Exhibit 4.2

CONFIDENTIAL

THIS NOTE HAS NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED, OR ANY STATE SECURITIES LAWS. IT MAY NOT BE SOLD, OFFERED FOR SALE, PLEDGED OR HYPOTHECATED IN THE ABSENCE OF AN EFFECTIVE REGISTRATION STATEMENT AS TO THE SECURITIES UNDER SAID ACT OR ANY APPLICABLE STATE SECURITIES LAWS, OR AN OPINION OF COUNSEL SATISFACTORY TO THE CORPORATION THAT SUCH REGISTRATION IS NOT REQUIRED.

NEUROSIGMA, INC.

PROMISSORY NOTE

October 14, 2013

FOR VALUE RECEIVED, NeuroSigma, Inc., a Delaware corporation (the “Company”) promises to pay to Jerry E. Shea, Jr. (the “Investor”), or its registered assigns, in lawful money of the United States of America the principal sum of $301,500, or such lesser amount as shall equal the outstanding principal amount hereof, together with simple interest from the date of this Promissory Note (the “Note”) on the unpaid principal balance at a rate equal to twelve percent (12%) per annum. Principal and accrued interest shall be due and payable in full on the earlier to occur of (a) July 1, 2015, or (b) the closing in one or more related transactions of the Company’s next equity financing in which gross aggregate proceeds to the Company exceeds $25,000,000 (excluding any and all notes which are converted) (“Next Equity Financing”); provided that the sale of the Company’s Common Stock to its employees, directors, and consultants pursuant to equity compensation plans, or the issuance of Common Stock upon exercise or conversion of securities outstanding prior to the date hereof, shall not constitute a Next Equity Financing. This Note is one of the “Notes” issued pursuant to the Note and Warrant Purchase Agreement dated as of October 14, 2013 (the “Note Purchase Agreement”). Capitalized terms not otherwise defined herein shall have the meaning set forth in the Note Purchase Agreement.

The following is a statement of the rights of the Investor and the conditions to which this Note is subject, and to which the Investor, by the acceptance of this Note, agrees:

1. Prepayment. Prepayment of principal, together with accrued interest, may be made at any time without penalty.

2. Waiver and Amendment. Any provision of this Note may be amended, waived or modified upon the written consent of Company and a Majority in Interest. Notwithstanding the foregoing, in the event an amendment, waiver, or modification of this Note adversely affects the rights of the Investor in a manner different than the other Investors other than by virtue of the amount of principal and interest then outstanding owed to such Investors, then the written

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consent of the Investor shall also be required to enforce such amendment, waiver or modification.

3. Notices. All notices, requests, demands, consents, instructions or other communications required or permitted hereunder shall in writing and faxed, mailed or delivered to each party at the respective addresses of the parties as set forth in the Note Purchase Agreement, or at such other address or facsimile number as Company shall have furnished to the Investor in writing. All such notices and communications shall be effective (a) when sent by Federal Express or other overnight service of recognized standing, on the business day following the deposit with such service; (b) when mailed, by registered or certified mail, first class postage prepaid and addressed as aforesaid through the United States Postal Service, upon receipt; (c) when delivered by hand, upon delivery; and (d) when faxed, upon confirmation of receipt.

4. Usury. In the event any interest is paid on this Note is deemed to be in excess of the then legal maximum rate, then that portion of the interest payment representing an amount in excess of the then legal maximum rate shall be deemed a payment of principal and applied against the principal of this Note.

5. Waivers. Company hereby waives notice of default, presentment or demand for payment, protest or notice of nonpayment or dishonor and all other notices or demands relative to this instrument.

6. Transfer of this Note. This Note and all rights hereunder may only be transferred, in whole or in part, to an affiliate of the holder hereof; provided, however, that (x) such affiliate shall have agreed with all parties hereto, in a written instrument reasonably satisfactory to the Company, (1) providing that such affiliate shall be bound by the terms of this Note and (2) that contains the representations and warranties set forth in Section 3 of the Note Purchase Agreement, and (y) as a condition to such transfer, the holder hereof shall surrender this Note to the Company to permit the Company to deliver a new Note in such affiliate’s name. Except as set forth in Section 6, this Note may not be transferred without the prior written consent of the Company in its sole discretion. All transfers of this Note must also be made in accordance with the Securities Act, and applicable state securities laws. Any attempted transfer of this Note in violation of this Section 6 shall be null and void ab initio. Upon surrender of this Note to the Company, together with instructions by the applicable holder hereof that all or a portion of this Note be assigned, the Company shall execute and deliver a new Note in the name of the affiliate or affiliates named in such instrument of assignment and, if the applicable holder’s entire interest is not being assigned, in the name of the prior holder, and this Note shall promptly be canceled. Each such new Note shall bear any legend as to the applicable restrictions on transferability in order to ensure compliance with such laws, including, without limitation, the legend set forth on the face of this Note. Prior to presentation of this Note to the Company for transfer, the Company shall treat the registered holder hereof as the owner and holder of this Note for the purpose of receiving all payments of principal and interest hereon and for all other

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purposes whatsoever, whether or not this Note shall be overdue and the Company shall not be affected by notice to the contrary.

7. Governing Law. This Note and all actions arising out of or in connection with this Note shall be governed by and construed in accordance with the laws of the State of California, without regard to the conflicts of law provisions of the State of California, or of any other state.

8. Counterparts. This Note may be executed in one or more counterparts, each of which will be deemed an original, but all of which together will constitute one and the same agreement. Facsimile copies of signed signature pages will be deemed binding originals.

[Signature Pages Follow]

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IN WITNESS WHEREOF, the Company has caused this Note to be issued as of the date first written above.

[Signature Pages Continue on the Following Page]

[Signature Page to the Promissory Note]

CONFIDENTIAL

ACKNOWLEDGED AND AGREED:

FOR INVESTORS THAT ARE INDIVIDUALS:

FOR INVESTORS THAT ARE TRUSTS:

FOR INVESTORS THAT ARE CORPORATIONS, LIMITED LIABILITY COMPANIES OR PARTNERSHIPS:

[Signature Page to the Promissory Note]