5,805 research outputs found
Qualitative modelling and analysis of regulations in multi-cellular systems using Petri nets and topological collections
In this paper, we aim at modelling and analyzing the regulation processes in
multi-cellular biological systems, in particular tissues.
The modelling framework is based on interconnected logical regulatory
networks a la Rene Thomas equipped with information about their spatial
relationships. The semantics of such models is expressed through colored Petri
nets to implement regulation rules, combined with topological collections to
implement the spatial information.
Some constraints are put on the the representation of spatial information in
order to preserve the possibility of an enumerative and exhaustive state space
exploration.
This paper presents the modelling framework, its semantics, as well as a
prototype implementation that allowed preliminary experimentation on some
applications.Comment: In Proceedings MeCBIC 2010, arXiv:1011.005
Abstracting Asynchronous Multi-Valued Networks: An Initial Investigation
Multi-valued networks provide a simple yet expressive qualitative state based
modelling approach for biological systems. In this paper we develop an
abstraction theory for asynchronous multi-valued network models that allows the
state space of a model to be reduced while preserving key properties of the
model. The abstraction theory therefore provides a mechanism for coping with
the state space explosion problem and supports the analysis and comparison of
multi-valued networks. We take as our starting point the abstraction theory for
synchronous multi-valued networks which is based on the finite set of traces
that represent the behaviour of such a model. The problem with extending this
approach to the asynchronous case is that we can now have an infinite set of
traces associated with a model making a simple trace inclusion test infeasible.
To address this we develop a decision procedure for checking asynchronous
abstractions based on using the finite state graph of an asynchronous
multi-valued network to reason about its trace semantics. We illustrate the
abstraction techniques developed by considering a detailed case study based on
a multi-valued network model of the regulation of tryptophan biosynthesis in
Escherichia coli.Comment: Presented at MeCBIC 201
ADAM: Analysis of Discrete Models of Biological Systems Using Computer Algebra
Background: Many biological systems are modeled qualitatively with discrete
models, such as probabilistic Boolean networks, logical models, Petri nets, and
agent-based models, with the goal to gain a better understanding of the system.
The computational complexity to analyze the complete dynamics of these models
grows exponentially in the number of variables, which impedes working with
complex models. Although there exist sophisticated algorithms to determine the
dynamics of discrete models, their implementations usually require
labor-intensive formatting of the model formulation, and they are oftentimes
not accessible to users without programming skills. Efficient analysis methods
are needed that are accessible to modelers and easy to use. Method: By
converting discrete models into algebraic models, tools from computational
algebra can be used to analyze their dynamics. Specifically, we propose a
method to identify attractors of a discrete model that is equivalent to solving
a system of polynomial equations, a long-studied problem in computer algebra.
Results: A method for efficiently identifying attractors, and the web-based
tool Analysis of Dynamic Algebraic Models (ADAM), which provides this and other
analysis methods for discrete models. ADAM converts several discrete model
types automatically into polynomial dynamical systems and analyzes their
dynamics using tools from computer algebra. Based on extensive experimentation
with both discrete models arising in systems biology and randomly generated
networks, we found that the algebraic algorithms presented in this manuscript
are fast for systems with the structure maintained by most biological systems,
namely sparseness, i.e., while the number of nodes in a biological network may
be quite large, each node is affected only by a small number of other nodes,
and robustness, i.e., small number of attractors
Modelling epistasis in genetic disease using Petri nets, evolutionary computation and frequent itemset mining
Petri nets are useful for mathematically modelling disease-causing genetic epistasis. A Petri net model of an interaction has the potential to lead to biological insight into the cause of a genetic disease. However, defining a Petri net by hand for a particular interaction is extremely difficult because of the sheer complexity of the problem and degrees of freedom inherent in a Petri net’s architecture.
We propose therefore a novel method, based on evolutionary computation and data mining, for automatically constructing Petri net models of non-linear gene interactions. The method comprises two main steps. Firstly, an initial partial Petri net is set up with several repeated sub-nets that model individual genes and a set of constraints, comprising relevant common sense and biological knowledge, is also defined. These constraints characterise the class of Petri nets that are desired. Secondly, this initial Petri net structure and the constraints are used as the input to a genetic algorithm. The genetic algorithm searches for a Petri net architecture that is both a superset of the initial net, and also conforms to all of the given constraints. The genetic algorithm evaluation function that we employ gives equal weighting to both the accuracy of the net and also its parsimony.
We demonstrate our method using an epistatic model related to the presence of digital ulcers in systemic sclerosis patients that was recently reported in the literature. Our results show that although individual “perfect” Petri nets can frequently be discovered for this interaction, the true value of this approach lies in generating many different perfect nets, and applying data mining techniques to them in order to elucidate common and statistically significant patterns of interaction
A structured approach for the engineering of biochemical network models, illustrated for signalling pathways
http://dx.doi.org/10.1093/bib/bbn026Quantitative models of biochemical networks (signal transduction cascades, metabolic pathways, gene regulatory circuits) are a central component of modern systems biology. Building and managing these complex models is a major challenge that can benefit from the application of formal methods adopted from theoretical computing science. Here we provide a general introduction to the field of formal modelling, which emphasizes the intuitive biochemical basis of the modelling process, but is also accessible for an audience with a background in computing science and/or model engineering. We show how signal transduction cascades can be modelled in a modular fashion, using both a qualitative approach { Qualitative Petri nets, and quantitative approaches { Continuous Petri Nets and Ordinary Differential Equations. We review the major elementary building blocks of a cellular signalling model, discuss which critical design decisions have to be made during model building, and present ..
Computational models for inferring biochemical networks
Biochemical networks are of great practical importance. The interaction of biological compounds in cells has been enforced to a proper understanding by the numerous bioinformatics projects, which contributed to a vast amount of biological information. The construction of biochemical systems (systems of chemical reactions), which include both topology and kinetic constants of the chemical reactions, is NP-hard and is a well-studied system biology problem. In this paper, we propose a hybrid architecture, which combines genetic programming and simulated annealing in order to generate and optimize both the topology (the network) and the reaction rates of a biochemical system. Simulations and analysis of an artificial model and three real models (two models and the noisy version of one of them) show promising results for the proposed method.The Romanian National Authority for Scientific Research, CNDI–UEFISCDI,
Project No. PN-II-PT-PCCA-2011-3.2-0917
Evolving concurrent Petri net models of epistasis
A genetic algorithm is used to learn a non-deterministic Petri netbased model of non-linear gene interactions, or statistical epistasis. Petri nets are computational models of concurrent processes. However, often certain global assumptions (e.g. transition priorities) are required in order to convert a non-deterministic Petri net into a simpler deterministic model for easier analysis and evaluation. We show, by converting a Petri net into a set of state trees, that it is possible to both retain Petri net non-determinism (i.e. allowing local interactions only, thereby making the model more realistic), whilst also learning useful Petri nets with practical applications. Our Petri nets produce predictions of genetic disease risk assessments derived from clinical data that match with over 92% accuracy
Analysis of signalling pathways using the prism model checker
We describe a new modelling and analysis approach for signal
transduction networks in the presence of incomplete data. We illustrate
the approach with an example, the RKIP inhibited ERK pathway
[1]. Our models are based on high level descriptions of continuous time
Markov chains: reactions are modelled as synchronous processes and concentrations
are modelled by discrete, abstract quantities. The main advantage
of our approach is that using a (continuous time) stochastic logic
and the PRISM model checker, we can perform quantitative analysis of
queries such as if a concentration reaches a certain level, will it remain at
that level thereafter? We also perform standard simulations and compare
our results with a traditional ordinary differential equation model. An
interesting result is that for the example pathway, only a small number
of discrete data values is required to render the simulations practically
indistinguishable
Exploring the concept of interaction computing through the discrete algebraic analysis of the Belousov–Zhabotinsky reaction
Interaction computing (IC) aims to map the properties of integrable low-dimensional non-linear dynamical systems to the discrete domain of finite-state automata in an attempt to reproduce in software the self-organizing and dynamically stable properties of sub-cellular biochemical systems. As the work reported in this paper is still at the early stages of theory development it focuses on the analysis of a particularly simple chemical oscillator, the Belousov-Zhabotinsky (BZ) reaction. After retracing the rationale for IC developed over the past several years from the physical, biological, mathematical, and computer science points of view, the paper presents an elementary discussion of the Krohn-Rhodes decomposition of finite-state automata, including the holonomy decomposition of a simple automaton, and of its interpretation as an abstract positional number system. The method is then applied to the analysis of the algebraic properties of discrete finite-state automata derived from a simplified Petri net model of the BZ reaction. In the simplest possible and symmetrical case the corresponding automaton is, not surprisingly, found to contain exclusively cyclic groups. In a second, asymmetrical case, the decomposition is much more complex and includes five different simple non-abelian groups whose potential relevance arises from their ability to encode functionally complete algebras. The possible computational relevance of these findings is discussed and possible conclusions are drawn
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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
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