12,304 research outputs found
Petri nets for systems and synthetic biology
We give a description of a Petri net-based framework for
modelling and analysing biochemical pathways, which uniĀÆes the qualita-
tive, stochastic and continuous paradigms. Each perspective adds its con-
tribution to the understanding of the system, thus the three approaches
do not compete, but complement each other. We illustrate our approach
by applying it to an extended model of the three stage cascade, which
forms the core of the ERK signal transduction pathway. Consequently
our focus is on transient behaviour analysis. We demonstrate how quali-
tative descriptions are abstractions over stochastic or continuous descrip-
tions, and show that the stochastic and continuous models approximate
each other. Although our framework is based on Petri nets, it can be
applied more widely to other formalisms which are used to model and
analyse biochemical networks
An integrative top-down and bottom-up qualitative model construction framework for exploration of biochemical systems
The authors would like to thank the support on this research by the CRISP project (Combinatorial Responses In Stress Pathways) funded by the BBSRC (BB/F00513X/1) under the Systems Approaches to Biological Research (SABR) Initiative.Peer reviewedPublisher PD
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An introduction to Biomodel engineering, illustrated for signal transduction pathways
BioModel Engineering is the science of designing, constructing
and analyzing computational models of biological systems. It is inspired
by concepts from software engineering and computing science.
This paper illustrates a major theme in BioModel Engineering, namely
that identifying a quantitative model of a dynamic system means building
the structure, finding an initial state, and parameter fitting. In our
approach, the structure is obtained by piecewise construction of models
from modular parts, the initial state is obtained by analysis of the structure
and parameter fitting comprises determining the rate parameters of
the kinetic equations. We illustrate this with an example in the area of
intracellular signalling pathways
Computing Difference Abstractions of Metabolic Networks Under Kinetic Constraints
International audienceAlgorithms based on abstract interpretation were proposed recently for predicting changes of reaction networks with partial kinetic information. Their prediction precision, however, depends heavily on which heuristics are applied in order to add linear consequences of the steady state equations of the metabolic network. In this paper we ask the question whether such heuristics can be avoided while obtaining the highest possible precision. This leads us to the first algorithm for computing the difference abstractions of a linear equation system exactly without any approximation. This algorithm relies on the usage of elementary flux modes in a nontrivial manner, first-order definitions of the abstractions, and finite domain constraint solving
Structural Kinetic Modeling of Metabolic Networks
To develop and investigate detailed mathematical models of cellular metabolic
processes is one of the primary challenges in systems biology. However, despite
considerable advance in the topological analysis of metabolic networks,
explicit kinetic modeling based on differential equations is still often
severely hampered by inadequate knowledge of the enzyme-kinetic rate laws and
their associated parameter values. Here we propose a method that aims to give a
detailed and quantitative account of the dynamical capabilities of metabolic
systems, without requiring any explicit information about the particular
functional form of the rate equations. Our approach is based on constructing a
local linear model at each point in parameter space, such that each element of
the model is either directly experimentally accessible, or amenable to a
straightforward biochemical interpretation. This ensemble of local linear
models, encompassing all possible explicit kinetic models, then allows for a
systematic statistical exploration of the comprehensive parameter space. The
method is applied to two paradigmatic examples: The glycolytic pathway of yeast
and a realistic-scale representation of the photosynthetic Calvin cycle.Comment: 14 pages, 8 figures (color
A unified view on bipartite species-reaction and interaction graphs for chemical reaction networks
The Jacobian matrix of a dynamic system and its principal minors play a
prominent role in the study of qualitative dynamics and bifurcation analysis.
When interpreting the Jacobian as an adjacency matrix of an interaction graph,
its principal minors correspond to sets of disjoint cycles in this graph and
conditions for various dynamic behaviors can be inferred from its cycle
structure. For chemical reaction systems, more fine-grained analyses are
possible by studying a bipartite species-reaction graph. Several results on
injectivity, multistationarity, and bifurcations of a chemical reaction system
have been derived by using various definitions of such bipartite graph. Here,
we present a new definition of the species-reaction graph that more directly
connects the cycle structure with determinant expansion terms, principal
minors, and the coefficients of the characteristic polynomial and encompasses
previous graph constructions as special cases. This graph has a direct relation
to the interaction graph, and properties of cycles and sub-graphs can be
translated in both directions. A simple equivalence relation enables to
decompose determinant expansions more directly and allows simpler and more
direct proofs of previous results.Comment: 27 pages. submitted to J. Math. Bio
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
On the foundations of cancer modelling: selected topics, speculations, & perspectives
This paper presents a critical review of selected topics related to the modelling of cancer onset, evolution and growth, with the aim of illustrating, to a wide applied mathematical readership, some of the novel mathematical problems in the field. This review attempts to capture, from the appropriate literature, the main issues involved in the modelling of phenomena related to cancer dynamics at all scales which characterise this highly complex system: from the molecular scale up to that of tissue. The last part of the paper discusses the challenge of developing a mathematical biological theory of tumour onset and evolution
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