Document:

Exhibit 10.5

 

February 15, 2021

 

Medicus Sciences Acquisition Corp. 

 152 West 57th Street, Floor 20

New York, New York 10019

 

Re: Initial Public
Offering

 

Ladies and Gentlemen:

 

This letter (this “Letter Agreement”)
is being delivered to you in accordance with the Underwriting Agreement (the “Underwriting Agreement”)
entered into by and between Medicus Sciences Acquisition Corp., a Cayman Islands exempted company (the “Company”)
and Maxim Group LLC, as representative (the “Representative”) of the several underwriters (the “Underwriters”),
relating to an underwritten initial public offering (the “Public Offering”) of 9,200,000 of the Company’s
units (including 1,200,000 units that may be purchased pursuant to the Underwriters’ option to purchase additional units,
the “Units”), each unit consisting of (i) one Class A ordinary share of the Company, par value $0.0001
per share (collectively, the “Ordinary Shares”), (ii) one-ninth of one redeemable warrant (the “outstanding
redeemable warrants”) and (iii) the contingent right to receive, in certain circumstances, following the initial
business combination redemption time, at least two-ninths of one redeemable warrant (the “distributable redeemable
warrants” and, together with the outstanding redeemable warrants, the “Warrants”), each
whole Warrant entitling the holder thereof to purchase one Ordinary Share at a price of $11.50 per share, subject to adjustment.
The Units will be sold in the Public Offering pursuant to a registration statement on Form S-1 and a prospectus (the “Prospectus”)
filed by the Company with the U.S. Securities and Exchange Commission (the “Commission”). Certain capitalized
terms used herein are defined in paragraph 1 hereof.

 

In order to induce the Company and the
Underwriters to enter into the Underwriting Agreement and to proceed with the Public Offering and for other good and valuable consideration,
the receipt and sufficiency of which are hereby acknowledged, Medicus Sciences Holdings LLC (the “Sponsor”)
and each of the undersigned (each, an “Insider” and, collectively, the “Insiders”)
hereby agree with the Company as follows:

 

1. Definitions. As used herein,
(i) “Business Combination” shall mean a merger, share exchange, asset acquisition, share purchase, reorganization
or similar business combination with one or more businesses or entities; (ii) “Founder Shares” shall
mean the 2,323,000 Class B ordinary shares of the Company, par value $0.0001 per share, outstanding prior to the consummation
of the Public Offering; (iii) “Private Placement Warrants” shall mean the warrants to purchase up to
4,755,556 Ordinary Shares of the Company (or 5,022,222
Ordinary Shares of the Company if the Underwriters’ option to purchase additional units is exercised in full) that the Sponsor
and the Representative have agreed to purchase for an aggregate purchase price of $4,280,000
(or up to $4,520,000 if the Underwriters’ option to purchase additional units is exercised
in full), or $0.90 per Warrant, in a private placement that shall close simultaneously with the consummation of the Public Offering;
(iv) “Public Shareholders” shall mean the holders of Ordinary Shares included in the Units issued in
the Public Offering; (v) “Public Shares” shall mean the Ordinary Shares included in the Units issued
in the Public Offering; (vi) “Trust Account” shall mean the trust account into which a portion of the
net proceeds of the Public Offering and the sale of the Private Placement Warrants shall be deposited; (vii) “Transfer”
shall mean the (a) sale of, offer to sell, contract or agreement to sell, hypothecate, pledge, grant of any option to purchase
or otherwise dispose of or agreement to dispose of, directly or indirectly, or establishment or increase of a put equivalent position
or liquidation with respect to or decrease of a call equivalent position within the meaning of Section 16 of the Securities Exchange
Act of 1934, as amended, and the rules and regulations of the Commission promulgated thereunder with respect to, any security,
(b) entry into any swap or other arrangement that transfers to another, in whole or in part, any of the economic consequences of
ownership of any security, whether any such transaction is to be settled by delivery of such securities, in cash or otherwise,
or (c) public announcement of any intention to effect any transaction specified in clause (a) or (b); and (viii) “Charter”
shall mean the Company’s Amended and Restated Memorandum and Articles of Association, as the same may be amended from time
to time.

 

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2. Representations and Warranties.

 

(a) The Sponsor and each Insider, with
respect to itself, herself or himself, represent and warrant to the Company that it, she or he has the full right and power, without
violating any agreement to which it, she or he is bound (including, without limitation, any non-competition or non-solicitation
agreement with any employer or former employer), to enter into this Letter Agreement, as applicable, and to serve as an officer
of the Company and/or a director on the Company’s Board of Director (the “Board”), as applicable,
and each Insider hereby consents to being named in the Prospectus, road show and any other materials as an officer and/or director
of the Company, as applicable.

 

(b) Each Insider represents and warrants,
with respect to herself or himself, that such Insider’s biographical information furnished to the Company (including any
such information included in the Prospectus) is true and accurate in all material respects and does not omit any material information
with respect to such Insider’s background. The Insider’s questionnaire furnished to the Company is true and accurate
in all material respects. Each Insider represents and warrants that such Insider is not subject to or a respondent in any legal
action for, any injunction, cease-and-desist order or order or stipulation to desist or refrain from any act or practice relating
to the offering of securities in any jurisdiction; such Insider has never been convicted of, or pleaded guilty to, any crime (i) involving
fraud, (ii) relating to any financial transaction or handling of funds of another person, or (iii) pertaining to any
dealings in any securities and such Insider is not currently a defendant in any such criminal proceeding; and such Insider has
never been suspended or expelled from membership in any securities or commodities exchange or association or had a securities or
commodities license or registration denied, suspended or revoked.

 

3. Business Combination Vote. It
is acknowledged and agreed that the Company shall not enter into a definitive agreement regarding a proposed Business Combination
without the prior consent of the Sponsor. The Sponsor and each Insider, with respect to itself or herself or himself, agrees that
if the Company seeks shareholder approval of a proposed initial Business Combination, then in connection with such proposed initial
Business Combination, it, she or he, as applicable, shall vote all Founder Shares and any Public Shares held by it, her or him,
as applicable, in favor of such proposed initial Business Combination (including any proposals recommended by the Board in connection
with such Business Combination) and not redeem any Public Shares held by it, her or him, as applicable, in connection with such
shareholder approval.

 

4. Failure to Consummate a Business
Combination; Trust Account Waiver.

 

(a) The Sponsor and each Insider hereby
agree, with respect to itself, herself or himself, that in the event that the Company fails to consummate its initial Business
Combination within the time period set forth in the Charter, the Sponsor and each Insider shall take all reasonable steps to cause
the Company to (i) cease all operations except for the purpose of winding up; (ii) as promptly as reasonably possible but not more
than 10 business days thereafter, redeem 100% of the Public Shares, at a per-share price, payable in cash, equal to the aggregate
amount then on deposit in the Trust Account, including interest earned on the funds held in the Trust Account and not previously
release to the Company to pay income taxes, if any (less up to $100,000 of interest to pay dissolution expenses), divided by the
number of then outstanding Public Shares, which redemption will completely extinguish Public Shareholders’ rights as shareholders
(including the right to receive further liquidation distributions, if any); and (iii) as promptly as reasonably possible following
such redemption, subject to the approval of the Company’s remaining shareholders and the Board, liquidate and dissolve, subject
in the case of clauses (ii) and (iii) to the Company’s obligations under Cayman Islands law to provide for claims of creditors
and in all cases subject to the other requirements of applicable law. The Sponsor and each Insider agree not to propose any amendment
to the Charter (i) that would modify the substance or timing of the Company’s obligation to provide holders of the Public
Shares the right to have their shares redeemed in connection with an initial Business Combination or to redeem 100% of the Public
Shares if the Company does not complete an initial Business Combination within the required time period set forth in the Charter
or (ii) with respect to any provision relating to the rights of holders of Public Shares unless the Company provides its Public
Shareholders with the opportunity to redeem their Public Shares upon approval of any such amendment at a per-share price, payable
in cash, equal to the aggregate amount then on deposit in the Trust Account, including interest earned on the funds held in the
Trust Account and not previously released to the Company to pay taxes, if any, divided by the number of then-outstanding Public
Shares.

 

 (b) The Sponsor and each
Insider, with respect to itself, herself or himself, acknowledges that it, she or he has no right, title, interest or claim
of any kind in or to any monies held in the Trust Account or any other asset of the Company as a result of any liquidation of
the Company with respect to the Founder Shares held by it, her or him, if any. The Sponsor and each of the Insiders hereby
further waive, with respect to any Founder Shares and Public Shares held by it, her or him, as applicable, any redemption
rights it, she or he may have in connection with the consummation of a Business Combination, including, without limitation,
any such rights available in the context of a shareholder vote to approve such Business Combination or a shareholder vote to
approve an amendment to the Charter (i) that would modify the substance or timing of the Company’s obligation to
provide holders of the Public Shares the right to have their shares redeemed in connection with an initial Business
Combination or to redeem 100% of the Public Shares if the Company has not consummated an initial Business Combination within
the time period set forth in the Charter or (ii) with respect to any provision relating to the rights of holders of Public
Shares (although the Sponsor and the Insiders shall be entitled to liquidation rights with respect to any Public Shares they
hold if the Company fails to consummate a Business Combination within the required time period set forth in the Charter).

 

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5. Lock-up; Transfer Restrictions.

 

(a) The Sponsor and the Insiders agree
that they shall not Transfer any Founder Shares (the “Founder Shares Lock-up”) until the earliest of
(A) one year after the completion of an initial Business Combination and (B) the date following the completion of an initial Business
Combination on which the Company completes a liquidation, merger, share exchange or other similar transaction that results in all
of the Company’s shareholders having the right to exchange their Ordinary Shares for cash, securities or other property (the
 “Founder Shares Lock-up Period”). Notwithstanding the foregoing, if, subsequent to a Business Combination,
the closing price of the Ordinary Shares equals or exceeds $12.00 per share (as adjusted for share sub-divisions, share capitalizations,
share consolidations, reorganizations, recapitalizations and the like) for any 20 trading days within a 30-trading day period commencing
at least 150 days after the Company’s initial Business Combination, the Founder Shares shall be released from the Founder
Shares Lock-up.

 

(b) The Sponsor and Insiders agree that
they shall not effectuate any Transfer of Private Placement Warrants or Ordinary Shares underlying such warrants until 30 days
after the completion of an initial Business Combination.

 

(c) Notwithstanding the provisions set
forth in paragraphs 5(a) and (b), Transfers of the Founder Shares, Private Placement Warrants and Ordinary Shares
underlying the Private Placement Warrants are permitted (a) to the Company’s officers or directors, any affiliates or family
members of any of the Company’s officers or directors, any members or partners of the Sponsor or its affiliates, any affiliates
of the Sponsor or any employees of such affiliates; (b) in the case of an individual, by gift to a member of one of the individual’s
immediate family or to a trust, the beneficiary of which is a member of the individual’s immediate family, an affiliate of
such person or to a charitable organization; (c) in the case of an individual, by virtue of laws of descent and distribution upon
death of the individual; (d) in the case of an individual, pursuant to a qualified domestic relations order; (e) by private sales
or transfers made in connection with the consummation of a Business Combination at prices no greater than the price at which the
Founder Shares, Private Placement Warrants or Ordinary Shares, as applicable, were originally purchased; (f) by virtue of the Sponsor’s
organizational documents upon liquidation or dissolution of the Sponsor; (g) to the Company for no value for cancellation in connection
with the consummation of an initial Business Combination; (h) in the event of the Company’s liquidation prior to the completion
of a Business Combination; or (i) in the event of completion of a liquidation, merger, share exchange or other similar transaction
which results in all of the Company’s Public Shareholders having the right to exchange their Ordinary Shares for cash, securities
or other property subsequent to the completion of an initial Business Combination; provided, however, that in the
case of clauses (a) through (f) these permitted transferees must enter into a written agreement agreeing to be bound by these transfer
restrictions and the other restrictions contained in this Letter Agreement.

 

(d) During the period commencing on the
effective date of the Underwriting Agreement and ending 180 days after such date, the Sponsor and each Insider shall not, without
the prior written consent of the Representative, Transfer any Units, Ordinary Shares, Warrants or any other securities convertible
into, or exercisable or exchangeable for, Ordinary Shares held by it, her or him, as applicable, subject to certain exceptions
enumerated in Section [6(h)] of the Underwriting Agreement.

 

6. Remedies. The Sponsor and
each of the Insiders hereby agree and acknowledge that (i) each of the Underwriters and the Company would be irreparably
injured in the event of a breach by the Sponsor or such Insider of its, her or his obligations, as applicable under paragraphs
3, 4, 5, 7, 10 and 11, (ii) monetary damages may not be an adequate remedy for such
breach and (iii) the non-breaching party shall be entitled to injunctive relief, in addition to any other remedy that such
party may have in law or in equity, in the event of such breach.

 

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7. Payments by the Company.
Except as disclosed in the Prospectus, neither the Sponsor nor any affiliate of the Sponsor nor any director or officer of the
Company nor any affiliate of the officers shall receive from the Company any finder’s fee, reimbursement, consulting fee,
monies in respect of any payment of a loan or other compensation prior to, or in connection with any services rendered in order
to effectuate, the consummation of the Company’s initial Business Combination (regardless of the type of transaction that
it is).

 

8. Director and Officer Liability Insurance.
The Company will maintain an insurance policy or policies providing directors’ and officers’ liability insurance, and
the Insiders shall be covered by such policy or policies, in accordance with its or their terms, to the maximum extent of the coverage
available for any of the Company’s directors or officers.

 

9. Termination. This Letter Agreement
shall terminate on the earlier of (i) the expiration of the Founder Shares Lock-up Period and (ii) the liquidation of the Company.

 

10. Indemnification. In the event
of the liquidation of the Trust Account upon the failure of the Company to consummate its initial Business Combination within the
time period set forth in the Charter, the Sponsor (the “Indemnitor”) agrees to indemnify and hold harmless
the Company against any and all loss, liability, claim, damage and expense whatsoever (including, but not limited to, any and all
legal or other expenses reasonably incurred in investigating, preparing or defending against any litigation, whether pending or
threatened) to which the Company may become subject as a result of any claim by (i) any third party for services rendered or products
sold to the Company (except for the Company’s independent auditors) or (ii) any prospective target business with which the
Company has discussed entering into a transaction agreement (a “Target”); provided, however,
that such indemnification of the Company by the Indemnitor (x) shall apply only to the extent necessary to ensure that such claims
by a third party for services rendered or products sold to the Company or a Target do not reduce the amount of funds in the Trust
Account to below the lesser of (i) $10.00 per Public Share and (ii) the actual amount per Public Share held in the Trust Account
as of the date of the liquidation of the Trust Account if less than $10.00 per Public Share due to reductions in the value of the
trust assets, in each case net of interest that may be withdrawn to pay the Company’s tax obligations, (y) shall not apply
to any claims by a third party or Target who executed a waiver of any and all rights to the monies held in the Trust Account (whether
or not such waiver is enforceable) and (z) shall not apply to any claims under the Company’s indemnity of the Underwriters
against certain liabilities, including liabilities under the Securities Act of 1933, as amended. The Indemnitor shall have the
right to defend against any such claim with counsel of its choice reasonably satisfactory to the Company if, within 15 days following
written receipt of notice of the claim to the Indemnitor, the Indemnitor notifies the Company in writing that it shall undertake
such defense.

 

11. Forfeiture of Founder Shares.
To the extent that the Underwriters do not exercise their option to purchase additional Units within 45 days from the date of the
Prospectus in full (as further described in the Prospectus), the Sponsor agrees to automatically surrender to the Company for no
consideration, for cancellation at no cost, an aggregate number of Founder Shares so that the number of Founder Shares will equal
of 20% of the sum of the total number of Ordinary Shares and Founder Shares outstanding at such time. The Sponsor and Insiders
further agree that to the extent that the size of the Public Offering is increased or decreased, the Company will effect a share
capitalization or a share repurchase, as applicable, with respect to the Founder Shares immediately prior to the consummation of
the Public Offering in such amount as to maintain the number of Founder Shares at 20% of the sum of the total number of Ordinary
Shares and Founder Shares outstanding at such time.

 

12. Entire Agreement. This Letter
Agreement constitutes the entire agreement and understanding of the parties hereto in respect of the subject matter hereof and
supersedes all prior understandings, agreements, or representations by or among the parties hereto, written or oral, to the extent
they relate in any way to the subject matter hereof or the transactions contemplated hereby. This Letter Agreement may not be changed,
amended, modified or waived (other than to correct a typographical error) as to any particular provision, except by a written instrument
executed by all parties hereto.

 

13. Assignment. No party
hereto may assign either this Letter Agreement or any of its rights, interests, or obligations hereunder without the prior
written consent of the other parties. Any purported assignment in violation of this paragraph shall be void and ineffectual
and shall not operate to transfer or assign any interest or title to the purported assignee. This Letter Agreement shall be
binding on the Sponsor, each of the Insiders and each of their respective successors, heirs, personal representatives and
assigns and permitted transferees.

 

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14. Counterparts. This Letter Agreement
may be executed in any number of original or facsimile counterparts, and each of such counterparts shall for all purposes be deemed
to be an original, and all such counterparts shall together constitute but one and the same instrument.

 

15. Effect of Headings. The paragraph
headings herein are for convenience only and are not part of this Letter Agreement and shall not affect the interpretation thereof.

 

16. Severability. This Letter Agreement
shall be deemed severable, and the invalidity or unenforceability of any term or provision hereof shall not affect the validity
or enforceability of this Letter Agreement or of any other term or provision hereof. Furthermore, in lieu of any such invalid or
unenforceable term or provision, the parties hereto intend that there shall be added as a part of this Letter Agreement a provision
as similar in terms to such invalid or unenforceable provision as may be possible and be valid and enforceable.

 

17. Governing Law. This Letter Agreement
shall be governed by and construed and enforced in accordance with the laws of the State of New York, without giving effect to
conflicts of law principles that would result in the application of the substantive laws of another jurisdiction. The parties hereto
(i) all agree that any action, proceeding, claim or dispute arising out of, or relating in any way to, this Letter Agreement shall
be brought and enforced in the courts of New York City, in the State of New York, and irrevocably submit to such jurisdiction and
venue, which jurisdiction and venue shall be exclusive, and (ii) waive any objection to such exclusive jurisdiction and venue or
that such courts represent an inconvenient forum.

 

18. Notices. Any notice, consent
or request to be given in connection with any of the terms or provisions of this Letter Agreement shall be in writing and shall
be sent by express mail or similar private courier service, by certified mail (return receipt requested), by hand delivery or facsimile
transmission.

 

[Signature Page Follows]

 

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	 	Sincerely,
	 	 	 
	                                     	
        Medicus
        Sciences Holdings LLC

        By: Structure Alpha LLC, its managing member

        By: Sio Capital Management, LLC, its investment manager

 

	 	By:	 /s/ Michael Castor
	                                    	Name: 	Michael Castor
	 	Title:	Managing Member

 

	 	By:	 /s/ Michael Castor 
	                                     	Name: 	Michael Castor

 

	                                     	By:	 /s/ Jacob Gottlieb
	                                     	Name:	 Jacob Gottlieb

 

	 	By:	 /s/ Eric Cheng
	                                     	Name: 	Eric Cheng

 

	 	By:	 /s/ Judah Drillick
	                                     	Name: 	Judah Drillick

 

	 	By:	 /s/ Kenneth Berkovitz
	                                     	Name: 	Kenneth Berkovitz
	 	 	 
	 	By:	 /s/ Christopher Kaster
	                                     	Name:	Christopher Kaster

 

	                                     	By:	 /s/ Ross Levine
	 	Name: 	Ross Levine

 

Acknowledged and Agreed:

 

Medicus
Sciences Acquisition Corp.

 

	By:	 /s/ Michael Castor	 
	 	Name: 	Michael Castor	                              
	 	Title:	Chief Executive Officer	 

 

    6Exhibit 10.6

 

Medicus Sciences Acquisition Corp.

152 West 57th Street, Floor 20

New York, New York 10019

 

February 15, 2021

 

Medicus Sciences Holdings LLC

152 West 57th Street, Floor 20

New York, New York 10019

Attn: Michael Castor

 

Re: Administrative
Support Agreement

 

Ladies and Gentlemen:

 

This letter agreement
by and between Medicus Sciences Acquisition Corp. (the “Company”) and Medicus Sciences Holdings LLC (“MSH”),
dated as of the date hereof, will confirm our agreement that, commencing on the date the securities of the Company are first listed
on The Nasdaq Capital Market (the “Listing Date”), pursuant to a Registration Statement on Form S-1 and prospectus
filed with the U.S. Securities and Exchange Commission (the “Registration Statement”) and continuing until the earlier
of the consummation by the Company of an initial business combination or the Company’s liquidation (in each case as described
in the Registration Statement) (such earlier date hereinafter referred to as the “Termination Date”):

 

(i) MSH shall make
available, or cause to be made available, to the Company, at 152 West 57th Street, Floor 20, New York, New York 10019 (or any successor
location of MSH), certain office space, utilities and secretarial and administrative support as may be reasonably required by the
Company. In exchange therefor, the Company shall pay MSH the sum of $10,000 per month on the Listing Date and continuing monthly
thereafter until the Termination Date; and

 

(ii) MSH hereby irrevocably
waives any and all right, title, interest, causes of action and claims of any kind as a result of, or arising out of, this letter
agreement (each, a “Claim”) in or to, and any and all right to seek payment of any amounts due to it out of, the trust
account established for the benefit of the public shareholders of the Company and into which substantially all of the proceeds
of the Company’s initial public offering will be deposited (the “Trust Account”) as a result of, or arising out
of, this letter agreement, and hereby irrevocably waives any Claim it may have in the future, which Claim would reduce, encumber
or otherwise adversely affect the Trust Account or any monies or other assets in the Trust Account, and further agrees not to seek
recourse, reimbursement, payment or satisfaction of any Claim against the Trust Account or any monies or other assets in the Trust
Account for any reason whatsoever.

 

This letter agreement
constitutes the entire agreement and understanding of the parties hereto in respect of its subject matter and supersedes all prior
understandings, agreements, or representations by or among the parties hereto, written or oral, to the extent they relate in any
way to the subject matter hereof or the transactions contemplated hereby.

 

This letter agreement
may not be amended, modified or waived as to any particular provision, except by a written instrument executed by the parties hereto.

 

No party hereto may
assign either this letter agreement or any of its rights, interests, or obligations hereunder without the prior written approval
of the other party. Any purported assignment in violation of this paragraph shall be void and ineffectual and shall not operate
to transfer or assign any interest or title to the purported assignee.

 

This letter agreement
constitutes the entire relationship of the parties hereto, and this letter agreement and any litigation between the parties (whether
grounded in contract, tort, statute, law or equity) shall be governed by, construed in accordance with, and interpreted pursuant
to the laws of the State of New York, without giving effect to its choice of law principles.

 

[Signature Page Follows]

 

     

     

    

 

	 	Very truly yours,
	 	 
	 	MEDICUS SCIENCES ACQUISITION CORP.
	 	 	 
	 	By:	/s/
    Michael castor
	 	 	Name:	Michael Castor
	 	 	Title:	Chief Executive Officer

 

AGREED TO AND ACCEPTED BY:

 

MEDICUS SCIENCES HOLDINGS LLC

By: Structure Alpha LLC, its managing member

By: Sio Capital Management, LLC, its investment manager

 

	By:	/s/ Michael Castor	 
	 	Name:	Michael Castor	 
	 	Title:  	Managing Member 	 

 

[Signature Page to Administrative Support
Agreement]

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