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### Writing and Compiling Code into Biochemistry

Example: FIR FilterExample: FIR FilterExample: FIR Filter

Marc Riedel

Assistant Professor, Electrical and Computer Engineering Graduate Faculty, Biomedical Informatics and Computational BiologyUniversity of Minnesota

PSB ─ Kona, Hawaii, Jan. 7, 2010

KeshabParhi

Distinguished McKnightUniversity Professor; Edgar F. Johnson Professor;Electrical & Computer Engineering University of Minnesota

Adam Shea

Brian Fett

StudentsElectrical & Computer Engineering University of Minnesota

Who is this guy?

- Most of the cells in his body are not his own!
- Most of the cells in his body are not even human!
- Most of the DNA in his body isalien!

“Minnesota Farmer”

Who is this guy?

He’s a human-bacteria hybrid:

- 100 trillion bacterial cells of at least 500 different types inhabit his body.

[like all of us]

vs.

- only 1 trillion human cells of 210 different types.

“Minnesota Farmer”

Who is this guy?

He’s a human-bacteria hybrid:

- 100 trillion bacterial cells of at least 500 different types inhabit his body.

[like all of us]

vs.

- only 1 trillion human cells of 210 different types.

“Minnesota Farmer”

“E. coli, a self-replicating object only a thousandth of a millimeter in size, can swim 35 diameters a second, taste simple chemicals in its environment, and decide whether life is getting better or worse.”

– Howard C. Berg

About 3 pounds of bacteria!

We should put these critters to work…

“Stimulus, response! Stimulus response! Don’t you ever think!”

Synthetic Biology

- Positioned as an engineering discipline.
- “Novel functionality through design”.
- Repositories of standardized parts.

- Driven by experimental expertise in particular domains of biology.
- Gene-regulation, signaling, metabolism, protein structures …

Biochemistry in a Nutshell

Nucleotides:

DNA: string of n nucleotides (n ≈ 109)

... ACCGTTGAATGACG...

Amino acid: coded by a sequence of 3 nucleotides.

Proteins: produced from a sequence of m amino acids (m ≈ 103) called a “gene”.

Biochemical Reactions

+

+

+

Relative rates or (reaction propensities):

slow

medium

fast

Discrete chemical kinetics; spatial homogeneity.

f

(

r

)

=

1

Mario

b

f

(

g

)

=

2

Luigi

[nearly]Rate Independent Biochemical Computation

Biochemical rules are inherently parallel.

Sequentialize?

Step 1:

M1

then

Step 2:

M2

Module Locking

slow

slow

slow

+

slow

Sequentialize computation

with only two rates:

“fast” and “slow”.

slow

+

+

fast

+

Lock phases or modules with keys.

Keys are generated by keysmiths; but indicators consume keysmiths.

Two-phase protocol to ensure only one type of key is present.

Synthesis

SPICE

Register Level Design

Integrated Circuits

Design Automation forBehavioral Specification(e.g., DSP function)

Structural Description

(e.g., memory and functional units)

Circuit-Level Description

(e.g., NAND2 and D flip-flops)

waveforms

Synthesis

SPICE

Register Level Design

Verilog

Elements of

Register-basedBiochemical computation

Brian’s Automated ModularBiochemical Instantiator

Biochemistry

Integrated Circuits

Design Automation forBehavioral Specification(e.g., DSP function)

Structural Description

(e.g., memory and functional units)

Biochemical Netlist

(e.g., Proteins, Enzymes)

Biochemical

Synthesis

STA Engine

SSA Engine

waveforms

“Stochastic Transient Analysis of Biochemical Systems”

Example: FIR Filter

Two-Tap Moving-Average Filter:

module MA(X, Y);

input X;

output Y;

reg Xn;

always

begin

Y = (1/2 * X) +

(1/2 * Xn);

Xn = X;

end

endmodule

Example: FIR Filter

module MA(X, Y);

input X;

output Y;

reg Xn;

always

begin

Y = (1/2 * X) +

(1/2 * Xn);

Xn = X;

end

endmodule

Example: FIR Filter

module MA(X, Y);

input X;

output Y;

reg Xn;

always

begin

Y = (1/2 * X) +

(1/2 * Xn);

Xn = X;

end

endmodule

Example: FIR Filter

module MA(X, Y);

input X;

output Y;

reg Xn;

always

begin

Y = (1/2 * X) +

(1/2 * Xn);

Xn = X;

end

endmodule

module MA(X, Y);

input X;

output Y;

reg Xn;

always

begin

Y = (1/2 * X) +

(1/2 * Xn);

Xn = X;

end

endmodule

module MA(X, Y);

input X;

output Y;

reg Xn;

always

begin

Y = (1/2 * X) +

(1/2 * Xn);

Xn = X;

end

endmodule

module MA(X, Y);

input X;

output Y;

reg Xn;

always

begin

Y = (1/2 * X) +

(1/2 * Xn);

Xn = X;

end

endmodule

Example: FIR Filter

Two-Tap Moving-Average Filter:

Example: IIR Filter

Biquad versatile infinite-impulse responses filter:

Example: IIR Filter

Biquad versatile infinite-impulse responses filter:

+

k2

+

k3

+

Stochastic Kinetics- Its rate.
- The quantities of its reactants.

The probability that a given reaction is the next to fire is proportional to:

See D. Gillespie, “Stochastic Chemical Kinetics”, 2006.

Reactions

Synthesizing Biological Computationinputs

computation

outputs

Molecular Triggers

Molecular Products

Biological Computation at the Populational Level

How can we control the quantity of molecular product at the populational level?

Synthesizing Stochasticity

Engineer a probabilistic response in each cell.

product

with Prob.0.3

trigger

product

with Prob.0.7

Biological Computation at the Populational Level

Obtain a fractional response.

Discussion

Synthesize a design for a precise, robust, programmable probability distribution on outcomes – for arbitrary types and reactions.

Computational Chemical Design

vis-a-vis

Technology-Independent Logic Synthesis

Experimental Design

vis-a-vis

Technology Mapping in Circuit Design

- Implement design by selecting specific types and reactions – say from “toolkit”.

DNA Strand Displacement

X1

X2

+

X3

Erik Winfree’s group at Caltech: “DNA as a Universal Substrate for Chemical Kinetics.”

Methods and CAD tools for generating nearly rate independent biochemical netlists for: nearly any memoryless function (e.g., curve-fitting).

Discussion

Where are we?

- Methods for generating any register-to-register computation (e.g., DSP functions).

Where are we headed?

- A technology-independent biochemical CPU.

MARCO (SRC/DoD) Contract 2003-NT-1107

CAREER Award 0845650

Biomedical Informatics & Computational BiologyUMN / Mayo Clinic / IBM

Blue Gene DevelopmentGroup. Rochester, MN

R2

R3

Playing by the Rules

Stochastic Chemical Kinetics

The probability that a given reaction is the next to fire is proportional to:

- Its rate.
- The number of ways that the reactants can combine.

SeeDan Gillespie,

- “Exact Stochastic Simulation of Coupled Chemical Reactions,”1977.
- “Stochastic Chemical Kinetics,” 2006.

Stochastic Simulation Algorithm (SSA)

R1

R2

R3

S1 = [5, 5, 5] 0

Ri

Choose the next reaction according to:

where

R2

R3

Stochastic Simulation Algorithm (SSA)

S1 = [5, 5, 5] 0

Ri

Choose the time of the next reaction according to:

Stochastic Simulation Algorithm (SSA)

S1 = [5, 5, 5] 0

Choose R3 and t = 3 seconds.

R1

R2

R3

S2 = [4, 7, 4]

3

Choose R1 and t = 1 seconds.

S3 = [2, 6, 7] 4

Choose R3 and t = 2 seconds.

S4 = [1, 8, 6] 6

Choose R2 and t = 1 seconds.

Stochastic Simulation Algorithm (SSA)

S1 = [5, 5, 5] 0

Choose R3 and t = 3 seconds.

S2 = [4, 7, 4]

3

7

Choose R1 and t = 1 seconds.

S3 = [2, 6, 7] 4

Choose R3 and t = 2 seconds.

S4 = [1, 8, 6] 6

Choose R2 and t = 1 seconds.

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