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## Biochemical Reactions

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**Biochemical**Reactions Synthesizing Biological Computation inputs computation outputs Molecular Triggers Molecular Products Protein-Protein Chemistry at the Cellular Level**Synthesizing Biological Computation**Biochemical Reactions Design a system that computes output quantitiesas functions of input quantities. given obtain Quantities of Different Types Quantities of Different Types**Synthesizing Biological Computation**X Biochemical Reactions Z Y Design a system that computes output quantitiesas functions of input quantities. specified independent for us to design**0**0 0 0 1 1 1 0 1 1 1 0 + 2a c b + Basic Mechanisms Logic Gates: how digital values are computed. “XOR” gate Biochemical Reactions: how types of molecules combine.**+**Biochemical Reactions cell species count 9 8 6 5 7 9 Discrete chemical kinetics; spatial homogeneity.**+**+ + Biochemical Reactions Relative rates or (reaction propensities): slow medium fast Discrete chemical kinetics; spatial homogeneity.**Biochemical**Reactions N M Synthesizing Biological Computation Design a system that computes output quantitiesas functionsof input quantities. given obtain Quantities of Different Types Quantities of Different Types independent specified for us to design**Example: Multiplication**Start with of type x. Start with of type y. X Y × Produce of type z. X Y x a v . fast y′ a a y z + + + × obtain of z X Y a Iterate! med . y′ y Use working types a,y′. slow fast**Produce of type n.**+ fast + a n a n 2 obtain 1 of n med a slow m b + v . fast + n b 2 c b M obtain of n 2 M 2 fast b med . c n Example: Exponentiation Start with M of type m. Use working types a,b,c. Start with anynon-zero amount of types aandn. Start with no amountof types bandc.**Functional Dependencies**Exponentiation Logarithm Linear Raising-to-a-Power**k1**+ 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.**Modular Synthesis**Deterministic Module Stochastic Module . . . . . . . . . initializing,reinforcing,stabilizing, purifying, andworking reactions linear,exponentiation, logarithm,raising-to-a-power,etc.**.**. . . StochasticModule DeterministicModule . . . . . . . . Modular Synthesis Compose modules to achieved desired probabilistic response. Composition requires “regulatory gluing”.**Modular Synthesis**Strategy: • Structure computation to obtain initial choice probabilistically. • Thenamplify this choice and inhibitother choices. Method is: • Precise. • Robust. • Programmable. With “locking”, produces designs that areindependentof rates.**CAD Tool**Brian’s Automated Modular Biochemical Instantiator (BAMBI) • Library of biochemical models. • Designated input and output types. • Specific quantities (or ranges) of input types. • Target functional dependencies. • Target probability distribution. 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. Farm of Cell B.E. processors (from Sony Playstations 3’s) IBM System Z Mainframe