LIMITED GUARANTY

Exhibit 10.6

LIMITED GUARANTY

LIMITED GUARANTY, dated as of August 14, 2008, made by FINANCIÈRE ELITECH S.A.S., a société par actions simplifiée incorporated under the laws of France and registered with the Clerk of the Commercial Court of Nanterre under the number 481 676 062 (the “Guarantor”), in favor of the holders from time to time of certain Guaranteed Notes (as defined below).

W I T N E S S E T H :

WHEREAS, Nanogen, Inc, a Delaware corporation (the “Company”), and each party listed as a “Investor” on the Schedule thereto (each an “Investor”, and collectively, the “Investors”) are parties to the Securities Purchase Agreement, dated as of August 14, 2008 (as amended, restated or otherwise modified from time to time, the “Securities Purchase Agreement”) pursuant to which the Company shall issue to the Investors the “Notes” (as defined in the Securities Purchase Agreement) numbered      to      (as may be amended, restated, replaced, exchanged or otherwise modified from time to time the “Guaranteed Notes”) in the aggregate principal amount of $5,000,000; for purposes of clarification, the Guaranteed Notes shall not include notes of the same series numbered      to      initially issued to the Guarantor pursuant to the terms of a separate securities purchase agreement between the Company and the Guarantor;

WHEREAS, the Securities Purchase Agreement requires that the Guarantor execute and deliver this Limited Guaranty guaranteeing the obligations of the Company under the Guaranteed Notes on the terms and subject to the limitations contained herein;

WHEREAS, the Guarantor has determined that the execution, delivery and performance of this Limited Guaranty directly benefits, and is in the best interest of, such Guarantor; and

NOW, THEREFORE, in consideration of the premises and the agreements herein and in order to induce the Investors to perform under the Securities Purchase Agreement and purchase the Guaranteed Notes, the Guarantor hereby agrees with each Investor as follows:

SECTION 1. Definitions. Reference is hereby made to the Securities Purchase Agreement and the Guaranteed Notes for a statement of the terms thereof. All terms used in this Limited Guaranty, which are defined in the Securities Purchase Agreement or the Guaranteed Notes and not otherwise defined herein, shall have the same meanings herein as set forth therein. As used in this Agreement, the following terms shall have the respective meanings indicated below, such meanings to be applicable equally to both the singular and plural forms of such terms:

“Event of Default” shall have the meaning set forth in the Guaranteed Notes.

“Governmental Authority” means any nation or government, any Federal, state, city, town, municipality, county, local or other political subdivision thereof or thereto and any department, commission, board, bureau, instrumentality, agency or other entity exercising executive, legislative, judicial, taxing, regulatory or administrative powers or functions of or pertaining to government.

“Insolvency Proceeding” means any proceeding commenced by or against any Person under any provision of the Bankruptcy Code (Chapter 11 of Title 11 of the United States Code) or under any other bankruptcy or insolvency law, assignments for the benefit of creditors, formal or informal moratoria, compositions, or extensions generally with creditors, or proceedings seeking reorganization, arrangement, or other similar relief from creditors.

“Noteholders” means the Investors and any assignees of the Guaranteed Notes.

“Person” means an individual, corporation, limited liability company, partnership, association, joint-stock company, trust, unincorporated organization, joint venture or other enterprise or entity or Governmental Authority.

SECTION 2. Limited Guaranty.

(a) The Guarantor hereby irrevocably, absolutely and unconditionally guarantees the prompt payment by the Company as and when due and payable (whether by scheduled maturity, required prepayment, acceleration, demand or otherwise), of (A) all principal of the Guaranteed Notes not to exceed an aggregate of $5,000,000 (the “Guaranteed Principal Amount”), and (B) interest on the Guaranteed Principal Amount at a rate per annum equal to twenty percent (20%) (including, without limitation, all such interest that accrues after the commencement of any Insolvency Proceeding of the Company or the Guarantor, whether or not the payment of such interest is unenforceable or is not allowable due to the existence of such Insolvency Proceeding) (collectively, the “Guaranteed Obligations”).

(b) Upon the occurrence of an Event of Default under any Guaranteed Note, the holder of such Guaranteed Note may declare any or all Guaranteed Obligations with respect to such Guaranteed Note due and payable hereunder by Guarantor within 90 days following the occurrence of such Event of Default, and such Noteholder shall be entitled to enforce all Guaranteed Obligations of the Guarantor hereunder.

(c) In addition to the foregoing, Guarantor agrees to pay any and all expenses (including reasonable counsel fees and expenses) reasonably incurred by any Noteholder in enforcing any rights under this Limited Guaranty.

SECTION 3. Guarantor’s Obligations Unconditional.

(a) The Guarantor hereby guarantees that the Guaranteed Obligations will be paid by the Guarantor strictly in accordance with the terms of this Limited Guaranty, regardless of any law, regulation or order now or hereafter in effect in any jurisdiction affecting any of such terms or the rights of any Noteholder with respect to any Guaranteed Note covered by this Limited Guaranty. The obligations of the Guarantor under this Limited Guaranty are independent of the Company’s obligations under each Guaranteed Note and the other Transaction Documents (as defined in the Guaranteed Notes), and a separate action or actions may be brought and prosecuted against the Guarantor to enforce this Limited Guaranty, irrespective of whether any action is brought against the Company or whether the Company is

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joined in any such action. The liability of the Guarantor hereunder shall be absolute and unconditional irrespective of: (i) any lack of validity or enforceability of the Guaranteed Notes or any other Transaction Document or any agreement or instrument relating thereto; (ii) any change in the time, manner or place of payment of, or in any other term in respect of, all or any of the Guaranteed Notes, or any other amendment or waiver of or consent to any departure from any provision of the Guaranteed Notes or any other Transaction Document other than this Limited Guaranty, including the creation or existence of any Guaranteed Obligations in excess of the amount evidenced by the Guaranteed Notes (provided, however, that the terms and conditions of the Guaranteed Notes shall not be amended without the prior written consent of the Guarantor); (iii) the existence of any claim, set-off, defense or other right that the Guarantor may have against any Person, including, without limitation, any Noteholder, or (iv) any other circumstance which might otherwise constitute a defense available to, or a discharge of, the Company or any other guarantor in respect of the Guaranteed Obligations or the Guarantor in respect hereof.

(b) This Limited Guaranty (i) is a continuing guaranty and shall remain in full force and effect until such date on which all of the Guaranteed Obligations and all other expenses to be paid by the Guarantor pursuant hereto shall have been satisfied in full, and (ii) shall continue to be effective or shall be reinstated, as the case may be, if at any time any payment of any of the Guaranteed Obligations is rescinded or must otherwise be returned by any Noteholder upon the insolvency, bankruptcy or reorganization of the Company or otherwise, all as though such payment had not been made.

SECTION 4. Waivers. The Guarantor hereby waives, to the extent permitted by applicable law, (i) promptness and diligence; (ii) notice of acceptance and notice of the incurrence of any Guaranteed Obligations by the Company; (iii) notice of any actions taken by any Noteholder or the Company under the Guaranteed Notes or any other Transaction Document or any other agreement or instrument relating thereto, other than this Limited Guaranty; (iv) all other notices, demands and protests, and all other formalities of every kind in connection with the enforcement of the Guaranteed Obligations, the omission of or delay in which, but for the provisions of this Section 4, might constitute grounds for relieving the Guarantor of its obligations hereunder; and (v) any right to compel or direct any Noteholder to seek payment or recovery of any amounts owed under this Limited Guaranty from any one particular fund or source.

SECTION 5. Subrogation. Until all obligations under the Guaranteed Notes have been paid in full in cash or otherwise converted in accordance with the terms thereof, the Guarantor hereby waives and irrevocably agrees it will not exercise any and all rights which it has or may have at any time or from time to time (whether arising directly or indirectly by operation of law or contract) to assert any claim against the Company on account of any payments made under this Limited Guaranty, including, without limitation, any and all existing and future rights of subrogation, reimbursement, exoneration, contribution and/or indemnity. If any amount shall be paid to the Guarantor on account of such subrogation rights at any time when all of the obligations under the Guaranteed Notes and all such other expenses shall not have been paid in full, such amount shall be held in trust for the benefit of the Noteholders, shall be segregated from the other funds of the Guarantor and shall forthwith be paid over to the Noteholders on a pro rata basis based on the aggregate principal amount outstanding under each

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Noteholder’s respective Guaranteed Note, to be applied in whole or in part by the Noteholders against the Company’s outstanding obligations under the Guaranteed Notes, whether matured or unmatured, and all such other expenses in accordance with the terms of the Guaranteed Notes.

SECTION 6. Representations and Warranties. The Guarantor hereby represents and warrants as follows:

(a) The Guarantor (i) is a société par actions simplifiée incorporated under the laws of France and registered with the Clerk of the Commercial Court of Nanterre under the number 481 676 062; and (ii) has all requisite corporate power and authority to execute, deliver and perform its obligations under this Limited Guaranty.

(b) The execution, delivery and performance by the Guarantor of this Limited Guaranty (i) have been duly authorized by all necessary corporate action, (ii) do not contravene its bylaws (statuts) or any applicable law, (iii) do not violate any contractual restriction binding on or otherwise affecting the Guarantor, and (iv) do not result in or require the creation of any lien, security interest or other charge or encumbrance upon or with respect to any of its properties.

(c) No authorization, approval or other action by, and no notice to or filing with, any Governmental Authority is required in connection with the due execution, delivery and performance by the Guarantor of this Limited Guaranty.

(d) This Limited Guaranty is a legal, valid and binding obligation of the Guarantor, enforceable against the Guarantor in accordance with its terms, except as may be limited by applicable bankruptcy, insolvency, reorganization, moratorium or other similar laws and general equity principles affecting the enforcement of creditors’ rights generally.

(e) The Guarantor now has and will continue to have independent means of obtaining information concerning the affairs, financial condition and business of the Company, and has no need of, or right to obtain from any Noteholder, any credit or other information concerning the affairs, financial condition or business of the Company that may come under the control of any Noteholder.

SECTION 7. Payments. Unless otherwise agreed in writing by the Guarantor and each Noteholder, the Guarantor will make each payment hereunder in lawful money of the United States of America (“Dollars”) and in immediately available funds to each Noteholder, at such address specified by such Person from time to time by notice to the Guarantor. The specification under this Limited Guaranty of Dollars is of the essence. Unless otherwise agreed in writing by the Guarantor and each Noteholder, the Guarantor’s obligation hereunder and under the other Transaction Documents to make payments in Dollars shall not be discharged or satisfied by any tender or recovery pursuant to any judgment expressed in or converted into any currency other than Dollars, except to the extent that such tender or recovery results in the effective receipt by each Noteholder of the full amount of Dollars expressed to be payable to such Noteholder under this Limited Guaranty or the other Transaction Documents. If, for the purpose of obtaining or enforcing judgment in any court, it is necessary to convert into or from any currency other than Dollars (such other currency being hereinafter referred to as the

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“Judgment Currency”) an amount due in Dollars, the rate of exchange used shall be that at which the Noteholder could, in accordance with normal lending procedures, purchase Dollars with the Judgment Currency on the Business Day preceding that on which final judgment is given. The obligation of the Guarantor in respect of any such sum due from it to any Noteholder hereunder shall, notwithstanding any judgment in such Judgment Currency, be discharged only to the extent that, on the Business Day immediately following the date on which such Noteholder receives any sum adjudged to be so due in the Judgment Currency, such Noteholder may, in accordance with normal banking procedures, purchase Dollars with the Judgment Currency. If the Dollars so purchased are less than the sum originally due to such Noteholder in Dollars, the Guarantor agrees, as a separate obligation and notwithstanding any such judgment, to indemnify such Noteholder against such loss, and if the Dollars so purchased exceed the sum originally due to such Noteholder in Dollars, such Noteholder agrees to remit to the Guarantor such excess.

SECTION 8. Indemnity and Expenses.

(a) The Guarantor agrees to indemnify and hold each Noteholder harmless from and against any and all claims, damages, losses, liabilities, obligations, penalties, costs and expenses (including, without limitation, the reasonable legal fees and disbursements of such Noteholder’s counsel) to the extent that they arise out of or otherwise result from this Limited Guaranty (including, without limitation, enforcement of this Limited Guaranty), except to the extent such claims, damages, losses, liabilities, obligations, penalties, costs or expenses result from such Noteholder’s gross negligence or willful misconduct as determined by a court of competent jurisdiction.

(b) The Guarantor will upon demand pay to each Noteholder the amount of any and all reasonable costs and expenses, including the reasonable fees and disbursements of such Noteholder’s counsel and of any experts and agents, which the Noteholder may incur in connection with (i) the amendment, waiver or other modification or termination of this Limited Guaranty, (ii) the exercise or enforcement of any of the rights of such Noteholder hereunder, or (iii) the failure by the Guarantor to perform or observe any of the provisions hereof.

SECTION 9. Notices, Etc. All notices and other communications provided for hereunder shall be in writing and shall be mailed (by certified mail, postage prepaid and return receipt requested), telecopied or delivered, if to the Guarantor, to it at the address specified below its signature at the end of this Limited Guaranty; if to the Noteholder, to it at its address set forth on Schedule A hereto; or, as to any such Person, at such other address as shall be designated by such Person in a written notice to such other Persons complying as to delivery with the terms of this Section 9. All such notices and other communications shall be effective (i) if sent by registered mail, return receipt requested, when received or three (3) Business Days after mailing, whichever first occurs, (ii) if telecopied, when transmitted and a confirmation is received, provided the same is on a Business Day and, if not, on the next Business Day, or (iii) if delivered, upon delivery, provided the same is on a Business Day and, if not, on the next Business Day.

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SECTION 10. CONSENT TO JURISDICTION; SERVICE OF PROCESS AND VENUE.

(c) ANY LEGAL ACTION, SUIT OR PROCEEDING WITH RESPECT TO THIS LIMITED GUARANTY OR ANY DOCUMENT RELATED HERETO MAY BE BROUGHT IN THE COURTS OF THE STATE OF NEW YORK IN THE COUNTY OF NEW YORK OR THE UNITED STATES OF AMERICA FOR THE SOUTHERN DISTRICT OF NEW YORK, AND APPELLATE COURTS THEREOF, AND, BY EXECUTION AND DELIVERY OF THIS LIMITED GUARANTY, THE GUARANTOR HEREBY ACCEPTS, GENERALLY AND UNCONDITIONALLY, THE JURISDICTION OF THE AFORESAID COURTS. THE GUARANTOR HEREBY EXPRESSLY AND IRREVOCABLY WAIVES, TO THE FULLEST EXTENT PERMITTED BY LAW, ANY OBJECTION, INCLUDING, WITHOUT LIMITATION, ANY OBJECTION TO THE LAYING OF VENUE OR BASED ON THE GROUNDS OF FORUM NON CONVENIENS, WHICH IT MAY NOW OR HEREAFTER HAVE TO THE BRINGING OF ANY SUCH ACTION, SUIT OR PROCEEDING IN SUCH RESPECTIVE JURISDICTIONS AND CONSENTS TO THE GRANTING OF SUCH LEGAL OR EQUITABLE RELIEF AS IS DEEMED APPROPRIATE BY THE COURT.

(d) The Guarantor hereby irrevocably appoints Capitol Services, Inc., with an office at 1218 Central Avenue, Suite 100, Albany, New York 12205 (the “Agent for Service of Process”) as agent to receive on its behalf, service of process in the State of New York for purposes of this Limited Guaranty. The Guarantor further agrees that such service of process may be made on the Agent for Service of Process by personal service on such Agent for Service of Process of the summons and complaint or other legal process in any suit, action or proceeding with respect to this Agreement, or by any other method of service provided for under applicable laws in effect in the State of New York, and hereby authorizes the Agent for Service of Process to accept such service on its behalf and to admit service with respect thereto. Service upon the Agent for Service of Process as aforesaid shall be deemed personal service on the Guarantor, for all purposes, notwithstanding any failure of the Agent for Service of Process to mail to the Guarantor copies of the legal process served upon it, or any failure by it to receive such copies.

(c) To the extent that the Guarantor has or hereafter may acquire any immunity from jurisdiction of any court or from any legal process (whether through service or notice, attachment prior to judgment, attachment in aid of execution or otherwise) with respect to itself or its property, the Guarantor hereby irrevocably waives such immunity in respect of its obligations under this Limited Guaranty and the other Transaction Documents.

SECTION 11. WAIVER OF JURY TRIAL. THE GUARANTOR AND, BY ACCEPTANCE HEREOF, EACH NOTEHOLDER, WAIVES TO THE MAXIMUM EXTENT PERMITTED BY APPLICABLE LAW, TRIAL BY JURY IN ANY LITIGATION IN ANY COURT WITH RESPECT TO, IN CONNECTION WITH OR ARISING OUT OF THIS GUARANTY, OR THE VALIDITY, PROTECTION, INTERPRETATION, COLLECTION OR ENFORCEMENT THEREOF.

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SECTION 12. Miscellaneous.

(e) No amendment of any provision of this Limited Guaranty shall be effective unless it is in writing and signed by the Guarantor and each Noteholder, and no waiver of any provision of this Limited Guaranty, and no consent to any departure by the Guarantor therefrom, shall be effective unless it is in writing and signed by each Noteholder, and then such waiver or consent shall be effective only in the specific instance and for the specific purpose for which given.

(f) No failure on the part of any Noteholder to exercise, and no delay in exercising, any right hereunder, under the Guaranteed Notes or any other Transaction Document shall operate as a waiver thereof, nor shall any single or partial exercise of any right preclude any other or further exercise thereof or the exercise of any other right. The rights and remedies of the Noteholders provided herein, in the Guaranteed Notes and in the other Transaction Documents are cumulative and are in addition to, and not exclusive of, any rights or remedies provided by law. The rights of the Noteholders under the Guaranteed Notes or any Transaction Document against any party thereto are not conditional or contingent on any attempt by any Noteholder to exercise any of its rights under its Guaranteed Note or any other Transaction Document against such party or against any other Person.

(g) Any provision of this Limited Guaranty which is prohibited or unenforceable in any jurisdiction shall, as to such jurisdiction, be ineffective to the extent of such prohibition or unenforceability without invalidating the remaining portions hereof or thereof or affecting the validity or enforceability of such provision in any other jurisdiction.

(h) This Limited Guaranty shall (i) be binding on the Guarantor and its respective successors and assigns, and (ii) inure, together with all rights and remedies of each Noteholder hereunder, to the benefit of such Noteholder and its successors, transferees and assigns. Without limiting the generality of clause (ii) of the immediately preceding sentence, solely to the extent permitted by Section 17 of such Guaranteed Note, each Noteholder may assign or otherwise transfer the Guaranteed Note held by it, and assign or otherwise transfer its rights under any other Transaction Document, to any other person, and such other person shall thereupon become vested with all of the benefits in respect thereof granted to the Noteholder herein or otherwise. None of the rights or obligations of the Guarantor hereunder may be assigned or otherwise transferred without the prior written consent of the Noteholders.

(i) This Limited Guaranty shall be governed by and construed in accordance with, the laws of the State of New York applicable to contracts made and to be performed therein without regard to conflict of law principles.

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IN WITNESS WHEREOF, the Guarantor has caused this Limited Guaranty to be executed and delivered by its officer thereunto duly authorized as of the date first above written.

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SCHEDULE A