S.T.


By: /s/ Jay R. Chiappa
   ------------------------------


/s/ Lawrence Chimerine
---------------------------------
Lawrence Chimerine


THE COOK ORGANIZATION, LTD.


By:______________________________


_________________________________
Katherine D. Crothall


/s/ John Dinapoli
---------------------------------
John Dinapoli

_________________________________


                                       9
<PAGE>   10


Michael Glassner and
  Lisa Glessner, JTWROS


Victor M. Goldberg, D.D.S.,
P.C. Veba Trust


By: /s/ Victor M. Goldberg
-------------------------------------------


/s/ Thomas K. Henson
-------------------------------------------
Thomas K. Henson


/s/ Peter Holland and Grace Holland
-------------------------------------------
Peter Holland and
  Grace Holland, JTWROS


/s/ Chris J. Hooven
-------------------------------------------
Chris J. Hooven


___________________________________________
Jeffrey Jacobs and
  Jaime Jacobs, JTWROS


/s/ Andrew S. Jacobson
-------------------------------------------
Andrew S. Jacobson


/s/ Timothy Margraf
-------------------------------------------
Timothy Margraf


/s/ Kurt E. Meyers and Linda Yedinak-Meyers
-------------------------------------------
Kurt E. Meyers and Linda
  Yedinak-Meyers, JTWROS


___________________________________________
Brett A. Richman and Laura


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<PAGE>   11


  Richman, JTWROS



Henry Rambo, D.D.S. and
Joseph A. Leonetti, DMD
Profit Sharing Plan FBO
Joseph A. Leonetti, DMD


By: /s/ Joseph A. Leonetti
   ----------------------------------------


Henry Rambo, D.D.S. and
Joseph A. Leonetti, DMD
Ltd. Profit Sharing Trust


By: /s/ Henry Rambo
   ----------------------------------------


___________________________________________
Marc S. Richman


/s/ David Rubenstein
-------------------------------------------
David Rubenstein


___________________________________________
Ralph A. Saggiomo


/s/ James J. Sheehan
-------------------------------------------
James J. Sheehan


/s/ Eugene Spinelli
-------------------------------------------
Eugene Spinelli


                                       11
<PAGE>   12


___________________________________________
Jon C. Wayland


/s/ Jospeh A. Leonetti
-------------------------------------------
Joseph A. Leonetti


/s/ Howard Salasin
-------------------------------------------
Howard Salasin


                                       12
<PAGE>   13


                                   SCHEDULE A

Howard Salasin

Solomon Kal Rudman

Joseph A. Leonetti

Henry M. Rambo, DDS and
  Joseph A. Leonetti, DMD
  Money Purchase Pension Plan

Henry M. Rambo, DDS and
  Joseph A. Leonetti, DMD
  Money Purchase Pension Plan
  FBO Joseph A. Leonetti, DMD

Henry M. Rambo, DDS and
  Joseph A. Leonetti, DMD
  Profit Sharing Plan
  FBO Joseph A. Leonetti, DMD

Brent Bailey

Richard Toltzis

Lawrence Cherry

Henry M. Rambo

George Longo

Palmetto Partners Ltd.

Donald R. Kendall, Jr. and Dianne S. Kendall,
  as Joint Tenants with Right of Survivorship

Beckman Instruments, Inc.


                                       13
<PAGE>   14


                                   SCHEDULE B

Brent Bailey

Scott A. Carr

Christopher J. Chambers

Jay R. Chiappa, D.D.S. P.S.T.

Lawrence Chimerine

Katherine D. Crothall

John Dinapoli

Michael Glassner IRA

Michael Glassner and
  Lisa Glessner, JTWROS

Victor M. Goldberg, D.D.S.,
P.C. Veba Trust

Thomas K. Henson

Peter Holland and
  Grace Holland, JTWROS

Chris J. Hooven

Jeffrey Jacobs and
  Jaime Jacobs, JTWROS

Andrew S. Jacobson

Timothy Margraf

Kurt E. Meyers and Linda
  Yedinak-Meyers, JTWROS

Brett A. Richman and Laura
  Richman, JTWROS


                                       14
<PAGE>   15


Henry Rambo, D.D.S. and
Joseph A. Leonetti, DMD
Profit Sharing Plan FBO
Joseph A. Leonetti, DMD

Henry Rambo, D.D.S. and
Joseph A. Leonetti, DMD
Ltd. Profit Sharing Trust

Marc S. Richman

David Rubenstein

Ralph A. Saggiomo

James J. Sheehan

Eugene Spinelli

Jon C. Wayland

Joseph A. Leonetti

Howard Salasin



                                       15
<PAGE>   16


                                   SCHEDULE C

Howard and Myrna Asher, as Tenants by the Entirety

Advest Inc. Custodian FBO Jeffrey D Barnes IRA

B-ETC., L.L.C.

J. Beyer Bray

Jay R. Chiappa, D.D.S. Profit Sharing Account

Jay R. Chiappa, D.D.S. Profit Sharing Segregate Account

Jay R. Chiappa, D.D.S. Profit Sharing Voluntary Account

Barbara M. Coffey IRA

Thomas J. Coffey

Thomas J. Coffey IRA

Joseph and Kay Dusek, as Joint Tenants

Thomas Fuelling

Richard I. Goldstein

Fayez Sarofim

David E. Jorden

Thomas J. Kelly, Jr.

Philip Kendall

Jeffrey C. Lee

Thomas A. Leonard & Kathleen M. Leonard, as Joint
Tenants

John M. McNamara

Kurt E. Meyers, D.D.S. and Linda Yedinak-Meyers, as
Joint Tenants


                                       16
<PAGE>   17


Henry Rambo and Sarah v. Rambo, as Joint Tenants

Brett A. Richman

Charles Sheedy

Larry C. Smedley, DDS

Eugene P. Spinelli


                                       17
<PAGE>   18


List of Additional Signatories to this Agreement in connection with the sale and
issuance of the Company's Series F Convertible Preferred Stock

Raye G. White

William K. McGee, Jr.

Russell M. Frankel

Charles E. Sheedy

Ralph B. Thomas

FSI No.2 Corporation

Fayez Sarofim

James A. Reynolds

David E. Jorden

Elliott Braunstein

Evans Attwell

Preston Moore

John Kirk/Margarite Kirk
(TIC)

Margarite Kirk, TTEE, Ward
Conover

Galman/Slipakoff

William D. Jones

Michael Anton

William M. Knapp

Jeri H. Campbell

Chet B. Hawkins


                                       18
<PAGE>   19


Brent Bailey

Jeff Jacobs

Christopher J. Chambers

Paul M. Chambers

Vince E. Spina

Marguerite B. Spina

Jon C. Wayland

Thomas Sheppard

Michael J. and Connie J.
Jones

Charles W. and Janet H.
Whitlock

Juanita Eggers

Alan Markowitz

Jim Sheehan

Kevin Mullen

Robert P. Brezina

SABA Holdings Limited

Adrian Kundanmal

Peter Holland

Andrew Jacobson


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