Stochasticity in gene regulation : molecular basis, motifs and Networks
Because the components of genetic networks are present in small quantities, the detailed behavior of network motifs are better described by stochastic models than by macroscopic kinetics. An exact solution is possible for a gene regulated by its own proteomic atmosphere, showing a dependence in the adiabaticity parameter measuring the relative speed of the binding/unbinding and synthesis/ degradation events. This solution deviates from the commonly used approximation based on the equilibrium law of mass action. The dynamics of small networks are shown to depend on the average number of proteins in the system, the repression strength and the adiabaticity parameter. Stochastic simulations of toggle switches show that strongly repressed systems are better candidates for "good switches". The discrete nature of these systems also defines the behavior of systems where the molecular species are on the verge of extinction, the death and resurrection of the species greatly modifying the attractor landscape. Deterministic models and the diffusion approximation to the master equation break down at the limits of protein populations, in a way very analogous to the breakdown of geometrical optics that occurs at distances smaller than one wavelength of light from edges. Our arguments suggest that the stability of lysogeny in the \[lambda\]-phage may be influenced by such extinction phenomena. The role of stochasticity and noise in controlling genetic circuits is investigated in the context of transitions into and from competence in Bacillus subtilis. Recent experiments have demonstrated that bistability is not necessary for this function, but that the existence of one stable fixed point (vegetation) and an excitable unstable one (competence) is sufficient. Stochasticity therefore plays a crucial role in this excitation. We consider the importance of the protein binding/unbinding to the DNA as a noise source. A theoretical model that includes this "nonadiabatic" mechanism appears to produce a better agreement with experiments than models where only the adiabatic limit is considered. The knowledge gained with the study of smaller motifs can be extended to larger networks. The network controlling the Bacillus subtilis decision between competence and sporulation is analyzed in the light of modularity.