ELIXIR PHARMACEUTICALS, INC. One Kendall Square

Exhibit 10.22

ELIXIR PHARMACEUTICALS, INC.

One Kendall Square

Building 1000, 5^th Floor

Cambridge, MA 02139

November 21, 2006

Hercules Technology Growth Capital, Inc.

Hercules Technology II, L.P.

525 University Avenue

Suite 700

Palo Alto, CA 94301

Attention: Mr. Manuel A. Henriquez

Ladies and Gentlemen:

For good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged by Elixir Pharmaceuticals, Inc., a Delaware corporation (the “Company”), the Company hereby grants to Hercules Technology Growth Capital, Inc., Hercules Technology II, L.P. and/or any one or more of their respective designated affiliates, assignees and/or nominees (collectively, “Hercules”) the right to participate in one Qualified Financing (as defined below) of the Company hereafter, as determined by Hercules in its sole discretion, by permitting Hercules to purchase up to $1,500,000 of Qualified Financing Securities (as defined below) in such Qualified Financing. Hercules shall have no obligation to purchase Qualified Financing Securities in any Qualified Financing. Any Hercules purchaser of Qualified Financing Securities shall be an “accredited investor” as defined in Regulation D promulgated under the Securities Act of 1933, as amended (the “Act”).

As used herein:

“Qualified Financing” means the sale and issuance by the Company, in a single transactions or series of related transactions, of shares of its convertible preferred stock or other equity securities (or instruments or securities convertible into or exercisable for such convertible preferred stock or other equity securities) to one or more institutional investors for financing purposes, other than a sale effected pursuant to an effective registration statement under the Act.

“Qualified Financing Securities” means, with respect to any Qualified Financing, the class and series of convertible preferred stock or other equity security of the Company (or instrument or security convertible into or exercisable for such convertible preferred stock or other equity security) sold and issued by the Company to the purchasers in such Qualified Financing.

The purchase, if any, by Hercules of Qualified Financing Securities in any Qualified Financing shall be made, subject to the provisions of this letter, upon the same terms and conditions (including, without limitation, price) as purchases by the other purchasers of Qualified Financing Securities in such Qualified Financing, and Hercules shall execute the definitive stock purchase agreement, investor rights agreement and other agreements (collectively, “Operative Documents”) executed by such other purchasers in connection with such Qualified Financing.

Until such time, if any, as Hercules participates in a Qualified Financing pursuant to the exercise of its rights hereunder, the Company shall give Hercules not less than ten (10) days written notice prior to the closing of each Qualified Financing, and shall provide such drafts and definitive copies of the Operative Documents and other documents and information in connection with such Qualified Financing as Hercules may reasonably request. Hercules may exercise its purchase rights hereunder by delivering written notice thereof to the Company no less than five (5) days prior to such closing.

The rights of Hercules to purchase Qualified Financing Securities in a Qualified Financing as set forth above shall survive the repayment by the Company of its indebtedness to Hercules and otherwise shall survive the expiration or other termination of that certain Loan and Security Agreement of even date herewith between the Company and Hercules, and shall terminate upon the earliest to occur of (i) consummation of the purchase by Hercules of Qualified Financing Securities in a Qualified Financing, (ii) the seventh anniversary of the date hereof, (iii) the date that is three (3) years following the effective date of the Company’s registration statement filed under the Act in connection with its initial public offering, and (iv) the consummation of a sale by the Company of all or substantially all of its assets or the merger or consolidation of the Company into or with another person or entity (other than a merger effected for the sole purpose of reincorporation in another jurisdiction or the creation of a holding company where the stockholders of the Company as of immediately prior to such merger continue to hold at least a majority of the issued and outstanding capital stock entitled to vote of such new holding company).

This Agreement shall be governed by, and interpreted and enforced in accordance with, the laws of the State of California, excluding its conflict of laws provisions.

2