TetraphasePharmaceuticals, Inc. Confidential

Exhibit 10.13

December 22, 2010

Patrick Horn, M.D.

295 Commonwealth Ave.

Newton, MA 02467

Dear Patrick:

On behalf of Tetraphase Pharmaceuticals, Inc. (the “Company”), I am very pleased to offer you employment with the Company. The purpose of this letter is to summarize the terms of your employment with the Company, should you accept our offer.

1. Employment. You will be employed to serve in the position of Chief Medical Officer, reporting to Guy Macdonald, President and Chief Executive Officer of Tetraphase Pharmaceuticals, Inc. Your start date will be January 3^rd, 2011. As Chief Medical Officer, you will have such duties and responsibilities as are customarily assigned to an employee with such title and such other duties and responsibilities as may be assigned to you by the Company. You agree to devote your full business time, best efforts, skill, knowledge, attention, and energies to the advancement of the Company’s business and interests and to the performance of your duties and responsibilities as an employee of the Company.

2. Compensation. Your base rate of compensation will be $315,000 on an annual basis, less all applicable federal, state and local taxes and withholdings, such base salary to be paid in installments in accordance with the Company’s standard payroll practices. Such base salary may be adjusted from time to time in accordance with normal business practices and in the sole discretion of the Company.

3. Bonus. If the Board of Directors approves an annual bonus in any fiscal year you may be eligible for a discretionary award of up to 25% of your annualized base salary in such year. The bonus award, if any, will be based on both individual and corporate performance and will be determined by the Board of Directors of the Company in its sole discretion. In order to be eligible for a bonus, if any, you must complete three months of continuous service and be an active employee of the Company on the date such bonus is distributed. Any bonus payable to you under this letter will be paid between January 1 and March 15 of the calendar year following the calendar year in which such bonus is earned and approved by the Board.

In addition, upon commencement of your employment with the Company, you will receive a Sign-on Bonus of $50,000 (less all applicable federal, state, and local taxes and withholdings). If you voluntarily terminate your employment with the Company before the first anniversary of date of hire, you will be required to refund the Sign-on Bonus to the Company.

4. Benefits. You shall be eligible to participate in any and all bonus and benefit programs that the Company establishes and makes available to its employees from time to time, provided that you are eligible under (and subject to all provisions of) the plan documents governing those programs. Such benefits may include: participation in group medical and dental

Tetraphase Pharmaceuticals, Inc. Confidential

insurance programs, term life insurance, long-term disability insurance and participation in the Company’s 401(k) plan. The benefits made available by the Company, and the rules, terms, and conditions for participation in such benefit plans may be changed by the Company at any time and from time to time without advance notice.

5. Stock Incentive Program. You will be eligible to participate in the Company’s stock incentive program. Subject to approval by the Company’s Board of Directors, the Company will grant to you an option to purchase 2,833,000 shares of the Company’s Common Stock (subject to adjustment for stock splits, combinations, or other recapitalizations) which will vest (i.e., become exercisable) as to 25% of the shares on the first anniversary of your first day of employment and as to 6.25% of the shares every three-months thereafter, subject to your continued employment by the Company. The option exercise price will be equal to the fair market value of one share of Common Stock on the date of grant of the option as determined by the Company’s Board of Directors. The option will be issued pursuant to the Company’s 2006 Stock Incentive Plan and the stock option agreement covering the option, which must be executed to effect the grant of any option.

6. At-Will Employment. Your employment with the Company will be on an “at-will” basis, meaning that either you or the Company may terminate the employment relationship at any time, for any reason, with or without cause and with or without notice. Although your job duties, title, compensation and benefits, as well as the Company’s personnel policies and procedures, may change from time to time, the “at-will” nature of your employment may only be changed by a written agreement signed by you and the principal executive officer of the Company, which expressly states the intention to modify the at-will nature of your employment. Notwithstanding the foregoing, however, should the Company terminate your employment without “cause,” as that term is defined in this paragraph, (a) you will receive as severance pay an amount equal to six (6) months of your then-current base salary (subject to all applicable federal, state and local taxes and withholdings, and payable in accordance with the Company’s regular payroll practices) and (b) during such six-month severance period, the Company will provide you with medical and dental insurance benefits to the extent you were receiving such benefits prior to such termination and to the extent that the Company is able to provide you with such benefits at a cost to the Company that is not in excess of the cost that the Company was paying for such benefits for you prior to such termination; provided, however, that if you become employed prior to the end of the six-month severance period and are eligible to receive medical or dental insurance benefits from your new employer, then the Company shall no longer be required to provide you with such benefits, each of the benefits provided above in clauses (a) and (b) to be provided in exchange for your execution of a separation agreement and release of claims in a form to be provided by, and satisfactory to, counsel for the Company. For purposes hereof “cause” shall mean (a) a good faith finding by the Board of Directors of the Company that (i) you have failed to substantially perform your assigned duties for the Company, which failure is not cured within 20 days following written notice from the Company to you specifying the duties not performed, (ii) you have engaged in dishonesty, gross negligence or misconduct or (iii) you have breached any employment agreement, confidentiality agreement, nondisclosure agreement or other agreement entered into between you and the Company or (b) your conviction of, or the entry of a pleading of guilty or nolo contendere by you to, any crime involving moral turpitude or any felony.

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7. Non-Competition, Non-Solicitation and Non-Disclosure Agreement. As a condition of your employment, you will be required to execute the Company’s Non-Competition, Non-Solicitation and Non-Disclosure Agreement, a copy of which is enclosed with this letter.

8. Proof of Legal Right to Work. For purposes of federal immigration law, you will be required to provide the Company with documentary evidence of your identity and eligibility for employment in the United States. Such documentation must be provided to the Company within three (3) business days of your date of hire, or our employment relationship with you may be terminated. You may need to obtain a work visa in order to be eligible to work in the United States. If that is the case, your employment with the Company will be conditioned upon your obtaining a work visa in a timely manner as determined by the Company.

9. Company Policies and Procedures. As an employee of the Company, you will be required to comply with all Company policies and procedures. Violations of the Company’s policies may lead to immediate termination of your employment. Further, the Company’s premises, including all workspaces, furniture, documents, and other tangible materials, and all information technology resources of the Company (including computers, data and other electronic files, and all internet and email) are subject to oversight and inspection by the Company at any time. Company employees should have no expectation of privacy with regard to any Company premises, materials, resources, or information.

10. Other Agreements and Governing Law. You represent that you are not bound by any employment contract, restrictive covenant or other restriction preventing you from entering into employment with or carrying out your responsibilities for the Company, or which is in any way inconsistent with the terms of this letter. Please note that this offer letter is your formal offer of employment and supersedes any and all prior or contemporaneous agreements, discussions and understandings, whether written or oral, relating to the subject matter of this letter or your employment with the Company. The resolution of any disputes under this letter will be governed by Massachusetts law.

11. Section 409A of the Code. Subject to the provisions in this Section 11, any severance payments or benefits under this letter will begin only upon the date of your “separation from service” (determined as set forth below) which occurs on or after the date of termination of your employment. The following rules shall apply with respect to distribution of the payments and benefits, if any, to be provided to you under this letter.

(a) It is intended that each installment of the severance payments and benefits provided under this letter shall be treated as a separate “payment” for purposes of Section 409A of the Code and the guidance issued thereunder (“Section 409A”). Neither you nor the Company will have the right to accelerate or defer the delivery of any such payments or benefits except to the extent specifically permitted or required by Section 409A.

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(b) The determination of whether and when your separation from service from the Company has occurred shall be made and in a manner consistent with, and based on the presumptions set forth in, Treasury Regulation Section 1.409A-l(h). Solely for purposes of this paragraph, “Company” shall include all persons with whom the Company would be considered a single employer under Section 414(b) and 414(c) of the Code.

(c) All reimbursements and in-kind benefits provided under this letter shall be made or provided in accordance with the requirements of Section 409A to the extent that such reimbursements or in-kind benefits are subject to Section 409A, including, where applicable, the requirements that (i) any reimbursement is for expenses incurred during your lifetime (or during a shorter period of time specified in your offer letter), (ii) the amount of expenses eligible for reimbursement during a calendar year may not affect the expenses eligible for reimbursement in any other calendar year, (iii) the reimbursement of an eligible expense will be made on or before the last day of the calendar year following the year in which the expense is incurred and (iv) the right to reimbursement is not subject to set off or liquidation or exchange for any other benefit.

(d) Notwithstanding anything herein to the contrary, the Company shall have no liability to you or to any other person if the payments and benefits provided in this letter that are intended to be exempt from or compliant with Section 409A are not so exempt or compliant.

If this letter correctly sets forth the initial terms under which you will be employed by the Company, please sign the enclosed duplicate of this letter in the space provided below and return it to my attention at Tetraphase. This offer is effective through December 28^th, 2010. This offer is contingent on satisfactory reference checks.

The foregoing correctly sets forth the terms of my at-will employment by the Company.

Tetraphase Pharmaceuticals, Inc. Confidential

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