Exhibit 3.1

AMENDED AND RESTATED

CERTIFICATE OF INCORPORATION OF

CAPNIA, INC.

Capnia, Inc., a corporation organized and existing under the laws of the State of Delaware (the “Corporation”), certifies that:

A. The name of the Corporation is Capnia, Inc. The Corporation’s original Certificate of Incorporation was filed with the Secretary of State of the State of Delaware on August 25, 1999.

B. This Amended and Restated Certificate of Incorporation (“Restated Certificate”) was duly adopted in accordance with Sections 242 and 245 of the General Corporation Law of the State of Delaware, and restates, integrates and further amends the provisions of the Corporation’s Certificate of Incorporation.

C. The text of the Certificate of Incorporation is amended and restated to read as set forth in EXHIBIT A attached hereto.

IN WITNESS WHEREOF, Capnia, Inc. has caused this Restated Certificate to be signed by Ernest Mario, a duly authorized officer of the Corporation, on February 5, 2010.

ARTICLE I

The name of this Corporation is Capnia, Inc.

ARTICLE II

The purpose of the Corporation is to engage in any lawful act or activity for which corporations may be organized under the DGCL.

ARTICLE III

The Corporation is to have perpetual existence.

ARTICLE IV

The address of the Corporation’s registered office in the State of Delaware is 1209 Orange Street, City of Wilmington, County of New Castle, State of Delaware 19801. The name of its registered agent at such address is The Corporation Trust Company.

ARTICLE V

1. Authorized Capital. The Corporation is authorized to issue two classes of stock to be designated, respectively, “Common Stock” and “Preferred Stock.” The total number of shares of Common Stock the Corporation shall have authority to issue is 29,500,000 with a par value of $0.001 per share. The total number of shares of Preferred Stock the Corporation shall have authority to issue is 21,702,428 with a par value of $0.001 per share, of which 459,375 shall be designated Series A Preferred Stock, 3,743,053 shall be designated Series B Preferred Stock and 17,500,000 shall be designated Series C Preferred Stock.

2. Dividends. The relative rights, preferences, privileges, limitations and restrictions granted to or imposed on the respective classes and/or series of the shares of capital stock or the holders thereof are as follows.

(A) Preferred Stock Preference. The holders of the Series A Preferred Stock, Series B Preferred Stock and Series C Preferred Stock shall be entitled to receive dividends, on a pari passu basis, out of any funds legally available therefor, prior and in preference to any declaration or payment of any dividend (payable other than in Common Stock or other securities or rights convertible into, or entitling the holder thereof to receive directly or indirectly, additional shares of Common Stock (hereinafter referred to as “Common Stock Equivalents”)) on the Corporation’s Common Stock, at the rate of (i) in the case of the Series A Preferred Stock, 8% of the Series A Original Issue Price per annum, (ii) in the case of the Series B Preferred Stock, 8% of the Series B Original Issue Price per annum, and (iii) in the case of the Series C Preferred Stock, 8% of the Series C Original Issue Price per annum. Such dividends shall be payable when, as and if declared by the Corporation’s Board of Directors (the “Board”), and shall not be cumulative.

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(B) Additional Dividends. After the payment or setting aside for payment of the dividends described in Section 2(A), any additional dividends (other than Common Stock Equivalents) declared or paid in any fiscal year shall be declared or paid among the holders of the Preferred Stock and Common Stock then outstanding in proportion to the greatest whole number of shares of Common Stock which would be held by each such holder if all shares of Preferred Stock were converted at the then-effective Conversion Rate (as defined in Section 4(A) hereof).

3. Liquidation Preference. In the event of any liquidation, dissolution or winding up of the Corporation, either voluntary or involuntary, distributions to the Corporation’s stockholders shall be made in the following manner:

(A) Preferred Stock Preference. The holders of Series A Preferred Stock, Series B Preferred Stock and Series C Preferred Stock shall be entitled to receive, on a pari passu basis, prior and in preference to any distribution of any of the Corporation’s assets or surplus funds to the holders of the Corporation’s Common Stock, an amount equal to (i) in the case of the Series A Preferred Stock, $4.00 per share (as adjusted for stock splits, stock dividends, reorganizations, recapitalizations or similar events with respect to such share) (the “Series A Original Issue Price”), plus an additional amount equal to any dividends declared but unpaid on each such share, (ii) in the case of the Series B Preferred Stock, $4.80 per share (as adjusted for stock splits, stock dividends, reorganizations, recapitalizations or similar events with respect to such share) (the “Series B Original Issue Price”), plus an additional amount equal to any dividends declared but unpaid on each such share, and (iii) in the case of the Series C Preferred Stock, $1.80 per share (as adjusted for stock splits, stock dividends, reorganizations, recapitalizations or similar events with respect to such share) (the “Series C Original Issue Price”), plus an additional amount equal to any dividends declared but unpaid on each such share. If, upon such liquidation, dissolution or winding up of the Corporation, the assets and funds distributed are insufficient to permit the payment to each holder of Series A Preferred Stock, Series B Preferred Stock and Series C Preferred Stock of the full aforesaid preferential amount, the entire assets and funds legally available for distribution shall be distributed ratably among such holders in proportion to the preferential amount each such holder is otherwise entitled to receive. The Series A Original Issue Price, the Series B Original Issue Price and the Series C Original Issue Price are sometimes collectively referred to herein as the “Original Issue Price”.

(B) Remaining Assets. Upon the completion of the distribution required by subsection (A) of this Section 3, the Corporation’s remaining assets and funds available for distribution to stockholders shall be distributed ratably to the holders of Series A Preferred Stock, Series B Preferred Stock, Series C Preferred Stock and Common Stock based on the number of shares of Common Stock held by each such holder (assuming full conversion into Common Stock of the Series A Preferred Stock, Series B Preferred Stock and Series C Preferred Stock).

(C) (1) Unless otherwise determined in writing by the holders of at least two-thirds (2/3) of the Preferred Stock then outstanding, for the purposes of this Section 3, a liquidation, dissolution or winding up of the Corporation shall be deemed to include (X) the acquisition of the Corporation by another entity by means of any transaction or series of related transactions (including, without limitation, any merger, consolidation or other form of reorganization) in which outstanding shares of the Corporation are exchanged for or converted into securities or other

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consideration issued, or caused to be issued, by the acquiring entity or its affiliate, unless the Corporation’s stockholders of record as constituted immediately prior to such transaction or series of related transactions will, immediately after such transaction or series of related transactions, hold at least a majority of the voting power of the surviving or acquiring entity on account of shares held by them prior to such transaction or series of related transactions or (Y) a sale, lease or other disposition of all or substantially all of the assets of the Corporation.

(2) In any of such events, if the consideration received by the Corporation is other than cash, its value will be deemed its fair market value. Any securities shall be valued as follows:

(a) For securities not subject to investment letter or other similar restrictions on free marketability,

(i) if traded on a securities exchange or The Nasdaq Global Market, the value shall be deemed to be the average of the closing prices of the securities on such exchange or market over the 30-day period ending three (3) days prior to the closing of such transaction;

(ii) if actively traded over-the-counter, the value shall be deemed to be the average of the closing bid prices of the securities over the 30-day period ending three (3) days prior to the closing of such transaction; and

(iii) if there is no active public market, the value shall be the fair market value thereof, as determined in good faith by the Board.

(b) The method of valuation of securities subject to investment letter or other restrictions on free marketability (other than restrictions arising solely by virtue of a stockholder’s status as an affiliate or former affiliate) shall take into account an appropriate discount (as determined in good faith by the Board) from the market value as determined pursuant to subsection (C)(2)(a) so as to reflect the approximate fair market value thereof.

(3) In the event the requirements of this subsection (C) are not complied with, the Corporation shall forthwith either:

(a) cause such closing to be postponed until such time as the requirements of this Section 3 have been complied with, or

(b) cancel such transaction, in which event the rights, preferences, privileges and restrictions of the holders of the Preferred Stock shall revert to and be the same as such rights, preferences, privileges and restrictions existing immediately prior to the date of the first notice referred to in subsection (C)(4).

(4) The Corporation shall give each holder of record of Preferred Stock written notice of a transaction described in subsection (C)(1) not later than twenty (20) days prior to the stockholders’ meeting called to approve such transaction, or twenty (20) days prior to the closing of such transaction, whichever is earlier, and shall also notify such holders in writing of the final

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approval of such transaction. The first of such notices shall describe the material terms and conditions of the impending transaction and the provisions of this Section 3, and the Corporation shall thereafter give such holders prompt notice of any material changes. The transaction shall in no event take place sooner than twenty (20) days after the Corporation has given the first notice provided for herein or sooner than ten (10) days after the Corporation has given notice of any material changes provided for herein; provided, however, that such periods may be shortened upon the written consent of the holders of at least two-thirds (2/3) of the shares of Preferred Stock then outstanding.

4. Conversion. The holders of the Preferred Stock have conversion rights as follows:

(A) Right to Convert. Each share of each series of Preferred Stock shall be convertible, at the option of the holder thereof, at any time after the date of issuance of such share and on or prior to the day prior to the Redemption Date, if any, as may have been fixed in any Redemption Notice with respect to the Preferred Stock, at the office of the Corporation or any transfer agent for the Preferred Stock, into such number of fully paid and nonassessable shares of Common Stock as is determined by dividing the Original Issue Price for such series of Preferred Stock by the Conversion Price for such series of Preferred Stock, determined as hereinafter provided, in effect at the time of the conversion (the “Conversion Rate”). The initial “Conversion Price” per share for the Series A Preferred Stock, the Series B Preferred Stock and the Series C Preferred Stock shall, as of the date of this Restated Certificate, initially be the Series A Original Issue Price, the Series B Original Issue Price and the Series C Original Issue Price, respectively. Such initial Conversion Price of each series of Preferred Stock shall be subject to adjustment as provided in subsection (D) of this Section 4.

(B) Automatic Conversion. Each share of each series of Preferred Stock shall automatically be converted into fully paid and nonassessable shares of Common Stock at its then effective Conversion Rate upon the earlier of (i) immediately prior to the closing of a firm commitment underwritten public offering pursuant to an effective registration statement under the Securities Act of 1933, as amended (the “1933 Act”), covering the offer and sale of Common Stock to the public for the account of the Corporation in which the public offering price (prior to underwriter’s discounts or commissions and offering expenses) exceeds $6.30 per share (subject to adjustment for stock splits, stock dividends, recapitalizations and similar events) and the aggregate gross proceeds raised exceeds $30,000,000 (a “Qualified IPO”) or (ii) on the date the holders of at least two-thirds (2/3) of the then outstanding shares of Preferred Stock so elect to convert in writing.

(C) Mechanics of Conversion.

(1) Before any holder of Preferred Stock shall be entitled to convert the same into shares of Common Stock, such holder shall surrender the certificate or certificates therefor, duly endorsed, at the office of the Corporation or of any transfer agent for such Preferred Stock, and shall give written notice to the Corporation at such office that such holder elects to convert the same and shall state therein the name or names in which such holder wishes the certificate or certificates for shares of Common Stock to be issued. The Corporation shall, as soon as practicable thereafter, issue and deliver at such office to such holder of Preferred Stock, a certificate or certificates for the number of shares of Common Stock to which such holder shall be

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entitled as aforesaid. Such conversion shall be deemed to have been made immediately prior to the close of business on the date of surrender of the shares of Preferred Stock to be converted, and the person or persons entitled to receive the shares of Common Stock issuable upon such conversion shall be treated for all purposes as the record holder or holders of such shares of Common Stock on such date; provided, however, that in the event of an automatic conversion in connection with a Qualified IPO, the outstanding shares of Preferred Stock shall be converted automatically without any further action by the holders of such shares and whether or not the certificates representing such shares are surrendered to the Corporation or its transfer agent; provided further, however, that the Corporation shall not be obligated to issue certificates evidencing the shares of Common Stock issuable upon such automatic conversion unless the certificates evidencing such shares of Preferred Stock are either delivered to the Corporation or its transfer agent as provided above.

(2) If the conversion is in connection with an underwritten offering of securities pursuant to the 1933 Act, the conversion may, at the option of any holder tendering shares of Preferred Stock for conversion, be conditioned upon the closing with the underwriters of the sale of securities pursuant to such offering, in which event the person(s) entitled to receive the Common Stock upon conversion of the Preferred Stock shall not be deemed to have converted such Preferred Stock until immediately prior to the closing of such sale of securities.

(D) Adjustment of Conversion Price. The Conversion Price of each series of Preferred Stock shall be subject to adjustment from time to time as follows:

(1) (a) If the Corporation shall issue, after the date of filing of this Restated Certificate, any Additional Stock (as defined in subsection (D)(2)) without consideration or for a consideration per share less than the Conversion Price for any series of Preferred Stock in effect immediately prior to the issuance of such Additional Stock, the Conversion Price for such series in effect immediately after each such issuance of Additional Stock shall forthwith (except as otherwise provided in this subsection (D)) be adjusted to a price equal to (calculated to the nearest cent) the product obtained by multiplying the Conversion Price for such series of Preferred Stock in effect immediately prior to such issuance of Additional Stock by a fraction, the numerator of which is equal to the sum of (x) the total number of shares of Common Stock outstanding (including any shares of Common Stock deemed to be issued pursuant to subsection (D)(1)(e)(i) or (ii) of this Section 4) immediately prior to such issuance of Additional Stock plus (y) the number of shares of Common Stock that the aggregate consideration received by the Corporation for such issuance of Additional Stock would purchase at the Conversion Price for such series of Preferred Stock in effect immediately prior to such issuance of Additional Stock, and the denominator of which is equal to the sum of (x) the total number of shares of Common Stock outstanding (including any shares of Common Stock deemed to be issued pursuant to subsection (D)(1)(e)(i) or (ii) of this Section 4) immediately prior to such issuance of Additional Stock plus (y) the number of shares of Additional Stock issued.

(b) No adjustment in the Conversion Price for any series of Preferred Stock need be made if such adjustment would result in a change in the Conversion Price of less than $0.01. Any adjustment of less than $0.01 which is not made shall be carried forward and shall be made at the time of and together with any subsequent adjustment that, on a cumulative basis, amounts to an adjustment of $0.01 or more in the Conversion Price. Except to the limited extent

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provided for in subsections (D)(1)(e)(iii) or (iv), no adjustment of such Conversion Price pursuant to this subsection (D)(1) shall have the effect of increasing the Conversion Price above the Conversion Price in effect immediately prior to such adjustment.

(c) In the case of the issuance of Common Stock for cash, the consideration shall be deemed to be the amount of cash paid therefor before deducting any discounts, commissions or other expenses allowed, paid or incurred by the Corporation for any underwriting or otherwise in connection with the issuance and sale thereof.

(d) In the case of the issuance of Common Stock for a consideration in whole or in part other than cash, the consideration other than cash shall be deemed to be the fair value thereof as determined by the Board in good faith irrespective of any accounting treatment.

(e) In the case of the issuance (whether before, on or after the date of filing of this Restated Certificate) of (x) options to purchase or rights to subscribe for Common Stock, (y) securities, by their terms, convertible into or exchangeable for Common Stock or (z) options to purchase or rights to subscribe for securities, by their terms, convertible into or exchangeable for Common Stock, the following provisions shall apply for all purposes of subsections (D)(1) and (2):

(i) The aggregate maximum number of shares of Common Stock deliverable upon exercise (assuming the satisfaction of any conditions to exercisability, including, without limitation, the passage of time) of such options to purchase or rights to subscribe for Common Stock shall be deemed to have been issued at the time such options or rights were issued and for a consideration equal to the consideration (determined in the manner provided in subsections (D)(1)(c) and (D)(1)(d)), if any, received by the Corporation upon the issuance of such options or rights plus the minimum purchase price provided in such options or rights for the Common Stock covered thereby.

(ii) The aggregate maximum number of shares of Common Stock deliverable upon conversion of or in exchange (assuming the satisfaction of any conditions to convertibility or exchangeability, including, without limitation, the passage of time) for any such convertible or exchangeable securities, or upon the exercise of options to purchase or rights to subscribe for such convertible or exchangeable securities and subsequent conversion or exchange thereof, shall be deemed to have been issued at the time such securities were issued or such options or rights were issued and for a consideration equal to the consideration (determined in the manner provided in subsections (D)(1)(c) and (D)(1)(d)), if any, received by the Corporation for any such securities and related options or rights (excluding any cash received on account of accrued interest or accrued dividends) plus the minimum additional consideration, if any, to be received by the Corporation upon the conversion or exchange of such securities or the exercise of any related options or rights.

(iii) In the event of any change in the number of shares of Common Stock deliverable upon exercise of any such options or rights or upon conversion of or in exchange for such convertible or exchangeable securities, or on any change in the minimum

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purchase price of such options, rights or securities, including, but not limited to, a change resulting from the antidilution provisions of such options, rights or securities, the Conversion Price of each series of Preferred Stock that was in any way affected by or computed using such options, rights or securities shall be recomputed to reflect such change, but no further adjustment shall be made for the actual issuance of Common Stock or any payment of such consideration upon the exercise of any such options or rights or the conversion or exchange of such securities.

(iv) Upon the expiration of any such options or rights, the termination of any such rights to convert or exchange or the expiration of any options or rights related to such convertible or exchangeable securities, the Conversion Price of each series of Preferred Stock that was in any way affected by or computed using such options, rights or securities related to such options or rights shall forthwith be readjusted to such Conversion Price as would have been obtained had the adjustment made upon the issuance of such options, rights, convertible or exchangeable securities or options or rights related to such convertible or exchangeable securities, as the case may be, been made upon the basis of the issuance of only the number of shares of Common Stock (and convertible or exchangeable securities that remain in effect) actually issued upon the exercise of such options or rights, upon the conversion or exchange of such convertible or exchangeable securities or upon the exercise of the options or rights related to such convertible or exchangeable securities, as the case may be.

(v) The number of shares of Common Stock deemed issued and the consideration deemed paid therefor pursuant to subsections (D)(1)(e)(i) and (ii) of this Section 4 shall be appropriately adjusted to reflect any change, termination or expiration of the type described in either subsection (D)(1)(e)(iii) or (iv) of this Section 5.

(2) “Additional Stock” shall mean any shares of Common Stock issued (or deemed to have been issued pursuant to subsection (D)(1)(e) of this Section 4) by the Corporation after the date of filing of this Restated Certificate other than:

(a) shares of Common Stock issued pursuant to an event or transaction described in subsection (D)(3) of this Section 4;

(b) shares of Series A Preferred Stock outstanding on the date hereof, Series B Preferred Stock outstanding on the date hereof and Series C Preferred Stock authorized on the date hereof and sold at a price not less than the Original Issue Price for such stock and the Common Stock into which such shares are convertible;

(c) shares of Common Stock or other securities issued as a dividend or distribution on the Preferred Stock;

(d) shares of Common Stock, warrants or options to purchase Common Stock or other securities issued to the Corporation’s employees, officers, directors, consultants, advisors or other service providers pursuant to any plan or arrangement, provided such plan or arrangement and issuance are approved by the Board, including a majority of those directors elected by the holders of Preferred Stock;

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(e) shares of Common Stock, warrants or options to purchase Common Stock or other securities issued to financial institutions or equipment lessors, provided such issuance is approved by the Board, including a majority of those directors elected by the holders of Preferred Stock;

(f) shares of Common Stock, warrants or options to purchase Common Stock or other securities issued in connection with corporate or strategic partnering agreements or agreements to license technology, provided such issuance is approved by the Board, including a majority of those directors elected by the holders of Preferred Stock;

(g) shares of Common Stock issued in a Qualified IPO; or

(h) shares of Common Stock or other securities issued in connection with a bona fide business acquisition by the Corporation (whether by merger, consolidation, sale of assets, sale or exchange of stock or otherwise), provided such acquisition is approved by the Board, including a majority of those directors elected by the holders of Preferred Stock.

(3) Subdivision, etc. In the event the Corporation should, at any time or from time to time after the date of filing of this Restated Certificate, fix a record date for the effectuation of a split or subdivision of the outstanding shares of Common Stock or the determination of holders of Common Stock entitled to receive a dividend or other distribution payable in additional shares of Common Stock or Common Stock Equivalents without payment of any consideration by such holder for the additional shares of Common Stock or the Common Stock Equivalents (including the additional shares of Common Stock issuable upon conversion or exercise thereof), then, as of such record date (or the date of such dividend distribution, split or subdivision if no record date is fixed), the Conversion Price of each series of Preferred Stock shall be appropriately decreased so that the number of shares of Common Stock issuable on conversion of each share of such series of Preferred Stock shall be increased in proportion to such increase of the aggregate shares of Common Stock outstanding and those issuable with respect to such Common Stock Equivalents.

(4) Combination. If the number of shares of Common Stock outstanding at any time after the date of filing of this Restated Certificate is decreased by a combination of the outstanding shares of Common Stock, then, on the effective date of such combination, the Conversion Price of each series of Preferred Stock shall be appropriately increased so that the number of shares of Common Stock issuable on conversion of each share of such series of Preferred Stock shall be decreased in proportion to such decrease in outstanding shares of Common Stock.

(E) Other Distributions. In the event the Corporation shall declare a distribution payable in securities of other persons, evidences of indebtedness issued by the Corporation or other persons, assets (excluding cash dividends) or options or rights not referred to in subsection (D)(3) of this Section 4, then, in each such case for the purpose of this subsection (F), the holders of Preferred Stock shall be entitled to a proportionate share of any such distribution as though they were the holders of the number of shares of Common Stock of the Corporation into which their respective

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shares of Preferred Stock are convertible as of the record date fixed for the determination of the holders of Common Stock of the Corporation entitled to receive such distribution.

(F) Recapitalizations. If, at any time or from time to time after the date of filing of this Restated Certificate, there shall be a recapitalization of the Corporation’s Common Stock (other than (x) a subdivision or combination provided for elsewhere in this Section 4 or (y) a merger or sale of assets referred to in Section 3(C)) provision shall be made so that the holders of each series of Preferred Stock shall thereafter be entitled to receive upon conversion of each such series of Preferred Stock the number of shares of stock or other securities or property of the Corporation or otherwise to which a holder of Common Stock deliverable upon conversion of such series of Preferred Stock would have been entitled on such recapitalization. In any such case, appropriate adjustment shall be made in the application of the provisions of this Section 4 with respect to the rights of the holders of each series of Preferred Stock after the recapitalization to the end that the provisions of this Section 4 (including adjustment of the Conversion Price then in effect and the number of shares issuable upon conversion of each series of Preferred Stock) shall be applicable after that event as nearly equivalent as prior to that event as may be practicable.

(G) No Impairment. The Corporation will not, by amendment of this Restated Certificate or through any reorganization, recapitalization, transfer of assets, consolidation, merger, dissolution, issue or sale of securities or any other voluntary action, avoid or seek to avoid the observance or performance of any of the terms to be observed or performed hereunder by the Corporation, but will at all times in good faith assist in the carrying out of all the provisions of this Section 4 and in the taking of all such action as may be necessary or appropriate in order to protect the conversion rights of the holders of Preferred Stock set forth in this Section 4 against impairment. This provision shall not restrict the Corporation’s right to amend this Restated Certificate with the requisite stockholder consent.

(H) No Fractional Shares and Certificate as to Adjustment.

(1) No fractional shares shall be issued upon the conversion of any share of any series of Preferred Stock and, in lieu of any fractional shares to which any holder of any series of Preferred Stock would otherwise be entitled, the Corporation shall pay cash equal to such fraction multiplied by the then effective Conversion Price for the applicable series of Preferred Stock. Whether or not fractional shares are issuable upon such conversion shall be determined on the basis of the total number of shares of the applicable series of Preferred Stock of each holder at the time converting into Common Stock and the number of shares of Common Stock issuable upon such aggregate conversion.

(2) Upon the occurrence of each adjustment or readjustment of the Conversion Rate for any series of Preferred Stock pursuant to this Section 4, the Corporation, at its expense, shall promptly compute such adjustment or readjustment in accordance with the terms hereof and prepare and furnish to each holder of such series of Preferred Stock a certificate setting forth such adjustment or readjustment and showing in detail the facts upon which such adjustment or readjustment is based. The Corporation shall, upon written request at any time of any holder of any series of Preferred Stock, furnish or cause to be furnished to such holder a like certificate setting forth (i) all such adjustments and readjustments, (ii) the Conversion Rate at the time in effect, and

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(iii) the number of shares of Common Stock and the amount, if any, of other property that at the time would be received upon the conversion of such holder’s shares of Preferred Stock.

(I) Notices of Record Date. In the event of any taking by the Corporation of a record of the holders of any class of securities for the purpose of determining the holders thereof who are entitled to receive any dividend (other than a cash dividend) or other distribution, any right to subscribe for, purchase or otherwise acquire any shares of stock of any class or any other securities or property or to receive any other right, the Corporation shall send by recognized express courier to each holder of Preferred Stock, at least twenty (20) days prior to such record date, a notice specifying the date on which any such record is to be taken for the purpose of such dividend or distribution or right, and the amount and character of such dividend, distribution or right.

(J) Reservation of Stock Issuable Upon Conversion. The Corporation shall at all times reserve and keep available out of its authorized but unissued shares of Common Stock solely for the purpose of effecting the conversion of the shares of Preferred Stock such number of its shares of Common Stock as shall from time to time be sufficient to effect the conversion of all outstanding shares of Preferred Stock; and if at any time the number of authorized but unissued shares of Common Stock shall not be sufficient to effect the conversion of all then outstanding shares of Preferred Stock, the Corporation will take such corporate action as may, in the opinion of its counsel, be necessary to increase its authorized but unissued shares of Common Stock to such number of shares as shall be sufficient for such purpose, including, without limitation, engaging its best efforts to obtain the requisite stockholder approval for any necessary amendment to this Restated Certificate.

5. Redemption.

(A) At any time after the fourth (4th) anniversary of the date on which the Corporation first issues shares of its Series C Preferred Stock, and upon receipt by the Corporation of a written request from the holders of at least two-thirds (2/3) of the then outstanding Preferred Stock that all shares of Preferred Stock be redeemed (the “Redemption Trigger Notice”), the Corporation shall, to the extent it may lawfully do so, redeem in two (2) annual installments (each payment date being referred to herein as a “Redemption Date”) the Preferred Stock by paying in cash therefor an amount per share equal to (i) in the case of the Series A Preferred Stock, the Series A Original Issue Price, plus an additional amount equal to any dividends declared but unpaid on each such share (the “Series A Redemption Price”), (ii) in the case of the Series B Preferred Stock, the Series B Original Issue Price, plus an additional amount equal to any dividends declared but unpaid on each such share (the “Series B Redemption Price”) and (iii) in the case of the Series C Preferred Stock, the Series C Original Issue Price, plus an additional amount equal to any dividends declared but unpaid on each such share (the “Series C Redemption Price”). The first Redemption Date shall be not more than 45 days after the Corporation’s receipt of the Redemption Trigger Notice. The number of shares of Preferred Stock that the Corporation shall be required to redeem on each Redemption Date shall be 50% of the Preferred Stock on the first Redemption Date and all remaining Preferred Stock on the second Redemption Date. Any redemption effected pursuant to this Section 5 shall be made on a pro rata basis among the holders of each series of Preferred Stock to be redeemed in proportion to the number of shares of such series of Preferred Stock then held by such holders. In the event the Corporation may not lawfully redeem the Preferred Stock as provided

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for herein, then the Corporation shall issue a promissory note in favor of the respective holders of shares of Preferred Stock to be redeemed having a principal amount equal to the Series A Redemption Price, the Series B Redemption Price and the Series C Redemption Price, as applicable, and accruing interest at an annual rate of ten percent (10%), and such promissory note shall be due and payable within one (1) year from the date of issuance.

(B) Redemption Procedure. As used in this subsection (B) and in subsection (C), the term “Redemption Price” shall collectively refer to the Series A Redemption Price, Series B Redemption Price and Series C Redemption Price. At least thirty (30) days prior to each Redemption Date, written notice (the “Redemption Notice”) shall be sent by recognized express courier, postage prepaid, to each holder of record (at the close of business on the business day next preceding the day on which notice is given) of the Preferred Stock to be redeemed, at the address last shown on the records of the Corporation for such holder or given by the holder to the Corporation for the purpose of notice or if no such address appears or is given, at the place where the principal executive office of the Corporation is located, notifying such holder of the redemption to be effected, specifying the number of shares to be redeemed from such holder, the Redemption Price, the place at which payment may be obtained and calling upon such holder to surrender to the Corporation, in the manner and at the place designated, its certificate or certificates representing the shares to be redeemed. Except as provided in subsection (C) below, on or after each Redemption Date, each holder of Preferred Stock to be redeemed shall surrender to the Corporation the certificate or certificates representing such shares, in the manner and at the place designated in the Redemption Notice, and thereupon the aggregate Redemption Price of such shares shall be payable to the order of the person whose name appears on such certificate or certificates as the owner thereof and each surrendered certificate shall be cancelled. In the event less than all the shares represented by any such certificate are redeemed, a new certificate shall be issued representing the unredeemed shares.

(C) Effect of Redemption. From and after each Redemption Date, unless there shall have been a default in payment of the Redemption Price, all rights of the holders of such shares as holders of Preferred Stock (except the right to receive their respective Redemption Price without interest upon surrender of their certificate or certificates) shall cease with respect to such shares, and such shares shall not thereafter be transferred on the books of the Corporation or be deemed to be outstanding for any purpose whatsoever. If the funds of the Corporation legally available for redemption on any Redemption Date are insufficient to redeem the total number of shares requested to be redeemed on such date, those funds which are legally available will be used to redeem the maximum possible number of such shares ratably among the holders of such shares to be redeemed based upon their holdings of Preferred Stock, provided that funds shall be allocated among the Series A Preferred Stock, Series B Preferred Stock and Series C Preferred proportionately based on their aggregate Redemption Price. The shares not redeemed shall remain outstanding and be entitled to all the rights and preferences provided herein. At any time thereafter when additional funds of the Corporation are legally available for the redemption of shares not redeemed, such funds will immediately be set aside for the redemption of the balance of the shares which the Corporation has become obligated to redeem on any Redemption Date but which it has not redeemed.

6. Voting.

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(A) General. Each holder of each share of each series of Preferred Stock shall be entitled to the number of votes equal to the number of shares of Common Stock into which such share of Preferred Stock could be converted, exclusive of any dividends, at the record date for determination of the stockholders entitled to vote on such matters, or, if no such record date is established, at the date such vote is taken or any written consent of stockholders is solicited, and, except as otherwise required by law, shall have voting rights and powers equal to the voting rights and powers of the Common Stock. Each holder of each share of Preferred Stock shall be entitled to notice of any stockholders’ meeting in accordance with the Corporation’s Bylaws and shall vote with holders of the Common Stock upon the election of directors (except as set forth in subsection (B) below) and upon any other matter submitted to a vote of stockholders (except those matters required by law to be submitted to a class vote and as set forth in Section 7). Fractional votes by the holders of Preferred Stock shall not, however, be permitted and any fractional voting rights shall (after aggregating all shares of Common Stock into which shares of Preferred Stock held by each holder could be converted, exclusive of any dividends) be rounded to the nearest whole number (with one-half being rounded upward). Each holder of each share of Common Stock shall be entitled to one vote.

(B) Election of Directors.

(1) The authorized number of directors of the Board shall be six (6). So long as at least 1,000,000 shares of Preferred Stock (as adjusted for stock splits, stock dividends, reorganizations, recapitalizations or similar events) are outstanding: (a) the holders of Preferred Stock, voting together as a single class, shall be entitled to elect three (3) members of the Board at each meeting or pursuant to each consent of the Corporation’s stockholders for the election of directors; (b) the holders of a majority of the Common Stock, voting as a single class, shall be entitled to elect one (1) member of the Board at each meeting or pursuant to each consent of the Corporation’s stockholders for the election of directors; and (c) the holders of Common Stock and Preferred Stock, voting together as a single class, shall be entitled the remaining members of the Board at each meeting or pursuant to each consent of the Corporation’s stockholders for the election of directors.

(2) Vacancies in the Board may be filled by at least a majority of the remaining directors originally elected by the class or classes of stock or series thereof that elected the member who created the vacancy (or the remaining director so elected if there is but one or in any event by (a) in the case of any vote conducted at a meeting of the holders of shares of that class or classes or series, the affirmative vote of the holders of a plurality of the shares of that class or classes or series or (b) in the case of any vote taken by written consent without a meeting, the affirmative vote of the holders of at least a majority of the shares of that class or classes or series). The stockholders entitled to vote upon the election of directors may elect a director or directors at any time to fill any vacancy or vacancies not filled by the directors.

(3) Any director who was elected by a specified class or classes of stock or series thereof may be removed during his or her term of office, either for or without cause, by, and only by, the affirmative vote of the holders of at least a majority of the shares of the class or classes of stock or series thereof that initially elected such director. Such vote may be given at a special meeting of such stockholders duly called or by an action by written consent for that purpose.

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(C) Adjustment in Authorized Common Stock. The number of authorized shares of Common Stock may be increased or decreased (but not below the number of shares of Common Stock then outstanding) by an affirmative vote of the holders of a majority of the stock of the Corporation.

7. Preferred Stock Protective Provisions. The Corporation shall not, without first obtaining the affirmative vote or written consent of the holders of at least two-thirds (2/3) of the Preferred Stock then outstanding, whether by way of amendment of this Restated Certificate or Bylaws, by merger, by consolidation, by reorganization or otherwise:

(A) increase or decrease (other than by conversion or redemption) the number of authorized shares of Preferred Stock;

(B) authorize any new class or series of equity securities having any preference or priority as to voting, dividends, redemption, conversion or distribution of assets upon liquidation, merger or otherwise which is superior to or on a parity with any such preference or priority of any series of Preferred Stock then outstanding;

(C) redeem, purchase or otherwise acquire (or pay into or set aside for a sinking fund for such purpose) any shares of Common Stock or Preferred Stock; provided, however, that this restriction shall not apply to the repurchase of shares of Common Stock from current or former employees, officers, directors, consultants or other persons performing services for the Corporation pursuant to agreements under which the Corporation has the right to repurchase such shares at a price equal to or below cost upon the occurrence of certain events, such as the termination of services;

(D) redeem, purchase or otherwise acquire for value (or pay into or set aside for a sinking fund for such purpose) any share or shares of Preferred Stock; provided, however, that this restriction shall not apply to any redemption in accordance with Section 5 of this ARTICLE V;

(E) pay or declare a dividend or make any other distribution in respect of any shares of Preferred Stock or Common Stock (payable other than in Common Stock or Common Stock Equivalents);

(F) take any action that would alter or change the rights, preferences or privileges of any series of Preferred Stock then outstanding;

(G) change the number of authorized directors of the Board (unless unanimously approved by the Board) or change the number of directors which the holders of Preferred Stock are entitled to elect;

(H) sell all or substantially all of the Corporation’s assets or lease or otherwise dispose of or encumber all or substantially all of the Corporation’s assets, or merge into or consolidate with any other entity, or effect any transaction or series of related transactions in which the Corporation’s stockholders as constituted immediately prior to such transaction or series of related transactions own immediately after such transaction or series of related transactions less than

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fifty percent (50%) of the voting power of the surviving or acquiring entity on account of shares held by them prior to such transaction or series of related transactions;

(I) dissolve, liquidate or wind up the Corporation;

(J) incur indebtedness or guarantee indebtedness in excess of $100,000 in the aggregate unless approved by the Board, including a majority of the directors elected by the Preferred Stock; or

(K) amend this Restated Certificate or Bylaws.

The provisions of this Section 7 shall not limit or restrict any rights which any holder of Preferred Stock may have under the DGCL.

8. Status of Redeemed or Converted Stock. In the event any shares of any series of Preferred Stock are converted pursuant to Section 4 or redeemed pursuant to Section 5, the Corporation shall never again issue the shares so converted or redeemed and all such shares so converted or redeemed shall, upon such conversion or redemption, cease to be a part of the Corporation’s authorized stock. This Restated Certificate shall be appropriately amended to effect the corresponding reduction in the Corporation’s authorized stock.

9. Notices. Any notice required by the provisions of Sections 3, 4 and 5 to be given to the holders of shares of any series of Preferred Stock shall be in writing and shall be delivered personally by hand or by recognized express courier, fees prepaid, directed to each holder of record at such holder’s address appearing on the Corporation’s books. Any such notice shall be deemed given upon personal delivery or on the date of delivery to the express courier.

ARTICLE VI

Explicitly subject to the limitations provided in this Restated Certificate, in furtherance and not in limitation of the powers conferred by the laws of the state of Delaware, the Board is expressly authorized to make, alter, amend or repeal the Corporation’s Bylaws.

ARTICLE VII

Election of directors need not be by written ballot unless the Corporation’s Bylaws shall so provide.

ARTICLE VIII

To the fullest extent permitted by the DGCL, as the same may be amended from time to time, a director of the Corporation shall not be personally liable to the Corporation or its stockholders for monetary damages for breach of fiduciary duty as a director. Any repeal or modification of the provisions of this ARTICLE VIII, by amendment of this ARTICLE VIII or by operation of law, shall not adversely affect any right or protection of a director of the Corporation with respect to any acts or omissions of such director occurring prior to such repeal or modification.

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ARTICLE IX

To the fullest extent permitted by applicable law, the Corporation is authorized to provide indemnification of (and advancement of expenses to) directors, officers, employees and other agents of the Corporation (and any other persons to which Delaware law permits the Corporation to provide indemnification), through Bylaw provisions, agreements with any such director, officer, employee or other agent or other person, vote of stockholders or disinterested directors, or otherwise, in excess of the indemnification and advancement otherwise permitted by Section 145 of the DGCL. Any repeal or modification of any of the provisions of this ARTICLE IX, by amendment of this ARTICLE IX or by operation of law, shall not adversely affect any right or protection of a director, officer, employee or other agent or other person existing at the time of, or increase the liability of any director of the Corporation with respect to any acts or omissions of such director, officer or agent occurring prior to, such repeal or modification.

ARTICLE X

Explicitly subject to the limitations in Section 7 of ARTICLE V, the Corporation reserves the right to amend, alter, change or repeal any provision contained in this Restated Certificate, in the manner now or hereafter prescribed by statute, and all rights conferred upon stockholders herein are granted subject to this reservation.

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CERTIFICATE OF AMENDMENT OF

AMENDED AND RESTATED CERTIFICATE OF INCORPORATION OF

CAPNIA, INC.

Capnia, Inc., a corporation organized and existing under the laws of the State of Delaware (the “Corporation”), certifies that:

FIRST: The name of the Corporation is Capnia, Inc. The Corporation’s original Certificate of Incorporation was filed with the Secretary of State of the State of Delaware on August 25, 1999. The Corporation’s Amended and Restated Certificate of Incorporation was filed with the Secretary of State of the State of Delaware on February 5, 2010.

SECOND: This Certificate of Amendment of Amended and Restated Certificate of Incorporation was duly adopted by the board of directors of the Corporation in accordance with Section 242 of the General Corporation Law of the State of Delaware, as the same may be amended from time to time (the “Corporation Law”), and by written consent of the stockholders of the Corporation entitled to vote thereon in accordance with the provisions of Section 228 of the Corporation Law.

THIRD: ARTICLE V, Section 6(B)(1) of the Corporation’s Amended and Restated Certificate of Incorporation is hereby amended, restated and replaced in its entirety to read as follows:

“ARTICLE V

(1) The authorized number of directors of the Board shall be seven (7). So long as at least 1,000,000 shares of Preferred Stock (as adjusted for stock splits, stock dividends, reorganizations, recapitalizations or similar events) are outstanding: (a) the holders of Preferred Stock, voting together as a single class, shall be entitled to elect two (2) members of the Board at each meeting or pursuant to each consent of the Corporation’s stockholders for the election of directors; (b) the holders of a majority of the Common Stock, voting as a single class, shall be entitled to elect two (2) members of the Board at each meeting or pursuant to each consent of the Corporation’s stockholders for the election of directors; and (c) the holders of Common Stock and Preferred Stock, voting together as a single class, shall be entitled to elect the remaining members of the Board at each meeting or pursuant to each consent of the Corporation’s stockholders for the election of directors.”

***

IN WITNESS WHEREOF, Capnia, Inc. has caused this Amended and Restated Certificate of Incorporation to be signed by Anish Bhatnagar, a duly authorized officer of the Corporation, on June 2, 2014.