LOCK-UP AGREEMENT

EXHIBIT 10.3

LOCK-UP AGREEMENT

Targacept, Inc.

100 North Main Street, Suite 1510

Winston-Salem, NC 27101

Catalyst Biosciences, Inc.

260 Littlefield Avenue

South San Francisco, CA 94080

Ladies and Gentlemen:

In connection with the proposed acquisition of Catalyst Biosciences, Inc. (the “Company”) by Targacept, Inc. (“Targacept”) whereby Talos Merger Sub, Inc. (“Merger Sub”), a wholly-owned subsidiary of Targacept, will merge with and into the Company (the “Merger”), and in consideration of Targacept, Merger Sub and the Company entering into the Agreement and Plan of Merger dated on or about March 5, 2015 (the “Merger Agreement;” all capitalized terms used in this Lock-Up Agreement without definition herein shall have the meanings ascribed to them in the Merger Agreement), the receipt and sufficiency of such consideration being hereby acknowledged and accepted, and in order to induce Targacept and the Company each to close the Merger, the undersigned (“Securityholder”), a holder of shares of Company Capital Stock, Company Stock Options and/or Company Warrants (collectively, the “Company Securities”) who will receive shares of Targacept Common Stock in exchange for his, her or its shares of Company Common Stock and/or upon exercise of Company Stock Options and/or Company Warrants, as the case may be, hereby agrees with Targacept and the Company as follows:

1. During the Lock-Up Period (as defined below), Securityholder shall not, directly or indirectly, (a) sell, assign, transfer, tender, or otherwise dispose of (whether by actual disposition or effective economic disposition due to cash settlement or otherwise, including, without limitation, by the creation of any liens, claims, charges or other encumbrances or restrictions of any kind whatsoever (“Liens”) on) any (i) Company Securities and (ii) shares of Targacept Common Stock and any securities convertible into, exchangeable for or that represent the right to receive shares of Targacept Common Stock, in each case whether now owned or hereinafter acquired, owned directly by the Securityholder (including holding as a custodian) or with respect to which the Securityholder has beneficial ownership within the rules and regulations of the Securities and Exchange Commission (collectively, the “Locked-Up Securities”), (b) effect any short sale or enter into any contract, option, commitment or other arrangement or understanding with respect to the direct or indirect sale, transfer, assignment or other disposition of (including, without limitation, by the creation of any Liens or by establishing or increasing a put equivalent position or liquidating or decreasing a call equivalent position within the meaning of Section 16 of the Securities Exchange Act of 1934, as amended (the “Exchange Act”), and the rules and regulations of the Securities and Exchange Commission promulgated thereunder with respect to, any Locked-Up Securities, or publicly announce an intention to effect any such transaction, during the Lock-Up Period) any Locked-Up Securities, or (c) take any action that would make any

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representation or warranty of Securityholder contained herein untrue or incorrect or have the effect of preventing or disabling Securityholder from performing Securityholder’s obligations under this Lock-Up Agreement. Notwithstanding the foregoing, and provided that transfers described in (a) through (e) of this sentence are not required to be reported in any public report or filing with the Securities and Exchange Commission (other than (i) a filing at any time on a Form 5 or (ii) a filing after the expiration of the Lock-Up Period on a Schedule 13D or Schedule 13G (or Schedule 13D/A or schedule 13G/A), Securityholder may make (a) transfers by will or by operation of law or other transfers for estate-planning purposes, in which case this Lock-Up Agreement shall bind the transferee, (b) with respect to such Securityholder’s Company Options which expire on or prior to the Expiration Date, transfers, sale, or other disposition of Locked-Up Securities to the Company as payment for the (i) exercise price of such Securityholder’s Company Options and (ii) taxes applicable to the exercise of such Securityholder’s Company Options or (c) if Securityholder is a partnership or limited liability company, a transfer to one or more partners or members of Securityholder or to an affiliated corporation, trust or other business entity under common control with Securityholder, or if Securityholder is a trust, a transfer to a beneficiary, provided that in each such case the applicable transferee has signed a lock-up agreement in substantially the form hereof, (d) any transfer to another holder of the capital stock of the Company that has signed a lock-up agreement in substantially the form hereof relating to the transferred Shares and (e) transfers of shares acquired on the open market following the Closing Date. In the event that any securities held by any other holder (the “Other Holder”) subject to a similar lock-up agreement in connection with the Merger are released from the restrictions of such lock-up agreement, the Locked-Up Securities held by the undersigned Securityholder shall likewise automatically be released from the restrictions contained herein in the same proportion as those securities released for the Other Holder.

2. As used in this Lock-Up Agreement, the term “Lock-Up Period” shall mean from and after the date hereof until the earlier to occur of (a) 120 days after the Closing Date or (b) such date and time as the Merger Agreement shall be terminated pursuant to Section 9 thereof or otherwise. Upon termination or expiration of this Lock-Up Agreement, no party shall have any further obligations or liabilities under this Lock-Up Agreement; provided, however, such termination or expiration shall not relieve any party from liability for any willful breach of this Lock-Up Agreement or acts of bad faith prior to termination hereof.

3. Securityholder also agrees and consents to the entry of stop transfer instructions with Targacept’s transfer agent and registrar against the transfer of Securityholders’ Locked-Up Securities, except in compliance with this Lock-Up Agreement. In furtherance of the foregoing, Targacept and its transfer agent are hereby authorized to decline to make any transfer of securities if such transfer would constitute a violation or breach of this Lock-Up Agreement.

4. Securityholder understands that Targacept, the Company and Merger Sub will proceed with the Merger in reliance on this Lock-Up Agreement. Moreover, Securityholder understands and agrees that Targacept, Merger Sub and the Company are relying upon the accuracy, completeness, and truth of Securityholder’s representations, warranties, agreements, and certifications contained in this Lock-Up Agreement.

[Remainder of Page has Intentionally Been Left Blank; Signature Page Follows]

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If a corporation, a limited partnership or other legal entity, please sign here:

[Signature Page to Lock-Up Agreement]

Date:                 , 2015

[Signature Page to Lock-Up Agreement]