FINANCIÈRE ELITECH S.A.S. 12-12 bis, rue Jean Jaurès

Exhibit 10.12

FINANCIÈRE ELITECH S.A.S.

12-12 bis, rue Jean Jaurès

92800 Puteaux

France

August 14, 2008

[Investor]¹ (the “Investor”)

Nanogen Inc.

10398 Pacific Center Court

San Diego, California 92121

Ladies and Gentlemen:

Reference is made to (i) the Securities Purchase Agreement, dated as of the date hereof, by and among Nanogen, Inc., a Delaware corporation, with headquarters located at 10398 Pacific Center Court, San Diego, California 92121 (the “Company”) and the Investor (the “Securities Purchase Agreement”) and (ii) the Second Amendment and Exchange Agreement, dated as of the date hereof, by and among the Company and the Investor (the “Amendment and Exchange Agreement”). Capitalized terms used but not otherwise defined herein shall have the meanings ascribed to them in the Securities Purchase Agreement and the Amendment and Exchange Agreement, as applicable.

In exchange for good and valuable consideration, the sufficiency of which is hereby acknowledged, and to induce the Investor to execute and deliver the Securities Purchase Agreement and the Amendment and Exchange Agreement, the undersigned hereby agree as follows:

1. Upon the occurrence and during the continuation of an Event of Default under any Note or any Amended Exchanged Note, then, at the written request of the Company, the Collateral Agent, any Co-Collateral Agent or any holder of Notes or Amended Exchange Notes (a “Request”), Financière Elitech SAS, a société par actions simplifiée formed under the laws of France (“Elitech”) shall deliver in writing a firm, binding irrevocable bid (the “Bid”) in accordance with the terms and conditions of this letter agreement (this “Agreement”) to the Company, the Collateral Agent and all Co-Collateral Agents to acquire all of the outstanding capital stock (the “Stock”) of Nanogen Advanced Diagnostics, S.r.l., a company with limited

liability (società a responsabilità limitata), incorporated under the laws of Italy, with its registered heaquarters in Italy, Trezzano sul Naviglio (MI), having registered share capital of Fifty Thousand Euros (€50,000) and share capital subscribed and paid in of Fifty Thousand Euros (€50,000), registered in the Companies Registry at n. 05239350969, Italian tax payer code n. 05239350969 (“NAD Sub”), for cash in an amount of not less than Seven Million Euros (€7.0 million) to be paid to or for the benefit of the Company, the Collateral Agent or any Co-Collateral Agent, as applicable, by wire transfer of immediately available Euro funds in accordance with any applicable sale or auction procedures. Duly authorized representatives of Elitech shall execute and deliver the Bid, upon such request, regardless of whether or not the Stock is (i) the subject of an auction or other sales process (a) under Section 363 of Chapter 11 of Title 11, United States Code (the “Bankruptcy Code”), (b) pursuant to a plan of reorganization of the Company under the Bankruptcy Code or (c) under any other applicable law; or (ii) proposed to be sold by the Company to Elitech outside of an auction or other sales process. Notwithstanding the foregoing, to the extent there is an ongoing auction or other sales process contemplated by (a) or (b) of the prior sentence, then a portion of the Bid may be in the form of a credit bid of any or all secured obligations then due and owing from the Company to Elitech (the “Credit Bid”), but only if the Credit Bid portion of the Bid is valued by the Company and/or the bankruptcy court, if applicable, as, and is deemed to be the equivalent of, cash on a dollar for dollar basis; provided, however, that if the cash portion of the Bid is less than Seven Million Euros (€7.0 million) and a competitive bid in an amount less than Seven Million Euros (€7.0 million) is determined to be a higher or better offer on the basis that it is an all cash bid, then Elitech shall promptly amend its Bid to be an all cash Bid of not less than Seven Million Euros (€7.0 million).

2. Elitech shall submit the Bid to the Company or such other person or entity as may be authorized to accept the Bid on the Company’s behalf, as soon as practicable after the Company, the Collateral Agent or any Co-Collateral Agent, or any other person or entity authorized to do so, has requested such Bid (but in any event within five (5) Business Days of such request).

3. Elitech’s Bid shall not be subject to any conditions to consummation of the transactions contemplated by the Bid (the “Closing”) other than the following: (i) the accuracy in all material respects of the representations and warranties specified in paragraph 6 below, (ii) the Company’s delivery of certificates in respect of the Stock at the Closing, (iii) assuming that Elitech has satisfied its obligations in full under the Elitech Guaranty, the receipt of documents reasonably satisfactory to Elitech evidencing the Investor’s release of any first-priority security interest relating to the Stock or the NAD Sub assets held by it, effective as of the Closing, (iv) the receipt of documents reasonably satisfactory to Elitech demonstrating the elimination of all intercompany debts between the NAD Sub, on the one hand, and the Company and all other subsidiaries of the Company, on the other hand, effective as of the Closing, and (v) the receipt of any required governmental approvals. Elitech’s Bid shall not be conditioned on Elitech obtaining financing, conducting due diligence or obtaining board, shareholder or any other corporate approval. The Company hereby covenants and agrees to cause the elimination of all intercompany debts between the NAD Sub, on the one hand, and the Company and all other subsidiaries of the Company, on the other hand, effective as of the Closing.

4. To the extent any notice, bidding and/or sale procedures are used in connection with any auction or other sales process referenced in paragraph 1 above, the Bid shall be subject to such procedures; provided, that the Bid shall be acceptable by the Company at any time after delivery.

5. Elitech shall cause the transactions contemplated by the Bid to be consummated as soon as is practicable but in any event within ten (10) days after Elitech receives notice of acceptance of the Bid. The Bid shall remain capable of being accepted until the closing of the sale of the Stock to a third party. Once accepted, the Bid shall remain valid, binding and enforceable until the Closing. For the avoidance of doubt, the parties hereto agree that if the Stock or the NAD Sub’s assets are sold to a third party, the proceeds of such sale, pursuant to the terms of the intercreditor agreement between the collateral agents for the holders of the Notes and the Amended Exchange Notes shall be applied to pay off all then existing obligations under the Notes prior to the application of such proceeds to repay the then existing obligations under the Amended Exchanged Notes. The parties hereto further agree, that, assuming that Elitech has satisfied its obligations in full under the Elitech Guaranty, Elitech will have the right to receive proceeds equal to any amounts that it has paid to Investors under the Elitech Guaranty prior to the application of any proceeds from such sale to repay additional amounts due to the Investors (other than Elitech) under the Notes or any amounts outstanding under the Amended Exchanged Notes.

6. Elitech and the Company agree to execute a definitive purchase agreement governing the purchase of the Stock from the Company (the “Purchase Agreement”) on an “as-is, where-is” basis on the following terms: (i) (a) customary interim operations of the business covenant in respect of NAD Sub, (b) a customary tax allocation covenant, (c) a covenant requiring the parties to use their respective best efforts to take all actions necessary to consummate the transaction, including the receipt of all required consents or approvals, (d) the release of the security interests and the elimination of intercompany indebtedness as set forth in paragraph 3(iii) and 3(iv) above and (e) a customary further assurances clause and (ii) the following representations and warranties made by each party: (w) the due authorization, execution and delivery of the transaction documents, (x) the enforceability of the transaction documents, (y) no conflicts of such definitive agreement with the such party’s organizational documents, any statute, rule or regulation applicable to the Company and any material contract of such party and (z) solely with respect to the Company, the ownership by the Company of the Stock. The Bid is not subject to the inclusion of any other representation, warranty, covenant or agreement or provision in the Purchase Agreement. If the Bid is accepted by the Company, Elitech agrees to execute the Purchase Agreement promptly upon the written request of the Company, the Collateral Agent and/or the Co-Collateral Agent, as applicable, but in any event within ten (10) Business Days of such request.

7. Elitech hereby represents and warrants that the summarized consolidated financial information attached hereto as Exhibit I presents fairly in all material respects the financial position and the results of operations and cash flows of Elitech and its subsidiaries, at the indicated dates and for the indicated periods, but excluding financial information for Elitech’s French subsidiary Elitech France SAS.

8. The Company hereby makes the following representations and warranties to Elitech with respect to NAD Sub as of the date hereof: (i) NAD Sub is duly organized, validly existing and in good standing under the laws of Italy, has all requisite power to own, lease and operate its properties and to carry on its business as now being conducted; (ii) NAD Sub has no subsidiaries; (iii) the Company has provided to Elitech audited financial statements for NAD Sub for the year ended December 31, 2007. There has been no material change in the financial condition of NAD Sub since the date of such financial statements; (iv) NAD Sub has timely filed all tax returns required to have been filed, and taxes owed by NAD Sub have been timely paid; (v) NAD Sub does not own any real property or interests in real property in fee. Each lease for real property to which NAD Sub is a party is in full force and effect; (vi) since December 31, 2007, (a) NAD Sub has not sold, leased, transferred or assigned any material property or assets, except for the sale of inventory in the ordinary course of business consistent with past practice, (b) NAD Sub has not incurred, assumed or guaranteed any indebtedness, or materially modified the terms of any indebtedness, (c) NAD Sub has not incurred any material liability or created or assumed any lien on any material asset, except for factoring of accounts receivable under the GE credit facility, on a basis consistent with past practice, and (d) there has not been any labor dispute, other than individual grievances, or any activity or proceeding by a labor union or representative thereof to organize any employees of NAD Sub; (vii) there is no legal action pending or, to the Company’s knowledge, threatened against or affecting NAD Sub, which would reasonably be expected to have, individually or in the aggregate, a material adverse effect; (viii) NAD Sub and the Company and/or subsidiaries of the Company have entered into the license, transfer price and service agreements that are reasonably required for NAD Sub to carry on its business as now being conducted. Notwithstanding the foregoing, Elitech’s obligation to make the Bid, to consummate the transactions contemplated by the Bid or to satisfy any of its obligations under this Agreement will not be conditioned on the truth or accuracy of the foregoing representations and warranties.

9. Any notices, consents, waivers or other communications required or permitted to be given under the terms of this Agreement must be in writing and shall be delivered in accordance with the terms of Section 9(f) of the Securities Purchase Agreement. The addresses and facsimile numbers for such communications to Elitech shall be:

Financière Elitech S.A.S.

12-12 bis, rue Jean Jaurès

92800 Puteaux

France

Attn: Pierre Debiais

Facsimile: +33 (1) 41 45 07 19

with a copy (for informational purposes only) to:

Jackson Walker, L.L.P.

901 Main Street, Suite 6000

Dallas, Texas 75202

Attn: L. Scott Brown

Facsimile: 214 ###-###-####

10. This Agreement constitutes the entire agreement among the parties hereto with respect to the subject matter hereof and supersedes all prior negotiations, letters and understandings relating to the subject matter hereof and is fully binding on the parties.

11. This Agreement may be executed simultaneously in any number of counterparts. Each counterpart shall be deemed to be an original, and all such counterparts shall constitute one and the same instrument. This Agreement may be executed and accepted by facsimile signature and any such signature shall be of the same force and effect as an original signature.

12. The terms of this Agreement shall be binding upon and shall inure to the benefit of the Investor and its respective successors and assigns.

13. This Agreement may not be amended or modified except in writing signed by each of the Company, the Investor and Elitech.

14. All questions concerning the construction, validity, enforcement and interpretation of this Agreement shall be governed by the internal laws of the State of New York, without giving effect to any choice of law or conflict of law provision or rule (whether of the State of New York or any other jurisdiction) that would cause the application of the laws of any jurisdictions other than the State of New York. Each party hereby irrevocably submits to the non-exclusive jurisdiction of the state and federal courts sitting in The City of New York, Borough of Manhattan, for the adjudication of any dispute hereunder or in connection herewith or with any transaction contemplated hereby or discussed herein, and hereby irrevocably waives, and agrees not to assert in any suit, action or proceeding, any claim that it is not personally subject to the jurisdiction of any such court, that such suit, action or proceeding is brought in an inconvenient forum or that the venue of such suit, action or proceeding is improper. Elitech hereby appoints Capitol Services, Inc., with offices at 1218 Central Avenue, Suite 100, Albany, New York 12205, as its agent for service of process in New York. Nothing contained herein shall be deemed to limit in any way any right to serve process in any manner permitted by law. To the extent Elitech breaches any terms of this Agreement, Elitech shall pay, upon demand, all costs and expenses (including fees and expenses of outside counsel) that any of the Company, the Collateral Agent, any Co-Collateral Agent or the Investor incurs in connection with such breach, including, without limitation, costs and expenses incurred by any such person or entity in the exercise of any permitted remedy or the enforcement of the provisions of this Agreement. Any amount payable in respect of a Bid shall bear interest from and including the date payment is due in respect of such Bid to and including the actual date payment is made by Elitech at the higher of (i) 10% and (ii) to the extent such payment is not made within 30 days of when due, the highest rate permitted under New York law, in each case, compounded quarterly. Such interest shall be payable at the same time as the payment to which it relates and shall be calculated daily on the basis of a year of 365 days and the actual number of days elapsed.

15. Each party hereby irrevocably waives personal service of process and consents to process being served in any such suit, action or proceeding by mailing a copy thereof to such party at the address for such notices to it under this Agreement and agrees that such service shall constitute good and sufficient service of process and notice thereof. Nothing contained herein shall be deemed to limit in any way any right to serve process in any manner permitted by law. Nothing contained herein shall be deemed to limit in any way any right to serve process in any manner permitted by law. Each party hereby irrevocably waives any right it may have, and agrees not to request, a jury trial for the adjudication of any dispute hereunder or in connection with or arising out of this Agreement or any transaction contemplated hereby.

16. Each party hereto acknowledges that, in view of the uniqueness of the transactions contemplated by this Agreement, the other parties hereto would not have an adequate remedy at law for money damages in the event that this Agreement has not been performed in accordance with its terms, and therefore agrees that such other parties shall be entitled to specific enforcement of the terms hereof in addition to any other remedy to which it may be entitled, at law or in equity, without the posting of a bond or provision of other security.

17. Each party hereto shall use its best efforts to comply with the terms of this Agreement and shall do and perform, or cause to be done and performed, all such further acts and things, and shall execute and deliver all such other agreements, certificates, instruments and documents, as the other party may reasonably request in order to carry out the intent and accomplish the purposes of this Agreement and the consummation of the transactions contemplated hereby.

18. With regard to all dates and time periods set forth or referred to in this Agreement, time is of the essence.

19. All amounts denominated in currencies other than the United States Dollars shall be converted in the US dollar equivalent amount in accordance with the Exchange Rate on the date of calculation. “Exchange Rate” means, in relation to any amount of currency to be converted into US dollars pursuant to this Agreement, the US dollar exchange rate as published in The Wall Street Journal on the relevant date of calculation.

20. If for the purpose of obtaining or enforcing judgment against Elitech in any court in any jurisdiction it becomes necessary to convert into any other currency (such other currency being hereinafter referred to as the “Judgment Currency”) an amount due in U.S. Dollars under this Agreement, the conversion shall be made at the Exchange Rate prevailing on the Business Day immediately preceding:

(i) the date of actual payment of the amount due, in the case of any proceeding in the courts of New York or in the courts of any other jurisdiction that will give effect to such conversion being made on such date: or

(ii) the date on which the foreign court determines, in the case of any proceeding in the courts of any other jurisdiction (the date as of which such conversion is made pursuant to this paragraph being hereinafter referred to as the “Judgment Conversion Date”).

If in the case of any proceeding in the court of any jurisdiction referred to in paragraph (ii) above, there is a change in the Exchange Rate prevailing between the Judgment Conversion Date and the date of actual payment of the amount due, the applicable party shall pay such adjusted amount as may be necessary to ensure that the amount paid in the Judgment Currency, when converted at the Exchange Rate prevailing on the date of payment, will produce the amount of US Dollars which could have been purchased with the amount of Judgment Currency stipulated in the judgment or judicial order at the Exchange Rate prevailing on the Judgment Conversion Date. Any amount due from the Company under this provision shall be due as a separate debt and shall not be affected by judgment being obtained for any other amounts due under or in respect of this Agreement.

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Please confirm your agreement with and acceptance of the foregoing, effective as of the date first above written, by signing this Agreement where indicated below.

Acknowledged and Agreed:

EXHIBIT I

Summarized Consolidated Financial Information of Elitech

(Excluding Elitech France SAS)