719 research outputs found
Uncoupled Analysis of Stochastic Reaction Networks in Fluctuating Environments
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 recent studies demonstrate the importance of accounting for such
extrinsic components, the resulting models are typically hard to analyze. In
this work we develop a general mathematical framework that allows to uncouple
the network from its dynamic environment by incorporating only the
environment's effect onto the network into a new model. More technically, we
show how such fluctuating extrinsic components (e.g., chemical species) can be
marginalized in order to obtain this decoupled model. We derive its
corresponding process- and master equations and show how stochastic simulations
can be performed. Using several case studies, we demonstrate the significance
of the approach. For instance, we exemplarily formulate and solve a marginal
master equation describing the protein translation and degradation in a
fluctuating environment.Comment: 7 pages, 4 figures, Appendix attached as SI.pdf, under submissio
Synchronization of stochastic hybrid oscillators driven by a common switching environment
Many systems in biology, physics and chemistry can be modeled through
ordinary differential equations, which are piecewise smooth, but switch between
different states according to a Markov jump process. In the fast switching
limit, the dynamics converges to a deterministic ODE. In this paper we suppose
that this limit ODE supports a stable limit cycle. We demonstrate that a set of
such oscillators can synchronize when they are uncoupled, but they share the
same switching Markov jump process. The latter is taken to represent the effect
of a common randomly switching environment. We determine the leading order of
the Lyapunov coefficient governing the rate of decay of the phase difference in
the fast switching limit. The analysis bears some similarities to the classical
analysis of synchronization of stochastic oscillators subject to common white
noise. However the discrete nature of the Markov jump process raises some
difficulties: in fact we find that the Lyapunov coefficient from the
quasi-steady-state approximation differs from the Lyapunov coefficient one
obtains from a second order perturbation expansion in the waiting time between
jumps. Finally, we demonstrate synchronization numerically in the radial
isochron clock model and show that the latter Lyapinov exponent is more
accurate
A Molecular Implementation of the Least Mean Squares Estimator
In order to function reliably, synthetic molecular circuits require
mechanisms that allow them to adapt to environmental disturbances. Least mean
squares (LMS) schemes, such as commonly encountered in signal processing and
control, provide a powerful means to accomplish that goal. In this paper we
show how the traditional LMS algorithm can be implemented at the molecular
level using only a few elementary biomolecular reactions. We demonstrate our
approach using several simulation studies and discuss its relevance to
synthetic biology.Comment: Molecular circuits, synthetic biology, least mean squares estimator,
adaptive system
Path mutual information for a class of biochemical reaction networks
Living cells encode and transmit information in the temporal dynamics of
biochemical components. Gaining a detailed understanding of the input-output
relationship in biological systems therefore requires quantitative measures
that capture the interdependence between complete time trajectories of
biochemical components. Mutual information provides such a measure but its
calculation in the context of stochastic reaction networks is associated with
mathematical challenges. Here we show how to estimate the mutual information
between complete paths of two molecular species that interact with each other
through biochemical reactions. We demonstrate our approach using three simple
case studies.Comment: 6 pages, 2 figure
Emergence of switch-like behavior in a large family of simple biochemical networks
Bistability plays a central role in the gene regulatory networks (GRNs)
controlling many essential biological functions, including cellular
differentiation and cell cycle control. However, establishing the network
topologies that can exhibit bistability remains a challenge, in part due to the
exceedingly large variety of GRNs that exist for even a small number of
components. We begin to address this problem by employing chemical reaction
network theory in a comprehensive in silico survey to determine the capacity
for bistability of more than 40,000 simple networks that can be formed by two
transcription factor-coding genes and their associated proteins (assuming only
the most elementary biochemical processes). We find that there exist reaction
rate constants leading to bistability in ~90% of these GRN models, including
several circuits that do not contain any of the TF cooperativity commonly
associated with bistable systems, and the majority of which could only be
identified as bistable through an original subnetwork-based analysis. A
topological sorting of the two-gene family of networks based on the presence or
absence of biochemical reactions reveals eleven minimal bistable networks
(i.e., bistable networks that do not contain within them a smaller bistable
subnetwork). The large number of previously unknown bistable network topologies
suggests that the capacity for switch-like behavior in GRNs arises with
relative ease and is not easily lost through network evolution. To highlight
the relevance of the systematic application of CRNT to bistable network
identification in real biological systems, we integrated publicly available
protein-protein interaction, protein-DNA interaction, and gene expression data
from Saccharomyces cerevisiae, and identified several GRNs predicted to behave
in a bistable fashion.Comment: accepted to PLoS Computational Biolog
Reaction-diffusion with stochastic decay rates
Understanding anomalous transport and reaction kinetics due to microscopic
physical and chemical disorder is a long-standing goal in many fields including
geophysics, biology, and engineering. We consider reaction-diffusion
characterized by fluctuations in both transitions times and decay rates. We
introduce and analyze a model framework that explicitly connects microscopic
fluctuations with the mescoscopic description. For broad distributions of
transport and reaction time scales we compute the particle density and derive
the equations governing its evolution, finding power-law decay of the survival
probability, and spatially heterogeneous decay that leads to subdiffusion and
an asymptotically stationary surviving-particle density. These anomalies are
clearly attributable to non-Markovian effects that couple transport and
chemical properties in both reaction and diffusion terms.Comment: Explain model and applications in more detail. 19 pages, 6 figure
Decision Making in an Intracellular Genetic Classifier
A model for an intracellular genetic classifier is introduced and studied to investigate how cellular decision making will function under the stochastic conditions. In particular, this provides a basis to investigate whether a binary classification under the effects of intrinsic noise is still possible. More precisely, a mathematical model of a genetic classifier is derived using a standard approach using Hill functions and its dynamical properties are explored. Classification mechanism is studied considering the effects of low copy number of mRNA and proteins in terms of the degree of cooperativity, inputs and transcription rates. It is shown that the intrinsic noise blurs the separation line between the classification classes, but the influence of stochasticity is qualitatively different for the case of monostable or bistable dynamics. Finally, potential applications are discussed
Phenotypic Variation and Bistable Switching in Bacteria
Microbial research generally focuses on clonal populations. However, bacterial cells with identical genotypes frequently display different phenotypes under identical conditions. This microbial cell individuality is receiving increasing attention in the literature because of its impact on cellular differentiation, survival under selective conditions, and the interaction of pathogens with their hosts. It is becoming clear that stochasticity in gene expression in conjunction with the architecture of the gene network that underlies the cellular processes can generate phenotypic variation. An important regulatory mechanism is the so-called positive feedback, in which a system reinforces its own response, for instance by stimulating the production of an activator. Bistability is an interesting and relevant phenomenon, in which two distinct subpopulations of cells showing discrete levels of gene expression coexist in a single culture. In this chapter, we address techniques and approaches used to establish phenotypic variation, and relate three well-characterized examples of bistability to the molecular mechanisms that govern these processes, with a focus on positive feedback.
Stochastic Simulation of Biomolecular Networks in Dynamic Environments
This is the final version of the article. Available from Public Library of Science via the DOI in this record.Simulation of biomolecular networks is now indispensable for studying biological systems, from small reaction networks to large ensembles of cells. Here we present a novel approach for stochastic simulation of networks embedded in the dynamic environment of the cell and its surroundings. We thus sample trajectories of the stochastic process described by the chemical master equation with time-varying propensities. A comparative analysis shows that existing approaches can either fail dramatically, or else can impose impractical computational burdens due to numerical integration of reaction propensities, especially when cell ensembles are studied. Here we introduce the Extrande method which, given a simulated time course of dynamic network inputs, provides a conditionally exact and several orders-of-magnitude faster simulation solution. The new approach makes it feasible to demonstrate-using decision-making by a large population of quorum sensing bacteria-that robustness to fluctuations from upstream signaling places strong constraints on the design of networks determining cell fate. Our approach has the potential to significantly advance both understanding of molecular systems biology and design of synthetic circuits.MV acknowledges support under an MRC Biomedical Informatics Fellowship. PT acknowledges support by the Royal Commission for the Exhibition of 1851. RG acknowledges support from the Leverhulme Trust (RPG-2013-171). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript
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