Exhibit 4.1

DESCRIPTION OF THE REGISTRANT’S SECURITIES REGISTERED PURSUANT TO SECTION 12 OF THE SECURITIES EXCHANGE ACT OF 1934

As of the date of our annual report on Form 10-K of which this Exhibit is a part, our only class of securities registered under Section 12 of the Securities Exchange Act of 1934, as amended, is our common stock, par value $0.0001 per share. As used below, the terms “PaxMedica,” “our company,” “we,” “us” and “our” refer to PaxMedica, Inc.

Description of Common Stock

Set forth below is a summary description of the material terms of our common stock, which does not purport to be complete. For more information, please see our Certificate of Incorporation, as amended (the “Certificate of Incorporation”) and bylaws, as amended and restated (the “Bylaws”), each of which is incorporated by reference as an exhibit to our annual report on Form 10-K of which this Exhibit is a part, and the applicable provisions of Delaware General Corporation Law (“DGCL”). We encourage you to read the Certificate of Incorporation and the Bylaws and the applicable provisions of the DGCL for additional information.

General

Our Certificate of Incorporation authorizes us to issue up to 210,000,000 shares of capital consisting of 200,000,000 shares of common stock with a par value of $0.0001 per share and 10,000,000 shares of preferred stock with a par value of $0.0001 per share.

Common Stock

Holders of our common stock are entitled to such dividends as may be declared by our board of directors out of funds legally available for such purpose. The shares of common stock are neither redeemable nor convertible. Holders of common stock have no preemptive or subscription rights to purchase any of our securities.

Each holder of our common stock is entitled to one vote for each such share outstanding in the holder’s name. No holder of common stock is entitled to cumulate votes in voting for directors.

In the event of our liquidation, dissolution or winding up, the holders of our common stock are entitled to receive pro rata our assets, which are legally available for distribution, after payments of all debts and other liabilities. All of the outstanding shares of our common stock are fully paid and non-assessable. The shares of common stock offered by this prospectus will also be fully paid and non-assessable.

Preferred Stock

Our board of directors has the authority, without further action by our stockholders, to issue up to 10,000,000 shares of preferred stock in one or more classes or series and to fix the designations, rights, preferences, privileges and restrictions thereof, without further vote or action by the stockholders. These rights, preferences and privileges could include dividend rights, conversion rights, voting rights, terms of redemption, liquidation preferences, sinking fund terms and the number of shares constituting, or the designation of, such class or series, any or all of which may be greater than the rights of common stock. The issuance of our preferred stock could adversely affect the voting power of holders of common stock and the likelihood that such holders will receive dividend payments and payments upon our liquidation. In addition, the issuance of preferred stock could have the effect of delaying, deferring or preventing a change in control of our company or other corporate action.

Series X Preferred Stock

In August 2022, a series of our preferred stock was designated as Series X Preferred Stock, consisting of 500,000 designated shares. As of December 31, 2022, 45,568 shares of Series X preferred stock were outstanding, with an aggregate stated value of $4,556,800.

Holders of Series X Preferred Stock are not entitled to receive dividends with respect to their shares of Series X Preferred Stock. The Series X Preferred Stock has no voting rights, other than the right to vote with respect to any amendment of the Certificate of Designations and with respect to any other adverse change to the voting or other powers, preferences, rights, privileges or restrictions of the Series X Preferred Stock contained in the Certificate of Designations. The Certificate of Designations contains beneficial ownership restrictions that restrict the conversion of shares of Series X Preferred Stock into shares of common stock.

Warrants

In connection with the October 2020 Notes, we also issued an aggregate of 1,034,176 warrants to purchase shares of common stock, which are exercisable at an exercise price of $3.00.

In connection with the 2022 Notes, we also issued an aggregate of 195,140 warrants to purchase shares of common stock, which are exercisable at an exercise price of $4.20.

In connection with the Lind Note (as defined below), we also issued to Lind a common stock purchase warrant (the “Lind Warrant”) to acquire 800,000 shares of our common stock until February 6, 2027 at an exercise price of $3.25 per share, subject to certain adjustments.

Representative’s Warrants

In connection with our initial public offering, we issued to Craft Capital Management LLC (“Craft”) and R.F. Lafferty & Co., Inc. (“Lafferty” and, together with Craft, the “Representatives”) warrants to purchase up to a total of 108,181 shares of common stock (7% of the shares of common stock sold in our initial public offering, excluding the over-allotment option) (the “Representative’s Warrants”). The Representative’s Warrants are exercisable at any time, and from time to time, in whole or in part, during the four and a half-year period commencing six months from the closing date of our initial public offering, and expiring four and a half years thereafter in compliance with FINRA Rule 5110(f)(2)(G). The Representative’s Warrants are exercisable at a per share price equal to 125% of the price per share as of our initial public offering. The Representative’s Warrants are subject to a 180-day lock-up pursuant to Rule 5110(g)(1) of FINRA.

The exercise price and number of shares issuable upon exercise of the Representative’s Warrants may be adjusted in certain circumstances including in the event of a stock dividend, extraordinary cash dividend or recapitalization, reorganization, merger or consolidation.

In January 2023, we issued additional Representative’s Warrants to purchase up to a total of 30,000 shares of our common stock. The warrants are exercisable at a per share price equal to $3.00.

In March 2023, we issued additional Representative’s Warrants to purchase up to a total of 112,000 shares of our common stock. The warrants are exercisable at a per share price equal to $3.50.

The exercise price and number of shares issuable upon exercise of the warrants may be adjusted in certain circumstances including in the event of a stock dividend, extraordinary cash dividend or recapitalization, reorganization, merger or consolidation.

2022 Convertible Promissory Notes

Between April and July 2022, we issued the 2022 Notes in an aggregate principal amount of approximately $1.5 million with an interest rate of 10% per annum. The 2022 Notes mature 12 months from the date of issuance and are convertible at a conversion price equal to $4.20 per share.

The 2022 Notes are subject to customary events of default, including, but not limited to, our failure to issue the shares issuable upon conversion of the 2022 Notes upon exercise of a holder’s conversion rights under the 2022 Notes, pay the principal or interest on the 2022 Notes when due, our liquidation, and our default or breach of any other financial instrument. Upon the occurrence of an event of default, the principal amount is accelerated and any accrued but unpaid interest thereon is multiplied by 120%, which the holder may determine to accept in common stock, cash, or any combination thereof.

Lind Transaction

On February 2, 2023, pursuant to a Securities Purchase Agreement with Lind Global Fund II LP, a Delaware limited partnership (“Lind”), we issued to Lind a secured, 18-month, interest free convertible promissory note in the principal amount of $3,680,000 (the “Lind Note”) and a common stock purchase warrant (the “Lind Warrant”) to acquire 800,000 shares of our common stock until February 6, 2027 at an exercise price of $3.25 per share, subject to certain adjustments. These shares were not registered under the Securities Act when issued, but we have agreed to file a registration statement with the Commission no later than 90 days from February 2, 2023, covering the resale of all of our shares of common stock issuable to Lind pursuant to the Lind Note and the Lind Warrant.

The Lind Note contains certain negative covenants, including restricting us from certain distributions, loans, issuance or future priced securities and sale of assets.

Upon the occurrence of an event of default as described in the Lind Note, the Lind Note will become immediately due and payable at a default interest rate of 110% of the then outstanding principal amount of the Note. Events of default include, but are not

limited to, a default in the payment of the principal amount or any accrued and unpaid interest under the Lind Note, failure to observe or perform any other covenant, condition or agreement contained in the Lind Note or any transaction documents, a change of control, a default in any indebtedness in excess of $250,000, our failure to instruct our transfer agent to issue unlegended certificates, the shares no longer publicly being traded, if after August 7, 2023 the shares are not available for immediate resale under Rule 144 and the Company’s market capitalization is below $10 million for 10 days. Upon an event of default, Lind can demand that all or a portion of the outstanding principal amount be converted into shares of common stock at the lower of the conversion price and 80% of the average of the three lowest daily VWAPs.

Registration rights

The securities purchase agreement pursuant to which we issued the 2022 Convertible Notes and 2022 Warrants grants the purchasers certain registration rights in respect of the “registrable securities” held by them, which securities include the shares of our common stock issued upon the conversion of the 2022 Convertible Notes and 2022 Warrants. The registration of shares of our common stock pursuant to the exercise of these registration rights would enable the holders thereof to sell such shares without restriction under the Securities Act when the applicable registration statement is declared effective. If Rule 144 is not available to the holders of registrable shares under the securities purchase agreement for the 2022 Convertible Notes and 2022 Warrants, we are required to file a resale registration statement six months after the issuance of the 2022 Convertible Notes covering those registrable shares and any holder of registrable shares may require us to file a resale registration statement covering their registrable shares at any time. The holders of registrable securities are also entitled to certain “piggyback” registration rights allowing them to include their registrable securities in any registration of securities under the Securities Act, subject to certain marketing and other limitations. As a result, whenever we propose to file a registration statement under the Securities Act other than with respect to a demand registration or a registration statement on S-8, these holders are entitled to notice of the registration and have the right to include their registrable securities in the registration subject to certain limitations.

Pursuant to the Registration Rights Agreement with Lincoln Park, Lincoln Park was granted registration rights related to the shares of Common Stock that have been or may be issued to Lincoln Park under the Purchase Agreement (collectively, the “LP Registrable Securities”). Under the Registration Rights Agreement, we are obligated to prepare and file a registration statement covering the resale of the LP Registrable Securities by Lincoln Park with the Commission within 20 business days of entering the Purchase Agreement with Lincoln Park. The registration statement of which this prospectus forms a part has satisfied this obligation.

Anti-Takeover Provisions

The provisions of Delaware law, our Certificate of Incorporation and our Bylaws described below may have the effect of delaying, deferring or discouraging another party from acquiring control of us.

Certificate of Incorporation and Bylaws

Our Certificate of Incorporation and Bylaws provide for:

· classifying our board of directors into three classes;

· authorizing the issuance of “blank check” preferred stock, the terms of which may be established and shares of which may be issued without stockholder approval;

· limiting the removal of directors by the stockholders;

· requiring a supermajority vote of stockholders to amend our Bylaws or certain provisions our Certificate of Incorporation;

· prohibiting stockholder action by written consent, thereby requiring all stockholder actions to be taken at a meeting of our stockholders;

· eliminating the ability of stockholders to call a special meeting of stockholders;

· establishing advance notice requirements for nominations for election to the board of directors or for proposing matters that can be acted upon at stockholder meetings; and

· establishing Delaware as the exclusive jurisdiction for certain stockholder litigation against us.

Section 203 of the DGCL

We are subject to Section 203 of the DGCL, which prohibits a Delaware corporation from engaging in any business combination with any interested stockholder for a period of three years after the date that such stockholder became an interested stockholder, with the following exceptions:

· before such date, the board of directors of the corporation approved either the business combination or the transaction that resulted in the stockholder becoming an interested stockholder;

· upon completion of the transaction that resulted in the stockholder becoming an interested stockholder, the interested stockholder owned at least 85% of the voting stock of the corporation outstanding at the time the transaction began, excluding for purposes of determining the voting stock outstanding (but not the outstanding voting stock owned by the interested stockholder) those shares owned (i) by persons who are directors and also officers and (ii) employee stock plans in which employee participants do not have the right to determine confidentially whether shares held subject to the plan will be tendered in a tender or exchange offer; or

· on or after such date, the business combination is approved by the board of directors and authorized at an annual or special meeting of the stockholders, and not by written consent, by the affirmative vote of at least 66 2/3% of the outstanding voting stock that is not owned by the interested stockholder.

In general, Section 203 defines business combination to include the following:

· any merger or consolidation involving the corporation and the interested stockholder;

· any sale, transfer, pledge or other disposition of 10% or more of the assets of the corporation involving the interested stockholder;

· subject to certain exceptions, any transaction that results in the issuance or transfer by the corporation of any stock of the corporation to the interested stockholder;

· any transaction involving the corporation that has the effect of increasing the proportionate share of the stock or any class or series of the corporation beneficially owned by the interested stockholder; or

· the receipt by the interested stockholder of the benefit of any loss, advances, guarantees, pledges or other financial benefits by or through the corporation.

In general, Section 203 defines an “interested stockholder” as an entity or person who, together with the person’s affiliates and associates, beneficially owns, or within three years prior to the time of determination of interested stockholder status did own, 15% or more of the outstanding voting stock of the corporation.

Potential Effects of Authorized but Unissued Stock

We have shares of common stock and preferred stock available for future issuance without stockholder approval. We may utilize these additional shares for a variety of corporate purposes, including future public offerings to raise additional capital, to facilitate corporate acquisitions or payment as a dividend on the capital stock.

The existence of unissued and unreserved common stock and preferred stock may enable our board of directors to issue shares to persons friendly to current management or to issue preferred stock with terms that could render more difficult or discourage a third-party attempt to obtain control of us by means of a merger, tender offer, proxy contest or otherwise, thereby protecting the continuity of our management. In addition, the board of directors has the discretion to determine designations, rights, preferences, privileges and restrictions, including voting rights, dividend rights, conversion rights, redemption privileges and liquidation preferences of each series of preferred stock, all to the fullest extent permissible under the DGCL and subject to any limitations set forth in our Certificate of Incorporation. The purpose of authorizing the board of directors to issue preferred stock and to determine the rights and preferences applicable to such preferred stock is to eliminate delays associated with a stockholder vote on specific issuances. The issuance of preferred stock, while providing desirable flexibility in connection with possible financings, acquisitions and other corporate purposes, could have the effect of making it more difficult for a third-party to acquire, or could discourage a third-party from acquiring, a majority of our outstanding voting stock.

Choice of Forum

Unless we consent in writing to the selection of an alternative forum, the Court of Chancery of the State of Delaware shall be the sole and exclusive forum for any stockholder to bring (i) any derivative action or proceeding brought on behalf of the Company, (ii) any action asserting a claim of breach of fiduciary duty owed by any director, officer or other employee of the Company or the Company’s stockholders, creditors or constituents, (iii) any action asserting a claim against the Company or any director or officer of the Company arising pursuant to, or a claim against the Company or any director or officer of the Company, with respect to the interpretation or application of any provision of, the DGCL, our Certificate of Incorporation or Bylaws, or (iv) any action asserting a claim governed by the internal affairs doctrine, except for, in each of the aforementioned actions, any claims to which the Court of Chancery of the State of Delaware determines it lacks jurisdiction. This provision will not apply to claims arising under the Exchange Act, or for any other federal securities laws which provide for exclusive federal jurisdiction. However, the exclusive forum provision provides that unless we consent in writing to the selection of an alternative forum, the federal district courts of the United States of America will be the exclusive forum for the resolution of any complaint asserting a cause of action arising under the Securities Act. Therefore, this provision could apply to a suit that falls within one or more of the categories enumerated in the exclusive forum

provision and that asserts claims under the Securities Act, inasmuch as Section 22 of the Securities Act creates concurrent jurisdiction for federal and state courts over all suits brought to enforce any duty or liability created by the Securities Act or the rules and regulations thereunder. There is uncertainty as to whether a court would enforce such an exclusive forum provision with respect to claims under the Securities Act.

We note that there is uncertainty as to whether a court would enforce the provision and that investors cannot waive compliance with the federal securities laws and the rules and regulations thereunder. Although we believe this provision benefits us by providing increased consistency in the application of Delaware law in the types of lawsuits to which it applies, the provision may have the effect of discouraging lawsuits against our directors and officers.

Limitations on Liability and Indemnification Matters

The Bylaws provide that we will indemnify each of our directors and executive officers to the fullest extent permitted by the DGCL. We intend to enter into indemnification agreements with each of our directors and executive officers that may, in some cases, be broader than the specific indemnification provisions contained under Delaware law. Further, we intend to indemnify each of our directors and executive officers against certain liabilities, costs and expenses, and to purchase a policy of directors' and officers' liability insurance that insures our directors and executive officers against the cost of defense, settlement or payment of a judgment under certain circumstances. In addition, as permitted by Delaware law, the Charter includes provisions that eliminate the personal liability of our directors for monetary damages resulting from breaches of certain fiduciary duties as a director. The effect of this provision is to restrict our rights and the rights of our stockholders in derivative suits to recover monetary damages against a director for breach of fiduciary duties as a director.

These provisions may be held not to be enforceable for violations of the federal securities laws of the United States.

Listing

Our common stock is traded on the Nasdaq Stock Market under the symbol “PXMD.”

Transfer Agent and Registrar

Our transfer agent is Computershare Trust N.A. The transfer agent’s address is 1290 Avenue of the Americas, 9th Floor, New York, NY 1010, and its telephone number is (212) 805-7100.