Control of protein concentrations in heterogeneous cell populations

In this work we propose a synthetic gene circuit for controlling the variability in protein concentration at a population level. The circuit, based on the use of an intracellular nonlinear controller coupled to a cell-to-cell communication mechanism, allows for independent control of the mean and variance of a signalling molecule across cell population. Via a piecewise affine approximation of the nonlinearity, we provide set invariance results that imply the stability of the closed loop system. We also obtain closed-form expressions for the mean and variance as a function of the tuneable parameters of the controller. The predictions offered by the theoretical analysis are in agreement with numerical simulations performed with physiologically realistic parameters in Escherichia coli.