Exhibit 4.1

FORM OF STOCK PURCHASE AGREEMENT

This Stock Purchase Agreement (this “Agreement”) is made as of February 5, 2020 (the “Effective Date”) by and between Cortexyme, Inc., a Delaware corporation (the “Company”), and [___________] (“Purchaser”).

1. Issuance of Shares. Effective as the Effective Date, the Company agrees to issue and sell to Purchaser [_________] shares (the “Shares”) of the Company’s Common Stock, $0.001 par value per share (the “Common Stock”). Purchaser will purchase the Shares at a price of $50.00 per Share in cash. The total purchase price payable by the Purchaser for the Shares is $[_______] (the “Total Purchase Price”).

2. Closing and Delivery.

(a) Closing. The closing (“Closing”) of the transactions contemplated hereby shall be held at the offices of Orrick, Herrington & Sutcliffe LLP, 1000 Marsh Road, Menlo Park, California 94025 within two Business Days of the date of this Agreement (such date, the “Closing Date”), or at such other time and place as the Company and the Purchaser mutually agree upon. “Business Day” shall mean any day except any Saturday, any Sunday, any day which is a federal legal holiday in the United States or any day on which banking institutions in the State of New York are authorized or required by law or other governmental action to close.

(b) Delivery. At the Closing, (i) the Company shall cause its transfer agent to transfer the Shares to the Purchaser in book entry form in such name(s) as the Purchaser may designate in writing and (ii) upon delivery by the Company to the Purchaser of the Shares in book entry form free and clear of any liens or other restrictions (other than the restrictions set forth in this Agreement, including the restrictions set forth in Section 5 hereof) and written notice from the Company or its transfer agent evidencing the issuance to the Purchaser of the Shares on and as of the Closing Date, the Purchaser shall pay the Company the applicable Total Purchase Price by wire transfer in immediately available funds to such account(s) as the Company shall designate in writing to the Purchaser.

3. Company Representations. The Company represents and warrants to Purchaser as follows:

(a) Organization and Standing. The Company is duly incorporated, validly existing, and in good standing under the laws of the State of Delaware. The Company has all requisite power and authority to own and operate its properties and assets and to carry on its business as presently conducted and as proposed to be conducted. The Company is qualified to do business as a foreign entity in every jurisdiction in which the failure to be so qualified would have, or would reasonably be expected to have, individually or in the aggregate, a material adverse effect upon the business, properties, assets, liabilities, operations, financial condition or results of operations of the Company, or the ability of the Company to perform its obligations under this Agreement (a “Material Adverse Effect”).

(b) Power. The Company has all requisite power to execute and deliver this Agreement, to sell and issue the Shares hereunder, and to carry out and perform its obligations under the terms of this Agreement.

(c) Authorization. The execution, delivery, and performance of this Agreement by the Company has been duly authorized by all requisite action on the part of the Company and its officers, directors and stockholders, and this Agreement constitutes the legal, valid, and binding obligation of the Company enforceable in accordance with its terms, except (i) as limited by applicable bankruptcy, insolvency, reorganization, moratorium, and other laws of general application affecting enforcement of creditors’ rights generally, and (ii) as limited by laws relating to the availability of specific performance, injunctive relief or other equitable remedies.

(d) Consents and Approvals. Except for any Current Report on Form 8-K or Notice of Exempt Offering of Securities on Form D to be filed by the Company in connection with the transaction contemplated hereby, the Company is not required to give any notice to, make any filing with, or obtain any authorization, consent, or approval of any government or governmental agency in order to consummate the transaction contemplated by this Agreement. Assuming the accuracy of the representations of the Purchaser in Section 4, no consent, approval, authorization or other order of, or registration, qualification or filing with, any court, regulatory body, administrative agency, self-regulatory organization, stock exchange or market (including The Nasdaq Stock Market), or other governmental body is required for the execution and delivery of this Agreement, or for the valid issuance, sale and delivery of the Shares to be sold pursuant to this Agreement other than such as have been or will be made or obtained, or for any securities filings required to be made, under federal or state securities laws applicable to the offering of the Shares.

(e) Non-Contravention. The execution and delivery of this Agreement, the issuance, sale and delivery of the Shares to be sold by the Company under this Agreement, the performance by the Company of its obligations under this Agreement and/or the consummation of the transaction contemplated hereby will not (a) conflict with, result in the breach or violation of, or constitute (with or without the giving of notice or the passage of time or both) a violation of, or default under, (i) any bond, debenture, note or other evidence of indebtedness, or under any lease, license, franchise, permit, indenture, mortgage, deed of trust, loan agreement, joint venture or other agreement or instrument to which the Company is a party or by which it or its properties may be bound or affected, (ii) the Company’s Amended and Restated Certificate of Incorporation as in effect on the date hereof, the Company’s Amended and Restated Bylaws as in effect on the date hereof, or (iii) any statute or law, judgment, decree, rule, regulation, ordinance or order of any court or governmental or regulatory body (including The Nasdaq Stock Market), governmental agency, arbitration panel or authority applicable to the Company or its respective properties, except in the case of clauses (i) and (iii), for such conflicts, breaches, violations or defaults that would not reasonably be expected to have, individually or in the aggregate, a Material Adverse Effect, or (b) result in the creation or imposition of any lien, encumbrance, claim, security interest or restriction whatsoever upon any of the properties or assets of the Company or an acceleration of indebtedness pursuant to any obligation, agreement or condition contained in any bond, debenture, note or any other evidence of indebtedness or any indenture, mortgage, deed of trust or any other agreement or instrument to which the Company is a party or by which the Company is bound or to which any of the property or assets of the Company is subject, except for such liens, encumbrances, claims, security interests, restrictions, accelerations of indebtedness that would not reasonably be expected to have, individually or in the aggregate, a Material Adverse Effect.

(f) Shares. The Shares are duly authorized and when issued pursuant to the terms of this Agreement will be validly issued, fully paid, and nonassessable, and will be free of any liens or encumbrances with respect to the issuance thereof; provided, however, that the Shares shall be subject to restrictions on transfer under state or federal securities laws as set forth in this Agreement, or as otherwise may be required under state or federal securities laws as set forth in this Agreement at the time a transfer is proposed. The issuance and delivery of the Shares is not subject to preemptive, co-sale, right of first refusal or any other similar rights of the stockholders of the Company or any other person, or any liens or encumbrances or result in the triggering of any anti-dilution or other similar rights under any outstanding securities of the Company.

(g) No Registration. Assuming the accuracy of each of the representations and warranties of the Purchaser, the issuance by the Company of the Shares is exempt from registration under the Securities Act of 1933, as amended (the “Securities Act”).

4. Investment Representations. In connection with the receipt of the Shares pursuant to this Agreement, Purchaser represents to the Company the following:

(a) The execution, delivery and performance by Purchaser of this Agreement do not and will not contravene or constitute a default under, or violation of, or be subject to penalties under, (i) any agreement (or require the consent of any party under any such agreement that has not been made or obtained) to which Purchaser is a party, or (ii) any judgment, injunction, order, decree or other instrument binding upon Purchaser, except where such contravention, default, violation or failure to obtain a consent, individually or in the aggregate, would not reasonably be expected to impair Purchaser’s ability to perform fully any obligation which Purchaser has or will have under this Agreement.

(b) Purchaser understands the definition of the term “accredited investor” within the meaning of Regulation D, Rule 501(a), as amended, under the Securities Act, and qualifies as an accredited investor. Purchaser was not organized solely for the purpose of acquiring the Shares and is not required to be registered as a broker-dealer under Section 15 of the Exchange Act.

(c) Purchaser acknowledges and affirms that, with the assistance of its advisors, it has conducted and completed its own investigation, analysis and evaluation related to the investment in the Shares. Purchaser has received or has had full access to all the information it considers necessary or appropriate to make an informed investment decision with respect to the Shares.

(d) Purchaser is acquiring the Shares hereunder for its own account for investment purposes only and not with a view to any public distribution thereof or with any intention of selling, distributing or otherwise disposing of the Shares in a manner that would violate the registration requirements of the Securities Act. Each Purchaser is able to bear the economic risk of holding the Shares for an indefinite period (including total loss of its investment), and has sufficient knowledge and experience in financial and business matters so as to be capable of evaluating the merits and risk of its investment.

(e) Purchaser understands that the Shares have not been registered under the Securities Act by reason of a specific exemption therefrom, which exemption depends upon, among other things, the bona fide nature of Purchaser’s investment intent as expressed herein.

(f) Purchaser understands that the Shares are “restricted securities” under applicable U.S. federal and state securities laws and that, pursuant to these laws, Purchaser must hold the Shares indefinitely unless they are registered with the SEC and qualified by state authorities, or an exemption from such registration and qualification requirements is available.

(g) No broker, finder or investment banker is entitled to any brokerage, finder’s or other fee or commission in connection with the transactions contemplated hereby based upon arrangements made by or on behalf of Purchaser.

(h) Between the time any of the Purchaser’s investment professionals learned about the offering contemplated by this Agreement and the public announcement of the offering, neither the Purchaser nor any Person acting on behalf of or pursuant to any understanding with such Purchaser, directly or indirectly executed any purchases or sales, including Short Sales (as defined below), of the securities of the Company. For purposes of this Agreement, “Person” shall mean an individual or corporation, partnership, trust, incorporated or unincorporated association, joint venture, limited liability company, joint stock company, government (or an agency or subdivision thereof) or other entity of any kind and “Short Sales” shall include, without limitation, (i) (A) all “short sales” as defined in Rule 200 promulgated under Regulation SHO under the Exchange Act, whether or not against the box, and (B) all types of direct and indirect stock pledges, forward sale contracts, options, puts, calls, short sales, swaps, “put equivalent positions” (as defined in Rule 16a-1(h) under the Exchange Act) and similar arrangements (including on a total return basis) that have an economically similar result to a “short sale” as defined in Rule 200, and (ii) sales and other transactions through non-U.S. broker dealers or foreign regulated brokers that have an economically similar result to a “short sale” as defined in Rule 200..

5. Restrictive Legends and Stop-Transfer Orders. It is understood that, except as provided below, book-entry notations evidencing the Shares may bear the following or any similar legend:

(a) “THE SECURITIES REPRESENTED HEREBY HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED (THE “ACT”), OR UNDER THE SECURITIES LAWS OF ANY OTHER JURISDICTIONS. THESE SECURITIES ARE SUBJECT TO RESTRICTIONS ON TRANSFERABILITY AND RESALE AND MAY NOT BE TRANSFERRED OR RESOLD EXCEPT AS PERMITTED UNDER THE ACT AND THE APPLICABLE SECURITIES LAWS OF OTHER STATES AND JURISDICTIONS, PURSUANT TO REGISTRATION OR EXEMPTION THEREFROM. INVESTORS SHOULD BE AWARE THAT THEY MAY BE REQUIRED TO BEAR THE FINANCIAL RISKS OF THIS INVESTMENT FOR AN INDEFINITE PERIOD OF TIME. THE ISSUER OF THESE SECURITIES MAY REQUIRE AN OPINION OF COUNSEL IN FORM AND SUBSTANCE REASONABLY SATISFACTORY TO THE ISSUER TO THE EFFECT THAT ANY PROPOSED TRANSFER OR RESALE IS IN COMPLIANCE WITH THE ACT.”

(b) “AS LONG AS THE HOLDER OF THESE SECURITIES IS AN AFFILIATE OF THE ISSUER, THESE SECURITIES MAY NOT BE SOLD, OR OFFERED FOR SALE, IN THE ABSENCE OF A REGISTRATION STATEMENT IN EFFECT WITH RESPECT TO THE SALE OF THESE SECURITIES UNDER THE SECURITIES ACT OF 1933, OR THE SALE OTHERWISE BEING EXEMPT FROM REGISTRATION UNDER SUCH ACT. THE ISSUER MAY REQUIRE AN OPINION OF COUNSEL REASONABLY SATISFACTORY TO THE ISSUER THAT SUCH REGISTRATION IS NOT REQUIRED.”

(c) If required by the authorities of any state in connection with the issuance of sale of the Shares, the legend required by such state authority.

6. Registration Rights.

(a) The Company shall use reasonable efforts to file a registration statement on Form S-1, or other appropriate form available to the Company, registering the resale of the Shares as promptly as practicable within 60 days following the Closing Date and to use reasonable efforts to cause such registration statement to be declared effective as soon as practicable after the filing thereof. The Company shall use reasonable efforts to keep such registration statement effective at all times until (1) the Shares may be sold without volume or manner-of-sale restrictions pursuant to Rule 144 under the Securities Act, or (2) the three (3) year anniversary of the Closing Date, whichever is the earliest to occur. Subject to the accuracy of the information provided by the Purchaser to the Company, the Company shall ensure that such registration statement (including any amendments or supplements thereto and prospectuses contained therein) shall not contain any untrue statement of a material fact or omit to state a material fact required to be stated therein, or necessary to make the statements therein (in the case of prospectuses, in the light of the circumstances in which they were made) not misleading. After the date hereof and during any

period in which a prospectus or prospectus supplement relating to any of the Securities subject to registration under this Section 7 is required to be delivered by Purchaser pursuant to the Securities Act (including in circumstances where such requirement may be satisfied pursuant to Rule 172 of the Securities Act), (i) the Company will notify the Purchaser promptly of the time when any subsequent amendment to such registration statement, other than documents incorporated by reference, has been filed with the SEC or has become effective or any subsequent supplement to the prospectus regarding such Shares or of the Purchasers or any subsequent amendment to the prospectus or any supplement or amendment to the prospectus supplement has been filed with the SEC and of any comment letter from the SEC or any request by the SEC for any amendment or supplement to such registration statement, any amendment to the prospectus, any supplement to the prospectus that relates to the Shares subject to such registration statement under this Section or the Purchaser, or any amendment or supplement to the prospectus supplement, provided that no notification of the Purchaser shall be required if such amendment, supplement, or comment, or request would not, and would not seek, to limit the rights of the Purchaser, (ii) the Company will prepare and file with the SEC, promptly upon Purchaser’s request, any amendments or supplements to such registration statement, prospectus or prospectus supplement that, in the Company’s reasonable opinion, may be necessary in connection with any resale of the Shares by Purchaser (provided, however, that the failure of such Purchaser to make such request shall not relieve the Company of any obligation or liability hereunder), (iii) the Company will not file any amendment or supplement to a registration statement, prospectus or prospectus supplement, other than documents incorporated by reference, relating to the Shares subject to registration under this Section unless a copy thereof has been submitted or made available to Purchaser within a reasonable period of time before the filing and Purchaser has not reasonably objected in writing thereto (provided, however, that (A) the failure of Purchaser to make such objection shall not relieve the Company of any obligation or liability hereunder, and (B) the Company has no obligation to provide Purchaser any advance copy of such filing or to provide such Purchaser an opportunity to object to such filing if such filing does not name Purchaser or specifically discuss the Shares subject to registration under this Section as contemplated hereby or would have the effect of limiting the rights of the Purchaser with respect to the Shares) and the Company will furnish or make available to Purchaser at the time of filing thereof a copy of any document that upon filing is deemed to be incorporated by reference into a registration statement, prospectus or prospectus supplement, except for those documents available via EDGAR, and (iv) the Company will cause each amendment or supplement to the prospectus or prospectus supplement, other than documents incorporated by reference, to be filed with the SEC as required pursuant to the applicable paragraph of Rule 424(b) of the Securities Act. All fees and expenses incident to the performance of or compliance with, this Section by the Company shall be borne by the Company whether or not any Shares are sold pursuant to a registration statement. Notwithstanding anything to the contrary contained herein, in no event shall the Company be permitted to name Purchaser or affiliate of a Purchaser as an underwriter without the prior written consent of Purchaser.

7. Fees and Expenses. Except as set forth in Section 6 hereof, each party shall pay its own fees and expenses in connection with the transactions contemplated hereby.

8. Miscellaneous.

(a) The Company acknowledges that the Purchaser will rely on the representations and warranties contained in this Agreement. The obligation of the Purchaser to consummate the Closing shall be subject to the satisfaction or valid waiver by the Purchaser of the condition that all representations and warranties of the Company set forth in this Agreement shall be true and correct in all material respects (other than representations and warranties that are qualified as to materiality or Material Adverse Effect, which representations and warranties shall be true in all respects) at and as of the Closing Date. Prior to the Closing, the Company agrees to promptly notify the Purchaser if it becomes aware that any of the representations or warranties of the Company set forth herein are no longer accurate in all material respects.

(b) This Agreement and all acts and transactions pursuant hereto and the rights and obligations of the parties hereto shall be governed, construed and interpreted in accordance with the laws of the State of California, without giving effect to principles of conflicts of law.

(c) This Agreement may be executed in two counterparts, each of which shall be deemed an original and all of which together shall constitute one instrument.

(d) The rights and benefits of this Agreement shall inure to the benefit of, and be enforceable by the Company’s successors and assigns. The rights and obligations of Purchaser under this Agreement may only be assigned with the prior written consent of the Company.

[Signature Pages Follow]

The undersigned has executed this Agreement as of the date first set forth above.

[Signature Page to Stock Purchase Agreement]

The undersigned has executed this Agreement as of the date first set forth above.

[Signature Page to Stock Purchase Agreement]