Related papers: Amplified biochemical oscillations in cellular sys…
The impact of quenched disorder on deterministic diffusion in chaotic dynamical systems is studied. As a simple example, we consider piecewise linear maps on the line. In computer simulations we find a complicated scenario of multiple…
Ordinary differential equations obtained as limits of Markov processes appear in many settings. They may arise by scaling large systems, or by averaging rapidly fluctuating systems, or in systems involving multiple time-scales, by a…
We discuss the effect of stochastic resonance in a simple model of magnetic reversals. The model exhibits statistically stationary solutions and bimodal distribution of the large scale magnetic field. We observe a non trivial amplification…
Gene regulatory circuits must contend with intrinsic noise that arises due to finite numbers of proteins. While some circuits act to reduce this noise, others appear to exploit it. A striking example is the competence circuit in Bacillus…
Auto-regulatory feedback loops are one of the most common network motifs. A wide variety of stochastic models have been constructed to understand how the fluctuations in protein numbers in these loops are influenced by the kinetic…
Stochastic fluctuations of molecule numbers are ubiquitous in biological systems. Important examples include gene expression and enzymatic processes in living cells. Such systems are typically modelled as chemical reaction networks whose…
We have developed a coarse-grained formulation for modeling the dynamic behavior of cells quantitatively, based on stochasticity and heterogeneity, rather than on biochemical reactions. We treat each reaction as a continuous-time stochastic…
Circadian rhythms in living organisms are temporal orders emerging from biochemical circuits driven out of equilibrium. Here, considering the KaiABC system, a minimal model in the synthetic biology, we study how the oscillation emerges from…
Chemically active systems such as living cells are maintained out of thermal equilibrium due to chemical events which generate heat and lead to active fluctuations. A key question is to understand on which time and length scales active…
Autonomous oscillations in biological systems may have a biochemical origin or result from an interplay between force-generating and visco-elastic elements. In molecular motor assemblies the force-generating elements are molecular engines…
Stochastic models of biochemical reaction networks are widely used to capture intrinsic noise in cellular systems. The typical formulation of these models are based on Markov processes for which there is extensive research on efficient…
The maximum amplitude of mechanical oscillators coupled to optical cavities are studied both analytically and numerically. The optical backaction on the resonator enables self-sustained oscillations whose limit cycle is set by the dynamic…
Chemical reactions inside cells are generally considered to happen within fixed-size compartments. Needless to say, cells and their compartments are highly dynamic. Thus, such stringent assumptions may not reflect biochemical reality, and…
We revisit the dynamics of a gene repressed by its own protein in the case where the transcription rate does not adapt instantaneously to protein concentration but is a dynamical variable. We derive analytical criteria for the appearance of…
Adaptation mechanism of cells on the basis of stochastic gene expression and epigenetic modification is proposed. From marginally stable states generated by epigenetic modification, a gene expression pattern that achieves greater cell…
Bioreactors are widely used in many industries to generate a range of products using various host cells e.g., yeast, insect, and mammalian cells. Depending on the process, product, and host cell, some bioreactors exhibit sustained periodic…
We review the mathematical formalism underlying the modelling of stochasticity in biological systems. Beginning with a description of the system in terms of its basic constituents, we derive the mesoscopic equations governing the dynamics…
Understanding how fluctuations propagate across spatial scales is central to our understanding of inanimate matter from turbulence to critical phenomena. In contrast to physical systems, biological systems are organized into a hierarchy of…
Dynamical systems with $\epsilon$ small random perturbations appear in both continuous mechanical motions and discrete stochastic chemical kinetics. The present work provides a detailed analysis of the central limit theorem (CLT), with a…
We propose a general approach to the question of how biological rhythms spontaneously self-regulate, based on the concept of ``stochastic feedback''. We illustrate this approach by considering the neuroautonomic regulation of the heart…