Exhibit 4.1

FORM OF REGISTRATION RIGHTS AGREEMENT

THIS REGISTRATION RIGHTS AGREEMENT (this “Agreement”), dated [●], 2026 (the “Agreement Effective Date”), is entered into by and among (i) Twist Bioscience Corporation, a Delaware corporation (the “Company”), and (ii) [●] (“Stockholder”). The Company and Stockholder may sometimes be referred herein individually as a “Party,” and collectively, as the “Parties.” Capitalized terms used but not defined in the Purchase Agreement (as defined below) shall have the respective meanings ascribed to such terms in the Agreement.

BACKGROUND

WHEREAS, concurrently with the execution of this Agreement, the Company and the Stockholder are parties to that Stock Purchase Agreement, of even date herewith (the “Purchase Agreement”), providing for the sale and issuance of a certain number of shares of the Company’s Common Stock, par value $0.00001 per share (the “Common Stock”), as more fully set forth in the Purchase Agreement (the “Twist Shares”). Capitalized terms used but not defined herein shall have the meaning assigned to them in the Purchase Agreement.

AGREEMENT

NOW, THEREFORE, the Parties, intending to be legally bound, hereby agree as follows:

1.             REGISTRATION RIGHTS.

(a)            The Company agrees to use commercially reasonable efforts to, within [●] ([●]) business days following [●], file with the SEC a prospectus supplement pursuant to Rule 424(b) (“Prospectus Supplement”) that constitutes part of the Twist Form S-3 or, if unavailable, a registration statement or post-effective amendment to an existing registration statement (the “Registration Statement”) covering the resale of the Twist Shares pursuant to this Agreement (such shares of Common Stock and, unless issued in a transaction registered under the Securities Act, any other equity security issued or issuable with respect to such purchased Common Stock by way of stock split, dividend, distribution, recapitalization, merger, exchange, replacement or similar event, the “Registrable Shares”); provided, that the Company’s obligations to include the Registrable Shares in the Prospectus Supplement are contingent upon Stockholder furnishing in writing to the Company such information regarding Stockholder or its permitted assigns, the securities of the Company held by Stockholder and the intended method of disposition of the Registrable Shares (which shall be limited to non-underwritten public offerings) as shall be reasonably requested by the Company to effect the registration of the Registrable Shares, and Stockholder shall execute such documents in connection with such registration as the Company may reasonably request that are customary of a selling stockholder in similar situations; provided, further that Stockholder shall not in connection with the foregoing be required to execute any lock-up or similar agreement or otherwise be subject to any contractual restriction on the ability to transfer the Registrable Shares, except as set forth in Section 1.1(d) of the Purchase Agreement. Any Registration Statement filed pursuant to this Section 1 shall be on Form S-3 (or a successor form) if the Company is eligible to use such form and shall be an automatically effective Registration Statement or supplement thereto if the Company is a “well-known seasoned issuer” (“WKSI”). In the event the Company loses WKSI eligibility at any time during the Registration Period (as defined below), the Company will (consistent with SEC C&DI 198.06) take reasonable efforts to (i) prepare and file a post-effective amendment to the Twist Form S-3 to convert such Registration Statement from an automatic shelf registration statement on Form S-3 filed in reliance on General Instruction I.D thereof to a non-automatic shelf Registration Statement on Form S-3 filed in reliance on General Instruction I.B.1 or I.B.2 thereof in order to avail itself of the 180-day grace period set forth in Rule 415(a)(5)(ii)(A) of the Securities Act and (ii) take all other actions consistent with SEC C&DI 198.06, including filing of a post-effective amendment or new Registration Statement on Form S-3 or, if the Company is no longer eligible to file on Form S-3, on Form S-1 promptly after the Company’s next Section 10(A)(3) update under the Securities Act.

(b)            At its expense, the Company shall:

(i)            except during such times as the Company is permitted hereunder to suspend the use of the prospectus forming part of a Registration Statement, use its commercially reasonable efforts to keep such registration, and any qualification, exemption or compliance under state securities laws which the Company determines to obtain, continuously effective with respect to Stockholder, and to keep the applicable Registration Statement or any subsequent shelf registration statement free of any material misstatements or omissions, until the earliest of the following: (1) Stockholder ceases to hold any Registrable Shares and (2) the date all Registrable Shares held by Stockholder may be sold without restriction under Rule 144 under the Securities Act. The period of time during which the Company is required hereunder to keep a Registration Statement effective is referred to herein as the “Registration Period”;

(ii)           during the Registration Period, promptly advise Stockholder:

(1)            when a Registration Statement or any amendment thereto has been filed with the SEC;

(2)            after it shall receive notice or obtain knowledge thereof, of the issuance by the SEC of any stop order suspending the effectiveness of any Registration Statement or the initiation of any proceedings for such purpose;

(3)            of the receipt by the Company of any notification with respect to the suspension of the qualification of the Registrable Shares included therein for sale in any jurisdiction or the initiation or threatening of any proceeding for such purpose; and

(4)            subject to the provisions in this Agreement, of the occurrence of any event that requires the making of any changes in any Registration Statement or prospectus so that, as of such date, the statements therein are not materially misleading and do not omit to state a material fact required to be stated therein or necessary to make the statements therein (in the case of a prospectus, in the light of the circumstances under which they were made) not misleading. Notwithstanding anything to the contrary set forth herein, the Company shall not, when so advising Stockholder of such events, provide Stockholder with any material, nonpublic information regarding the Company other than to the extent that providing notice to Stockholder of the occurrence of the events listed in (1) through (4) above constitutes material, nonpublic information regarding the Company;

(iii)          during the Registration Period, use its commercially reasonable efforts to obtain the withdrawal of any order suspending the effectiveness of any Registration Statement as soon as reasonably practicable;

(iv)          during the Registration Period, upon the occurrence of any event contemplated in Section 1(b)(ii)(4), except for such times as the Company is permitted hereunder to suspend the use of a prospectus forming part of a Registration Statement, use its commercially reasonable efforts to, as soon as reasonably practicable, prepare a post-effective amendment to such Registration Statement or a supplement to the related prospectus, or file any other required document so that, as thereafter delivered to purchasers of the Registrable Shares included therein, such prospectus will not include any untrue statement of a material fact or omit to state any material fact necessary to make the statements therein, in the light of the circumstances under which they were made, not misleading; (v)           during the Registration Period, use its commercially reasonable efforts to cause all Registrable Shares to be listed on the national securities exchange on which the Common Stock is then listed; and

(vi)          during the Registration Period, use its commercially reasonable efforts to allow Stockholder to review disclosure regarding Stockholder in the Prospectus Supplement or Registration Statement, as applicable.

(c)            Notwithstanding anything to the contrary in this Agreement, the Company shall be entitled to delay the filing or effectiveness of, or terminate or suspend the use of, the Registration Statement (or any prospectus therein) if (i) it determines that in order for the Registration Statement not to contain a material misstatement or omission, (1) an amendment thereto would be needed to include information that would at that time not otherwise be required in a current, quarterly or annual report under the Exchange Act, or (2) the negotiation or consummation of a transaction by the Company or its affiliates is contemplated or pending or an event has occurred, which negotiation, consummation or event that the Company reasonably believes would require additional disclosure by the Company in the Registration Statement of material information that the Company has a bona fide business purpose for keeping confidential and the non-disclosure of which in the Registration Statement would be expected, in the reasonable judgment of the Company to cause the Registration Statement to fail to comply with applicable disclosure requirements, or (ii) in the good faith judgment of the Company, such filing or effectiveness or use of such Registration Statement would require the disclosure of material non-public information concerning the Company that at the time is not, in the good faith judgment of the Company, in the best interests of the Company to disclose and is not otherwise required to be disclosed, and in either case, the Company concludes as a result to defer such filing or terminate or suspend the use of such Registration Statement (or any prospectus included therein) (each such circumstance, a “Suspension Event”); provided that the Company may not delay or suspend the use of such Registration Statement on more than four (4) occasions or for more than ninety (90) consecutive calendar days, or more than one hundred and eighty (180) total calendar days, in each case during any twelve (12) month period. Upon receipt of any written notice from the Company of the happening of any Suspension Event during the period that the Registration Statement is effective or if as a result of a Suspension Event the Registration Statement or related prospectus contains any untrue statement of a material fact or omits to state any material fact required to be stated therein or necessary to make the statements therein (in light of the circumstances under which they were made, in the case of the prospectus) not misleading, Stockholder agrees that (A) it will immediately discontinue offers and sales of the Registrable Shares under the Registration Statement (until Stockholder receives copies of a supplemental or amended prospectus that corrects the misstatement(s) or omission(s) referred to above and receives notice that any post-effective amendment has become effective or unless otherwise notified by the Company that it may resume such offers and sales) and (B) it will maintain the confidentiality of any information included in such written notice delivered by the Company unless otherwise required by law or subpoena.

(d)            If the Twist Shares are either eligible to be sold (i) pursuant to an effective Registration Statement or (ii) without restriction under, and without the Company being in compliance with the current public information requirements of, Rule 144 under the Securities Act, then at Stockholder’s written request, each of the Company and Stockholder will reasonably cooperate with the Company’s transfer agent, such that any remaining restrictive legend set forth on such Twist Shares will be removed in connection with a sale of such shares, subject to receipt from Stockholder by the Company and its transfer agent of customary representations and other documentation reasonably requested by the Company and its transfer agent in connection therewith, including, if required by the Company’s transfer agent, an opinion of counsel, in a form reasonably acceptable to its transfer agent, regarding the removal of such restrictive legends.

(e)            Following such time as Rule 144 under the Securities Act is available, with a view to making available to Stockholder the benefits of Rule 144, the Company agrees, for so long as Stockholder holds the Twist Shares purchased pursuant to the Purchase Agreement, to:

(i)            make and keep public information available, as those terms are understood and defined in Rule 144; and

(ii)           file with the SEC in a timely manner all reports and other documents required of the Company under the Securities Act and the Exchange Act so long as the Company remains subject to such requirements and the filing of such reports and other documents is required for the applicable provisions of Rule 144.

(f)            Indemnification.

(i)            the Company agrees to indemnify, to the extent permitted by applicable law, Stockholder (to the extent a seller under the Registration Statement or Prospectus Supplement, as applicable), its directors and officers and each person who controls Stockholder (within the meaning of the Securities Act), to the extent permitted by applicable law, against all losses, claims, damages, liabilities and reasonable and documented out-of-pocket expenses (including reasonable and documented outside attorneys’ fees of one law firm (and one firm of local counsel)) caused by any untrue or alleged untrue statement of material fact contained in any Registration Statement, prospectus included in any Registration Statement (“Prospectus”) or any amendment thereof or supplement thereto or any omission or alleged omission of a material fact required to be stated therein or necessary to make the statements therein (in the case of a Prospectus, in the light of the circumstances under which they were made) not misleading, except insofar as the same are caused by or contained in any information or affidavit so furnished in writing to the Company by or on behalf of Stockholder expressly for use therein.

(ii)           In connection with any Registration Statement in which Stockholder is participating, Stockholder shall furnish (or cause to be furnished) to the Company in writing such information and affidavits as the Company reasonably requests for use in connection with any such Registration Statement or Prospectus and, to the extent permitted by applicable law, shall indemnify the Company, its directors and officers and each person or entity who controls the Company (within the meaning of the Securities Act) against any losses, claims, damages, liabilities and expenses (including, without limitation, reasonable and documented outside attorneys’ fees) resulting from any untrue or alleged untrue statement of material fact contained or incorporated by reference in any Registration Statement, Prospectus or any amendment thereof or supplement thereto or any omission or alleged omission of a material fact required to be stated therein or necessary to make the statements therein (in the case of a Prospectus, in the light of the circumstances under which they were made) not misleading, but only to the extent that such untrue statement or omission is contained (or not contained in, in the case of an omission) in any information or affidavit so furnished in writing by on behalf of Stockholder expressly for use therein; provided, that the liability of Stockholder shall be several and not joint with any other investor and shall be in proportion to and limited to the net proceeds received by Stockholder from the sale of Registrable Shares giving rise to such indemnification obligation.

(iii)          Any person or entity entitled to indemnification herein shall (1) give prompt written notice to the indemnifying party of any claim with respect to which it seeks indemnification (provided that the failure to give prompt notice shall not impair any person’s or entity’s right to indemnification hereunder to the extent such failure has not prejudiced the indemnifying party) and (2) unless in such indemnified party’s reasonable judgment a conflict of interest between such indemnified and indemnifying parties may exist with respect to such claim, permit such indemnifying party to assume the defense of such claim with counsel reasonably satisfactory to the indemnified party. If such defense is assumed, the indemnifying party shall not be subject to any liability for any settlement made by the indemnified party without its consent (but such consent shall not be unreasonably withheld). An indemnifying party who is not entitled to, or elects not to, assume the defense of a claim shall not be obligated to pay the fees and expenses of more than one counsel for all parties indemnified by such indemnifying party with respect to such claim, unless in the reasonable judgment of any indemnified party a conflict of interest may exist between such indemnified party and any other of such indemnified parties with respect to such claim. No indemnifying party shall, without the consent of the indemnified party, consent to the entry of any judgment or enter into any settlement which cannot be settled in all respects by the payment of money (and such money is so paid by the indemnifying party pursuant to the terms of such settlement) or which settlement includes a statement or admission of fault and culpability on the part of such indemnified party or which does not include as an unconditional term thereof the giving by the claimant or plaintiff to such indemnified party of a release from all liability in respect to such claim or litigation.

(iv)          The indemnification provided for under this Agreement shall remain in full force and effect regardless of any investigation made by or on behalf of the indemnified party or any officer, director or controlling person or entity of such indemnified party and shall survive the transfer of the Registrable Shares purchased pursuant to the Purchase Agreement.

(v)           If the indemnification provided under this Section 1(f) from the indemnifying party is unavailable or insufficient to hold harmless an indemnified party in respect of any losses, claims, damages, liabilities and expenses referred to herein, then the indemnifying party, in lieu of indemnifying the indemnified party, shall contribute to the amount paid or payable by the indemnified party as a result of such losses, claims, damages, liabilities and expenses in such proportion as is appropriate to reflect the relative fault of the indemnifying party and the indemnified party, as well as any other relevant equitable considerations; provided, that the liability of Stockholder shall be limited to the net proceeds received by Stockholder from the sale of Registrable Shares giving rise to such indemnification obligation. The relative fault of the indemnifying party and indemnified party shall be determined by reference to, among other things, whether any action in question, including any untrue or alleged untrue statement of a material fact or omission or alleged omission to state a material fact, was made by (or not made by, in the case of an omission), or relates to information supplied by (or not supplied by, in the case of an omission), such indemnifying party or indemnified party, and the indemnifying party’s and indemnified party’s relative intent, knowledge, access to information and opportunity to correct or prevent such action. The amount paid or payable by a party as a result of the losses or other liabilities referred to above shall be deemed to include, subject to the limitations set forth in Sections 1(f)(i), (ii) and (iii) above, any legal or other fees, charges or expenses reasonably incurred by such party in connection with any investigation or proceeding. No person guilty of fraudulent misrepresentation (within the meaning of Section 11(f) of the Securities Act) shall be entitled to contribution pursuant to this Section 1(f)(v) from any person or entity who was not guilty of such fraudulent misrepresentation.

2.            MISCELLANEOUS PROVISIONS.

2.1            Expenses. Each Party shall pay the expenses and costs incurred by such Party that are incidental to the preparation of this Agreement, the performance and compliance with all agreements contained in this Agreement to be performed or complied with by such Party and the consummation of the transactions contemplated hereby.

2.2            Assignment. Neither Party may assign or otherwise transfer this Agreement or any of its rights or obligations hereunder to any person or entity without the prior written consent of the other Parties.

2.3            Entire Agreement; Amendment. This Agreement and the documents referred to herein or executed and delivered at the Closing, together with all exhibits hereto and thereto, constitute the entire agreement and understanding among the Parties with respect to the subject matter hereof. This Agreement may be amended, modified, waived, discharged, or terminated only by an instrument in writing signed by the Parties.

2.4            Governing Law and Venue. This Agreement shall be governed by and construed in accordance with the laws of the State of Delaware in all respects as such laws are applied to agreements among Delaware residents entered into and performed entirely within the State of Delaware, without giving effect to conflict of law principles thereof that would result in the application of any other laws. Each Party (i) hereby irrevocably and unconditionally submits to the jurisdiction of the Court of Chancery of the State of Delaware and to the jurisdiction of the Federal courts located in Delaware for the purpose of any suit, action or other proceeding arising out of or based upon this Agreement, (ii) agrees not to commence any suit, action or other proceeding arising out of or based upon this Agreement except in the Court of Chancery of the State of Delaware or Federal courts located in Delaware, and (iii) hereby waives, and agrees not to assert, by way of motion, as a defense, or otherwise, in any such suit, action or proceeding, any claim that it is not subject personally to the jurisdiction of the above-named courts, that its property is exempt or immune from attachment or execution, that the suit, action or proceeding is brought in an inconvenient forum, that the venue of the suit, action or proceeding is improper or that this Agreement or the subject matter hereof may not be enforced in or by such court.

2.5            WAIVER OF JURY TRIAL. EACH PARTY HEREBY WAIVES ITS RIGHTS TO A JURY TRIAL OF ANY CLAIM OR CAUSE OF ACTION BASED UPON OR ARISING OUT OF THIS AGREEMENT OR THE SUBJECT MATTER HEREOF. THE SCOPE OF THIS WAIVER IS INTENDED TO BE ALL-ENCOMPASSING OF ANY AND ALL DISPUTES THAT MAY BE FILED IN ANY COURT AND THAT RELATE TO THE SUBJECT MATTER OF THE TRANSACTIONS CONTEMPLATED HEREBY, INCLUDING, WITHOUT LIMITATION, CONTRACT CLAIMS, TORT CLAIMS (INCLUDING NEGLIGENCE), BREACH OF DUTY CLAIMS, AND ALL OTHER COMMON LAW AND STATUTORY CLAIMS. THIS SECTION HAS BEEN FULLY DISCUSSED BY EACH PARTY AND THESE PROVISIONS WILL NOT BE SUBJECT TO ANY EXCEPTIONS. EACH PARTY HEREBY FURTHER WARRANTS AND REPRESENTS THAT SUCH PARTY HAS REVIEWED THIS WAIVER WITH ITS LEGAL COUNSEL, AND THAT SUCH PARTY KNOWINGLY AND VOLUNTARILY WAIVES ITS JURY TRIAL RIGHTS FOLLOWING CONSULTATION WITH LEGAL COUNSEL.

2.6            Counterparts. This Agreement may be executed in counterparts, each of which is an original, but all of which shall constitute one instrument. Counterparts may be delivered via facsimile, electronic mail (including pdf or any electronic signature) or other transmission method and any counterpart so delivered shall be deemed to have been duly and validly delivered and be valid and effective for all purposes.

2.7            Successors and Assigns. This Agreement shall be binding upon and inure to the benefit of each Party, and such Party’s respective executors, administrators, estates, heirs, successors, and assigns.

2.8            Third Party Beneficiaries. Nothing herein, expressed, or implied, is intended or shall be construed to confer upon or give to any person or entity other than the parties hereto, any rights, remedies, or other benefits under or by reason of this Agreement.

2.9            Specific Enforcement. Notwithstanding anything to the contrary set forth herein, it is agreed and understood that monetary damages would not adequately compensate an injured Party for the breach of this Agreement by another Party, that this Agreement shall be specifically enforceable, and that any breach or threatened breach of this Agreement shall be the proper subject of a temporary or permanent injunction or restraining order. Further, each Party waives any claim or defense that there is an adequate remedy at law for such breach or threatened breach.

2.10          Attorneys’ Fees. If any action at law or in equity (including, arbitration) 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.

2.11          Severability. If one or more provisions of this Agreement are held to be unenforceable under applicable law, such provision shall be excluded from this Agreement and the balance of the Agreement shall be interpreted as if such provision were so excluded and shall be enforceable in accordance with its terms.

2.12          Notices. All notices, requests, consents and other communications hereunder will be in writing and will be given or made (and will be deemed to have been duly given or made upon receipt) by delivery in person, by overnight courier service, or by email with receipt confirmed (followed by delivery of an original via overnight courier service) to the respective Parties at the addresses indicated at the signature page hereto.

2.13          Titles and Subtitles. The titles and subtitles used in this Agreement are used for convenience only and are not to be considered in construing or interpreting this Agreement.

[Signature Pages Follow]

IN WITNESS WHEREOF, each Party has caused this Agreement to be executed and delivered as of the Agreement Effective Date.

Exhibit 5.1

Orrick, Herrington & Sutcliffe LLP The Orrick Building 405 Howard Street San Francisco, CA 94105-2669   +1 415 773 5700   orrick.com

Twist Bioscience Corporation
681 Gateway Blvd.
South San Francisco, CA 94080

Registration Statement on Form S-3 (No. 333-272428); Up to 632,328 shares of common stock

Ladies and Gentlemen:

At your request, we have examined the Prospectus Supplement (as defined below), filed with the Securities and Exchange Commission (the “Commission”) relating to the offering from time to time, pursuant to Rule 415 of the General Rules and Regulations of the Commission promulgated under the Securities Act of 1933 (the “Securities Act”), by the selling stockholders named in the Prospectus Supplement (the “Selling Securityholders”), of up to 632,328 shares of common stock, par value $0.00001 per share (the “Shares”) of Twist Bioscience Corporation, a Delaware Corporation (the “Company”). The Shares will be issued pursuant to Stock Purchase Agreements, dated as of February 11, 2026, between the Company and the Selling Securityholders (collectively, the “Stock Purchase Agreements”). The resale of the Shares is being registered pursuant to a registration statement on Form S-3 under the Securities Act, filed with the Commission on June 5, 2023 (Registration No. 333-272428) (the “Registration Statement”), a base prospectus dated June 5, 2023 included in the Registration Statement at the time it originally became effective (the “Base Prospectus”), and a prospectus supplement dated February 17, 2026 filed with the Commission pursuant to Rule 424(b) under the Act (the “Prospectus Supplement,” and together with the Base Prospectus, the “Prospectus”).

We have examined the originals, or copies identified to our satisfaction, of such corporate records of the Company, certificates of public officials, officers of the Company, and other persons, and such other documents, agreements and instruments as we have deemed relevant and necessary for the basis of our opinions hereinafter expressed. In such examination, we have assumed the following: (a) the authenticity of original documents and the genuineness of all signatures; (b) the conformity to the originals of all documents submitted to us as copies; and (c) the truth, accuracy, and completeness of the information, representations, and warranties contained in the records, documents, instruments, and certificates we have reviewed.

February 17, 2026 Page 2

Based on and subject to the foregoing, we are of the opinion that the Shares have been duly authorized and, when issued pursuant to the Stock Purchase Agreements, will be validly issued, fully paid and nonassessable.

We express no opinion as to laws other than the laws of the State of Delaware with respect to the opinion set forth above, and we express no opinion with respect to the applicability thereto, or the effect thereon, of any other laws, or as to any matters of municipal law or the laws of any local agencies within any state.

We hereby consent to the reference to us under the heading “Legal Matters” in the Prospectus and to the filing of this opinion as Exhibit 5.1 to the Registration Statement. By giving this consent, we do not admit that we are within the category of persons whose consent is required under Section 7 of the Securities Act and the rules and regulations promulgated thereunder.

Very truly yours,

/s/ Orrick, Herrington & Sutliffe LLP

ORRICK, HERRINGTON & SUTCLIFFE LLP