Large system in a small cell: A hypothetical pathway from a microscopic stochastic process towards robust genetic regulation

We provide a theoretical basis for the treatment of genetic regulation by stochastic differential equations, considering a discrete structural transition of a giant DNA molecule together with intracellular chemical species as environmental factors. Starting from a microscopic description with discrete state variables for genetic products represented as small natural numbers, we derive a set of nonlinear stochastic differential equations with continuous variables by introducing a new concept of system size on the environmental factors, existing in large numbers even in an intracellular space. Our theoretical model may provide novel insight into experimental studies on the regulatory mechanism in living cells.