Dynamics of gene switches and bimodality in their expression profiles. A) A synthetic genetic switch  that contains a repressed positive feedback is stimulated by an inhibitor of the repressor. B) The stimulation-response curve of the genetic circuit. C) The histogram of the steady-state gene expression level of 100 random sample simulations of the genetic switch shown in A. Simulations are performed with randomly (uniformly) generated initial conditions (initial gene expression level) and 20% Gaussian variance in the parameters. D) A synthetic genetic toggle switch  that contains double negative feedbacks. E) The state space of the gene expression levels. Each trajectory (blue lines) is the response curve with respect to a particular initial condition. The red arrows represent the asymptotes of the response curves, i.e. all trajectories converge to the two attractor-states. F) The histogram of the steady state gene expression level of 100 random sample simulations of the genetic switch shown in B. Simulations are performed with uniformly generated initial conditions (initial gene expression level) and 20% Gaussian variance in parameters. G) Schematic representation of a phase plane of a gene switch. Single cell dose response experiments should be able to measure the response curve and uncover the switch-like behavior. H) Experimental measurements of the average expression level of a cell population will mask the switching behavior. A Gaussian distribution is plotted to represent the cell-cell variances in the population. Different cells, according to their initial gene expression level, could have different response curve (blue trajectories). The averaging of the variation in the responses results in a seemingly graded response. I) Experiments across a range of different conditions allowing for the sampling of a large state space recover the switch-like behavior. Each sample could fall in the neighborhood of a possible steady state (points on the blue trajectory). The steady states (on/off states of the gene switch) are the dense regions of the possible response curves in the state space, i.e. the samples occurs at higher frequencies in these states, which results in a bimodal distribution in the observed profiles.
Wu et al. BMC Genomics 2011 12:547 doi:10.1186/1471-2164-12-547