BiochemicalReactions

computationinputs outputs

Molecular Triggers

Molecular Products

Synthesizing Biological ComputationSynthesizing Biological Computation

Protein-Protein Chemistry at the Cellular Level

Design a system that computes output quantitiesas functions of input quantities.

Synthesizing Biological ComputationSynthesizing Biological Computation

BiochemicalReactions

given obtain

Quantities of Different

Types

Quantities of Different

Types

Design a system that computes output quantitiesas functions of input quantities.

Synthesizing Biological ComputationSynthesizing Biological Computation

BiochemicalReactions

independentfor us to design

specified

Z=X×Y

X

Y

Z

Logic Gates: how digital values are computed.

Biochemical Reactions: how types of molecules combine.

“XOR” gate

0011

0101

0110

1x 2x g

Basic Mechanisms

+

1x

2x

g

+2a b c

Biochemical Reactions

9

6

7

cellspecies count

+

8

5

9

Discrete chemical kinetics; spatial homogeneity.

Biochemical Reactions

+

+

+

slow

medium

fast

Relative rates or (reaction propensities):

Discrete chemical kinetics; spatial homogeneity.

Design a system that computes output quantitiesas functions of input quantities.

Synthesizing Biological Computation

BiochemicalReactions

given obtain

Quantities of Different

Types

Quantities of Different

TypesM NM2

independent

for us to design

specified

Example: MultiplicationExample: Multiplication

Use working types a, y′.

slow ax

med.yy′

fasta

v. fastzy′ya a

obtain of zYX

Produce of type z.YXStart with of type x. X Start with of type y. Y

Iterate!

Start with no amount of types b and c.

Example: ExponentiationStart with M of type m. Produce of type n.

M2Use working types a, b, c.

Start with any non-zero amount of types a and n.

nana fast2meda

obtain 1 of n

bmslow

cbnb 2v. fast

fastb

ncmed.

obtain of n M2

Functional Dependencies

Logarithm

Linear

Raising-to-a-Power

2MN 2MN Exponentiation

)(log2 MN )(log2 MN

MN MN

PMN PMN

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

• Its rate.• The quantities of its reactants.

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

Stochastic Kinetics

+

+

+

k1

k2

k3

12

Modular SynthesisModular Synthesis

Deterministic Deterministic ModuleModule

..

..

..

Stochastic Stochastic ModuleModule

..

..

..

..

..

..

initializing, reinforcing,stabilizing,purifying, and working reactions

linear, exponentiation, logarithm,raising-to-a-power, etc.

13

Modular SynthesisModular Synthesis

StochasticModule

DeterministicModule

..

..

..

..

..

..

Compose modules to achieved desired probabilistic response.

Composition requires “regulatory gluing”.

02MN 02MN

)(log 02 NP )(log 02 NP

00

PNQ 00

PNQ

..

..

..

..

..

..

• Structure computation to obtain initial choice probabilistically.

• Then amplify this choice and inhibit other choices.

Method is:

• Precise.• Robust.• Programmable.

Strategy:

With “locking”, produces designs that are independent of rates.

Modular SynthesisModular Synthesis

CAD Tool

• Library of biochemical models.

• Designated input and output types.

• Specific quantities (or ranges) of input types.

• Target functional dependencies.

• Target probability distribution.

Brian’s Automated Modular Biochemical Instantiator (BAMBI)

Given:

Outputs:• Reactions/parameters implementing specification.• Detailed measures of accuracy and robustness.

Targets can be nearly any analytic function or data set.

Computational Infrastructure• Implementing a “front-end” database of biochemical models in

Structured Query Language (SQL) from online repositories: BioBricks, SBML.org, …

• Implementing “back-end” number crunching algorithms for analysis and synthesis on a farm of high-performance processors.

IBM System Z MainframeFarm of Cell B.E.

processors (from Sony Playstations 3’s)