Amendment No. Two to Asset Purchase Agreement, dated August 21, 2012, by and between Royalty Pharma Collection Trust, Proprius, Inc. and the Registrant

Exhibit 10.12

AMENDMENT NO. TWO TO ASSET PURCHASE AGREEMENT

This Amendment No. Two is made as of this 21^st day of August, 2012 by and among Royalty Pharma Collection Trust, a Delaware statutory trust (“Seller”), as assignee of Cypress Bioscience, Inc., a Delaware corporation, Proprius, Inc., a Delaware corporation (“Subsidiary”), and Exagen Diagnostics, Inc., a Delaware corporation (“Purchaser” and, collectively with Seller and Subsidiary, the “Parties”), the parties to that certain Asset Purchase Agreement, dated as of October 8, 2010 and amended on March 10, 2011, by and among the Parties (the “Agreement”). Capitalized terms used but not defined herein shall have the respective meanings given to such terms in the Agreement.

RECITALS

WHEREAS, pursuant to the terms of the Agreement, at the Closing, Purchaser purchased the Diagnostic Business from Seller and Subsidiary;

WHEREAS, following the Closing, certain issues have arisen between the Parties concerning, among others, claims alleging fraud, misrepresentation, unfair business practices under Cal. Bus. & Prof. Code § 17200 et seq., intentional interference with contractual relations, and intentional interference with prospective economic relations, including claims related to the collection of receivables by Seller and Subsidiary, which claims are detailed in letters from Purchaser’s counsel to Seller and its counsel (the “Matter”); and

WHEREAS, the Parties desire to resolve the Matter by setting forth herein amendments to certain provisions of the Agreement.

AMENDMENT

NOW, THEREFORE, in consideration of the foregoing and for other good and valuable consideration, the receipt and adequacy of which being hereby acknowledged, the Parties hereby agree as follows:

1. Amendment and Restatement of Section 1.3(c). Section 1.3(c) of the Agreement is amended and restated to read as follows:

“(c) (i) Issuance of Note.

On the second anniversary of the date hereof, Purchaser will issue to Seller a promissory note (the “Note”) in the aggregate principal amount of $2,000,000, the form of which is attached hereto as Exhibit A. The Note shall be secured in accordance with Section 5.9 of the Agreement. The Note shall accrue interest at a rate of 10% per annum which interest shall be payable on the last Friday of each month following the date of issuance of the Note. The outstanding principal balance on the Note shall be repaid at the rate of $41,666.67 per month on the last Friday of each month following the date of issuance of the Note. The amount of interest and principal due on the last Friday of each month following the date of issuance of the Note are as set forth on Schedule A attached to the Note.

(ii) Mandatory Prepayment.

The Note shall be subject to the following mandatory prepayment conditions:

2. Amendment to First Sentence of Section 1.9(a). The first sentence of Section 1.9(a) of the Agreement shall be deleted and replaced with the following: “If any Trigger Event occurs prior to the date on which the Purchaser issues and delivers the Note to Seller, Purchaser shall become immediately obligated to pay the sum of $2,000,000 to Seller by wire transfer of immediately available funds.”

3. Amendment of Section 1.10. The phrase “Second Cash Payment” in Section 1.10 of the Agreement shall be deleted and replaced with the following: “payment obligations under the Note, subject to the acceleration of such payment obligations under Section 1.3(c)(ii)(1) of the Agreement.”

4. Release and Waiver. In consideration of the mutual agreements contained herein, the adequacy and sufficiency of which are hereby acknowledged, Purchaser hereby waives, releases, acquits and forever discharges Seller and Subsidiary and their respective Affiliates,

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predecessors, successors and assigns from any and all claims, demands, actions, causes of action, liabilities and damages in law or in equity, arising out of, in connection with, or relating to, the Matter, and all matters directly and indirectly related thereto.

5. Miscellaneous. Except as expressly amended hereby, the Agreement and the Ancillary Agreements shall remain in full force and effect in accordance with the terms thereof. This Amendment No. Two will be construed in accordance with, and governed in all respects by, the laws of the State of California (without giving effect to principles of conflicts of law) and may be executed in several counterparts, each of which will constitute an original and all of which, when taken together, will constitute one agreement.

6. Trustee Capacity of Wilmington Trust Company. Notwithstanding anything contained herein to the contrary, it is expressly understood and agreed by the parties hereto that (i) this Agreement is executed and delivered by Wilmington Trust Company, not individually or personally but solely in its trustee capacity, in the exercise of the powers and authority conferred and vested in it under the Amended and Restated Trust Agreement dated as of August 9, 2011, among State Street Custodial Services (Ireland) Limited, as Trustee of Royalty Pharma Select, and Wilmington Trust Company, as owner trustee of Seller, (ii) each of the representations, undertakings and agreements herein made on the part of Seller is made and intended not as a personal representation, undertaking and agreement by Wilmington Trust Company but is made and intended for the purpose of binding only Seller and (iii) under no circumstances shall Wilmington Trust Company be personally liable for the payment of any indebtedness or expenses of Seller or be liable for the breach or failure of any obligation, representation, warranty or covenant made or undertaken by Seller under this Agreement or any related documents.

[Signatures Follow]

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The Parties have caused this Amendment No. Two to be executed as of the date first written above.

[Signature Page to Amendment No. Two]

EXHIBIT A

Form of Note

SECURED PROMISSORY NOTE

Subject to the terms and conditions of this Note, for value received, Exagen Diagnostics, Inc., a Delaware corporation (the “Borrower”), hereby promises to pay to Royalty Pharma Collection Trust, a Delaware statutory trust (the “Lender”), the principal sum of Two Million Dollars and Zero Cents ($2,000,000.00) (the “Principal Amount”), together with interest thereon accruing on and from the date hereof until the entire Balance is paid, at an annual rate equal to ten percent (10%) (the “Interest Rate”). Interest shall be calculated based on a 365-day year, compounded monthly, but in no event shall the rate of interest exceed the maximum rate, if any, allowable under applicable law. The amount of interest and principal due on the last Friday of each month following the date of issuance of this Note is as set forth on Schedule A hereto. “Balance” means, at the applicable time, the sum of all then outstanding principal of this Note, all then accrued but unpaid interest and all other amounts then accrued but unpaid under this Note.

1. Terms of Note. This Note is issued pursuant to, and is subject to the terms and entitled to the benefits of, the Asset Purchase Agreement, dated as of October 8, 2010, as amended, modified or supplemented from time to time (the “Asset Purchase Agreement”), among the Borrower, the Lender (as assignee of Seller) and Subsidiary. Terms used herein and not otherwise defined shall have the meanings set forth in the Asset Purchase Agreement.

2. Maturity. Subject to any prepayment of this Note, the principal amount of this Note shall be payable on the dates and in the amounts as set forth on Schedule A hereto.

3. Interest. Interest on this Note will accrue at the Interest Rate from the date hereof. Interest on this Note shall be payable on the dates and in the amounts as set forth on Schedule A hereto, subject to any prepayment of this Note. Following any prepayment of this Note, the interest amounts payable on this Note shall be adjusted accordingly. Notwithstanding the foregoing, in the event any payment due hereunder is not made when due, Section 1.11 of the Asset Purchase Agreement shall be applicable to such late payment.

4. Prepayment. This Note may be prepaid at any time, without premium or penalty, in whole or in part. Any prepayment of this Note shall be applied to installments of the Principal Amount in the inverse order of maturity. This Note is subject to the mandatory prepayment conditions set forth in Section 3.1(c)(ii) of the Asset Purchase Agreement. Such mandatory prepayments shall be made at the times and in the amounts as specified in the Asset Purchase Agreement.

5. Security. This Note is secured under the Intellectual Property Security Agreement, entered into concurrently with the execution and delivery of the Asset Purchase Agreement. Reference is hereby made to the Intellectual Property Security Agreement for a

description of the nature and extent of the security for this Note and the rights with respect to such security of the holder of this Note.

6. No Impairment. No provision of the Asset Purchase Agreement or this Note shall alter or impair the obligation of the Borrower, which is absolute and unconditional, to pay the principal and interest on this Note at the times, places and rates, and in the coin or currency provided in the Asset Purchase Agreement or herein.

7. No Waivers; Amendments. No failure or delay on the part of the payee hereof in exercising any right, power or remedy hereunder or under the Asset Purchase Agreement shall operate as a waiver thereof, nor shall any single or partial exercise of any such right, power or remedy preclude any other or further exercise thereof or the exercise of any other right, power or remedy. The remedies provided for herein and in the Asset Purchase Agreement are cumulative and are not exclusive of any remedies that may be available to the payee hereof at law or in equity or otherwise. This Note may not be amended and the provisions hereof may not be waived, except in accordance with the terms of the Asset Purchase Agreement.

8. Assignment. The Lender may assign this Note and its rights under the Intellectual Property Security Agreement to an Affiliate of such Lender. Such assignee shall be deemed a “Lender” for purposes of this Note. The Borrower may not assign its obligations under this Note without the prior written consent of the Lender.

9. Replacement of Note. Upon receipt by the Borrower of evidence reasonably satisfactory to it of ownership of and the loss, theft, destruction or mutilation of this Note, and (a) in the case of loss, theft or destruction of indemnity reasonably satisfactory to it, or (b) in the case of mutilation, upon surrender and cancellation of this Note, the Borrower, at its own expense, shall execute and deliver a new Note, dated and bearing interest from the date to which interest shall have been paid on this lost, stolen, destroyed or mutilated Note or dated the date of this lost, stolen, destroyed or mutilated Note if no interest shall have been paid hereon.

10. Collection Expenses. The Borrower further agrees, subject only to any limitation imposed by applicable law, to pay all expenses, including reasonable attorneys’ fees, incurred by the holder of this Note in endeavoring to collect any amounts payable hereunder which are not paid when due.

11. Payments in U.S. Dollars. All payments of principal and interest with respect to this Note are to be made in lawful money of the United States of America.

12. Governing Law. This Note shall be deemed to be a contract made under the laws of the State of California, and for all purposes shall be governed by and construed in accordance with the laws of the State of California without regard to principles of conflicts of laws thereof.

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IN WITNESS WHEREOF, the Borrower has caused this Note to be duly executed and delivered as a sealed instrument on the date set forth above by the duly authorized representative of the Borrower.

[Signature Page for Form of Note]