BIOCEPT, INC. AMENDMENT TO NOTE AND WARRANT PURCHASE AGREEMENT

Exhibit 10.18.4

BIOCEPT, INC.

AMENDMENT TO NOTE AND WARRANT PURCHASE AGREEMENT

This AMENDMENT TO NOTE AND WARRANT PURCHASE AGREEMENT (this “Amendment”), amending the Note and Warrant Purchase Agreement by and among BIOCEPT, INC., a California corporation (the “Company”), and the investors listed on the Schedule of Investors attached thereto (the “Investors”), dated as of February 1, 2011, and amended as of July 1, 2011, August 1, 2011 and September 30, 2011 (as amended, the “Purchase Agreement”), is entered into as of June 23, 2012. Capitalized terms used herein which are not defined herein shall have the definition ascribed to them in the Purchase Agreement.

RECITALS

WHEREAS, the Company and the Investors have previously entered into the Purchase Agreement;

WHEREAS, Section 6.7 of the Purchase Agreement provides that the Purchase Agreement may be amended with the written consent of (i) the Company and (ii) the holders of at least a majority in interest of the outstanding Securities (the “Required Holders”); and

WHEREAS, the undersigned constitute (i) the Company and (ii) the Required Holders.

AGREEMENT

NOW, THEREFORE, in consideration of the foregoing and the promises and covenants contained herein and in the Purchase Agreement, and for other good and valuable consideration, the receipt of which is hereby acknowledged, the parties hereto agree as follows:

1. Section 2.8 of the Purchase Agreement. The first sentence of Section 2.8 of the Purchase Agreement shall be amended and restated to read in its entirety as follows:

“At any time prior to December 31, 2012, the Company may sell up to the balance of the authorized Notes and Warrants not sold at the Seventh Closing, Sixth Closing, Fifth Closing, Fourth Closing, Third Closing, Second Closing and Initial Closing to such persons as may be approved by the Chief Executive Officer of the Company (the “Additional Investors”).”

2. Effect of Amendment. Except as expressly modified by this Amendment, the Purchase Agreement shall remain unmodified and in full force and effect.

3. Governing Law. This Amendment shall be governed by and construed under the laws of the State of California as applied to agreements among California residents, made and to be performed entirely within the State of California without giving effect to its conflicts of laws principles.

4. Counterparts. This Amendment may be executed in any number of counterparts and signatures delivered by facsimile, each of which shall be deemed an original, but all of which together shall constitute one instrument.

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IN WITNESS WHEREOF, the parties have executed this AMENDMENT TO NOTE AND WARRANT PURCHASE AGREEMENT as of the date first written above.