11,798 research outputs found
BlenX-based compositional modeling of complex reaction mechanisms
Molecular interactions are wired in a fascinating way resulting in complex
behavior of biological systems. Theoretical modeling provides a useful
framework for understanding the dynamics and the function of such networks. The
complexity of the biological networks calls for conceptual tools that manage
the combinatorial explosion of the set of possible interactions. A suitable
conceptual tool to attack complexity is compositionality, already successfully
used in the process algebra field to model computer systems. We rely on the
BlenX programming language, originated by the beta-binders process calculus, to
specify and simulate high-level descriptions of biological circuits. The
Gillespie's stochastic framework of BlenX requires the decomposition of
phenomenological functions into basic elementary reactions. Systematic
unpacking of complex reaction mechanisms into BlenX templates is shown in this
study. The estimation/derivation of missing parameters and the challenges
emerging from compositional model building in stochastic process algebras are
discussed. A biological example on circadian clock is presented as a case study
of BlenX compositionality
Iterative Approximate Solutions of Kinetic Equations for Reversible Enzyme Reactions
We study kinetic models of reversible enzyme reactions and compare two
techniques for analytic approximate solutions of the model. Analytic
approximate solutions of non-linear reaction equations for reversible enzyme
reactions are calculated using the Homotopy Perturbation Method (HPM) and the
Simple Iteration Method (SIM). The results of the approximations are similar.
The Matlab programs are included in appendices.Comment: 28 pages, 22 figure
A model reduction method for biochemical reaction networks
Background: In this paper we propose a model reduction method for biochemical reaction networks governed by a variety of reversible and irreversible enzyme kinetic rate laws, including reversible Michaelis-Menten and Hill kinetics. The method proceeds by a stepwise reduction in the number of complexes, defined as the left and right-hand sides of the reactions in the network. It is based on the Kron reduction of the weighted Laplacian matrix, which describes the graph structure of the complexes and reactions in the network. It does not rely on prior knowledge of the dynamic behaviour of the network and hence can be automated, as we demonstrate. The reduced network has fewer complexes, reactions, variables and parameters as compared to the original network, and yet the behaviour of a preselected set of significant metabolites in the reduced network resembles that of the original network. Moreover the reduced network largely retains the structure and kinetics of the original model.
Results: We apply our method to a yeast glycolysis model and a rat liver fatty acid beta-oxidation model. When the number of state variables in the yeast model is reduced from 12 to 7, the difference between metabolite concentrations in the reduced and the full model, averaged over time and species, is only 8%. Likewise, when the number of state variables in the rat-liver beta-oxidation model is reduced from 42 to 29, the difference between the reduced model and the full model is 7.5%.
Conclusions: The method has improved our understanding of the dynamics of the two networks. We found that, contrary to the general disposition, the first few metabolites which were deleted from the network during our stepwise reduction approach, are not those with the shortest convergence times. It shows that our reduction approach performs differently from other approaches that are based on time-scale separation. The method can be used to facilitate fitting of the parameters or to embed a detailed model of interest in a more coarse-grained yet realistic environment
FluxSimulator: An R Package to Simulate Isotopomer Distributions in Metabolic Networks
The representation of biochemical knowledge in terms of fluxes (transformation rates) in a metabolic network is often a crucial step in the development of new drugs and efficient bioreactors. Mass spectroscopy (MS) and nuclear magnetic resonance spectroscopy (NMRS) in combination with ^13C labeled substrates are experimental techniques resulting in data that may be used to quantify fluxes in the metabolic network underlying a process. The massive amount of data generated by spectroscopic experiments increasingly requires software which models the dynamics of the underlying biological system. In this work we present an approach to handle isotopomer distributions in metabolic networks using an object-oriented programming approach, implemented using S4 classes in R. The developed package is called FluxSimulator and provides a user friendly interface to specify the topological information of the metabolic network as well as carbon atom transitions in plain text files. The package automatically derives the mathematical representation of the formulated network, and assembles a set of ordinary differential equations (ODEs) describing the change of each isotopomer pool over time. These ODEs are subsequently solved numerically. In a case study FluxSimulator was applied to an example network. Our results indicate that the package is able to reproduce exact changes in isotopomer compositions of the metabolite pools over time at given flux rates.
Systems approaches to modelling pathways and networks.
Peer reviewedPreprin
Enzyme economy in metabolic networks
Metabolic systems are governed by a compromise between metabolic benefit and
enzyme cost. This hypothesis and its consequences can be studied by kinetic
models in which enzyme profiles are chosen by optimality principles. In
enzyme-optimal states, active enzymes must provide benefits: a higher enzyme
level must provide a metabolic benefit to justify the additional enzyme cost.
This entails general relations between metabolic fluxes, reaction elasticities,
and enzyme costs, the laws of metabolic economics. The laws can be formulated
using economic potentials and loads, state variables that quantify how
metabolites, reactions, and enzymes affect the metabolic performance in a
steady state. Economic balance equations link them to fluxes, reaction
elasticities, and enzyme levels locally in the network. Economically feasible
fluxes must be free of futile cycles and must lead from lower to higher
economic potentials, just like thermodynamics makes them lead from higher to
lower chemical potentials. Metabolic economics provides algebraic conditions
for economical fluxes, which are independent of the underlying kinetic models.
It justifies and extends the principle of minimal fluxes and shows how to
construct kinetic models in enzyme-optimal states, where all enzymes have a
positive influence on the metabolic performance
Qualitative System Identification from Imperfect Data
Experience in the physical sciences suggests that the only realistic means of
understanding complex systems is through the use of mathematical models.
Typically, this has come to mean the identification of quantitative models
expressed as differential equations. Quantitative modelling works best when the
structure of the model (i.e., the form of the equations) is known; and the
primary concern is one of estimating the values of the parameters in the model.
For complex biological systems, the model-structure is rarely known and the
modeler has to deal with both model-identification and parameter-estimation. In
this paper we are concerned with providing automated assistance to the first of
these problems. Specifically, we examine the identification by machine of the
structural relationships between experimentally observed variables. These
relationship will be expressed in the form of qualitative abstractions of a
quantitative model. Such qualitative models may not only provide clues to the
precise quantitative model, but also assist in understanding the essence of
that model. Our position in this paper is that background knowledge
incorporating system modelling principles can be used to constrain effectively
the set of good qualitative models. Utilising the model-identification
framework provided by Inductive Logic Programming (ILP) we present empirical
support for this position using a series of increasingly complex artificial
datasets. The results are obtained with qualitative and quantitative data
subject to varying amounts of noise and different degrees of sparsity. The
results also point to the presence of a set of qualitative states, which we
term kernel subsets, that may be necessary for a qualitative model-learner to
learn correct models. We demonstrate scalability of the method to biological
system modelling by identification of the glycolysis metabolic pathway from
data
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