Form of Preferred Stock Purchase Warrant issued to Capital Royalty Partners and related advisors by the Registrant in connection with the Term Loan Agreement, by and between Capital Royalty Partners II L.P., Capital Royalty Partners IIParallel Fund A L.P., Parallel Investment Opportunities Partners II L.P. and the Registrant

Exhibit 4.5

THE SECURITIES REPRESENTED BY THIS INSTRUMENT HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED, OR THE SECURITIES LAWS OF ANY STATE, AND MAY NOT BE SOLD, TRANSFERRED, ASSIGNED, PLEDGED OR HYPOTHECATED UNLESS AND UNTIL REGISTERED UNDER SUCH ACT AND/OR APPLICABLE STATE SECURITIES LAWS, OR UNLESS THE COMPANY HAS RECEIVED AN OPINION OF COUNSEL OR OTHER EVIDENCE, REASONABLY SATISFACTORY TO THE COMPANY AND ITS COUNSEL, THAT SUCH REGISTRATION IS NOT REQUIRED.

Warrant No.

EXAGEN DIAGNOSTICS, INC.

PREFERRED STOCK PURCHASE WARRANT

THIS CERTIFIES that                                          (the “Holder”) is entitled, upon the terms and subject to the conditions hereinafter set forth, at any time on or after the date of this warrant (this “Warrant”) and on or prior to                          (the “Expiration Date”), but not thereafter, to subscribe for and purchase from Exagen Diagnostics, Inc., a Delaware corporation (the “Company”),                                          (                ) shares of Series D Convertible Preferred Stock in the Company (the “Shares”) at an exercise price of $         per share (the “Exercise Price”).

1. Exercise of Warrant.

(a) Unless earlier terminated under Section 7, the purchase rights represented by this Warrant to purchase Shares are exercisable, in whole or in part, before the close of business on the Expiration Date, by the surrender of this Warrant and the Notice of Exercise annexed hereto duly executed at the principal executive office of the Company (or such other office or agency of the Company as it may designate by notice in writing to the Holder at the address of the Holder appearing on the books of the Company), and upon payment of the Exercise Price of the Shares thereby purchased (by cash or by check or bank draft payable to the order of the Company in an amount equal to the Exercise Price of the shares thereby purchased).

(b) Unless earlier terminated under Section 7, in lieu of exercising this Warrant by payment of cash or check pursuant to Section 1(a), the Holder may elect to receive Shares equal to the value of this Warrant (or the portion thereof being exercised), by surrender of this Warrant at the principal executive office of the Company, together with the Notice of Conversion annexed hereto, in which event the Company will issue to the Holder Shares in accordance with the following formula:

For purposes of this Section 1(b), the fair market value of a Share shall be the price per Share that the Company could obtain from a willing buyer for Shares sold by the Company from authorized but unissued Shares, as such price shall be determined in good faith by the Company’s Board of Directors. If the Shares are traded on the over-the-counter market or on an exchange, the fair market value of a Share shall be the average of the closing bid and asked prices of Shares quoted in the over-the-counter market in which the Shares are traded or the closing price quoted on any exchange on which the Shares are listed, whichever is applicable, as published in the Western Edition of The Wall Street Journal for the ten (10) trading days prior to the date of determination of fair market value (or such shorter period of time during which such stock was traded over-the-counter or on such exchange).

(c) 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 expense will cause to be issued in the name of, and delivered to, the Holder, or such other name as specified on the Notice of Exercise delivered to the Company:

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

(ii) in case such exercise is in part only, a 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 equal (without giving effect to any adjustments therein) to the number of Shares called for on the face of this Warrant minus the number of such Shares purchased by the Holder upon such exercise as provide in Sections 1(a) or (b) above.

2. Shares to be Fully Paid; Reservation of Shares. The Company covenants that all Shares which may be issued upon the exercise of rights represented by this Warrant (together with all shares of Common Stock issuable upon conversion of such Shares) will, upon issuance, be duly authorized, validly issued, fully paid and nonassessable and free from all preemptive rights of any stockholder and free from all taxes, liens and charges in respect of the issue thereof. Certificates for Shares purchased hereunder shall be delivered to the Holder within a reasonable time after the date on which this Warrant shall have been exercised as aforesaid. The Company further covenants and agrees that during the period within which the rights represented by this Warrant may be exercised, the Company will at all times have authorized and reserved (or will

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have provided for the ability to accomplish the same through a voting contract amongst sufficient stockholders), for the purpose of issue or transfer upon exercise of the subscription rights evidenced by this Warrant, a sufficient number of shares of authorized but unissued Shares (together with the number of shares of Common Stock issuable upon conversion of such Shares), or other securities and property, when and as required for the exercise of the rights represented by this Warrant.

3. Adjustment of Exercise Price and Number of Shares. The Exercise Price and the number of shares purchasable upon the exercise of this Warrant shall be subject to adjustment from time to time upon the occurrence of certain events described in this Section 3. Whenever the number of Shares purchasable upon the exercise of this Warrant is adjusted as herein provided the Exercise Price payable upon exercise of this Warrant shall be adjusted by multiplying the Exercise Price in effect immediately prior to such adjustment by a fraction, of which the numerator shall be the number of Shares purchasable upon the exercise of this Warrant immediately prior to such adjustment, and of which the denominator shall be the number of Shares so purchasable immediately thereafter.

(a) Conversion of Shares. If all of the outstanding Shares of the Company for which this Warrant is exercisable are converted into shares of Common Stock, the number of Shares purchasable upon exercise of this Warrant immediately prior to such conversion shall be adjusted so that the Holder of this Warrant shall be entitled to receive the number of shares of Common Stock which the Holder would have owned or have been entitled to receive had this Warrant been exercised immediately prior to such conversion and the Shares received thereupon had been simultaneously converted into shares of Common Stock immediately prior to such event.

(b) Dilutive Issuances. 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 issuable upon conversion of the Shares of the Company which occur after the date of this Warrant and prior to the exercise of this Warrant, including, without limitation, any increase in the number of shares of Common Stock issuable upon conversion as a result of a dilutive issuance of capital stock.

(c) Split, Subdivision or Combination of Shares. If the Company at any time while this Warrant, or any portion hereof, remains outstanding and unexpired shall split, subdivide or combine the Shares, into a different number of securities of the same class, the number of Shares purchasable upon exercise of this Warrant immediately prior thereto shall be adjusted so that the holder of this Warrant shall be entitled to receive the kind and number of Shares or other securities of the Company which the Holder would have owned or have been entitled to receive after the happening of any of the events described above, had this Warrant been exercised immediately prior to the happening of such event or any record date with respect thereto. An adjustment made pursuant to this Section 3(c) shall become effective immediately after the effective date of such event retroactive to the record date, if any, for such event.

(d) Reclassification. If the Company, at any time while this Warrant, or any portion hereof, remains outstanding and unexpired by reclassification of securities or otherwise, shall change the Shares into the same or a different number of securities or any other class or

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classes, this Warrant shall thereafter represent the right to receive the kind and number of Shares or other securities of the Company which the Holder would have owned or have been entitled to receive after the happening of the event described above, had this Warrant been exercised immediately prior to the happening of such event or any record date with respect thereto. An adjustment made pursuant to this Section 3(d) shall become effective immediately after the effective date of such event retroactive to the record date, if any, for such event.

(e) Cash Distributions. No adjustment on account of cash dividends or interest on the Shares will be made to the Exercise Price under this Warrant.

(f) De Minimus Adjustments. No adjustment in the number of Shares purchasable hereunder shall be required unless such adjustment would require an increase or decrease of at least one percent (1%) in the number of Shares purchasable upon the exercise of this Warrant; provided, however, that any adjustments which by reason of this Section 3(f) are not required to be made shall be carried forward and taken into account in any subsequent adjustment. All calculations shall be made to the nearest cent and to the nearest one-hundredth of a Share, as the case may be.

(g) Notice of Adjustment. Upon any adjustment of the Exercise Price or any increase or decrease in the number of shares purchasable upon the exercise of this Warrant, the Company shall give written notice thereof, by first class mail postage prepaid, addressed to the registered Holder of this Warrant at the address of such Holder as shown on the books of the Company. The notice shall be signed by the Company’s chief financial officer and shall state the Exercise Price resulting from such adjustment and the increase or decrease, if any, in the number of shares purchasable at such price upon the exercise of this Warrant, setting forth in reasonable detail the method of calculation and the facts upon which such calculation is based.

(h) Other Notices. If at any time:

(i) The Company shall declare any cash dividend upon its Shares (or Common Stock issuable upon conversion thereof);

(ii) There shall be any acquisition or capital reorganization or reclassification of the capital stock of the Company;

(iii) There shall be a voluntary or involuntary dissolution, liquidation or winding-up of the Company; or

(iv) There shall be an initial public offering of the Company’s securities;

then, in any one or more of said cases, the Company shall give, by first class mail, postage prepaid, addressed to the Holder of this Warrant at the address of such Holder as shown on the books of the Company, (a) at least ten (10) days prior written notice of the date on which the books of the Company shall close or a record shall be taken for such dividend or for determining rights to vote in respect of any such acquisition, reorganization, reclassification, dissolution, liquidation, winding-up or public offering, and (b) in the case of any such acquisition, reorganization, reclassification, dissolution, liquidation, winding-up or public offering, at least

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ten (10) days prior written notice of the date when the same shall take place; provided, however, that the Holder shall make a best efforts attempt to respond to such notice as early as possible after the receipt thereof. Any notice given in accordance with the foregoing clause (a) shall also specify, in the case of any such dividend, the date on which the holders of Shares (or Common Stock issuable upon conversion thereof) shall be entitled thereto. Any notice given in accordance with the foregoing clause (b) shall also specify the date on which the holders of Shares (or Common Stock issuable upon conversion thereof) shall be entitled to exchange their Shares (or Common Stock issuable upon conversion thereof) for securities or other property deliverable upon such acquisition, reorganization, reclassification, dissolution, liquidation, winding-up, conversion or public offering, as the case may be.

4. No Fractional Shares or Scrip. No fractional shares or scrip representing fractional shares shall be issued upon the exercise of this Warrant. With respect to any fraction of a share called for upon the exercise of this Warrant, an amount equal to such fraction multiplied by the then current price at which each Share may be purchased hereunder shall be paid in cash to the Holder.

5. Charges, Taxes and Expenses. Issuance of certificates for Shares upon the exercise of this Warrant shall be made without charge to the Holder hereof for any issue or transfer tax or other incidental expense in respect of the issuance of such certificate, all of which taxes and expenses shall be paid by the Company, and such certificates shall be issued in the name of the Holder or such other name as specified on the Notice of Exercise delivered to the Company.

6. No Rights as Stockholders. This Warrant does not entitle the Holder to any voting rights or other rights as a stockholder of the Company prior to the exercise thereof.

7. Early Termination on Merger, Initial Public Offering, etc. If at any time the Company proposes to merge, reorganize or consolidate with or into any other entity, sell all or substantially all of the assets of the Company, effect any other transaction or series of related transactions in which the holders of the Company’s capital stock immediately prior to the consummation of such transaction(s) hold less than fifty percent (50%) of the voting power of the surviving entity (or its parent), or conduct an initial public offering of its capital stock, then the Company shall give the Holder notice of such transaction pursuant to Section 3(h), and if the Warrant has not been exercised by the effective date of the transaction, the Warrant shall terminate.

8. Loss, Theft, Destruction or Mutilation of Warrant. Upon receipt by the Company of evidence reasonably satisfactory to it of the loss, theft, destruction or mutilation of this Warrant, and in case of loss, theft or destruction, of indemnity or security reasonably satisfactory to it, and upon reimbursement to the Company of all reasonable expenses incidental thereto, and upon surrender and cancellation of this Warrant, if mutilated, the Company will make and deliver a new warrant of like tenor and dated as of such cancellation, in lieu of this Warrant.

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9. Miscellaneous.

(a) Issue Date. The provisions of this Warrant shall be construed and shall be given effect in all respects as if it had been issued and delivered by the Company on the date set forth below.

(b) Governing Law. THIS WARRANT SHALL BE GOVERNED BY, AND CONSTRUED IN ACCORDANCE WITH, THE LAWS OF THE STATE OF DELAWARE WITHOUT REGARD TO CONFLICTS OF LAWS PRINCIPLES.

(c) Restrictions. By acceptance hereof, the Holder acknowledges that the Shares acquired upon the exercise of this Warrant may have restrictions upon their resale imposed by state and federal securities laws, and that certain 2008 Stockholders’ Agreement, as amended.

(d) Saturdays, Sundays, Holidays, etc. If the last or appointed day for the taking of any action or the expiration of any right required or granted herein shall be a Saturday or a Sunday or shall be a legal holiday, then such action may be taken or such right may be exercised on the next succeeding day not a Saturday, Sunday or legal holiday.

(e) Waivers and Amendments. Any provision of this Warrant may be amended and the observance of any term of this Warrant may be waived (either generally or in a particular instance and either retroactively or prospectively), only with the written consent of the Company and the Holder.

(f) Assignment. This Warrant may be assigned or transferred by the Holder only with the prior written approval of the Company.

IN WITNESS WHEREOF, the Company has caused this Warrant to be executed by its officer thereunto duly authorized.

Dated:

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NOTICE OF EXERCISE

1. The undersigned hereby elects to purchase                  shares of Series D Convertible Preferred Stock (the “Shares”) of Exagen Diagnostics, Inc. pursuant to the terms of the attached Warrant, and tenders herewith payment of the purchase price in full.

2. Please issue a certificate or certificates representing the Shares in the name of the undersigned or in such other name as is specified below:

3. The undersigned confirms that the Shares are being acquired for the account of the undersigned for investment only and not with a view to, or for resale in connection with, the distribution thereof and that the undersigned has no present intention of distributing or selling the Shares.