18,244 research outputs found
On the Complexity of Reconstructing Chemical Reaction Networks
The analysis of the structure of chemical reaction networks is crucial for a
better understanding of chemical processes. Such networks are well described as
hypergraphs. However, due to the available methods, analyses regarding network
properties are typically made on standard graphs derived from the full
hypergraph description, e.g.\ on the so-called species and reaction graphs.
However, a reconstruction of the underlying hypergraph from these graphs is not
necessarily unique. In this paper, we address the problem of reconstructing a
hypergraph from its species and reaction graph and show NP-completeness of the
problem in its Boolean formulation. Furthermore we study the problem
empirically on random and real world instances in order to investigate its
computational limits in practice
A symbolic network-based nonlinear theory for dynamical systems observability
EBM and MSB acknowledge the Engineering and Physical Sciences Research Council (EPSRC), grant Ref. EP/I032608/1. ISN acknowledges partial support from the Ministerio de Economía y Competitividad of Spain under project FIS2013-41057-P and from the Group of Research Excelence URJC-Banco de Santander.Peer reviewedPublisher PD
Markov chain aggregation and its application to rule-based modelling
Rule-based modelling allows to represent molecular interactions in a compact
and natural way. The underlying molecular dynamics, by the laws of stochastic
chemical kinetics, behaves as a continuous-time Markov chain. However, this
Markov chain enumerates all possible reaction mixtures, rendering the analysis
of the chain computationally demanding and often prohibitive in practice. We
here describe how it is possible to efficiently find a smaller, aggregate
chain, which preserves certain properties of the original one. Formal methods
and lumpability notions are used to define algorithms for automated and
efficient construction of such smaller chains (without ever constructing the
original ones). We here illustrate the method on an example and we discuss the
applicability of the method in the context of modelling large signalling
pathways
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
Formulating genome-scale kinetic models in the post-genome era.
The biological community is now awash in high-throughput data sets and is grappling with the challenge of integrating disparate data sets. Such integration has taken the form of statistical analysis of large data sets, or through the bottom-up reconstruction of reaction networks. While progress has been made with statistical and structural methods, large-scale systems have remained refractory to dynamic model building by traditional approaches. The availability of annotated genomes enabled the reconstruction of genome-scale networks, and now the availability of high-throughput metabolomic and fluxomic data along with thermodynamic information opens the possibility to build genome-scale kinetic models. We describe here a framework for building and analyzing such models. The mathematical analysis challenges are reflected in four foundational properties, (i) the decomposition of the Jacobian matrix into chemical, kinetic and thermodynamic information, (ii) the structural similarity between the stoichiometric matrix and the transpose of the gradient matrix, (iii) the duality transformations enabling either fluxes or concentrations to serve as the independent variables and (iv) the timescale hierarchy in biological networks. Recognition and appreciation of these properties highlight notable and challenging new in silico analysis issues
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