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Self-Consistent Proteomic Field Theory of Stochastic Gene Switches

Aleksandra M. Walczak ^*, Masaki Sasai  and Peter G. Wolynes ^* 

^* Department of Physics, Center for Theoretical Biological Physics, University of California at San Diego, La Jolla, California; Department of Complex Systems Science, Graduate School of Information Science, Nagoya University, Nagoya, Japan; and Department of Chemistry and Biochemistry, University of California at San Diego, La Jolla, California

Correspondence: Address reprint requests to Peter Wolynes, University of California at San Diego, Chemistry and Biochemistry, 9500 Gilman Drive, MC 0371, La Jolla, CA 92093-0371. Tel.: 858-822-4825; E-mail: pwolynes{at}ucsd.edu.

We present a self-consistent field approximation approach to the problem of the genetic switch composed of two mutually repressing/activating genes. The protein and DNA state dynamics are treated stochastically and on an equal footing. In this approach the mean influence of the proteomic cloud created by one gene on the action of another is self-consistently computed. Within this approximation a broad range of stochastic genetic switches may be solved exactly in terms of finding the probability distribution and its moments. A much larger class of problems, such as genetic networks and cascades, also remain exactly solvable with this approximation. We discuss, in depth, certain specific types of basic switches used by biological systems and compare their behavior to the expectation for a deterministic switch.

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