[Statistical fluctuations of the filling level of operator by repressor determine the level of noise of reporter gene expression].

ABSTRACT

The regulation of the reporter gene activity in a single bacterial cell by means of lambda-phage C1 repressor has been described by the methods of statistical thermodynamics. The equations for the calculation of the mean production rate of the reporter protein and its standard deviation as a function of C1 repressor concentration in the cell have been obtained. The stochastic nature of C1 repressor binding with OR1 and OR2 operator sites becomes apparent when both repressor molecules and operators are present in the bacterial cell in a small number of copies. In this case, the number of repressor molecules that bind to OR1 and OR2 sites fluctuates considerably. The in vitro binding of C1 repressor to OR1 and OR2 sites, their mutant forms, and nonspecific DNA regions has been well studied. Using the binding constants of in vitro binding of C1 repressor to OR1, OR2 and nonspecific DNA regions and also the value of the cooperativity parameter for C1 repressor binding to OR1 and OR2 sites, we calculated the mean rate of synthesis of the reporter protein and its standard deviation as a function of repressor concentration in cell. The theoretical relations fit well the experimental results. The results of calculations confirm the assumption that gene expression noise in a single cell at a repressor concentration exceeding 100 nM is related to the stochastic nature of binding of repressor dimers to OR1 and OR2 sites. Other mechanisms of the generation of gene expression noise (for example, monomer-dimer balance) make a significant contribution at concentrations less than 100 nM.