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Efficient, correct simulation of biological processes in the stochastic picalculus
 Gilmore (Eds.), Proc. Int. Conf. Computational Methods in Systems Biology (CMSB’07
, 2007
"... Abstract. This paper presents a simulation algorithm for the stochastic πcalculus, designed for the efficient simulation of biological systems with large numbers of molecules. The cost of a simulation depends on the number of species, rather than the number of molecules, resulting in a significant ..."
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Abstract. This paper presents a simulation algorithm for the stochastic πcalculus, designed for the efficient simulation of biological systems with large numbers of molecules. The cost of a simulation depends on the number of species, rather than the number of molecules, resulting in a significant gain in efficiency. The algorithm is proved correct with respect to the calculus, and then used as a basis for implementing the latest version of the SPiM stochastic simulator. The algorithm is also suitable for generating graphical animations of simulations, in order to visualise system dynamics. 1
A Process Model of Rho GTPbinding Proteins in the Context of Phagocytosis
"... At the early stages of the phagocytic signalling, Rho GTPbinding proteins play a key role. With the stimulus from the cell membrane and with the help from the regulators (GEF, GAP, Effector, GDI), these proteins serve as switches that interact with their environment in a complex manner. We present ..."
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Cited by 6 (1 self)
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At the early stages of the phagocytic signalling, Rho GTPbinding proteins play a key role. With the stimulus from the cell membrane and with the help from the regulators (GEF, GAP, Effector, GDI), these proteins serve as switches that interact with their environment in a complex manner. We present a generic process model for the Rho GTPbinding proteins, and compare it with a previous model that uses ordinary differential equations. We then extend the basic model to include the behaviour of the GDIs. We discuss the challenges this extension brings and directions of further research. Keywords: phagocytosis, GTPbinding proteins, stochastic πcalculus, process modeling
Stochastic Simulation of Biological Systems with Dynamical Compartment Structure
"... The Gillespie stochastic simulation algorithm represents one of the main physical abstractions exploited for the simulation of biological systems modeled by means of concurrent calculi. While the faithful modelling of biosystems often requires multicompartment semantics, the original Gillespie alg ..."
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Cited by 5 (1 self)
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The Gillespie stochastic simulation algorithm represents one of the main physical abstractions exploited for the simulation of biological systems modeled by means of concurrent calculi. While the faithful modelling of biosystems often requires multicompartment semantics, the original Gillespie algorithm considers only one fixedsize volume. In this paper we introduce an extended formalisation of the above algorithm which preserves the original model but allows the stochastic simulation in presence of multiple compartments with dynamical structure and variable sizes. The presented algorithm can be then used as basis for simulating systems expressed in an extended version of the stochastic πCalculus, the Sπ @ language, obtained by means of polyadic synchronisation. Despite of its conservativeness, Sπ @ is showed to allow flexible modelling of multiple compartments with dynamical structure and to provide increased biological faithfulness. 1
A Language for Biochemical Systems: Design and Formal Specification
"... Abstract. This paper introduces a Language for Biochemical Systems (LBS) which combines rulebased approaches to modelling with modularity. It is based on the Calculus of Biochemical Systems (CBS) which affords modular descriptions of metabolic, signalling and regulatory networks in terms of reactio ..."
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Cited by 4 (3 self)
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Abstract. This paper introduces a Language for Biochemical Systems (LBS) which combines rulebased approaches to modelling with modularity. It is based on the Calculus of Biochemical Systems (CBS) which affords modular descriptions of metabolic, signalling and regulatory networks in terms of reactions between modified complexes, occurring concurrently inside a hierarchy of compartments and with possible crosscompartment interactions and transport. Additional features of LBS, targeted towards practical and largescale applications, include species expressions for manipulating large complexes in a concise manner, parameterised modules with a notion of subtyping for writing reusable modules, and nondeterminism for handling combinatorial explosion. These features are demonstrated through examples. A formal specification of LBS is then given through an abstract syntax and a general semantics which is parametric on a structure pertaining to the specific choice of target semantical objects. Examples of such structures for the specific cases of Petri nets, coloured Petri nets, ODEs and continuous time Markov chains are also given. Keywords: Largescale, parametrised modules, subtyping, combinatorial
A Process Model of Rho GTPbinding Proteins
"... Rho GTPbinding proteins play a key role as molecular switches in many cellular activities. In response to extracellular stimuli and with the help from regulators (GEF, GAP, Effector, GDI), these proteins serve as switches that interact with their environment in a complex manner. Based on the struct ..."
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Cited by 3 (0 self)
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Rho GTPbinding proteins play a key role as molecular switches in many cellular activities. In response to extracellular stimuli and with the help from regulators (GEF, GAP, Effector, GDI), these proteins serve as switches that interact with their environment in a complex manner. Based on the structure of a published ordinary differential equations (ODE) model, we first present a generic process model for the Rho GTPbinding proteins, and compare it with the ODE model. We then extend the basic model to include the behaviour of the GDIs and explore the parameter space for the extended model with respect to biological data from the literature. We discuss the challenges this extension brings and the directions of further research. Keywords: GTPbinding proteins, stochastic πcalculus, process modeling This paper is electronically published in
M.: Computational selfassembly
"... The object of this paper is to appreciate the computational limits inherent in the combinatorics of an applied concurrent (aka agentbased) language κ. That language is primarily meant as a visual and concise notation for biological signalling pathways. Descriptions in κ, when enriched with suitable ..."
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Cited by 2 (1 self)
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The object of this paper is to appreciate the computational limits inherent in the combinatorics of an applied concurrent (aka agentbased) language κ. That language is primarily meant as a visual and concise notation for biological signalling pathways. Descriptions in κ, when enriched with suitable kinetic information, generate simulations as continuous time Markov chains. However, κ can be studied independently of the intended application, in a purely computational fashion, and this is what we are doing here. Specifically, we define a compilation of κ into a language where interactions can involve at most two agents at a time. That compilation is generic, the blow up in the number of rules is linear in the total rule set size, and the methodology used in deriving the compilation relies on an implicit causality analysis. The correctness proof is given in details, and correctness is spelt out in terms of the existence of a specific weak bisimulation. To compensate for the binary restriction, one allows components to create unique identifiers (aka names). An interesting byproduct of the analysis is that when using acyclic rules, one sees that name creation is not needed, and κ can be fully reduced to binary form. 1
A Hybrid Linear Logic for Constrained Transition Systems
, 2009
"... Linear implication can represent state transitions, but real transition systems operate under temporal, stochastic or probabilistic constraints that are not directly representable in ordinary linear logic. We propose a general modal extension of intuitionistic linear logic where logical truth is ind ..."
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Linear implication can represent state transitions, but real transition systems operate under temporal, stochastic or probabilistic constraints that are not directly representable in ordinary linear logic. We propose a general modal extension of intuitionistic linear logic where logical truth is indexed by constraints and hybrid connectives combine constraint reasoning with logical reasoning. The logic has a focused cutfree sequent calculus that can be used to internalize the rules of particular constrained transition systems; we illustrate this with an adequate encoding of the synchronous stochastic picalculus. We also present some preliminary experiments of direct encoding of biological systems in the logic. 1
A Deductive Compositional Approach to Petri Nets for Systems Biology
"... We introduce the language CP, a compositional language for place transition petri nets for the purpose of modelling signalling pathways in complex biological systems. We give the operational semantics of the language CP by means of a proof theoretical deductive system which extends multiplicative e ..."
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We introduce the language CP, a compositional language for place transition petri nets for the purpose of modelling signalling pathways in complex biological systems. We give the operational semantics of the language CP by means of a proof theoretical deductive system which extends multiplicative exponential linear logic with a selfdual noncommutative logical operator. This allows to express parallel and sequential composition of processes at the same syntactic level as in process algebra, and perform logical reasoning on these processes. We demonstrate the use of the language on a model of a signaling pathway for Fc receptormediated phagocytosis.
Visualization in Process Algebra Models of Biological Systems
"... In a recent paper, Nobel laureate Paul Nurse calls for a better understanding of living organisms through “both the development of the appropriate languages to describe information processing in biological systems and the generation of more effective methods to translate biochemical descriptions int ..."
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In a recent paper, Nobel laureate Paul Nurse calls for a better understanding of living organisms through “both the development of the appropriate languages to describe information processing in biological systems and the generation of more effective methods to translate biochemical descriptions into the functioning of the logic circuits that underpin biological phenomena. ” [1] The language that Nurse wishes to see is a formal language that can be automatically translated into machine executable code and that enables simulation and analysis techniques for proving properties of biological systems. Although there are many approaches to the formal modeling of living systems, only a few provide executable descriptions that highlight the mechanistic steps that make a system move from one state to another [2]. Almost all the techniques related to mathematical modeling abstract from these individual steps to produce global behavior, usually averaged over time. Computer science provides the key elements to describe mechanistic steps: algorithms and programming languages [3]. Following the metaphor of molecules as processes introduced in [4], process calculi have been identified as a promising tool to model biological systems that are
Abstract A Chart Semantics for the PiCalculus
"... We present a graphical semantics for the picalculus, that is easier to visualize and better suited to expressing causality and temporal properties than conventional relational semantics. A pichart is a finite directed acyclic graph recording a computation in the picalculus. Each node represents a ..."
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We present a graphical semantics for the picalculus, that is easier to visualize and better suited to expressing causality and temporal properties than conventional relational semantics. A pichart is a finite directed acyclic graph recording a computation in the picalculus. Each node represents a process, and each edge either represents a computation step, or a messagepassing interaction. Picharts enjoy a natural pictorial representation, akin to message sequence charts, in which vertical edges represent control flow and horizontal edges represent data flow based on message passing. A pichart represents a single computation starting from its top (the nodes with no ancestors) to its bottom (the nodes with no descendants). Unlike conventional reductions or transitions, the edges in a pichart induce ancestry and other causal relations on processes. We give both compositional and operational definitions of picharts, and illustrate the additional expressivity afforded by the chart semantics via a series of examples.