Related papers: Emergent L\'evy behavior in single-cell stochastic…
The study of biological cells in terms of mesoscopic, nonequilibrium, nonlinear, stochastic dynamics of open chemical systems provides a paradigm for other complex, self-organizing systems with ultra-fast stochastic fluctuations, short-time…
In the development of multiscale biological models it is crucial to establish a connection between discrete microscopic or mesoscopic stochastic models and macroscopic continuous descriptions based on cellular density. In this paper a…
Selection among autocatalytic species fundamentally depends on their growth law: exponential species, whose number of copies grows exponentially, are mutually exclusive, while sub-exponential ones, whose number of copies grows polynomially,…
Single-cell experiments have revealed cell-to-cell variability in generation times and growth rates for genetically identical cells. Theoretical models relating the fluctuating generation times of single cells to the population growth rate…
This paper analyses of a stochastic model of a chemical reaction network with three types of chemical species ${\cal R}$, ${\cal M}$ and ${\cal U}$ that interact to transform a flow of external resources, the chemical species ${\cal Q}$, to…
Cell fate determination, the process through which cells commit to differentiated states is commonly mediated by gene regulatory motifs with mutually exclusive expression states. The classical deterministic picture for cell fate…
The digital nature of genes combined with the associated low copy numbers of proteins regulating them is a significant source of stochasticity, which affects the phase of biochemical oscillations. We provide a theoretical framework for…
In this paper we study a class of stochastic individual-based models that describe the evolution of haploid populations where each individual is characterised by a phenotype and a genotype. The phenotype of an individual determines its…
By examining the deterministic limit of a general $\epsilon$-dependent generator for Markovian dynamics, which includes the continuous Fokker-Planck equations and discrete chemical master equations as two special cases, the intrinsic…
We present an algorithm for the stochastic simulation of gene expression and heterogeneous population dynamics. The algorithm combines an exact method to simulate molecular-level fluctuations in single cells and a constant-number Monte…
We present a simple mathematical model that captures the evolutionary capabilities of a prebiotic compartment or protocell. In the model the protocell contains an autocatalytic set whose chemical dynamics is coupled to the growth-division…
We study the limit of a kinetic evolution equation involving a small parameter and perturbed by a smooth random term which also involves the small parameter. Generalizing the classical method of perturbed test functions, we show the…
We consider a model for Darwinian evolution in an asexual population with a large but non-constant populations size characterized by a natural birth rate, a logistic death rate modelling competition and a probability of mutation at each…
This paper describes the stochastic Levy--Lorentz gas driven by general long-range reference random walk on correlated and entangled random medium. Further consideration has been laid on the stochastic reinforcement of the underlying random…
Recent imaging data for single bacterial cells reveal that their mean sizes grow exponentially in time and that their size distributions collapse to a single curve when rescaled by their means. An analogous result holds for the…
Here we develop an effective approach to simplify two-time-scale Markov chains with infinite state spaces by removal of states with fast leaving rates, which improves the simplification method of finite Markov chains. We introduce the…
The dynamics of stochastic reaction networks within cells are inevitably modulated by factors considered extrinsic to the network such as for instance the fluctuations in ribsome copy numbers for a gene regulatory network. While several…
The origin of stochastic fluctuations in gene expression has received considerable attention recently. Fluctuations in gene expression are particularly pronounced in cellular systems because of the small copy number of species undergoing…
The dynamics of molecular collisions in a macroscopic body are encoded by the parameter Thermodynamic entropy - a statistical measure of the number of molecular configurations that correspond to a given macrostate. Directionality in the…
Many mathematical models of statistical physics in two dimensions are either known or conjectured to exhibit conformal invariance. Over the years, physicists proposed predictions of various exponents describing the behavior of these models.…