Showing papers presented at "Computational Methods in Systems Biology in 2006"
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18 Oct 2006TL;DR: This work compares results obtained using implicit numerical differentiation formulae to those obtained using approximate stochastic simulation thereby exposing a flaw in the use of the differentiation procedure producing misleading results.
Abstract: Starting from a biochemical signalling pathway model expressed in a process algebra enriched with quantitative information we automatically derive both continuous-space and discrete-state representations suitable for numerical evaluation. We compare results obtained using implicit numerical differentiation formulae to those obtained using approximate stochastic simulation thereby exposing a flaw in the use of the differentiation procedure producing misleading results.
53 citations
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01 Jan 2006TL;DR: This paper presents an automated abstraction methodology that systematically reduces the small-scale complexity found in genetic regulatory network models, while broadly preserving the large-scale system behavior.
Abstract: In order to efficiently analyze the complicated regulatory systems often encountered in biological settings, abstraction is essential. This paper presents an automated abstraction methodology that systematically reduces the small-scale complexity found in genetic regulatory network models, while broadly preserving the large-scale system behavior. Our method first reduces the number of reactions by using rapid equilibrium and quasi-steady-state approximations as well as a number of other stoichiometry-simplifying techniques, which together result in substantially shortened simulation time. To further reduce analysis time, our method can represent the molecular state of the system by a set of scaled Boolean (or n-ary) discrete levels. This results in a chemical master equation that is approximated by a Markov chain with a much smaller state space providing significant analysis time acceleration and computability gains. The genetic regulatory network for the phage λ lysis/lysogeny decision switch is used as an example throughout the paper to help illustrate the practical applications of our methodology.
43 citations
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18 Oct 2006TL;DR: Based on the logical description of gene regulatory networks developed by R. Thomas, an enhanced modelling approach that uses timed automata yields a refined qualitative description of the dynamics of the system incorporating information not only on ratios of kinetic constants related to synthesis and decay, but also on the time delays occurring in the operations of theSystem.
Abstract: Based on the logical description of gene regulatory networks developed by R. Thomas, we introduce an enhanced modelling approach that uses timed automata. It yields a refined qualitative description of the dynamics of the system incorporating information not only on ratios of kinetic constants related to synthesis and decay, but also on the time delays occurring in the operations of the system. We demonstrate the potential of our approach by analysing an illustrative gene regulatory network of bacteriophage λ.
42 citations
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18 Oct 2006TL;DR: A new qualitative model for genetic regulatory networks based on Petri nets based on Boolean networks is proposed and a process for automatically constructing these models using logic minimization is detailed.
Abstract: In order to understand complex genetic regulatory networks researchers require automated formal modelling techniques that provide appropriate analysis tools In this paper we propose a new qualitative model for genetic regulatory networks based on Petri nets and detail a process for automatically constructing these models using logic minimization We take as our starting point the Boolean network approach in which regulatory entities are viewed abstractly as binary switches The idea is to extract terms representing a Boolean network using logic minimization and to then directly translate these terms into appropriate Petri net control structures The resulting compact Petri net model addresses a number of shortcomings associated with Boolean networks and is particularly suited to analysis using the wide range of Petri net tools We demonstrate our approach by presenting a detailed case study in which the genetic regulatory network underlying the nutritional stress response in Escherichia coli is modelled and analysed
36 citations
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18 Oct 2006TL;DR: This work proposes a numerical algorithm based on a similar partitioning but without resorting to simulation that exploits the connection to continuous-time Markov chains and decomposes the overall problem to significantly smaller subproblems that become tractable.
Abstract: Computational models of biochemical systems are usually very large, and moreover, if reaction frequencies of different reaction types differ in orders of magnitude, models possess the mathematical property of stiffness, which renders system analysis difficult and often even impossible with traditional methods. Recently, an accelerated stochastic simulation technique based on a system partitioning, the slow-scale stochastic simulation algorithm, has been applied to the enzyme-catalyzed substrate conversion to circumvent the inefficiency of standard stochastic simulation in the presence of stiffness. We propose a numerical algorithm based on a similar partitioning but without resorting to simulation. The algorithm exploits the connection to continuous-time Markov chains and decomposes the overall problem to significantly smaller subproblems that become tractable. Numerical results show enormous efficiency improvements relative to accelerated stochastic simulation.
31 citations
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18 Oct 2006
TL;DR: This paper introduces a new approach to the biclustering problem using the Possibilistic Clustering paradigm, and applies the proposed algorithm to the Yeast database, obtaining fast convergence and good quality solutions.
Abstract: The important research objective of identifying genes with similar behavior with respect to different conditions has recently been tackled with biclustering techniques. In this paper we introduce a new approach to the biclustering problem using the Possibilistic Clustering paradigm. The proposed Possibilistic Biclustering algorithm finds one bicluster at a time, assigning a membership to the bicluster for each gene and for each condition. The biclustering problem, in which one would maximize the size of the bicluster and minimizing the residual, is faced as the optimization of a proper functional. We applied the algorithm to the Yeast database, obtaining fast convergence and good quality solutions. We discuss the effects of parameter tuning and the sensitivity of the method to parameter values. Comparisons with other methods from the literature are also presented.
24 citations
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18 Oct 2006TL;DR: A new model called Membrane Systems with Peripheral and Integral Proteins with a circadian clock and the G-protein cycle in yeast saccharomyces cerevisiae is introduced and a quantitative analysis using an implemented simulator is presented.
Abstract: Membrane systems were introduced as models of computation inspired by the structure and functioning of biological cells. Recently, membrane systems have also been shown to be suitable to model cellular processes. We introduce a new model called Membrane Systems with Peripheral and Integral Proteins. The model has compartments enclosed by membranes, floating objects, objects associated to the internal and external surfaces of the membranes and also objects integral to the membranes. The floating objects can be processed within the compartments and can interact with the objects associated to the membranes. The model can be used to represent cellular processes that involve compartments, surface and integral membrane proteins, transport and processing of chemical substances. As examples we model a circadian clock and the G-protein cycle in yeast saccharomyces cerevisiae and present a quantitative analysis using an implemented simulator.
22 citations
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18 Oct 2006TL;DR: The results suggest that the currently identified ensemble of cells is inadequate to produce rhythmic neural activity and that several key elements of the CPG remain to be identified.
Abstract: The buccal ganglia of Aplysia contain a central pattern generator (CPG) that mediates rhythmic movements of the foregut during feeding. This CPG is a multifunctional circuit and generates at least two types of buccal motor patterns (BMPs), one that mediates ingestion (iBMP) and another that mediates rejection (rBMP). The present study used a computational approach to examine the ways in which an ensemble of identified cells and synaptic connections function as a CPG. Hodgkin-Huxley-type models were developed that mimicked the biophysical properties of these cells and synaptic connections. The results suggest that the currently identified ensemble of cells is inadequate to produce rhythmic neural activity and that several key elements of the CPG remain to be identified.
17 citations
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18 Oct 2006TL;DR: The Brane Logic, a modal logic for expressing formally properties about systems in Brane Calculus, is introduced and a model checker for a decidable fragment of this logic is presented.
Abstract: The Brane Calculus is a calculus of mobile processes, intended to model the transport machinery of a cell system. In this paper, we introduce the Brane Logic, a modal logic for expressing formally properties about systems in Brane Calculus. Similarly to previous logics for mobile ambients, Brane Logic has specific spatial and temporal modalities. Moreover, since in Brane Calculus the activity resides on membrane surfaces and not inside membranes, we need to add a specific logic (akin Hennessy-Milner’s) for reasoning about membrane activity.
We present also a proof system for deriving valid sequents in Brane Logic. Finally, we present a model checker for a decidable fragment of this logic.
14 citations
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18 Oct 2006TL;DR: A game-theoretic foundation for gene regulatory analysis based on the recent formalism of rewriting game theory is presented and it is shown that their models are specific instances of a C/P game deduced from the K parameter.
Abstract: We present a game-theoretic foundation for gene regulatory analysis based on the recent formalism of rewriting game theory. Rewriting game theory is discrete and comes with a graph-based framework for understanding compromises and interactions between players and for computing Nash equilibria. The formalism explicitly represents the dynamics of its Nash equilibria and, therefore, is a suitable foundation for the study of steady states in discrete modelling. We apply the formalism to the discrete analysis of gene regulatory networks introduced by R. Thomas and S. Kauffman. Specifically, we show that their models are specific instances of a C/P game deduced from the K parameter.
9 citations
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18 Oct 2006TL;DR: In this article, the decidability of divergence for the fragment with mate, bud and drip operations was extended to a broader class of properties and to a larger set of interaction primitives.
Abstract: Brane calculi are a family of biologically inspired process calculi proposed in [5] for modeling the interactions of dynamically nested membranes and small molecules.
Building on the decidability of divergence for the fragment with mate, bud and drip operations in [1], in this paper we extend the decidability results to a broader class of properties and to larger set of interaction primitives. More precisely, we provide the decidability of divergence, control state maintainabiliy, inevitability and boundedness properties for the calculus with molecules and without the phago operation.
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18 Oct 2006TL;DR: In this paper, a mathematical model for regulatory interactions based on the work of Thomas et al. extended with a stochastic element and an algorithm for reconstruction of such models from gene expression time series is presented.
Abstract: This paper presents a method for regulatory network reconstruction from experimental data. We propose a mathematical model for regulatory interactions, based on the work of Thomas et al. [25] extended with a stochastic element and provide an algorithm for reconstruction of such models from gene expression time series. We examine mathematical properties of the model and the reconstruction algorithm and test it on expression profiles obtained from numerical simulation of known regulatory networks. We compare the reconstructed networks with the ones reconstructed from the same data using Dynamic Bayesian Networks and show that in these cases our method provides the same or better results. The supplemental materials to this article are available from the website http://bioputer.mimuw.edu.pl/papers/cmsb06
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18 Oct 2006TL;DR: This article presents a framework for modeling genetic regulatory networks in a modular yet faithful manner based on the mathematically well-founded formalism of differential inclusions, and proposes a compositional algorithm to efficiently analyze reachability properties of the model.
Abstract: Genetic regulatory networks have been modeled as discrete transition systems by many approaches, benefiting from a large number of formal verification algorithms available for the analysis of discrete transition systems. However, most of these approaches do not scale up well. In this article, we explore the use of compositionality for the analysis of genetic regulatory networks. We present a framework for modeling genetic regulatory networks in a modular yet faithful manner based on the mathematically well-founded formalism of differential inclusions. We then propose a compositional algorithm to efficiently analyze reachability properties of the model. A case study shows the potential of this approach.
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18 Oct 2006TL;DR: This paper considers the Systems Biology Markup Language SBML and the Biochemical Abstract Machine BIOCHAM with their repositories of models of biochemical systems, and shows that the analysis of biochemical models by type inference provides accurate and useful information.
Abstract: Type checking and type inference are important concepts and methods of programming languages and software engineering. Type checking is a way to ensure some level of consistency, depending on the type system, in large programs and in complex assemblies of software components. Type inference provides powerful static analyses of pre-existing programs without types, and facilitates the use of type systems by freeing the user from entering type information. In this paper, we investigate the application of these concepts to systems biology. More specifically, we consider the Systems Biology Markup Language SBML and the Biochemical Abstract Machine BIOCHAM with their repositories of models of biochemical systems. We study three type systems: one for checking or inferring the functions of proteins in a reaction model, one for checking or inferring the activation and inhibition effects of proteins in a reaction model, and another one for checking or inferring the topology of compartments or locations. We show that the framework of abstract interpretation elegantly applies to the formalization of these abstractions and to the implementation of linear time type checking as well as type inference algorithms. Through some examples, we show that the analysis of biochemical models by type inference provides accurate and useful information. Interestingly, such a mathematical formalization of the abstractions used in systems biology already provides some guidelines for the extensions of biochemical reaction rule languages.
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18 Oct 2006
TL;DR: In this article, an enhanced specification of VICE, a hypothetical prokaryote with a genome as basic as possible, is presented. But it does not have a regulatory feedback circuit based on the enzyme phosphofructokinase.
Abstract: We analyse an enhanced specification of VICE, a hypothetical prokaryote with a genome as basic as possible. Besides the most common metabolic pathways of prokaryotes in interphase, VICE also posseses a regulatory feedback circuit based on the enzyme phosphofructokinase. We use as formal description language a fragment of the stochastic π-calculus. Simulations are run on BEAST, an abstract machine specially tailored to run in silico experimentations. Two kinds of virtual experiments have been carried out, depending on the way nutrients are supplied to VICE. The result of our experimentations in silico confirm that our virtual cell “survives” in an optimal environment, as it exhibits the homeostatic property similary to real living cells. Additionally, oscillatory patterns in the concentration of fructose-6-phosphate and fructose-1,6-bisphosphate show up, similar to the real ones.
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18 Oct 2006TL;DR: A low-resolution system analogue in which space, events, and time are discretized; object interaction uses a two-dimensional grid similar to a cellular automaton to facilitate experimental exploration of outcomes from changing components and features.
Abstract: In vitro model systems are used to study epithelial cell growth, morphogenesis, differentiation, and transition to cancer-like forms. MDCK cell lines (from immortalized kidney epithelial cells) are widely used examples. Prominent in vitro phenotypic attributes include stable cyst formation in embedded culture, inverted cyst formation in suspension culture, and lumen formation in overlay culture. We present a low-resolution system analogue in which space, events, and time are discretized; object interaction uses a two-dimensional grid similar to a cellular automaton. The framework enables “cell” agents to act independent using an embedded logic based on axioms. In silico growth and morphology can mimic in vitro observations in four different simulated environments. Matched behaviors include stable “cyst” formation. The in silico system is designed to facilitate experimental exploration of outcomes from changing components and features, including the embedded logic (the in silico analogue of a mutation or epigenetic change). Some simulated behaviors are sensitive to changes in logic. In two cases, the change caused cancer-like growth patterns to emerge.
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18 Oct 2006TL;DR: In this article, a graph decimation algorithm called "leaf-removal" is used to evaluate the feedback in a random graph ensemble, where the diagonal of the adjacency matrix has a fixed number of nonzero entries.
Abstract: Having in mind the large-scale analysis of gene regulatory networks, we review a graph decimation algorithm, called “leaf-removal”, which can be used to evaluate the feedback in a random graph ensemble. In doing this, we consider the possibility of analyzing networks where the diagonal of the adjacency matrix is structured, that is, has a fixed number of nonzero entries. We test these ideas on a network model with fixed degree, using both numerical and analytical calculations. Our results are the following. First, the leaf-removal behavior for large system size enables to distinguish between different regimes of feedback. We show their relations and the connection with the onset of complexity in the graph. Second, the influence of the diagonal structure on this behavior can be relevant.
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18 Oct 2006TL;DR: This paper integrates network architecture data with genome-wide gene expression measurements in order to determine which regulatory relations are actually confirmed by the expression data, and obtains non-trivial submodules of the regulatory network using two distinct algorithms, a naive exhaustive algorithm and a spectral algorithm based on the eigendecomposition of an affinity matrix.
Abstract: Recent high throughput techniques in molecular biology have brought about the possibility of directly identifying the architecture of regulatory networks on a genome-wide scale. However, the computational task of estimating fine-grained models on a genome-wide scale is daunting. Therefore, it is of great importance to be able to reliably identify submodules of the network that can be effectively modelled as independent subunits. In this paper we present a procedure to obtain submodules of a cellular network by using information from gene-expression measurements. We integrate network architecture data with genome-wide gene expression measurements in order to determine which regulatory relations are actually confirmed by the expression data. We then use this information to obtain non-trivial submodules of the regulatory network using two distinct algorithms, a naive exhaustive algorithm and a spectral algorithm based on the eigendecomposition of an affinity matrix. We test our method on two yeast biological data sets, using regulatory information obtained from chromatin immunoprecipitation.
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18 Oct 2006TL;DR: The power to uncover TF activity is demonstrated by focusing on a small, homogeneous, yet well defined set of chemostat cultivation experiments, where the transcriptional response of yeast grown under four different nutrient limitations, both aerobically as well as anaerobically was measured.
Abstract: Regulatory networks are usually presented as graph structures showing the (combinatorial) regulatory effect of transcription factors (TF’s) on modules of similarly expressed or otherwise related genes. However, from these networks it is not clear when and how TF’s are activated. The actual conditions or perturbations that trigger a change in the activity of TF’s should be a crucial part of the generated regulatory network.
Here, we demonstrate the power to uncover TF activity by focusing on a small, homogeneous, yet well defined set of chemostat cultivation experiments, where the transcriptional response of yeast grown under four different nutrient limitations, both aerobically as well as anaerobically was measured. We define a condition transition as an instant change in yeast’s extracellular environment by comparing two cultivation conditions, where either the limited nutrient or the oxygen availability is different. Differential gene expression as a consequence of such a condition transition is represented in a tertiary matrix, where zero indicates no change in expression; 1 and -1 respectively indicate an increase and decrease in expression as a consequence of a condition transition. We uncover TF activity by assessing significant TF binding in the promotor region of genes that behave accordingly at a condition transition. The interrelatedness of the conditions in the combinatorial setup is exploited by performing specific hypergeometric tests that allow for the discovery of both individual and combined effects of the cultivation parameters on TF activity. Additionally, we create a weight-matrix indicating the involvement of each TF in each of the condition transitions by posing our problem as an orthogonal Procrustes problem. We show that the Procrustes analysis strengthens and broadens the uncovered relationships.
The resulting regulatory network reveals nutrient-limitation-specific effects of oxygen presence on expression behavior and TF activity. Our analysis identifies many TF’s that seem to play a very specific regulatory role at the nutrient and oxygen availability transitions.
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18 Oct 2006TL;DR: A model of viral phenotypic mutations from R5 to X4 strains which reflect HIV late infection dynamics is presented and the action of Tumor Necrosis Factor in AIDS progression is investigated and suggestions on better design of HAART therapy are made.
Abstract: We have modelled the within-patient evolutionary process during HIV infection. We have studied viral evolution at population level (competition on the same receptor) and at species level (competitions on different receptors). During the HIV infection, several mutants of the virus arise, which are able to use different chemokine receptors, in particular the CCR5 and CXCR4 coreceptors (termed R5 and X4 phenotypes, respectively). Phylogenetic inference of chemokine receptors suggests that virus mutational pathways may generate R5 variants able to interact with a wide range of chemokine receptors different from CXCR4. Using the chemokine tree topology as conceptual framework for HIV viral speciation, we present a model of viral phenotypic mutations from R5 to X4 strains which reflect HIV late infection dynamics. Our model investigates the action of Tumor Necrosis Factor in AIDS progression and makes suggestions on better design of HAART therapy.
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18 Oct 2006TL;DR: This paper introduces Beta-binders, a process calculus for representing molecular complexation driven by the shape of the ligands involved and the subsequent molecular changes, and starts from process calculi theory to integrate information from molecular docking into systems biology paradigm.
Abstract: Drugs are small molecules designed to regulate the activity of specific biological receptors. Design new drugs is long and expensive, because modifying the behavior of a receptor may have unpredicted side effects. Two paradigms aim to speed up the drug discovery process: molecular docking estimates if two molecules can bind, to predict unwanted interactions; systems biology studies the effects of pharmacological intervention from a system perspective, to identify pathways related to the disease. In this paper we start from process calculi theory to integrate information from molecular docking into systems biology paradigm. In particular, we introduce Beta-binders${^\mathbb D}$, a process calculus for representing molecular complexation driven by the shape of the ligands involved and the subsequent molecular changes.
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18 Oct 2006
TL;DR: In this article, a phase ordering process mediated by phosphoinositide diffusion and driven by the distribution of chemotactic signal is proposed to explain the ability of eukaryotic cells to migrate directionally.
Abstract: Many eukaryotic cell types share the ability to migrate directionally in response to external chemoattractant gradients. This ability is central in the development of complex organisms, and is the result of billion years of evolution. Cells exposed to shallow gradients in chemoattractant concentration respond with strongly asymmetric accumulation of several signaling factors, such as phosphoinositides and enzymes. This early symmetry-breaking stage is believed to trigger effector pathways leading to cell movement. Although many factors implied in directional sensing have been recently discovered, the physical mechanism of signal amplification is not yet well understood. We have proposed that directional sensing is the consequence of a phase ordering process mediated by phosphoinositide diffusion and driven by the distribution of chemotactic signal. By studying a realistic computational model that describes enzymatic activity, recruitment to the plasmamembrane, and diffusion of phosphoinositide products we have shown that the effective enzyme-enzyme interaction induced by catalysis and diffusion introduces an instability of the system towards phase separation for realistic values of physical parameters. In this framework, large reversible amplification of shallow chemotactic gradients, selective localization of chemical factors, macroscopic response timescales, and spontaneous polarization arise.