Exhibit 3.1

AMENDED AND RESTATED

CERTIFICATE OF INCORPORATION

OF

COLUCID PHARMACEUTICALS, INC.

1. The name of the Corporation is: CoLucid Pharmaceuticals, Inc.

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

3. The nature of the business and the purposes to be conducted and promoted by the Corporation are to conduct any lawful business, to promote any lawful purpose and to engage in any lawful act or activity for which corporations may be organized under the DGCL.

4. The total number of shares of stock which the Corporation shall have authority to issue is one-hundred (100) shares of common stock, $0.001 par value per share (the “Common Stock”). Shares of the Common Stock may be issued from time to time as the board of directors of the Corporation (the “Board”) shall determine and on such terms and for such consideration as shall be fixed by the Board. The amount of the authorized Common Stock of the Corporation may be increased or decreased by the affirmative vote of the holders of a majority of the outstanding shares of Common Stock of the Corporation entitled to vote.

5. Elections of directors need not be by written ballot unless required by the Bylaws of the Corporation. Any director may be removed from office either with or without cause at any time by the affirmative vote of the holders of a majority of the outstanding Common Stock of the Corporation entitled to vote, given at a meeting of the stockholders called for that purpose, or by the consent of the holders of a majority of the outstanding Common Stock of the Corporation entitled to vote, given in accordance with DGCL Section 228.

6. In furtherance and not in limitation of the powers conferred upon the Board by law, the Board shall have the power to make, adopt, alter, amend and repeal from time to time the Bylaws of the Corporation subject to the right of the stockholders entitled to vote with respect thereto to alter, amend and repeal Bylaws made by the Board.

7. The personal liability of the directors of the Corporation shall be eliminated to the fullest extent permitted by law. If the DGCL is amended to authorize corporate action further eliminating or limiting the personal liability of directors, then the liability of a director of the

Corporation shall be eliminated or limited to the fullest extent permitted by the DGCL, as so amended.

8. (a) Each person who was or is made a party or is threatened to be made a party to or is involved in any action, suit or proceeding, whether civil, criminal, administrative or investigative (hereinafter a “proceeding”), by reason of the fact that he or she, or a person of whom he or she is the legal representative, is or was a director or officer of the Corporation or is or was serving at the request of the Corporation as a director, officer, employee or agent of another corporation or of a partnership, joint venture, limited liability company, trust or other enterprise, including service with respect to employee benefit plans maintained or sponsored by the Corporation, whether the basis of such proceeding is alleged action in an official capacity as a director, officer, employee or agent or in any other capacity while serving as a director, officer, employee or agent, shall be indemnified and held harmless by the Corporation to the fullest extent authorized by the DGCL, as the same exists or may hereafter be amended (but, in the case of any such amendment, to the fullest extent permitted by law, only to the extent that such amendment permits the Corporation to provide broader indemnification rights than said law permitted the Corporation to provide prior to such amendment), against all expense, liability and loss (including attorneys’ fees, judgments, fines, amounts paid or to be paid in settlement, and excise taxes or penalties arising under the Employee Retirement Income Security Act of 1974) reasonably incurred or suffered by such person in connection therewith and such indemnification shall continue as to a person who has ceased to be a director, officer, employee or agent and shall inure to the benefit of his or her heirs, executors and administrators; provided, however, that, except as provided in paragraph (b) below, the Corporation shall indemnify any such person seeking indemnification in connection with a proceeding (or part thereof) initiated by such person only if such proceeding (or part thereof) was authorized by the Board. The right to indemnification conferred in this Article shall be a contract right and shall include the right to be paid by the Corporation the expenses incurred in defending any such proceeding in advance of its final disposition; provided, however, that, if the DGCL requires, the payment of such expenses incurred by a director or officer in his or her capacity as a director or officer (and not in any other capacity in which service was or is rendered by such person while a director or officer, including, without limitation, service to an employee benefit plan) in advance of the final disposition of a proceeding, shall be made only upon delivery to the Corporation of an undertaking, by or on behalf of such director or officer, to repay all amounts so advanced if it shall ultimately be determined that such director or officer is not entitled to be indemnified under this Article or otherwise. The Corporation may, by action of the

Board, provide indemnification to employees and agents of the Corporation with the same scope and effect as the foregoing indemnification of directors and officers.

(b) If a claim under paragraph (a) above is not paid in full by the Corporation within 30 days after a written claim has been received by the Corporation, the claimant may at any time thereafter bring suit against the Corporation to recover the unpaid amount of the claim and, if successful in whole or in part, the claimant shall be entitled to be paid also the expense of prosecuting such claim. It shall be a defense to any such action (other than an action brought to enforce a claim for expenses incurred in defending any proceeding in advance of its final disposition where the required undertaking, if any is required, has been tendered to the Corporation) that the claimant has not met the standards of conduct which make it permissible under the DGCL for the Corporation to indemnify the claimant for the amount claimed, but the burden of proving such defense shall be on the Corporation. Neither the failure of the Corporation (including its board of directors, independent legal counsel, or its stockholders) to have made a determination prior to the commencement of such action that indemnification of the claimant is proper in the circumstances because he or she has met the applicable standard of conduct set forth in the DGCL, nor an actual determination by the Corporation (including its board of directors, independent legal counsel, or its stockholders) that the claimant has not met such applicable standard of conduct, shall be a defense to the action or create a presumption that the claimant has not met the applicable standard of conduct.

(c) The right to indemnification and the payment of expenses incurred in defending a proceeding in advance of its final disposition conferred in this Article shall not be exclusive of any other right which any person may have or hereafter acquire under any statute, provision of the Certificate of Incorporation (as it may be amended from time to time), by-law, agreement, vote of stockholders or disinterested directors or otherwise.