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Statistical model checking: An overview
 RV 2010
, 2010
"... Quantitative properties of stochastic systems are usually specified in logics that allow one to compare the measure of executions satisfying certain temporal properties with thresholds. The model checking problem for stochastic systems with respect to such logics is typically solved by a numerical a ..."
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Quantitative properties of stochastic systems are usually specified in logics that allow one to compare the measure of executions satisfying certain temporal properties with thresholds. The model checking problem for stochastic systems with respect to such logics is typically solved by a numerical approach [31,8,35,22,21,5] that iteratively computes (or approximates) the exact measure of paths satisfying relevant subformulas; the algorithms themselves depend on the class of systems being analyzed as well as the logic used for specifying the properties. Another approach to solve the model checking problem is to simulate the system for finitely many executions, and use hypothesis testing to infer whether the samples provide a statistical evidence for the satisfaction or violation of the specification. In this tutorial, we survey the statistical approach, and outline its main advantages in terms of efficiency, uniformity, and simplicity.
Statistical Model Checking in BioLab: Applications to the automated analysis of TCell Receptor Signaling Pathway ⋆
"... Abstract. We present an algorithm, called BioLab, for verifying temporal properties of rulebased models of cellular signalling networks. BioLab models are encoded in the BioNetGen language, and properties are expressed as formulae in probabilistic bounded linear temporal logic. Temporal logic is a ..."
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Abstract. We present an algorithm, called BioLab, for verifying temporal properties of rulebased models of cellular signalling networks. BioLab models are encoded in the BioNetGen language, and properties are expressed as formulae in probabilistic bounded linear temporal logic. Temporal logic is a formalism for representing and reasoning about propositions qualified in terms of time. Properties are then verified using sequential hypothesis testing on executions generated using stochastic simulation. BioLab is optimal, in the sense that it generates the minimum number of executions necessary to verify the given property. BioLab also provides guarantees on the probability of it generating TypeI (i.e., falsepositive) and TypeII (i.e., falsenegative) errors. Moreover, these error bounds are prespecified by the user. We demonstrate BioLab by verifying stochastic effects and bistability in the dynamics of the Tcell receptor signaling network. 1
Faeder J: Compartmental rulebased modeling of biochemical systems
 Proceedings of the 2009 Winter Simulation Conference (WSC), IEEE 2009
"... Rulebased modeling is an approach to modeling biochemical kinetics in which proteins and other biological components are modeled as structured objects and their interactions are governed by rules that specify the conditions under which reactions occur. BIONETGEN is an opensource platform that prov ..."
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Rulebased modeling is an approach to modeling biochemical kinetics in which proteins and other biological components are modeled as structured objects and their interactions are governed by rules that specify the conditions under which reactions occur. BIONETGEN is an opensource platform that provides a simple yet expressive language for rulebased modeling (BNGL). In this paper we describe compartmental BNGL (cBNGL), which extends BNGL to enable explicit modeling of the compartmental organization of the cell and its effects on system dynamics. We show that by making localization a queryable attribute of both molecules and species and introducing appropriate volumetric scaling of reaction rates, the effects of compartmentalization can be naturally modeled using rules. These properties enable the construction of new rule semantics that include both universal rules, those defining interactions that can take place in any compartment in the system, and transport rules, which enable movement of molecular complexes between compartments. 1
G.E.: Rulebender: integrated modeling, simulation and visualization for rulebased intracellular biochemistry
 BMC bioinformatics 13(Suppl
, 2012
"... This thesis was presented by ..."
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Thermodynamic graphrewriting
"... Abstract. We develop a new ‘thermodynamic ’ approach to stochastic graphrewriting. The ingredients are a finite set of reversible graphrewriting rules G (called generating rules), a finite set of connected graphs P (called energy patterns), and an energy cost function : P → R. The idea is that G ..."
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Abstract. We develop a new ‘thermodynamic ’ approach to stochastic graphrewriting. The ingredients are a finite set of reversible graphrewriting rules G (called generating rules), a finite set of connected graphs P (called energy patterns), and an energy cost function : P → R. The idea is that G defines the qualitative dynamics by showing which transformations are possible, while P and specify the longterm probability pi of any graph reachable under G. Given G, P, we construct a finite set of rules GP which (i) has the same qualitative transition system as G, and (ii) when equipped with suitable rates, defines a continuoustime Markov chain of which pi is the unique fixed point. The construction relies on the use of site graphs and a technique of ‘growth policy ’ for quantitative rule refinement which is of independent interest. The ‘division of labour ’ between the qualitative and the longterm quantitative aspects of the dynamics leads to intuitive and concise descriptions for realistic models (see the example in §4). It also guarantees thermodynamical consistency (aka detailed balance), otherwise known to be undecidable, which is important for some applications. Finally, it leads to parsimonious parameterizations of models, again an important point in some applications. 1
FORMAL REPRESENTATION OF THE HIGH OSMOLARITY GLYCEROL PATHWAY IN YEAST
, 2009
"... The high osmolarity glycerol (HOG) signalling system in yeast belongs to the class of Mitogen Activated Protein Kinase (MAPK) pathways that are found in all eukaryotic organisms. It includes at least three scaffold proteins that form complexes, and involves reactions that are strictly dependent on t ..."
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The high osmolarity glycerol (HOG) signalling system in yeast belongs to the class of Mitogen Activated Protein Kinase (MAPK) pathways that are found in all eukaryotic organisms. It includes at least three scaffold proteins that form complexes, and involves reactions that are strictly dependent on the set of species bound to a certain complex. The scaffold proteins lead to a combinatorial increase in the number of possible states. To date, representations of the HOG pathway have used simplifying assumptions to avoid this combinatorial problem. Such assumptions are hard to make and may obscure or remove essential properties of the system. This paper presents a detailed generic formal representation of the HOG system without such assumptions, showing the molecular interactions known from the literature. The model takes complexes into account, and summarises existing knowledge in an unambiguous and detailed representation. It can thus be used to anchor discussions about the HOG system. In the commonly used Systems Biology Markup Language (SBML), such a model would need to explicitly enumerate all state variables. The Kappa modelling language which we use supports representation of complexes without such enumeration. To conclude, we compare Kappa with a few other modelling languages and software tools that could also be used to represent and model the HOG system.
Systems biology
"... Efficient stochastic simulation of reaction–diffusion processes via direct compilation ..."
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Efficient stochastic simulation of reaction–diffusion processes via direct compilation
Review Spatial Simulations in Systems Biology: From Molecules to Cells
, 2012
"... Abstract: Cells are highly organized objects containing millions of molecules. Each biomolecule has a specific shape in order to interact with others in the complex machinery. Spatial dynamics emerge in this system on length and time scales which can not yet be modeled with full atomic detail. This ..."
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Abstract: Cells are highly organized objects containing millions of molecules. Each biomolecule has a specific shape in order to interact with others in the complex machinery. Spatial dynamics emerge in this system on length and time scales which can not yet be modeled with full atomic detail. This review gives an overview of methods which can be used to simulate the complete cell at least with molecular detail, especially Brownian dynamics simulations. Such simulations require correct implementation of the diffusioncontrolled reaction scheme occurring on this level. Implementations and applications of spatial simulations are presented, and finally it is discussed how the atomic level can be included for instance in multiscale simulation methods.