Form of Warrant to Purchase Series B Preferred Stock issued to Square 1 Bank

Exhibit 4.2

THIS WARRANT AND THE SHARES ISSUABLE HEREUNDER HAVE NOT BEEN REGISTERED UNDER. THE SECURITIES ACT OF 1933, AS AMENDED, AND MAY NOT BE SOLD, PLEDGED OR OTHERWISE TRANSFERRED EXCEPT IN ACCORDANCE WITH APPLICABLE LAW.

SECOND WARRANT TO PURCHASE STOCK

THIS WARRANT CERTIFIES THAT, for good and valuable consideration, the receipt of which is hereby acknowledged, SQUARE 1 BANK or its assignee (“Holder”) is entitled to purchase at any time and from time to time prior to the Expiration Date, the number of fully paid and nonassessable shares of the class of securities (the “Shares”) of the corporation (the “Company”) at the initial exercise price per Share (the “Warrant Price”) all as set forth above and as adjusted pursuant to Article 2 of this warrant, subject to the provisions and upon the terms and conditions set forth in this warrant.

ARTICLE 1

EXERCISE

1.1 Method of Exercise. Holder may exercise this warrant prior to the Expiration Date by delivering this warrant and a duly executed Notice of Exercise in substantially the form attached as Appendix 1 to the principal office of the Company. Unless Holder is exercising the conversion right set forth in Section 1.2, Holder shall also deliver to the Company a check for aggregate Warrant Price for the Shares being purchased.

1.2 Conversion Right. In lieu of exercising this warrant as specified in Section 1.1, Holder may from time to time convert this warrant, in whole or in part, into a number of Shares determined by dividing (a) the aggregate fair market value of the Shares or other securities otherwise issuable upon exercise of this warrant minus the aggregate Warrant Price of such Shares by (b) the fair market value of one Share. The fair market value of the Shares shall be determined pursuant to Section 1.3. If the fair market value of one Share as determined pursuant to Section 1.3 is less than the exercise price per Share hereunder at the time of any automatic conversion pursuant to Section 1.6.2, then the warrant shall not be automatically converted into Shares under Section 1.6.2 but instead upon the occurrence of such Acquisition shall expire unexercised and be of no further force and effect.

1.3 Fair Market Value. If the Shares are traded regularly in a public market, the fair market value of the Shares shall be the closing price of the Shares (or the closing price of the Company’s stock into which the Shares are convertible) reported for the business day immediately before Holder delivers its Notice of Exercise to the Company. If the Shares are not

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regularly traded in a public market, the Board of Directors of the Company shall determine fair market value in its reasonable good faith judgment.

1.4 Delivery of Certificate and New Warrant. Promptly after Holder exercises or converts this warrant, the Company shall deliver to Holder certificates for the Shares acquired and, if this warrant has not been fully exercised or converted and has not expired, a new warrant representing the Shares not so acquired.

1.5 Replacement of Warrants. On receipt of evidence reasonably satisfactory to the Company of the loss, theft, destruction or mutilation of this warrant and, in the case of loss, theft or destruction, on delivery of an indemnity agreement reasonably satisfactory in form and amount to the Company or, in the case of mutilation, on surrender and cancellation of this warrant, the Company at its expense shall execute and deliver, in lieu of this warrant, a new warrant of like tenor.

1.6 Conversion on Sale, Merger, or Consolidation of the Company.

1.6.1 “Acquisition.” For the purpose of this warrant, “Acquisition” means (a) any sale, license, or other disposition of all or substantially all of the assets (including intellectual property) of the Company, or (b) any reorganization, consolidation, merger or sale of the voting securities of the Company or any other transaction where the holders of the Company’s securities before the transaction beneficially own less than 50% of the outstanding voting, securities of the surviving entity after the transaction.

1.6.2 Conversion of Warrant upon Acquisition. If, upon the closing of any Acquisition, Holder has not otherwise exercised this warrant in full, then this warrant shall be deemed to have been automatically converted pursuant to Section 1.2, and thereafter Holder shall participate in the Acquisition on the same terms as other holders of the same class of securities of the Company.

ARTICLE 2

ADJUSTMENTS TO THE SHARES

2.1 Stock Dividends, Splits, Etc. If the Company declares or pays a dividend on its common stock payable in common stock, or other securities, or subdivides the outstanding common stock into a greater amount of common stock, then upon exercise of this warrant, for each Share acquired, Holder shall receive, without cost to Holder, the total number and kind of securities to which Holder would have been entitled had Holder owned the Shares of record as of the date the dividend or subdivision occurred.

2.2 Reclassification, Exchange or Substitution. Upon any reclassification, exchange, substitution, or other event that results in a change of the number and/or class of the securities issuable upon exercise or conversion of this warrant, Holder be entitled to receive, upon exercise or conversion of this warrant, the number and kind of securities and property that Holder would have received for the Shares if this warrant had been exercised immediately before such reclassification, exchange, substitution, or other event. Such an event shall include any automatic conversion of the outstanding or issuable securities of the Company

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of the same class or series as the Shares to common stock pursuant to the terms of the Company’s Articles of Incorporation upon the closing of a registered public offering of the Company’s common stock. The Company or its successor shall promptly issue to Holder a new warrant for such new securities or other property. The new warrant shall provide for adjustments which shall be as nearly equivalent as may be practicable to the adjustments provided for in this Article 2 including, without limitation, adjustments to the Warrant Price and to the number of securities or property issuable upon exercise of the new warrant. The provisions of this Section 2.2 shall similarly apply to successive reclassifications, exchanges, substitutions, or other events.

2.3 Adjustments for Combinations, Etc. If the outstanding Shares are combined or consolidated, by reclassification or otherwise, into a lesser number of shares, the Warrant Price shall be proportionately increased. If the outstanding Shares are combined or consolidated, by reclassification or otherwise, into a greater number of shares, the Warrant Price shall be proportionately decreased.

2.4 Certificate as to Adjustments. Upon each adjustment of the Warrant Price, the Company at its expense shall promptly compute such adjustment, and furnish Holder with a certificate of its Chief Financial Officer setting forth such adjustment and the facts upon which such adjustment is based. The Company shall, upon written request, furnish Holder a certificate setting forth the Warrant Price in effect upon the date thereof and the series of adjustments leading to such Warrant Price.

2.5 Fractional Shares. No fractional Shares shall be issuable upon exercise or conversion of the Warrant and the Number of Shares to be issued shall be rounded down to the nearest whole Share. If a fractional share interest arises upon any exercise or conversion of the Warrant, the Company shall eliminate such fractional share interest by paying Holder amount computed by multiplying the fractional interest by the fair market value of a full Share.

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ARTICLE 3

REPRESENTATIONS AND COVENANTS OF THE COMPANY AND THE HOLDER

3.1 Representation and Warranties of the Company. The Company hereby represents and warrants to the Holder as follows:

(a) All Shares which may be issued upon the exercise of the purchase right represented by this warrant, and all securities, if any, issuable upon conversion of the Shares, shall, upon issuance, be duly authorized, validly issued, fully paid and nonassessable, and free of any liens and encumbrances except for restrictions on transfer provided for herein or under applicable federal and state securities laws.

(b) The Company’s capitalization table attached to this warrant is true and complete in all material respects as of the Issue Date.

3.2 Notice of Certain Events. The Company shall provide Holder with not less than 10 days prior written notice, including a description of the material facts surrounding the impact on the Holder’s Warrant of, any of the following events: (a) declaration of any dividend or distribution upon its common stock, whether in cash, property, stock, or other securities and whether or not a regular cash dividend; (b) offering for subscription pro rata to the holders of any class or series of its stock any additional shares of stock of any class or series or other rights; (c) effecting any reclassification or recapitalization of common stock; or (d) the merger or consolidation with or into any other corporation, or sale, lease, license, or conveyance of all or substantially all of its assets, or liquidation, dissolution or winding up.

3.3 Information Rights. So long as the Holder holds this warrant and/or any of the Shares, the Company shall deliver to the Holder (a) promptly after mailing, copies of all communiques to the shareholders of the Company, (b) within one hundred eighty (180) days after the end of each fiscal year of the Company, the annual audited financial statements of the Company certified by independent public accountants of recognized standing and (c) within forty-five (45) days after the end of each of the first three quarters of each fiscal year, the Company’s quarterly, unaudited financial statements.

3.4 Registration Under Securities Act of 1933, as amended and Other Rights and Obligations. The Company and the Holder agree that the Shares or, if the Shares are convertible into common stock of the Company, such common stock, shall be “Registrable Securities”, and Holder shall be a “holder of Registrable Securities” under the Investors’ Rights Agreement among the Company and other persons dated as of August 16, 2007 (as it may be amended and/or restated, the “IRA”) solely for the purposes of receiving the registration rights (and being subject to the related obligations) set forth in Sections 4 through 11 thereof. In addition, prior to the issuance of the shares of Common Stock issuable upon exercise of this Warrant, the Holder agrees to be bound to the Stockholders Agreement dated among the Company arid other persons dated as of August 16, 2007 (as it may be amended and/or restated, the “Stockholders Agreement”) as a “Holder” pursuant thereto. The Company has provided to the Holder the current copies of the IRA and the Stockholders Agreement as of the Issue Date. Upon request of the Company, the Holder will execute joinders to the IRA and the Stockholders

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Agreement or a separate agreement evidencing the provisions that the Holder agrees to be bound by pursuant to this Section 3.4. In the event of a conflict between the provisions of either the IRA or the Stockholders Agreement, and this warrant, the provisions of this warrant shall govern.

3.5 Representations and Warranties of the Holder. The Holder represents and warrants to the Company as follows:

(a) It is acquiring the Warrant, and (if and when it exercises this Warrant) it will acquire the Shares, for its own account for investment and not with a view to, or for sale in connection with, any distribution thereof, nor with any present intention of distributing or selling the same; and the Holder has no present or contemplated agreement, undertaking, arrangement, obligation, indebtedness or commitment providing for the disposition thereof.

(b) The Holder is an “accredited investor” as defined in Rule 501(a) under the Securities Act of 1933, as amended (the “Act”).

(c) The Holder has made such inquiry concerning the Company and its business and personnel as it has deemed appropriate; and the Holder has sufficient knowledge and experience in finance and business that it is capable of evaluating the risks and merits of its investment in the Company.

ARTICLE 4

MISCELLANEOUS

4.1 Term: Exercise Upon Expiration. This warrant is exercisable in whole or in part, at any time and from time to time during the Exercise Period. If this warrant has not been exercised prior to the end of the Exercise Date, this warrant shall be deemed to have been automatically exercised on the Exercise Date by “cashless” conversion pursuant to Section 1.2.

4.2 Legends. This warrant and the Shares (and the securities issuable, directly or indirectly, upon conversion of the Shares, if any) shall be imprinted with a legend in substantially the following form together with any other legend required under the IRA, the Stockholders Agreement or to implement the other provisions of Section 3.4 hereof:

THIS SECURITY HAS NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933, AS AMENDED, AND MAY NOT BE SOLD, PLEDGED OR OTHERWISE TRANSFERRED EXCEPT IN ACCORDANCE WITH APPLICABLE LAW AND IN ACCORDANCE WITH SECTION 4.3 OF THE WARRANT PURSUANT TO WHICH THIS SECURITY WAS ISSUED.

4.3 Compliance with Securities Laws on Transfer. This warrant and the Shares issuable upon exercise of this warrant (and the securities issuable, directly or indirectly, upon conversion of the Shares, if any) may not be transferred or assigned in whole or in part without compliance with applicable federal and state securities laws by the transferor and the transferee. The Company may require Holder to provide an opinion of counsel, except if the transfer is to

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an affiliate of Holder or if there is no material question as to the availability of current information as referenced in Rule 144(c), Holder represents that it has complied with Rule 144 (d) and (e) in reasonable detail, the selling broker represents that it has complied with Rule 144(f), and the Company is provided with a copy of Holder’s notice of proposed sale.

4.4 Transfer Procedure. Subject to the provisions of Section 4.3, Holder may transfer all or part of this warrant or the Shares issuable upon exercise of this warrant (or the securities .issuable, directly or indirectly, upon conversion of the Shares, if any) by giving the Company notice of the portion of the warrant being transferred setting forth the name, address and taxpayer identification number of the transferee and surrendering this warrant to the Company for reissuance to the transferee(s) (and Holder, if applicable). No surrender or reissuance shall be required if the transfer is to an affiliate of Holder.

4.5 Notices. All notices and other communications from the Company to the Holder, or vice versa, shall be deemed delivered and effective when given personally or mailed by first-class registered or certified mail, postage prepaid, at such address as may have been furnished to the Company or the Holder, as the case may be, in writing by the Company or such Holder from time to time. All notices to the Holder shall be addressed as follows:

Square 1 Bank

Attn: Warrant Administrator

406 Blackwell Street, Suite 240

Crowe Building .

Durham, NC 27701

4.6 Amendments. This warrant and any term hereof may be changed, waived, discharged or terminated only by an instrument in writing signed by the party against which enforcement of such change, waiver, discharge or termination is sought.

4.7 Attorneys’ Fees. In the event of any dispute between the parties concerning the terms and provisions of this warrant, the party prevailing in such dispute shall be entitled to collect from the other party all costs incurred in such dispute, including reasonable attorneys’ fees.

4.8 Governing Law. This warrant shall be governed by and construed in accordance with the laws of the State of North Carolina, without giving effect to its principles regarding conflicts of law.

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APPENDIX 1

NOTICE OF EXERCISE

1. The undersigned hereby elects to purchase                          shares of the                          stock of BIONANOMATRIX, INC. pursuant to the terms of the attached warrant, and tenders herewith payment of the purchase price of such shares in full.

1. The undersigned hereby elects to convert the attached warrant into shares in the manner specified in the warrant. This conversion is exercised with respect to                          of the shares covered by the warrant.

[Strike paragraph that does not apply.]

2. Please issue a certificate or certificates representing said shares in the name of the undersigned or in such other name as is specified below:

Square 1 Bank

Attn: Warrant Administrator

406 Blackwell Street, Suite 240

Fowler Building

Durham, NC 27701

3. The undersigned represents it is acquiring the shares solely for its own account and not as a nominee for any other party and not with a view toward the resale or distribution thereof except in compliance with applicable securities laws.

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