Mixed Poisson distributions in exact solutions of Stochastic Auto-regulation Models

Details Mixed Poisson distributions in exact solutions of Stochastic Auto-regulation Models Mixed Poisson distributions in exact solutions of Stochastic Auto-regulation Models

2011-10-12

arxiv.org/abs/1110.2804v1

Biology

Quantitative Biology

Quantitative Methods

Paper and Supplementary Section, 4+11 pages

Scientific paper

In this paper we study the interplay between stochastic gene expression and system design using simple stochastic models of auto-activation and auto-inhibition. Using the Poisson Representation, a technique whose usefulness in the context of non-linear gene regulation models we elucidate, we are able to write down exact results for these feedback models in the steady state. We exploit this representation to analyze the parameter-spaces and demarcate where different behaviors including power-law, conventional bimodal, a novel bimodal with graded characteristics and sub-Poisson noise occur. Using our results, we reexamine how well the auto-inhibition and auto-activation models serve their conventional roles as paradigms for noise suppression and noise exploitation respectively.

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