Related papers: Distributed delay stabilizes bistable genetic netw…
Based on previously published experimental observations and mathematical models for Hes1, p53 and NF-kB gene expression, we improve these models through a distributed delay formulation of the time lag between transcription factor binding…
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…
This paper deals with the global stability of time-delayed dynamical networks. We show that for a time-delayed dynamical network with non-distributed delays the network and the corresponding non-delayed network are both either globally…
The expression of genes usually follows a two-step procedure. First, a gene (encoded in the genome) is transcribed resulting in a strand of (messenger) RNA. Afterwards, the RNA is translated into protein. Classically, this gene expression…
We study delay-independent stability in nonlinear models with a distributed delay which have a positive equilibrium. Such models frequently occur in population dynamics and other applications. In particular, we construct a relevant…
The regulation of cellular function is often controlled at the level of gene transcription. Such genetic regulation usually consists of interacting networks, whereby gene products from a single network can act to control their own…
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…
A perturbation framework is developed to analyze metastable behavior in stochastic processes with random internal and external states. The process is assumed to be under weak noise conditions, and the case where the deterministic limit is…
In real-world networks the interactions between network elements are inherently time-delayed. These time-delays can not only slow the network but can have a destabilizing effect on the network's dynamics leading to poor performance. The…
In this paper we investigate a structured population model with distributed delay. Our model incorporates two different types of nonlinearities. Specifically we assume that individual growth and mortality are affected by scramble…
We introduce simple models of genetic regulatory networks and we proceed to the mathematical analysis of their dynamics. The models are discrete time dynamical systems generated by piecewise affine contracting mappings whose variables…
We assess the impact of cell cycle noise on gene circuit dynamics. For bistable genetic switches and excitable circuits, we find that transitions between metastable states most likely occur just after cell division and that this…
Many transcription factors bind to DNA with a remarkable lack of specificity, so that regulatory binding sites compete with an enormous number of non-regulatory 'decoy' sites. For an auto-regulated gene, we show decoy sites decrease noise…
Previously we showed how delay communication between globally coupled self-propelled agents causes new spatio-temporal patterns to arise when the delay coupling is fixed among all agents \cite{Forgoston08}. In this paper, we show how…
Delays are an important phenomenon arising in a wide variety of real world systems. They occur in biological models because of diffusion effects or as simplifying modeling elements. We propose here to consider delayed stochastic reaction…
Gene products (RNAs, proteins) often occur at low molecular counts inside individual cells, and hence are subject to considerable random fluctuations (noise) in copy number over time. Not surprisingly, cells encode diverse regulatory…
A simple stochastic model of a self regulating gene that displays bistable switching is analyzed. While on, a gene transcribes mRNA at a constant rate. Transcription factors can bind to the DNA and affect the gene's transcription rate.…
Systems with time delay play an important role in modeling of many physical and biological processes. In this paper we describe generic properties of systems with time delay, which are related to the appearance and stability of periodic…
For cellular biochemical reaction systems where the numbers of molecules is small, significant noise is associated with chemical reaction events. This molecular noise can give rise to behavior that is very different from the predictions of…
A general class of stochastic gene expression models with self regulation is considered. One or more genes randomly switch between regulatory states, each having a different mRNA transcription rate. The gene or genes are self regulating…