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Symmetries (and their spontaneous rupturing) can be used to protect and engender novel quantum phases and lead to interesting collective phenomena. In Ref. 1, the authors described a general dynamical decoupling (polyfractal) protocol that…
Changes in a cell's external or internal conditions are usually reflected in the concentrations of the relevant transcription factors. These proteins in turn modulate the expression levels of the genes under their control and sometimes need…
The phenomenon of self-induced stochastic resonance (SISR) requires a nontrivial scaling limit between the deterministic and the stochastic timescales of an excitable system, leading to the emergence of coherent oscillations which are…
Genetic oscillators play important roles in cell life regulation. The regulatory efficiency usually depends strongly on the emergence of stable collective dynamic modes, which requires designing the interactions between genetic networks. We…
We study the noise activated dynamics of a model {\it autapse} neuron system that consists of a subcritical Hopf oscillator with a time delayed nonlinear feedback. The coherence of the noise driven pulses of the neuron exhibits a novel…
We study the noise effects in a driven system of globally coupled oscillators, with particular attention to the interplay between driving and noise. The self-consistency equation for the order parameter, which measures the collective…
The stochastic mutual repressor model is analysed using perturbation methods. This simple model of a gene circuit consists of two genes and three promotor states. Either of the two protein products can dimerize, forming a repressor molecule…
Certain cellular processes take the form of activity pulses that can be interpreted in terms of noise-driven excitable dynamics. Here we present an overview of different gene circuit architectures that exhibit excitable pulses of protein…
Pluripotent embryonic stem cells are of paramount importance for biomedical research thanks to their innate ability for self-renewal and differentiation into all major cell lines. The fateful decision to exit or remain in the pluripotent…
Bistable biological regulatory systems need to cope with stochastic noise to fine-tune their function close to bifurcation points. Here, we study stability properties of this regime in generic systems to demonstrate that cooperative…
Recent whole genome polymerase binding assays have shown that a large proportion of unexpressed genes have pre-assembled RNA pol II transcription initiation complex stably bound to their promoters. Some such promoter proximally paused genes…
We study the properties of large systems of globally coupled oscillators in the presence of noise. When the distribution of the natural frequencies of the oscillators is bimodal and its analytical continuation in the complex plane has only…
We report relationships between the effects of noise and applied constant currents on the behavior of a system of excitable elements. The analytical approach based on the nonlinear Fokker-Planck equation of a mean-field model allows us to…
We investigate a model where strong noise in a sub-population creates a metastable state in an otherwise unstable two-population system. The induced metastable state is vortex-like, and its persistence time grows exponentially with the…
We consider effect of stochastic sources upon self-organization process being initiated with creation of the limit cycle. General expressions obtained are applied to the stochastic Lorenz system to show that departure from equilibrium…
The effects of intrinsic noise on stochastic delay systems is studied within an expansion in the inverse system size. We show that the stochastic nature of the underlying dynamics may induce oscillatory behaviour in parameter ranges where…
Inside individual cells, expression of genes is inherently stochastic and manifests as cell-to-cell variability or noise in protein copy numbers. Since proteins half-lives can be comparable to the cell-cycle length, randomness in…
We consider the dynamics of a population of organisms containing two mutually inhibitory gene regulatory networks, that can result in a bistable switch-like behaviour. We completely characterize their local and global dynamics in the…
Biological systems are notoriously noisy. Noise, therefore, also plays an important role in many models of neural impulse generation. Noise is not only introduced for more realistic simulations but also to account for cooperative effects…
Timing is essential for many cellular processes, from cellular responses to external stimuli to the cell cycle and circadian clocks. Many of these processes are based on gene expression. For example, an activated gene may be required to…