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How many computers can fit into a drop of water ? Udi Shapiro Ehud Shapiro
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How many computers can fit into a drop of water? Udi Shapiro Ehud Shapiro.

Dec 22, 2015

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Page 1: How many computers can fit into a drop of water? Udi Shapiro Ehud Shapiro.

How many computers can fit into a drop of water?

Udi Shapiro

Ehud Shapiro

Page 2: How many computers can fit into a drop of water? Udi Shapiro Ehud Shapiro.
Page 3: How many computers can fit into a drop of water? Udi Shapiro Ehud Shapiro.

Medicine in 2050: “Doctor in a Cell”

Programmable Computer

Molecular Input

Molecular Output

Page 4: How many computers can fit into a drop of water? Udi Shapiro Ehud Shapiro.

micronmicronin Pentium IIin Pentium II

Scaling electro and bio devices

Page 5: How many computers can fit into a drop of water? Udi Shapiro Ehud Shapiro.

E. ColiE. Coli

1 micron1 micron

micronmicronin Pentium IIin Pentium II

Scaling electro and bio devices

Page 6: How many computers can fit into a drop of water? Udi Shapiro Ehud Shapiro.

E. Coli

Page 7: How many computers can fit into a drop of water? Udi Shapiro Ehud Shapiro.

E. Coli internals

(1Mbyte)

Page 8: How many computers can fit into a drop of water? Udi Shapiro Ehud Shapiro.

Ribosomes in operation

Ribosomes translate RNA to Proteins

RNA Polymerase transcribes DNA to RNA

Page 9: How many computers can fit into a drop of water? Udi Shapiro Ehud Shapiro.

A mechanical computer

Page 10: How many computers can fit into a drop of water? Udi Shapiro Ehud Shapiro.

1122

33

4455

AA

Page 11: How many computers can fit into a drop of water? Udi Shapiro Ehud Shapiro.

BB

FrontFront BackBack

1a1a

1b1b

2a2a

2b2b3a3a

3b3b

4a4a

4b4b

5a5a

5b5b

5a5a

5b5b

4a4a4b4b

3a3a

3b3b

Page 12: How many computers can fit into a drop of water? Udi Shapiro Ehud Shapiro.

Medicine in 2050: “Doctor in a Cell”

Programmable ComputerProgrammable Computer

Page 13: How many computers can fit into a drop of water? Udi Shapiro Ehud Shapiro.
Page 14: How many computers can fit into a drop of water? Udi Shapiro Ehud Shapiro.

S0 S1

a a

b

b

A1: even number of b’s

Automaton A1 accepting inputs with an even number of b ’s

Page 15: How many computers can fit into a drop of water? Udi Shapiro Ehud Shapiro.

0 1 0 0 1 1 0 0 1 0 0 1 1 0 ............

S0,0 S0

S1,0 S1

S0,1 S1

S1,1 S0

State transition rules

Turing Machine and Finite AutomatonTuring Machine and Finite Automaton

S0 S1

1

1

00

State transition diagram

Page 16: How many computers can fit into a drop of water? Udi Shapiro Ehud Shapiro.

Example ComputationExample Computation

S0,0 S0

S1,0 S1

S0,1 S1

S1,1 S0

State transition rules

0 1 0 0 1 0 0

S0

initial state: S0

<S0, 0100100>

S1

0 1 0 0 1 0 0 <S1, 00100>

S0,1 S1

S1

0 1 0 0 1 0 0 <S1, 0100>

S1,0 S1

S1

0 1 0 0 1 0 0 <S1, 100>

S1,0 S1

0 1 0 0 1 0 0

S0

<S0, 00>

S1,1 S0

0 1 0 0 1 0 0

S0

final state: S0 <S0, 0>

S0,0 S0

0 1 0 0 1 0 0

S0

<S0, 100100>

S0,0 S0

S0 S1

1

1

00

State transition diagram

Page 17: How many computers can fit into a drop of water? Udi Shapiro Ehud Shapiro.

S0-abaaba (S0 S0)

S0-baaba (S0 S1)

S1-aaba (S1 S1)

S1-aba (S1 S1)

S1-ba (S1 S0)

S0-a (S0 S0)

S0 (final state)

The input is accepted

⏐ →⏐ a

⏐ →⏐ a

⏐ →⏐ a

⏐ →⏐ a

⏐ →⏐ b

⏐ →⏐ b

An example computation over abaaba

Page 18: How many computers can fit into a drop of water? Udi Shapiro Ehud Shapiro.

T1: S0 S0

T2: S0 S1

T3: S0 S0

T4: S0 S1

T5: S1 S0

T6: S1 S1

T7: S1 S0

T8: S1 S1

⏐ →⏐ a

⏐ →⏐ a

⏐ →⏐ a

⏐ →⏐ a

⏐ →⏐ b

⏐ →⏐ b

⏐ →⏐ b

⏐ →⏐ b

A list of all 8 possible transition rules

Page 19: How many computers can fit into a drop of water? Udi Shapiro Ehud Shapiro.

S0 S1

a a

b

A2: at most one b

b

A6: no a after b

S0 S1

a b

S0 S1

a

b

a

A4: no two consecutive b’s

S0

a

A5: only a’s

S0 S1

a a

b b

A3: at least one b

S0 S1

b a

a b

A7: starts with a and ends with b

Automata programs used to test the molecular implementation

Page 20: How many computers can fit into a drop of water? Udi Shapiro Ehud Shapiro.

Molecular realization of Finite Automata

•Input: DNAS, a rest a’

•Software: DNA

S, aFokI

•Hardware: Class-II restriction enzyme FokI, DNA Ligase, ATP as fuel

Fok I Ligase