13,890 research outputs found
On Chemical Reaction Network Design by a Nested Evolution Algorithm
International audienceOne goal of synthetic biology is to implement useful functions with biochemical reactions, either by reprogramming living cells or programming artificial vesicles. In this perspective, we consider Chemical Reaction Networks (CRN) as a programming language, and investigate the CRN program synthesis problem. Recent work has shown that CRN interpreted by differential equations are Turing-complete and can be seen as analog computers where the molecular concentrations play the role of information carriers. Any real function that is computable by a Turing machine in arbitrary precision can thus be computed by a CRN over a finite set of molecular species. The proof of this result gives a numerical method to generate a finite CRN for implementing a real function presented as the solution of a Polynomial Initial Values Problem (PIVP). In this paper, we study an alternative method based on artificial evolution to build a CRN that approximates a real function given on finite sets of input values. We present a nested search algorithm that evolves the structure of the CRN and optimizes the kinetic parameters at each generation. We evaluate this algorithm on the Heaviside and Cosine functions both as functions of time and functions of input molecular species. We then compare the CRN obtained by artificial evolution both to the CRN generated by the numerical method from a PIVP definition of the function, and to the natural CRN found in the BioModels repository for switches and oscillators
Exploiting network topology for large-scale inference of nonlinear reaction models
The development of chemical reaction models aids understanding and prediction
in areas ranging from biology to electrochemistry and combustion. A systematic
approach to building reaction network models uses observational data not only
to estimate unknown parameters, but also to learn model structure. Bayesian
inference provides a natural approach to this data-driven construction of
models. Yet traditional Bayesian model inference methodologies that numerically
evaluate the evidence for each model are often infeasible for nonlinear
reaction network inference, as the number of plausible models can be
combinatorially large. Alternative approaches based on model-space sampling can
enable large-scale network inference, but their realization presents many
challenges. In this paper, we present new computational methods that make
large-scale nonlinear network inference tractable. First, we exploit the
topology of networks describing potential interactions among chemical species
to design improved "between-model" proposals for reversible-jump Markov chain
Monte Carlo. Second, we introduce a sensitivity-based determination of move
types which, when combined with network-aware proposals, yields significant
additional gains in sampling performance. These algorithms are demonstrated on
inference problems drawn from systems biology, with nonlinear differential
equation models of species interactions
Stochastic kinetic models: Dynamic independence, modularity and graphs
The dynamic properties and independence structure of stochastic kinetic
models (SKMs) are analyzed. An SKM is a highly multivariate jump process used
to model chemical reaction networks, particularly those in biochemical and
cellular systems. We identify SKM subprocesses with the corresponding counting
processes and propose a directed, cyclic graph (the kinetic independence graph
or KIG) that encodes the local independence structure of their conditional
intensities. Given a partition of the vertices, the graphical
separation in the undirected KIG has an intuitive chemical
interpretation and implies that is locally independent of given . It is proved that this separation also results in global independence of
the internal histories of and conditional on a history of the jumps in
which, under conditions we derive, corresponds to the internal history of
. The results enable mathematical definition of a modularization of an SKM
using its implied dynamics. Graphical decomposition methods are developed for
the identification and efficient computation of nested modularizations.
Application to an SKM of the red blood cell advances understanding of this
biochemical system.Comment: Published in at http://dx.doi.org/10.1214/09-AOS779 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Model validation of simple-graph representations of metabolism
The large-scale properties of chemical reaction systems, such as the
metabolism, can be studied with graph-based methods. To do this, one needs to
reduce the information -- lists of chemical reactions -- available in
databases. Even for the simplest type of graph representation, this reduction
can be done in several ways. We investigate different simple network
representations by testing how well they encode information about one
biologically important network structure -- network modularity (the propensity
for edges to be cluster into dense groups that are sparsely connected between
each other). To reach this goal, we design a model of reaction-systems where
network modularity can be controlled and measure how well the reduction to
simple graphs capture the modular structure of the model reaction system. We
find that the network types that best capture the modular structure of the
reaction system are substrate-product networks (where substrates are linked to
products of a reaction) and substance networks (with edges between all
substances participating in a reaction). Furthermore, we argue that the
proposed model for reaction systems with tunable clustering is a general
framework for studies of how reaction-systems are affected by modularity. To
this end, we investigate statistical properties of the model and find, among
other things, that it recreate correlations between degree and mass of the
molecules.Comment: to appear in J. Roy. Soc. Intefac
Variable-free exploration of stochastic models: a gene regulatory network example
Finding coarse-grained, low-dimensional descriptions is an important task in
the analysis of complex, stochastic models of gene regulatory networks. This
task involves (a) identifying observables that best describe the state of these
complex systems and (b) characterizing the dynamics of the observables. In a
previous paper [13], we assumed that good observables were known a priori, and
presented an equation-free approach to approximate coarse-grained quantities
(i.e, effective drift and diffusion coefficients) that characterize the
long-time behavior of the observables. Here we use diffusion maps [9] to
extract appropriate observables ("reduction coordinates") in an automated
fashion; these involve the leading eigenvectors of a weighted Laplacian on a
graph constructed from network simulation data. We present lifting and
restriction procedures for translating between physical variables and these
data-based observables. These procedures allow us to perform equation-free
coarse-grained, computations characterizing the long-term dynamics through the
design and processing of short bursts of stochastic simulation initialized at
appropriate values of the data-based observables.Comment: 26 pages, 9 figure
Simulation and inference algorithms for stochastic biochemical reaction networks: from basic concepts to state-of-the-art
Stochasticity is a key characteristic of intracellular processes such as gene
regulation and chemical signalling. Therefore, characterising stochastic
effects in biochemical systems is essential to understand the complex dynamics
of living things. Mathematical idealisations of biochemically reacting systems
must be able to capture stochastic phenomena. While robust theory exists to
describe such stochastic models, the computational challenges in exploring
these models can be a significant burden in practice since realistic models are
analytically intractable. Determining the expected behaviour and variability of
a stochastic biochemical reaction network requires many probabilistic
simulations of its evolution. Using a biochemical reaction network model to
assist in the interpretation of time course data from a biological experiment
is an even greater challenge due to the intractability of the likelihood
function for determining observation probabilities. These computational
challenges have been subjects of active research for over four decades. In this
review, we present an accessible discussion of the major historical
developments and state-of-the-art computational techniques relevant to
simulation and inference problems for stochastic biochemical reaction network
models. Detailed algorithms for particularly important methods are described
and complemented with MATLAB implementations. As a result, this review provides
a practical and accessible introduction to computational methods for stochastic
models within the life sciences community
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