Synthesizing stochasticity in biochemical systems.

Abstract

The science of Biology is evolving from a science of words and pictures to a science of hard numbers and equations. Biological systems are modeled mathematically, and computers are used to compute how systems will evolve using either differential equations or stochastic techniques. These techniques help scientists to understand the complex systems of interaction that Biology encompasses. The problem of designing such systems, however, is often relegated to simply finding similar behavior in a system and grafting that element into a new system. We, however, propose a method for designing biochemical pathways in organisms according to arbitrary design. Specifically, we examine the problem of designing a system that makes a stochastic response to some input stimuli. The method allows the designer to implement a wide variety of responses to various environments. We verify our designs, modeling the cell stochastically, using Gillespie simulations. We assume that the environment can be inferred by the chemistry within a cell and that the time-scales we operate on are short enough that the effect of diffusion across the membrane is negligible. Our designs consist of theoretical sets of reactions that if given suitable initial conditions will perform calculation within the system as well as make stochastic choices according to probabilities defined by the environment and the design. Our method employs a modular design methodology that allows us to create functional modules working at the reaction level and create larger systems by composing those modules together. We create modules and methods for choosing between multiple outcomes as well as performing addition, subtraction, multiplication, logarithm, and exponentiation. This design system could be the first step to creating biochemical systems for carrying out arbitrary designs.