INVESTOR RIGHTS AGREEMENT BETWEEN BELLICUMPHARMACEUTICALS, INC. AND ARIAD GENE THERAPEUTICS, INC. AND ARIADPHARMACEUTICALS, INC.

Exhibit 4.3

INVESTOR RIGHTS AGREEMENT

BETWEEN

BELLICUM PHARMACEUTICALS, INC.

AND

ARIAD GENE THERAPEUTICS, INC.

AND

ARIAD PHARMACEUTICALS, INC.

Exhibit 4.3

INVESTOR RIGHTS AGREEMENT

This INVESTOR RIGHTS AGREEMENT (the “Agreement”) is made as of July 25, 2006, by and between Bellicum Pharmaceuticals, Inc., a Delaware corporation (the “Company” or “Bellicum”) having a place of business at Twelve Greenway Plaza, Suite 1380, Houston, Texas 77046, and ARIAD Pharmaceuticals, Inc., and ARIAD Gene Therapeutics, Inc., both Delaware corporations with their principal place of business at 26 Landsdowne Street, Cambridge, Massachusetts 02139 (collectively, the “Investor”).

WHEREAS, the Company and the Investor have entered into a License Agreement (the “License Agreement”) regarding certain proprietary Licensed Patents and Licensed Technology (as those terms are defined in the License Agreement; and

WHEREAS, the Company has issued and sold (and in the future will issue and sell) to the Investor certain shares of its common stock, par value $.01 per share (the “Common Stock”) pursuant to a Stock Purchase Agreement of even date herewith (the “Stock Purchase Agreement”); and

WHEREAS, as a condition to entering into the Stock Purchase Agreement, the Company has agreed to grant the Investor certain rights and covenants set forth herein;

NOW, THEREFORE, in consideration of the premises and mutual agreements set forth herein and for other good and valuable consideration, the receipt and sufficiency of which are hereby mutually acknowledged, and intending to be legally bound hereby, the parties hereto agree as follows. Initially capitalized terms not otherwise defined herein shall have the meanings ascribed to them in the Stock Purchase Agreement:

1. Registration Rights. The Company hereby covenants and agrees with the Investor that at such time as the Company extends piggyback registration rights to any purchaser

of the Company’s preferred stock or Convertible Securities it will extend piggyback registration rights to the Investor, which will be identical in scope and priority, with the initial grant of piggyback registration rights granted to any purchaser of at least one million dollars ($1,000,000) of the Company’s preferred stock or Convertible Securities and will be transferable to any person or entity to which Investor transfers not less than 50,000 shares of Common Stock, as adjusted to reflect stock splits, stock dividends, recapitalizations similar divisions and combinations.

2. Covenants of the Company.

2.1 Delivery of Financial Statements to Investor. The Company shall deliver to the Investor, as long as the Investor holds not less than 100,000 shares of Common Stock of the Company, as adjusted to reflect stock splits, stock dividends, recapitalizations similar divisions and combinations:

(a) as soon as practicable, but in any event within one hundred eighty (180) days after the end of each fiscal year of the Company, an income statement for such fiscal year, a balance sheet of the Company and statement of stockholder’s equity as of the end of such year, such year-end financial reports to be in reasonable detail, prepared in accordance with generally accepted accounting principles (“GAAP”), and audited and certified by independent public accountants of nationally recognized standing selected by the Company;

(b) as soon as practicable, but in any event within thirty (30) days after the end of each of the first three (3) quarters of each fiscal year of the Company, beginning with the quarter ending June 30, 2006, an unaudited profit or loss statement for such fiscal quarter and an unaudited balance sheet as of the end of such fiscal quarter.

(c) with respect to the financial statements called for in subsection (b) of this Section 2.1, an instrument executed by the Chief Financial Officer or Chief Executive

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Officer of the Company and certifying that such financial statements were prepared in accordance with GAAP consistently applied with prior practice for earlier periods (with the exception of footnotes that may be required by GAAP) and fairly present the financial condition of the Company and its results of operations for the period specified, subject to year-end audit adjustment.

(d) at such time at substantially similar financial reporting rights are granted to a purchaser of the Company’s preferred stock, the provisions of Section 2.1 shall be automatically amended to conform to the provisions of such grant, and the entitlement of the Investor to receive financial information pursuant to Section 2.1 shall be deemed satisfied by the delivery to Investor of the information required to be provided to such preferred stock investors.

2.2 Limitation on Access to Information. The information provided by the Company pursuant to Section 2.1 shall be treated as Confidential Information as defined in the License Agreement and shall be subject to Article 5 thereof; provided, that, notwithstanding anything to the contrary in Section 2.1 above, the Company reserves the right not to provide information to the Investor (i) if delivery of such information to the Investor would result in disclosure to the Investor of (A) proprietary or strategic information relating to the Company’s corporate partnering programs other than those involving a Sublicense under the License Agreement, (B) the Company’s know-how or confidential trade secrets other than Bellicum Technology (as defined in the License Agreement) or (C) information subject to attorney-client privilege, provided, further, that nothing contained in this Section 2.2 shall limit the Investor’s rights or the Company’s obligations under the License Agreement or the Stock Purchase Agreement.

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2.3 Termination of Information; Assignment. The covenants set forth in Section 2.1 shall terminate as to the Investor and be of no further force or effect on the earlier of the Equity Termination Date or when the Company first becomes subject to the periodic reporting requirements of Sections 12(g) or 15(d) of the 1934 Act. The rights to receive and have access to information relating to the Company pursuant to Section 2.1 may be assigned (but only with all related obligations) by the Investor in the event of a merger, consolidation or sale of all or substantially all of the assets of the Investor or as a result of the assignment by the Investor of all of its rights hereunder, provided (a) the Company is, within a reasonable time after such transfer, furnished with written notice of the name and address of such transferee or assignee and the securities with respect to which such information rights are being assigned; and (b) such transferee or assignee agrees in writing to be bound by and subject to the terms and conditions of this Agreement and enters into a confidentiality agreement with the Company containing substantially similar confidentiality obligations to the Company as those contained in the License Agreement.

3. Co-Sale Rights.

3.1 (a) In the event that Kevin Slawin, M.D. or any transferee of his in a transaction not subject to this Article 3 pursuant to Section 3.1(d) (the “Co-Sale Offeree”) receives a bona fide offer from a third party or parties, other than the Company or any Permitted Transferee (as defined below) (the “Co-Sale Offeror”), to acquire any of his equity in the Company (the “Take-Along Shares”) for a specified price payable in cash or otherwise and on specified terms and conditions (the “Co-Sale Offer”), and the Co-Sale Offeree proposes to sell or otherwise transfer any or all of the Take-Along Shares to the Co-Sale Offeror pursuant to the Co-Sale Offer, Investor shall have the right to sell to the Co-Sale Offeror, at the same price per

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share and on the same terms and conditions as stated in the Co-Sale Offer, such number of shares equal to the Take-Along Shares multiplied by a fraction, the numerator of which shall be the number of shares of Common Stock owned by Investor and the denominator of which shall be the sum of the number of shares of Common Stock (assuming exercise or conversion of all Convertible Securities) owned by the Co-Sale Offeree plus the number of shares of Common Stock (assuming exercise or conversion of all Convertible Securities) owned by the Investor. Promptly upon receipt of a Co-Sale Offer, the Co-Sale Offeree will send a copy of the document outlining the terms of the proposed transfer to the Investor (with a copy to the Company), which shall include the name of the proposed transferee, the proposed purchase price per share, the terms of payment of such purchase price and all other matters relating to such sale (the “Proposal”).

(b) If Investor wishes to participate in any sale pursuant to Section 3.1(a) it shall notify the Co-Sale Offeree in writing of such intention and the number of shares it wishes to sell pursuant to this Section 3.1(b) not later than twenty (20) days after delivery of the Proposal. If the Co-Sale Offeree does not receive such notice from Investor within such twenty (20) day period, the Co-Sale Offeree shall, subject to the provision of Section 3.1(b), be free to consummate the proposed transaction without any obligation to include shares owned by Investor in such transaction.

(c) The Co-Sale Offeree and Investor, after having provided timely notice, shall sell to the Co-Sale Offeror all of the shares proposed to be sold by them at not less than the price and upon other terms and conditions, if any, not more favorable to the Co-Sale Offeror than those stated in the Co-Sale Offer.

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(d) The restrictions on transfer contained in this Section 3.1 shall not apply to transfers by any Co-Sale Offeree (a) to such Co-Sale Offeree’s children or other member of such Co-Sale Offeree’s immediate family, or to a trust for the sole benefit of such persons, (b) to a limited liability company or family limited partnership controlled by such Co-Sale Offeree, (c) to such Co-Sale Offeree’s guardian or conservator, (d) in the event of such Co-Sale Offeree’s death, to such Co-Sale Offeree’s executor(s) or administrator(s), or (e) to Bellicum pursuant to the Plan and any related restricted stock agreement or stock option agreement; provided that such transferee agrees in writing to be bound by the provisions of this Section 3 as a Co-Sale Offeree.

(e) The Co-Sale rights set forth in this Article 3 (i) shall be transferable to any person or entity to which Investor transfers not less than 100,000 shares of Common Stock, as adjusted to reflect stock splits, stock dividends, recapitalizations similar divisions and combinations, and (ii) shall terminate on the Equity Termination Date as defined in the Stock Purchase Agreement.

4. Percentage Maintenance.

4.1 Notice of New Issuance. From and after the date of consummation of a Qualified Financing, except with respect to “Exempt Issuances” as defined in Paragraph 4.3 below, in the event that the Company issues any shares of Common Stock or any Convertible Securities, the Company will deliver to Investor a written notice (the “Offer Notice”) upon the completion of such issuance (the “New Issuance”), stating the price and other terms and conditions thereof.

4.2 Right to Purchase Shares or Convertible Securities. Subject to Paragraph 3.3 hereof, in the event of a New Issuance (other than an Exempt Issuance), Investor

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shall have the right to purchase all (or any portion) of a number of shares of Common Stock or Convertible Securities at the price and on the terms upon which the New Issuance was made, such price to be paid in full in cash or by check at the time of issuance of such securities to Investor so that, after giving effect to the issuance to Investor and the conversion, exercise and exchange into or for (whether directly or indirectly) shares of Common Stock of all such Convertible Securities, Investor will continue to maintain its same proportionate ownership of Common Stock as of the date immediately preceding the New Issuance, treating Investor for the purpose of such computation, as the holder of the number of shares of Common Stock which would be issuable to it upon conversion, exercise and exchange of all Convertible Securities held by them on the date immediately preceding the New Issuance and assuming the like conversion, exercise and exchange of all such securities held by other persons. The rights set forth in this Paragraph 4.2 shall be exercised by Investor, if at all, by written notice to the Company delivered not later than thirty (30) days after the receipt by Investor of the Offer Notice in accordance with the terms and conditions stated therein, and such right shall expire at the end of the thirtieth day after the day of the receipt by Investor of the Offer Notice.

4.3 Exempt Issuances. The issuances referred to in Paragraph 4.1 which will not give Investor the rights described in Paragraph 4.2 (the “Exempt Issuances”) are issuances in which shares of Common Stock or Rights or Convertible Securities of the Company are issued (i) upon conversion of the preferred stock of the Company or any other Convertible Securities outstanding as of the date of this Agreement, (ii) as a dividend, stock split or distribution payable pro rata to all holders of Common Stock or Convertible Securities; (iii) to employees, officers, directors or consultants of the Company pursuant to the Company’s Stock Plan, (iv) in a Dilutive Financing or (v) in a transaction the primary purpose of which is other than financing the Company, including but not limited to an equipment lease or loan, a license, a strategic alliance or an acquisition.

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4.4. Assignment. The rights granted to Investor under this Paragraph 4 shall be assignable to any party to which the Investor transfers not less than 100,000 shares of Common Stock, as adjusted to reflect stock splits, stock dividends, recapitalizations similar divisions and combinations.

4.5 Termination. The rights granted under this Paragraph 4 shall terminate immediately before the consummation by the Company of an Initial Public Offering or a Company Sale.

5. Observer Rights. For so long as the Investor owns not less than 100,000 shares of Common Stock, as adjusted to reflect stock splits, stock dividends, recapitalizations similar divisions and combinations, from and after the Effective Date, one representative of Investor (the “Observer”), shall be entitled to (a) be present at all meetings of the Board of Directors of Bellicum or any Executive Committee thereof, and (b) notification of any such meetings, including such meetings’ time and place, in the same manner as the Directors of the Company. The Observer shall have the same access to information concerning the business and operations of Bellicum and at the same time as the directors of Bellicum. Notwithstanding the above, the Observer shall not be a director. As such, the Observer shall not have the right to vote at any meetings. Bellicum, in its sole discretion, reserves the right to exclude any Observer from all or part of any meeting of the Board of Directors of Bellicum to the extent reasonably necessary to protect confidential information of Bellicum to which Investor is not entitled under the License Agreement or maintain a legal privilege with respect to information of Bellicum. Notwithstanding anything to the contrary herein, the prohibitions and rights provided in this Section 4 will terminate upon the Equity Termination Date. The rights granted under this Paragraph 5 are personal to the Investor and may not be assigned.

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6. Miscellaneous.

6.1 Successors and Assigns; Subsequent Parties. The terms and conditions of this Agreement shall inure to the benefit of and be binding upon the respective successors and permitted assigns of the parties. Nothing in this Agreement, express or implied, is intended to confer upon any party other than the parties hereto or their respective successors and assigns any rights, remedies, obligations, or liabilities under or by reason of this Agreement. Subject to the terms of this Agreement, no party hereby may assign its rights or obligations hereunder without the prior written consent of the other parties; provided, however, that either party may, without the written consent of the other party, assign this Agreement and its rights and delegate its obligations hereunder in connection with the transfer or sale of all or substantially all of such party’s assets or business related to this Agreement or in the event of its merger, consolidation, change in control or similar transaction. Any permitted assignee shall assume all obligations of its assignor under this Agreement. Any purported assignment in violation of this Section 6.1 or another express provision of this Agreement shall be void.

6.2 Governing Law. This Agreement will be construed, interpreted and applied in accordance with the laws of the State of Delaware (excluding its body of law controlling conflicts of law).

6.3 Counterparts. This Agreement may be executed simultaneously in one or more counterparts, each of which shall be deemed an original, but all of which together shall constitute one and the same instrument.

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6.4 Waiver. The terms or conditions of this Agreement may be waived only by a written instrument executed by the Party waiving compliance. The failure of either party at any time or times to, require performance of any provision hereof shall in no manner affect its rights at a later time to enforce the same. No waiver by either party of any condition or term shall be deemed as a continuing waiver of such condition or term or of another condition or term.

6.5 Headings. Section and subsection headings are inserted for convenience of reference only and do not form part of this Agreement.

6.6 Force Majeure. Neither party shall be liable for failure of or delay in performing obligations set forth in this Agreement, and neither shall be deemed in breach of its obligations, if such failure or delay is due to natural disasters or any causes beyond the reasonable control of such party. In event of such force majeure, the party affected thereby shall use reasonable efforts to cure or overcome the same and resume performance of its obligations hereunder.

6.7 Notices. Unless otherwise provided, all notices, requests, consents and other communications hereunder shall be in writing, shall be addressed to the receiving party’s address set forth below or to such other address as a party may designate by notice hereunder, and shall be either (i) delivered by hand, (ii) made by telecopy or facsimile transmission, (iii) sent by overnight courier providing evidence of delivery, or (iv) sent by registered or certified mail, return receipt requested, postage prepaid.

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All notices, requests, consents and other communications hereunder shall be deemed to have been given either (i) if by hand, at the time of the delivery thereof to the receiving party at the address of such party set forth above, (ii) if made by telecopy or facsimile transmission, at the time that receipt thereof has been acknowledged by electronic confirmation or otherwise, (iii) if sent by overnight courier, on the next business day following the day such notice is delivered to the courier service, or (iv) if sent by registered or certified mail, on the fifth business day following the day such mailing is made.

6.8 Expenses. If any action at law or in equity is necessary to enforce or interpret the terms of this Agreement, the prevailing party shall be entitled to reasonable attorneys’ fees, costs and necessary disbursements in addition to any other relief to which such party may be entitled.

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6.9 Amendments. Any term of this Agreement may be amended only with the written consent of the Company and the Investor; provided, however, that any amendment to the provisions of Section 3 shall require the written consent of Kevin M. Slawin, M.D.

6.10 Severability. If any provision(s) of this Agreement are or become invalid, are ruled illegal by any court of competent jurisdiction or are deemed unenforceable under then current applicable law from time to time in effect during the term hereof, it is the intention of the parties that the remainder of this Agreement shall not be affected thereby provided that a party’s rights under this Agreement are not materially affected. The parties hereto covenant and agree to renegotiate any such term, covenant or application thereof in good faith in order to provide a reasonably acceptable alternative to the term, covenant or condition of this Agreement or the application thereof that is invalid, illegal or unenforceable, it being the intent of the parties that the basic purposes of this Agreement are to be effectuated.

6.11 Entire Agreement. This is the entire Agreement between the Parties with respect to the subject matter hereof and supersedes all prior representations, understandings and agreements between the Parties with respect to the subject matter hereof.

6.12 Construction. The parties hereby acknowledge and agree that: (i) each party and its counsel reviewed and negotiated the terms and provisions of this Agreement and have contributed to its revision; (ii) the rule of construction to the effect that any ambiguities are resolved against the drafting party shall not be employed in the interpretation of this Agreement; and (iii) the terms and provisions of this Agreement shall be construed fairly as to all parties hereto and not in a favor of or against any party, regardless of which party was generally responsible for the preparation of this Agreement.

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6.13 Remedies. It is specifically understood and agreed that any breach of the provisions of this Agreement by any person subject hereto will result in irreparable injury to the other parties hereto, that the remedy at law alone will be an inadequate remedy for such breach, and that, in addition to any other remedies which they may have, such other parties may enforce their respective rights by actions for specific performance (to the extent permitted by law).

6.14 Status. Nothing in this Agreement is intended or shall be deemed to constitute a partner, agency, employer-employee, or joint venture relationship between the parties.

6.15 Further Assurances. Each party agrees to execute, acknowledge and deliver such further instructions, and to do all such other acts, as may be necessary or appropriate in order to carry out the purposes and intent of this Agreement.

6.16 Counterparts. This Agreement may be executed simultaneously in one or more counterparts, each of which shall be deemed an original, but all of which together shall constitute one and the same instrument.

6.17 Authority of ARIAD Pharmaceuticals, Inc. ARIAD Gene Therapeutics, Inc. (“AGTI”) hereby appoints ARIAD Pharmaceuticals, Inc. (“API”) as its exclusive proxy and agent with respect to its ownership of Common Stock and for all purposes of this Agreement, and hereby instructs Bellicum to deal solely with API and to treat API as if it is the sole owner of the Common Stock owned by AGTI and API. Subject to this Section 6.17, AGTI and API may freely transfer their interest in the Common Stock between them. AGTI and API jointly and severally agree to indemnify and hold Bellicum harmless from any and all loss, costs, liability, claim or expense incurred by the Company as the result of claims against the Company with respect to actions taken in compliance with this instruction. The proxy and grant

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of agency authority granted hereby is coupled with an interest and shall not be revocable without the written consent an acknowledgement of the Company, which shall not be unreasonably withheld.

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IN WITNESS WHEREOF, the parties hereto have executed this Investor Rights Agreement or caused this Agreement to be executed by their duly authorized representatives, as of the date first written above.

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