AMENDMENT NO. 1 TO RIGHTS AGREEMENT

EXHIBIT 4.5

AMENDMENT NO. 1 TO RIGHTS AGREEMENT

Amendment No. 1, dated as of March 15, 2005 (the “Amendment”), to the Rights Agreement, dated as of May 16, 2001 (the “Rights Agreement”), by and between Insmed Incorporated, a Virginia corporation (the “Company “), and Wachovia Bank, National Association (formerly known as First Union National Bank), a national banking association (the “Rights Agent”). Capitalized terms not defined herein shall have the meanings ascribed to them in the Rights Agreement.

W I T N E S S E T H

WHEREAS, Section 27 of the Rights Agreement provides generally that prior to the Distribution Date, the Company may, and the Rights Agent shall, if the Company so directs, supplement or amend any provision of the Rights Agreement without the approval of any holders of the Rights;

WHEREAS, the Company intends to enter into several Purchase Agreements (the “Purchase Agreements”) with certain persons (the “Purchasers”) dated March 15, 2005, pursuant to which the Company will offer and sell up to $35,000,000 in aggregate principal amount of 5.5% Convertible Notes due 2008-2010, which notes will be convertible into Common Stock, and warrants to purchase shares of the Common Stock, in a private offering exempt from the registration requirements of the Securities Act of 1933, as amended;

WHEREAS, the securities sold pursuant the Purchase Agreements include restrictions on the conversion and exercise of such securities into Common Stock intended to prevent any Purchaser from becoming a Beneficial Owner of more than 9.9% of the shares of Common Stock for purposes of Section 16 of the 1934 Act and the rules promulgated thereunder (the “9.9% Limitation”);

WHEREAS, due to the 9.9% Limitation, no Purchaser may become an Acquiring Person under the Rights Agreement as a result of the sales of securities pursuant to the Purchase Agreements;

WHEREAS, prior to the issuance and sale of any securities pursuant to the Purchase Agreements, for the avoidance of any uncertainty as to whether application of the 9.9% Limitation would prevent any Purchaser from becoming an Acquiring Party under the Rights Agreement as a result of the sales of Securities pursuant to the Purchase Agreements, the Company desires to amend and clarify certain provisions of the Rights Agreement.

NOW, THEREFORE, in consideration of the premises and the mutual agreements herein set forth, the parties hereby agree as follows:

1. This Amendment is contingent upon, and shall take effect immediately prior to, the Closing (as defined in the Purchase Agreements).

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2. Section 1(kk) of the Rights Agreement is amended by deleting said section and inserting the following new paragraph:

“(kk) “Substantial Block” shall mean, (A) in the case of any Person other than an Exempt Person, either (i) a number of shares of Voting Stock having in the aggregate 15% or more of the general voting power or (ii) 15% or more of the Rights, or (B) in the case of an Exempt Person, any amount in excess of such Exempt Person’s Exempt Amount.”

3. Section 1 of the Rights Agreement is amended by adding at the end of said section the following:

“(qq) “Exempt Amount” as to any Exempt Person shall mean either (1) the sum of (A) the number of shares of Common Stock Beneficially Owned by such Exempt Person immediately prior to the Exempt Closing and (B) the number of shares of Common Stock issuable upon (i) the conversion of the note (the “Note”) sold to such Exempt Person pursuant to the Purchase Agreement and (ii) the exercise of the warrant sold to such Exempt Person pursuant to the Purchase Agreement (the “Warrant”), or (2) the sum of (A) the number of Rights Beneficially Owned by such Exempt Person immediately prior to the Exempt Closing and (B) the number of shares of Common Stock issuable upon (i) the conversion of the Note and (ii) the exercise of the Warrant (as such amounts in clause (1) or (2) may be increased or decreased based on any adjustments to the number of shares of Common Stock issuable upon conversion of the Note or upon exercise of the Warrant in accordance with the respective terms of the Note and the Warrant). The determination of the Beneficial Ownership specified in clauses (1) and (2) of this Section 1(qq) shall be made without regard to the application of Section 6(g) of the Note and Section 2(c) of the Warrant.

(rr) “Exempt Person” shall mean each of Alexandra Global Master Fund, Ltd., Baker Bros. Investments, L.P, Baker/Tisch Investments, L.P., Baker Biotech Fund I, L.P., Baker Biotech Fund II, L.P. and Baker Biotech Fund III, L.P. and their respective Affiliates and Associates (within the meaning of Affiliates and Associates set forth in Rule 13d-3 of the General Rules and Regulations of the Exchange Act) if immediately following the Exempt Closing such entity and its Affiliates and Associates Beneficially Own more than (i) a number of shares of Voting Stock having in the aggregate 15% or more of the general voting power or (ii) 15% or more of the Rights. An Exempt Person shall cease to be an Exempt Person when such Exempt Person’s Exempt Amount is less than a Substantial Block for any Person other than the Exempt Person.

(ss) “Exempt Closing” shall mean the time of the closing of the purchase and sale of the securities sold pursuant to the Purchase Agreements.

(tt) As to any Exempt Person, “Purchase Agreement” shall mean the Purchase Agreement between such Exempt Person and the Company dated March 15, 2005.”

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4. By execution of this Agreement, the Company shall not be deemed to have compromised or waived any of its rights under the Rights Agreement.

IN WITNESS WHEREOF, the parties hereto have caused this Amendment to be duly executed as of the day and year first above written. This Amendment may be executed in one or more counterparts all of which shall be considered one and the same amendment and each of which shall be deemed to be an original.

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