216,181 research outputs found
Asymptotic analysis of multiscale approximations to reaction networks
A reaction network is a chemical system involving multiple reactions and
chemical species. Stochastic models of such networks treat the system as a
continuous time Markov chain on the number of molecules of each species with
reactions as possible transitions of the chain. In many cases of biological
interest some of the chemical species in the network are present in much
greater abundance than others and reaction rate constants can vary over several
orders of magnitude. We consider approaches to approximation of such models
that take the multiscale nature of the system into account. Our primary example
is a model of a cell's viral infection for which we apply a combination of
averaging and law of large number arguments to show that the ``slow'' component
of the model can be approximated by a deterministic equation and to
characterize the asymptotic distribution of the ``fast'' components. The main
goal is to illustrate techniques that can be used to reduce the dimensionality
of much more complex models.Comment: Published at http://dx.doi.org/10.1214/105051606000000420 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
Perfect Sampling of the Master Equation for Gene Regulatory Networks
We present a Perfect Sampling algorithm that can be applied to the Master
Equation of Gene Regulatory Networks (GRNs). The method recasts Gillespie's
Stochastic Simulation Algorithm (SSA) in the light of Markov Chain Monte Carlo
methods and combines it with the Dominated Coupling From The Past (DCFTP)
algorithm to provide guaranteed sampling from the stationary distribution. We
show how the DCFTP-SSA can be generically applied to genetic networks with
feedback formed by the interconnection of linear enzymatic reactions and
nonlinear Monod- and Hill-type elements. We establish rigorous bounds on the
error and convergence of the DCFTP-SSA, as compared to the standard SSA,
through a set of increasingly complex examples. Once the building blocks for
GRNs have been introduced, the algorithm is applied to study properly averaged
dynamic properties of two experimentally relevant genetic networks: the toggle
switch, a two-dimensional bistable system, and the repressilator, a
six-dimensional genetic oscillator.Comment: Minor rewriting; final version to be published in Biophysical Journa
A Taxonomy of Causality-Based Biological Properties
We formally characterize a set of causality-based properties of metabolic
networks. This set of properties aims at making precise several notions on the
production of metabolites, which are familiar in the biologists' terminology.
From a theoretical point of view, biochemical reactions are abstractly
represented as causal implications and the produced metabolites as causal
consequences of the implication representing the corresponding reaction. The
fact that a reactant is produced is represented by means of the chain of
reactions that have made it exist. Such representation abstracts away from
quantities, stoichiometric and thermodynamic parameters and constitutes the
basis for the characterization of our properties. Moreover, we propose an
effective method for verifying our properties based on an abstract model of
system dynamics. This consists of a new abstract semantics for the system seen
as a concurrent network and expressed using the Chemical Ground Form calculus.
We illustrate an application of this framework to a portion of a real
metabolic pathway
The thermodynamic landscape of carbon redox biochemistry
Redox biochemistry plays a key role in the transduction of chemical energy in all living systems. Observed redox reactions in metabolic networks represent only a minuscule fraction of the space of all possible redox reactions. Here we ask what distinguishes observed, natural redox biochemistry from the space of all possible redox reactions between natural and non-natural compounds. We generate the set of all possible biochemical redox reactions involving linear chain molecules with a fixed numbers of carbon atoms. Using cheminformatics and quantum chemistry tools we analyze the physicochemical and thermodynamic properties of natural and non-natural compounds and reactions. We find that among all compounds, aldose sugars are the ones with the highest possible number of connections (reductions and oxidations) to other molecules. Natural metabolites are significantly enriched in carboxylic acid functional groups and depleted in carbonyls, and have significantly higher solubilities than non-natural compounds. Upon constructing a thermodynamic landscape for the full set of reactions as a function of pH and of steady-state redox cofactor potential, we find that, over this whole range of conditions, natural metabolites have significantly lower energies than the non-natural compounds. For the set of 4-carbon compounds, we generate a Pourbaix phase diagram to determine which metabolites are local energetic minima in the landscape as a function of pH and redox potential. Our results suggest that, across a set of conditions, succinate and butyrate are local minima and would thus tend to accumulate at equilibrium. Our work suggests that metabolic compounds could have been selected for thermodynamic stability, and yields insight into thermodynamic and design principles governing nature’s metabolic redox reactions.https://www.biorxiv.org/content/10.1101/245811v1Othe
Emergence of event cascades in inhomogeneous networks
There is a commonality among contagious diseases, tweets, urban crimes,
nuclear reactions, and neuronal firings that past events facilitate the future
occurrence of events. The spread of events has been extensively studied such
that the systems exhibit catastrophic chain reactions if the interaction
represented by the ratio of reproduction exceeds unity; however, their
subthreshold states for the case of the weaker interaction are not fully
understood. Here, we report that these systems are possessed by nonstationary
cascades of event-occurrences already in the subthreshold regime. Event
cascades can be harmful in some contexts, when the peak-demand causes vaccine
shortages, heavy traffic on communication lines, frequent crimes, or large
fluctuations in nuclear reactions, but may be beneficial in other contexts,
such that spontaneous activity in neural networks may be used to generate
motion or store memory. Thus it is important to comprehend the mechanism by
which such cascades appear, and consider controlling a system to tame or
facilitate fluctuations in the event-occurrences. The critical interaction for
the emergence of cascades depends greatly on the network structure in which
individuals are connected. We demonstrate that we can predict whether cascades
may emerge in a network, given information about the interactions between
individuals. Furthermore, we develop a method of reallocating connections among
individuals so that event cascades may be either impeded or impelled in a
network.Comment: 16 pages, 5 figure
Short relaxation times but long transient times in both simple and complex reaction networks
When relaxation towards an equilibrium or steady state is exponential at
large times, one usually considers that the associated relaxation time ,
i.e., the inverse of that decay rate, is the longest characteristic time in the
system. However that need not be true, and in particular other times such as
the lifetime of an infinitesimal perturbation can be much longer. In the
present work we demonstrate that this paradoxical property can arise even in
quite simple systems such as a chain of reactions obeying mass action kinetics.
By mathematical analysis of simple reaction networks, we pin-point the reason
why the standard relaxation time does not provide relevant information on the
potentially long transient times of typical infinitesimal perturbations.
Overall, we consider four characteristic times and study their behavior in both
simple chains and in more complex reaction networks taken from the publicly
available database "Biomodels." In all these systems involving mass action
rates, Michaelis-Menten reversible kinetics, or phenomenological laws for
reaction rates, we find that the characteristic times corresponding to
lifetimes of tracers and of concentration perturbations can be much longer than
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