WARRANT TO PURCHASE SHARES OF COMMON STOCK, PAR VALUE $.001 PER SHARE,

Exhibit 4.13

THIS WARRANT HAS NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933 OR THE SECURITIES LAWS OF ANY STATE AND MAY NOT BE SOLD OR OTHERWISE DISPOSED OF EXCEPT PURSUANT TO AN EFFECTIVE REGISTRATION STATEMENT UNDER SUCH ACT AND APPLICABLE STATE SECURITIES LAWS OR AN OPINION OF COUNSEL REASONABLY ACCEPTABLE TO THE COMPANY TO THE EFFECT THAT THE TRANSACTION PURSUANT TO WHICH SUCH WARRANTS WILL BE OFFERED FOR SALE OR OTHERWISE DISPOSED OF IS SUBJECT TO AN APPLICABLE EXEMPTION TO THE REGISTRATION REQUIREMENTS OF SUCH ACT OR SUCH LAWS.

WARRANT TO PURCHASE

SHARES OF COMMON STOCK,

PAR VALUE $.001 PER SHARE,

OF

PRECISION THERAPEUTICS, INC.

This certifies that, for good and valuable consideration, [Investor Name] (the “Warrantholder”), is entitled to purchase from Precision Therapeutics, Inc., a corporation incorporated under the laws of the State of Delaware (the “Corporation”), subject to the terms and conditions hereof, at any time at or after the Issue Date (as defined herein) and before 5:00 P.M., Pittsburgh, PA time on the Expiration Date (as defined herein), the Exercise Number (as defined herein) of fully paid and non-assessable shares of Common Stock, par value $.001 per share, of the Corporation at the Exercise Price (as defined herein).

ARTICLE I

Section 1.01: Definition of Terms. As used in this Warrant, the following capitalized terms shall have the following respective meanings:

The Exercise Number shall be subject to adjustment in accordance with Article III.

ARTICLE II

DURATION AND EXERCISE OF WARRANT

Section 2.01: Duration of Warrant. The Warrantholder may exercise this Warrant at any time and from time to time after the Issue Date, and before 5:00 P.M., Pittsburgh, PA time, on the Expiration Date. If this Warrant is not exercised on or prior to the Expiration Date, it shall become void, and all rights and obligations hereunder shall thereupon cease.

Section 2.02: Exercise of Warrant.

(a) The Warrantholder may exercise this Warrant, in whole or in part, by presentation and surrender of this Warrant to the Corporation at its principal corporate office or at the office of its stock transfer agent, if any, with the subscription form attached hereto as Exhibit A (the “Subscription Form”) duly executed and accompanied by payment of the full Exercise Price for each Warrant Share to be purchased. Payment of the Exercise Price shall be made in cash.

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(b) In lieu of payment of the Exercise Price pursuant to the preceding paragraph, the Warrantholder shall have the right to require the Corporation to convert the Warrants, in whole or in part and at any time or times (the “Conversion Right”), into shares of Common Stock by surrendering to the Corporation the certificate or certificates evidencing the Warrant to be converted with the form of notice of conversion attached hereto as Exhibit B duly filled in and signed. Upon exercise of the Conversion Right, the Corporation shall deliver to the Warrantholder (without payment by the holder of the Warrant of any Exercise Price) that number of shares of Common Stock which is equal to the quotient obtained by dividing (x) the value of the number of Warrants being converted at the time the Warrants are converted (determined by subtracting the aggregate Exercise Price for all such Warrants immediately prior to the conversion of the Warrants from the aggregate Current Market Price (as defined in Section 2.05) of that number of Warrant Shares purchasable upon exercise of such Warrants immediately prior to the conversion of the Warrants (taking into account all applicable adjustments pursuant to Article III) by (y) the Current Market Price of one share of Common Stock immediately prior to the conversion of the Warrants.

(c) Upon receipt of this Warrant with the Subscription Form duly executed and accompanied by payment of the aggregate Exercise Price for the Warrant Shares for which this Warrant is then being exercised (or by exercise of the Conversion Right), the Corporation shall cause to be issued certificates for the total number of whole shares of Common Stock for which this Warrant is being exercised in such denominations as are requested for delivery to the Warrantholder registered in the name of the Warrantholder or its nominee, and the Corporation shall thereupon deliver such certificates to the Warrantholder. The Warrantholder shall be deemed to be the holder of record of the shares of Common Stock issuable upon such exercise, notwithstanding that the stock transfer books of the Corporation shall then be closed or that certificates representing such shares of Common Stock shall not then be actually delivered to the Warrantholder.

(d) In case the Warrantholder shall exercise this Warrant (or exercise the Conversion Right) with respect to less than all of the Warrant Shares that may be purchased under this Warrant, the Corporation shall execute a new warrant in the form of this Warrant for the balance of such Warrant Shares and deliver such new warrant to the Warrantholder.

(e) The Corporation shall pay any and all stock transfer and similar taxes which may be payable in respect of the issue of any Warrant Shares to the Warrantholder.

Section 2.03: Reservation of Shares. The Corporation hereby agrees that it will use its best efforts so that at all times there shall be reserved for issuance and delivery upon exercise of this Warrant such number of shares of Common Stock from time to time issuable upon exercise of this Warrant.

Section 2.04: Listing. Prior to the issuance of any shares of Common Stock upon exercise of this Warrant, the Corporation shall secure the listing of such shares of Common Stock upon each national securities exchange or automated quotation system, if any, upon which shares of Common Stock are then listed (subject to official notice of issuance upon exercise of this Warrant) and shall maintain, so long as any other shares of Common Stock shall be so listed, such listing of all shares of Common Stock from time to time issuable upon the exercise of this Warrant.

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Section 2.05: Current Market Price. For the purpose of any computation under this Section, the current market price (the “Current Market Price”) per share of Common Stock of the Corporation (the “Applicable Share”) on any date shall be the daily closing price of such Applicable Share on the principal national securities exchange, on which the Applicable Shares are listed or admitted to trading or, if the Applicable Shares are not so listed, the closing asked price of such Applicable Shares on the NASDAQ National Market System if the Applicable Shares are quoted thereon. If, on any date on which computation of the Current Market Price is to be made hereunder, the Applicable Shares are not so listed or quoted on a national securities exchange or the NASDAQ National Market System, the Current Market Price shall be determined in good faith by the Board of Directors, or, if such Warrantholder disputes such determination, the Current Market Price shall be determined by an Independent Financial Expert in accordance with Section 2.06.

Section 2.06: Independent Financial Expert. To the extent that the Current Market Price is required to be determined in accordance with the last sentence of Section 2.05, an independent appraisal firm or investment bank experienced in the valuation of such securities and which is not affiliated with the Warrantholder (the “Independent Financial Expert”) shall be selected in good faith by the Warrantholder exercising the Conversion Right and approved by the Corporation (excluding those directors affiliated with the Warrantholder exercising the Conversion Right), which approval shall not be unreasonably withheld or delayed. If the Corporation and the Warrantholder exercising the Conversion Right are unable to agree on the selection of an independent appraiser within 30 days of the date when the Warrantholder exercising the Conversion Right first delivered notice in writing to the Corporation of the name of a proposed independent appraiser, then the Warrantholder exercising the Conversion Right may request the President of the American Arbitration Association to appoint an independent appraiser and such appointment shall be final and binding for purposes of determination of the Current Market Price in question. The Independent Financial Expert shall determine the Current Market Price. The determination of the Current Market Price for the Applicable Share by the Independent Financial Expert as of the date of determination shall mean the price that a willing buyer would pay to a willing seller for the Applicable Share in an arm’s length transaction, with neither party being under any immediate obligation or need to consummate the transaction, it being understood that the buyer and seller in arriving at such price in determining the value of the Applicable Share would each consider, among other factors: (a) the past and prospective earnings of the Corporation; (b) the initial public offering value of the Corporation if shares of Common Stock of the Corporation were to be offered to the public in a widely distributed initial public offering and listed on one or more major stock exchanges or quoted on the NASDAQ National Market; (c) comparable stock market valuations assuming such shares of Common Stock were publicly traded and widely distributed; and (d) the value of the Corporation in connection with an auction of the Corporation as a going concern; provided that such valuation shall exclude any minority discount or discount for lack of liquidity. The Corporation shall furnish to the Independent Financial Expert all reasonably available information requested by the Independent Financial Expert. The Current Market Price established by the Independent Financial Expert shall be final and binding with respect to each Conversion Right. The Corporation and Warrantholder shall split all fees and expenses of the Independent Financial Expert.

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ARTICLE III

ADJUSTMENT OF SHARES OF COMMON STOCK

PURCHASABLE

The number and kind of Warrant Shares shall be subject to adjustment from time to time upon the happening of certain events as provided in this Article III.

Section 3.01: Mechanical Adjustments.

(a) In case the Corporation shall at any time or from time to time after the date hereof (i) pay any dividend, or make any distribution, on the outstanding shares of Common Stock (or Common Stock Equivalents) in shares of Common Stock, (ii) subdivide the outstanding shares of Common Stock, (iii) combine the outstanding shares of Common Stock into a smaller number of shares or (iv) issue by reclassification of the shares of Common Stock any shares of capital stock of the Corporation, then and in each such case, the number and type of Warrant Shares into which this Warrant is exercisable immediately prior to such event or the record date therefor, whichever is earlier, shall be adjusted so that the Warrantholder shall be entitled to receive the number and type of shares of Common Stock which such Warrantholder would have owned or have been entitled to receive after the happening of any of the events described above, had such Warrant been converted into Common Stock immediately prior to the happening of such event or the record date therefor, whichever is earlier. An adjustment made pursuant to this Section 3.01 (a) shall become effective (x) in the case of any such dividend or distribution, immediately after the close of business on the record date for the determination of holders of shares of Common Stock entitled to receive such dividend or distribution, or (y) in the case of such subdivision, reclassification or combination, at the close of business on the day upon which such corporate action becomes effective.

(b) If the Corporation shall take a record of the holders of its Common Stock for the purpose of entitling them to receive a dividend or other distribution and shall thereafter, and before such dividend or distribution is paid or delivered to stockholders entitled thereto, legally abandon its plan to pay or deliver such dividend or distribution, then no adjustment in the number of Warrant Shares then in effect shall be made by reason of the taking of such record, and any such adjustment previously made as a result of the taking of such record shall be reversed.

(c) As used in this Section 3.01 the term “Common Stock” shall mean and include the Corporation’s authorized Common Stock, par value $.001 per share, as constituted on the date hereof, and shall also include any capital stock of any class of the Corporation thereafter authorized which shall neither be limited to a fixed sum or percentage in respect of the rights of the holders thereof to participate in dividends nor be entitled to a preference in the distribution of assets upon the voluntary or involuntary liquidation, dissolution or winding up of the Corporation.

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(d) In the case of a Sale of the Corporation or a proposed reorganization of the Corporation or a proposed reclassification of the capital stock of the Corporation (except a transaction for which provision for adjustment is otherwise made in this Section 3.01), the Warrant shall thereafter be exerciseable into the number of shares of stock or other securities or property to which a holder of the number of shares of Common Stock of the Corporation deliverable upon exercise of such Warrant would have been entitled upon such Sale of the Corporation, reorganization or reclassification; and, in any such case, appropriate adjustment shall be made in the application of the provisions, herein set forth with respect to the rights and interest thereafter of the holders of the Warrant, to the end that the provisions set forth herein (including provisions with respect to changes in and other adjustments of the applicable number of shares of stock issuable upon exercise) shall thereafter be applicable, as nearly as reasonably may be, in relation to any shares of stock or other property thereafter deliverable upon the exercise of the Warrant.

(e) Whenever the number of Warrant Shares issuable upon exercise of this Warrant is adjusted pursuant to paragraphs (a), (d) or (h) of this Section 3.01, the Exercise Price shall simultaneously be adjusted by multiplying the initial Exercise Price by a fraction, the numerator of which shall be the number of Warrant Shares initially issuable upon exercise of the Warrant (as set forth on the front page of this Warrant) by the number of Warrant Shares issuable under this Warrant, as adjusted. Notwithstanding anything in this Section 3.01 to the contrary, the Exercise Price shall not be reduced to less than the then existing par value of the Common Stock as a result of any adjustment made hereunder.

(f) No adjustment in the number of Warrant Shares shall be required unless such adjustment would require an increase or decrease of at least one Warrant Share; provided, however, that any adjustments which by reason of this paragraph (f) are not required to be made shall be carried forward and taken into account in any subsequent adjustment. All calculations under this Section 3.01 shall be made to the nearest one-thousandth of a share, as the case may be.

(g) In the event that at any time, as a result of any adjustment made pursuant to Section 3.01(a), the Warrantholder thereafter shall become entitled to receive any shares of capital stock of the Corporation other than Common Stock, thereafter the number of such other shares so receivable upon exercise of any Warrant shall be subject to adjustment from time to time in a manner and on terms as nearly equivalent as practicable to the provisions with respect to the Common Stock contained in Section 3.01(a).

(h) If any corporate action shall occur as to which the provisions of this Section 3.01 are not strictly applicable but as to which the failure to make any adjustment would adversely affect the purchase rights or value represented by the Warrants in accordance with the essential intent and principles of such Section 3.01 (which are to place the Warrantholder in a position as nearly equal as possible to the position the Warrantholder would have occupied had the Warrantholder purchased shares of Common Stock on the

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date hereof), then, in each such case, the Corporation shall appoint a firm of independent certified public accountants (which may be the regular auditors of the Corporation) to give their opinion upon the adjustment, if any, on a basis consistent with the essential intent and principles established in this Section 3.01, necessary to preserve, without dilution, the purchase rights represented by Warrants. Upon receipt of such opinion, the Corporation will promptly mail a copy thereof to Warrantholder and will make the adjustments described therein.

Section 3.02: Notices of Adjustment. Whenever the number of Warrant Shares is adjusted as herein provided, the Corporation shall prepare and deliver forthwith to the Warrantholder a certificate signed by its Chief Financial Officer, President or a Vice President, or by the Treasurer or an Assistant Treasurer or the Secretary or an Assistant Secretary, setting forth the adjusted number of shares purchasable upon the exercise of this Warrant after such adjustment, setting forth a brief statement of the facts requiring such adjustment and setting forth the computation by which adjustment was made.

Section 3.03: Form of Warrant After Adjustments. The form of this Warrant need not be changed because of any adjustments in the number or kind of the Warrant Shares, and Warrants theretofore or thereafter issued may continue to express the same price and number and kind of shares as are stated in this Warrant, as initially issued.

Section 3.04: Treatment of Warrantholder. Prior to due presentment for registration of transfer of this Warrant, the Corporation may deem and treat the Warrantholder as the absolute owner of this Warrant (notwithstanding any notation of ownership or other writing hereon) for all purposes and shall not be affected by any notice to the contrary.

ARTICLE IV

OTHER PROVISIONS RELATING TO RIGHTS OF WARRANTHOLDER

Section 4.01: No Rights as Shareholders; Notice to Warrantholders. Nothing contained in this Warrant shall be construed as conferring upon the Warrantholder the right to vote or to receive dividends or to consent or to receive notice as a shareholder in respect of any meeting of shareholders for the election of directors of the Corporation or of any other matter, or any rights whatsoever as shareholders of the Corporation. The Corporation shall give notice to the Warrantholder by certified mail if at any time prior to the expiration or exercise in full of the Warrants, any of the following events shall occur:

(a) the Corporation shall declare any dividend or distribution with respect to its capital stock;

(b) a dissolution, liquidation or winding up of the Corporation shall be proposed;

(c) a capital reorganization or reclassification of the capital stock of the Corporation; or

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(d) a Sale of the Corporation.

Such giving of notice shall be initiated at least five Business Days prior to the date fixed as a record date or effective date or the date of closing of the Corporation’s stock transfer books for the determination of the shareholders entitled to such dividend or distribution, or for the determination of the shareholders entitled to vote on such proposed capital reorganization or reclassification, merger, consolidation, transaction, sale, conveyance, dissolution, liquidation or winding up. Such notice shall specify such record date or the date of closing the stock transfer books, as the case may be.

Section 4.02: Lost, Stolen, Mutilated or Destroyed Warrants. If this Warrant is lost, stolen, mutilated or destroyed, the Corporation may, on such reasonable terms as to indemnity or otherwise as it may in its reasonable discretion impose (which shall, in the case of a mutilated Warrant, include the surrender thereof), issue a new Warrant of like denomination and tenor as, and in substitution for, this Warrant.

ARTICLE V

SPLIT-UP, COMBINATION,

EXCHANGE AND TRANSFER OF WARRANTS

Section 5.01: Split-Up, Combination, Exchange and Transfer of Warrants. Subject to the provisions of Section 5.02 hereof, this warrant may be split up, combined or exchanged for another Warrant or Warrants containing the same terms to purchase a like aggregate number of Warrant Shares. If the Warrantholder desires to split up, combine or exchange this Warrant, the Warrantholder shall make such request in writing delivered to the Corporation and shall surrender to the Corporation this Warrant and any other Warrants to be so split-up, combined or exchanged. Upon any such surrender for a split-up, combination or exchange, the Corporation shall execute and deliver to the person entitled thereto a Warrant or Warrants, as the case may be, as so requested. The Corporation shall not be required to effect any split-up, combination or exchange which will result in the issuance of a Warrant entitling the Warrantholder to purchase upon exercise a fraction of a share of Common Stock or a fractional Warrant. The Corporation may require such Warrantholder to pay a sum sufficient to cover any tax or governmental charge that may be imposed in connection with any split-up, combination or exchange of Warrants.

Section 5.02: Transfer. This Warrant and all rights hereunder may not be sold, transferred or otherwise disposed of, without the prior written consent of the Corporation.

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Section 5.03: Restrictive Legend. Each Warrant Share issued upon exercise of this Warrant shall bear a legend containing the following words:

“THE SHARES EVIDENCED BY THIS CERTIFICATE HAVE NOT BEEN REGISTERED UNDER THE SECURITIES ACT OF 1933 OR THE SECURITIES LAWS OF ANY STATE AND MAY NOT BE SOLD OR OTHERWISE DISPOSED OF EXCEPT PURSUANT TO AN EFFECTIVE REGISTRATION STATEMENT UNDER SUCH ACT AND APPLICABLE STATE SECURITIES LAWS OR AN OPINION OF COUNSEL REASONABLY ACCEPTABLE TO THE COMPANY TO THE EFFECT THAT THE TRANSACTION PURSUANT TO WHICH SUCH SHARES WILL BE OFFERED FOR SALE OR OTHERWISE DISPOSED OF IS SUBJECT TO AN APPLICABLE EXEMPTION TO THE REGISTRATION REQUIREMENTS OF SUCH ACT OR SUCH LAWS.”

The requirement that the above securities legend be placed upon certificates evidencing shares of Stock shall cease and terminate upon the earliest of the following events: (i) when such shares are transferred in a public offering registered under the Securities Act, (ii) when such shares are transferred pursuant to Rule 144 under the Securities Act or (iii) when such shares are transferred in any other transaction if the seller delivers to the Corporation an opinion of its counsel, which counsel and opinion shall be reasonably satisfactory to the Corporation, or a “no-action” letter from the staff of the Securities and Exchange Commission, in either case to the effect that such legend is no longer necessary in order to protect the Corporation against a violation by it of the Securities Act upon any sale or other disposition of such shares without registration thereunder. Upon the occurrence of such event, the requirement that the above legend regarding this Agreement be placed upon certificates evidencing shares of Stock shall cease and terminate. Upon the consummation of any event requiring the removal of a legend hereunder, the Corporation, upon the surrender of certificates containing such legend, shall, at its own expense, deliver to the holder of any such shares as to which the requirement for such legend shall have terminated, one or more new certificates evidencing such shares not bearing such legend.

ARTICLE VI

OTHER MATTERS

Section 6.01: Successors and Assigns. The terms and provisions of this Warrant shall bind and inure to the benefit of the Warrantholder and its successors and assigns.

Section 6.02: No Inconsistent Agreements. The Corporation will not on or after the date of this Warrant enter into any agreement with respect to its securities which is inconsistent with the rights granted to the Warrantholder or otherwise conflicts with the provisions hereof. The rights granted to the Warrantholder hereunder do not in any way conflict with and are not inconsistent with the rights granted to holders of the Corporation’s securities under any other agreements.

Section 6.03: Entire Agreement. This Warrant and the Exhibits hereto contain the entire agreement among the parties with respect to the subject matter hereof and supersede all prior and contemporaneous arrangements or understandings with respect thereto.

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Section 6.04: Amendments and Waivers. The terms and provisions of this Warrant, including the provisions of this sentence, may be modified or amended, or any of the provisions hereof waived, temporarily or permanently, pursuant to the written consent of the Corporation and the Warrantholder.

Section 6.05: Counterparts. This Warrant may be executed in any number of counterparts, and each such counterpart hereof, when executed and delivered to the other party, shall be deemed to be an original instrument, but all such counterparts together shall constitute but one agreement.

Section 6.06: Governing Law. This Warrant shall be governed by and construed in accordance with the laws of the Commonwealth of Pennsylvania without giving effect to the principles of conflicts of law.

Section 6.07: Notice. Any notice provided for in this Agreement shall be in writing and shall be either personally delivered or sent by facsimile or reputable overnight courier service (charges prepaid) to the Corporation at the address set forth below and to the Warrantholder at such address as the Corporation maintains on its books and records, or at such address or to the attention of such other person as the recipient party has specified by prior written notice to the sending party. Notices will be deemed to have been given hereunder when delivered personally or on receipt.

The Corporation’s address is:

Precision Therapeutics, Inc.

2516 Jane Street

Pittsburgh, PA 15203

Attention: Chief Executive Officer

All such notices, requests, consents and other communications shall be deemed to have been given when received.

Section 6.08: Severability. Whenever possible, each provision of this Warrant shall be interpreted in such manner as to be effective and valid, but if any provision of this Warrant is held to be invalid or unenforceable in any respect, such invalidity or unenforceability shall not render invalid or unenforceable any other provision of this Warrant.

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IN WITNESS WHEREOF, this Warrant Agreement has been duly executed by the Corporation under its corporate seal as of the 22nd day of August, 2003.

Exhibit A to Warrant

FORM OF SUBSCRIPTION

[To be executed only upon exercise of Warrant]

PRECISION THERAPEUTICS, INC.

The undersigned registered holder of the within Warrant hereby irrevocably exercises such Warrant for, and purchases thereunder, __________¹ shares of Common Stock covered by the within Warrant and requests that the certificates for such shares be issued in the name of, and delivered to, _____________ whose address is ________________. The undersigned herewith makes payment in full of the Exercise Price therefor (or $________ in the aggregate).

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Exhibit B to Warrant

FORM OF NOTICE OF CONVERSION

[To be executed only upon conversion of Warrant]

PRECISION THERAPEUTICS, INC.

The undersigned hereby irrevocably elects to exercise the right, represented by this Warrant certificate, to convert Warrants represented hereby into ______ shares of Common Stock in accordance with the terms hereof.

The undersigned requests that a certificate for such shares be registered in the name of _____________, whose address is ____________ and that such shares be delivered to __________________ whose address is _______________.

If said number of Warrant Shares is less than all of the shares of Common Stock purchasable hereunder, the undersigned requests that a new Warrant certificate representing the remaining balance of such shares be registered in the name of _______________, whose address is ___________________, and that such Warrant certificate be delivered to _____________, whose address is ____________.

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Bridge Warrant

The series of warrants represented by this form are substantially identical in all material respects except as to the details below. Accordingly, pursuant to Instruction 2 to Item 601(b) of Regulation S-K, we have filed the form of warrant herewith.