Exhibit 99.1

4550 Towne Centre Court | San Diego, California 92121

May 6, 2020

Board of Directors

Tetraphase Pharmaceuticals, Inc.

480 Arsenal Way, Suite 100

Watertown, MA 02472

Dear Members of the Board:

On behalf of La Jolla Pharmaceutical Company, I am pleased to submit this non-binding proposal to acquire 100% of the equity of Tetraphase Pharmaceuticals, Inc. for $22 million in cash plus an additional $12.5 million potentially payable under CVRs to be issued in the transaction. The $22 million upfront consideration would include amounts payable under the Black-Scholes put provisions in Tetraphase’s outstanding warrants and be subject to a minimum, to-be-agreed-upon closing net cash balance. The terms of the CVRs would match those set forth in Tetraphase’s merger agreement with AcelRx Pharmaceuticals, Inc., except that payments pursuant to the CVRs would be made in cash instead of cash or stock at the acquiror’s option.

We are impressed with the growth potential of XERAVA and excited about the potential benefits of combining two companies focused on delivering important therapies to patients in the ICU. Like Tetraphase, La Jolla is dedicated to the development and commercialization of therapies that improve outcomes in critically ill patients. In 2017, La Jolla’s first product, GIAPREZA (angiotensin II), was approved by the FDA as a treatment for septic or other distributive shock. In 2019, GIAPREZA was approved by the European Commission. GIAPREZA net sales were $23.1 million in 2019, up 129% from $10.1 million in 2018. La Jolla’s second product, LJPC‑0118 (artesunate), is under FDA review as a potential treatment for severe malaria.

As of March 31, 2020, La Jolla had $77.2 million of cash and no debt. La Jolla would fund 100% of the purchase price with cash on hand. Accordingly, this offer is not subject to any financing contingencies and would not require a vote by the La Jolla shareholders.

This proposal is subject to due diligence, which we believe we can complete by May 11, 2020. Following completion of our diligence review, we would expect to deliver an execution-ready version of a definitive merger agreement on the same day.

We look forward to discussing our proposal with you further.

Sincerely,

Kevin Tang

Chairman