FORM 4 Check this box if no longer subject to Section 16. Form 4 or Form 5 obligations may continue. See Instruction 1(b).

UNITED STATES SECURITIES AND EXCHANGE COMMISSION Washington, D.C. 20549 STATEMENT OF CHANGES IN BENEFICIAL OWNERSHIP OF SECURITIES Filed pursuant to Section 16(a) of the Securities Exchange Act of 1934, Section 17(a) of the Public Utility Holding Company Act of 1935 or Section 30(h) of the Investment Company Act of 1940

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(Print or Type Responses)

1. Name and Address of Reporting Person * PETERSON JEFFREY N   2. Issuer Name and Ticker or Trading Symbol PRESSURE BIOSCIENCES INC [PBIO] 5. Relationship of Reporting Person(s) to Issuer (Check all applicable) __X__ Director _____ 10% Owner _____ Officer (give title below) _____ Other (specify below) (Last) (First) (Middle) 110 WINCHESTER CT. 3. Date of Earliest Transaction (Month/Day/Year) 06/11/2018 (Street) FOSTER CITY, CA 94404 4. If Amendment, Date Original Filed(Month/Day/Year) 6. Individual or Joint/Group Filing(Check Applicable Line) _X_ Form filed by One Reporting Person ___ Form filed by More than One Reporting Person (City) (State) (Zip) Table I - Non-Derivative Securities Acquired, Disposed of, or Beneficially Owned

1.Title of Security (Instr. 3) 2. Transaction Date (Month/Day/Year) 2A. Deemed Execution Date, if any (Month/Day/Year) 3. Transaction Code (Instr. 8) 4. Securities Acquired (A) or Disposed of (D) (Instr. 3, 4 and 5) 5. Amount of Securities Beneficially Owned Following Reported Transaction(s) (Instr. 3 and 4) 6. Ownership Form: Direct (D) or Indirect (I) (Instr. 4) 7. Nature of Indirect Beneficial Ownership (Instr. 4) Code V Amount (A) or (D) Price

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Table II - Derivative Securities Acquired, Disposed of, or Beneficially Owned
(e.g., puts, calls, warrants, options, convertible securities)

1. Title of Derivative Security (Instr. 3)

2. Conversion or Exercise Price of Derivative Security

3. Transaction Date (Month/Day/Year)

3A. Deemed Execution Date, if any (Month/Day/Year)

4. Transaction Code (Instr. 8)

5. Number of Derivative Securities Acquired (A) or Disposed of (D) (Instr. 3, 4, and 5)

6. Date Exercisable and Expiration Date (Month/Day/Year)

7. Title and Amount of Underlying Securities (Instr. 3 and 4)

8. Price of Derivative Security (Instr. 5)

9. Number of Derivative Securities Beneficially Owned Following Reported Transaction(s) (Instr. 4)

10. Ownership Form of Derivative Security: Direct (D) or Indirect (I) (Instr. 4)

11. Nature of Indirect Beneficial Ownership (Instr. 4)

Code

V

(A)

(D)

Date Exercisable

Expiration Date

Title

Amount or Number of Shares

SERIES AA CONVERTIBLE PREFERRED STOCK

$ 2.5

06/11/2018

J

38.5

06/11/2018

06/11/2019

COMMON STOCK

38,500

$ 2,500

38.5

D

COMMON STOCK WARRANT

$ 3.5

06/11/2018

J

38,500

06/11/2018

06/11/2023

COMMON STOCK

38,500

(1)

38,500

D

COMMON STOCK WARRANT

$ 3.5

06/11/2018

J

2,500

03/31/2016(1)

03/31/2021

COMMON STOCK

2,500

(1)

2,500

D

Reporting Owners

Reporting Owner Name / Address	Relationships
	Director	10% Owner	Officer	Other
PETERSON JEFFREY N 110 WINCHESTER CT. FOSTER CITY, CA 94404	X

Signatures

/s/ Jeffrey N. Peterson		06/13/2018
**Signature of Reporting Person		Date

Explanation of Responses:

*	If the form is filed by more than one reporting person, see Instruction 4(b)(v).
**	Intentional misstatements or omissions of facts constitute Federal Criminal Violations. See 18 U.S.C. 1001 and 15 U.S.C. 78ff(a).
(1)	On June 11, 2018, Pressure BioSciences, Inc. (the "Issuer") entered into a letter agreement with Mr. Peterson (the "Reporting Person"). The Reporting Person previously held a convertible debenture with a face value of $46,200 (the "Debenture") and warrants to purchase common stock (the "Debenture Warrants"). Pursuant to the letter agreement, the Reporting Person agreed to convert the principal due to him pursuant to the Debenture into shares of Series AA Convertible Preferred Stock with a conversion price of $2.50 per share. The Reporting Person was also: (a) issued amended Debenture Warrants (originally issued on March 31, 2016) such that the exercise price is now $3.50 per share; and (b) issued a new warrant with an exercise price of $3.50 per share to purchase such number of shares of common stock as equal 100% of the number of shares of common stock issuable upon conversion of the Series AA Convertible Preferred Stock shares received as a result of the Debenture conversion.

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