Noise-induced multistability in the regulation of cancer by genes and pseudogenes.

We extend a previously introduced model of stochastic gene regulation of cancer to a nonlinear case having both gene and pseudogene messenger RNAs (mRNAs) self-regulated. The model consists of stochastic Boolean genetic elements and possesses noise-induced multistability (multimodality). We obtain analytical expressions for probabilities for the case of constant but finite number of microRNA molecules which act as a noise source for the competing gene and pseudogene mRNAs. The probability distribution functions display both the global bistability regime as well as even-odd number oscillations for a certain range of model parameters. Statistical characteristics of the mRNA's level fluctuations are evaluated. The obtained results of the extended model advance our understanding of the process of stochastic gene and pseudogene expressions that is crucial in regulation of cancer.

Oscillations in probability distributions for stochastic gene expression.

The phenomenon of oscillations in probability distribution functions of number of components is found for a model of stochastic gene expression. It takes place in cases of low levels of molecules or strong intracellular noise. The oscillations distinguish between more probable even and less probable odd number of particles. The even-odd symmetry restores as the number of molecules increases with the probability distribution function tending to Poisson distribution. We discuss the possibility of observation of the phenomenon in gene, protein, and mRNA expression experiments.

Influence of noise on the synchronization of the stochastic Kuramoto model.

We consider the Kuramoto model of globally coupled phase oscillators subject to Ornstein-Uhlenbeck and non-Gaussian colored noise and investigate the influence of noise on the order parameter of the synchronization process. We use numerical methods to study the dependence of the threshold as well as the maximum degree of synchronization on the correlation time and the strength of the noise, and find that the threshold of synchronization strongly depends on the nature of the noise. It is found to be lower for both the Ornstein-Uhlenbeck and non-Gaussian processes compared to the case of white noise. A finite correlation time also favors the achievement of the full synchronization of the system, in contract to the white noise process, which does not allow that. Finally, we discuss possible applications of the stochastic Kuramoto model to oscillations taking place in biochemical systems.

Nonequilibrium Lyapunov function and a fluctuation relation for stochastic systems: Poisson-representation approach.

We present a statistical physics framework for the description of nonlinear nonequilibrium stochastic processes, modeled via a chemical master equation, in the weak-noise limit. Using the Poisson-representation approach and applying the large-deviation principle, we first solve the master equation. Then we use the notion of the nonequilibrium free energy to derive an integral fluctuation relation for nonlinear nonequilibrium systems under feedback control. We point out that the free energy as well as some functionals can serve as a nonequilibrium Lyapunov function which has an important property to decay monotonously to its minimal value at all times. The Poisson-representation technique is illustrated via exact stochastic treatment of biophysical processes, such as bacterial chemosensing and molecular evolution.

Anomalous latent heat in nonequilibrium phase transitions.

We study first-order phase transitions in a two-temperature system, where due to the time-scale separation all the basic thermodynamical quantities (free energy, entropy, etc.) are well defined. The sign of the latent heat is found to be counterintuitive: it is positive when going from the phase where the temperatures and the entropy are higher to the one where these quantities are lower. The effect exists only out of equilibrium and requires conflicting interactions. It is displayed on a lattice gas model of ferromagnetically interacting spin-1/2 particles.