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

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 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 O R 1 and O R 2 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 O R 1 and O R 2 sites fluctuates considerably. The in vitro binding of C1 repressor to O R 1 and O R 2 sites, their mutant forms, and nonspecific DNA regions has been well studied. Using the binding constants of in vitro binding of C1 repressor to O R 1, O R 2, and nonspecific DNA regions and also the value of the cooperativity parameter for C1 repressor binding to O R 1 and O R 2 sites, we calculated the mean rate of synthesis of the reporter protein and its standard deviation as a function of repressor concentration in the 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 O R 1 and O R 2 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.