Related papers: Stochastic Description of a Bistable Frustrated Un…
Collective oscillation of cells in a population has been reported under diverse biological contexts and with vastly different molecular constructs. Could there be common principles similar to those that govern spontaneous oscillation in…
Prokaryotic gene expression is dynamic and noisy, and can lead to phenotypic variations. Previous work has shown that the selection of such variation can be modeled through basic reaction networks described by O.D.E. displaying a bistable…
We consider the stochastic patterns of a system of communicating, or coupled, self-propelled particles in the presence of noise and communication time delay. For sufficiently large environmental noise, there exists a transition between a…
Phase separation accompanied by further domain growth and coarsening is a phenomenon common to a broad variety of dynamical systems. In this connection, controlling such processes represents a relevant interdisciplinary problem. Using…
Delays and stochasticity have both served as crucially valuable ingredients in mathematical descriptions of control, physical, and biological systems. In this work, we investigate how explicitly dynamical stochasticity in delays modulates…
Coherent oscillatory activity can arise spontaneously as a result of increased coupling in a system of excitable and passive cells, each being quiescent in isolation. This can potentially explain the appearance of spontaneous rhythmic…
Fluctuations and noise may alter the behavior of dynamical systems considerably. For example, oscillations may be sustained by demographic fluctuations in biological systems where a stable fixed point is found in the absence of noise. We…
The model of a double-well oscillator with nonlinear dissipation is studied. The self-sustained oscillations regime and the excitable one are described. The first regime consists in the coexistence of two stable limit cycles in the phase…
The two-state Togashi-Kaneko model demonstrates how, at finite system sizes, autocatalysis can lead to noise-induced bistability between the cellular concentrations of different molecular species. Here, we show that, in the biologically…
We study the noise characteristics of stochastic oscillations in protein number dynamics of simple genetic oscillatory systems. Using the three-component negative feedback transcription regulatory system called the repressilator as a…
In this paper we study how to shape temporal pulses to switch a bistable system between its stable steady states. Our motivation for pulse-based control comes from applications in synthetic biology, where it is generally difficult to…
Oscillatory chemical reactions often serve as a timing clock of cellular processes in living cells. The temporal dynamics of protein concentration levels is thus of great interest in biology. Here we propose a theoretical framework to…
Stochastic gene expression has been implicated in a variety of cellular processes, including cell differentiation and disease. In this issue of Cell, Weinberger et al. (2005) take an integrated computational-experimental approach to study…
We study an alternative approach to model the dynamical behaviors of biological feedback loop, that is, a type-dependent spin system, this class of stochastic models was introduced by Fern\'andez et. al (2009), and are useful since take…
Biological systems are characterized by the ubiquitous roles of weak, that is, non-covalent molecular interactions, small, often very small, numbers of specific molecules per cell, and Brownian motion. These combine to produce stochastic…
Due to inherent noise in intracellular networks cellular decisions can be random, so genetically identical cells can display different phenotypic behavior even in identical environments. Most previous work in understanding the…
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…
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…
We analyze three simple genetic circuits which involve transcriptional regulation and feedback: the autorepressor, the switch and the repressilator, that consist of one, two and three genes, respectively. Such systems are commonly simulated…
Ring topologies of repressing genes have qualitatively different long-term dynamics if the number of genes is odd (they oscillate) or even (they exhibit bistability). However, these attractors may not fully explain the observed behavior in…