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Rulebased Modelling of Cellular Signalling
 PROCEEDINGS OF THE 18 TH INTERNATIONAL CONFERENCE ON CONCURRENCY THEORY (CONCUR’07), LECTURE NOTES IN COMPUTER SCIENCE
, 2007
"... Modelling is becoming a necessity in studying biological signalling pathways, because the combinatorial complexity of such systems rapidly overwhelms intuitive and qualitative forms of reasoning. Yet, this same combinatorial explosion makes the traditional modelling paradigm based on systems of di ..."
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Cited by 104 (22 self)
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Modelling is becoming a necessity in studying biological signalling pathways, because the combinatorial complexity of such systems rapidly overwhelms intuitive and qualitative forms of reasoning. Yet, this same combinatorial explosion makes the traditional modelling paradigm based on systems of differential equations impractical. In contrast, agentbased or concurrent languages, such as κ [1–3] or the closely related BioNetGen language [4–10], describe biological interactions in terms of rules, thereby avoiding the combinatorial explosion besetting differential equations. Rules are expressed in an intuitive graphical form that transparently represents biological knowledge. In this way, rules become a natural unit of model building, modification, and discussion. We illustrate this with a sizeable example obtained from refactoring two models of EGF receptor signalling that are based on differential equations [11, 12]. An exciting aspect of the agentbased approach is that it naturally lends itself to the identification and analysis of the causal structures that deeply shape the dynamical, and perhaps even evolutionary, characteristics of complex distributed biological systems. In particular, one can adapt the notions of causality and conflict, familiar from concurrency theory, to κ, our representation language of choice. Using the EGF receptor model as an example, we show how causality enables the formalization of the colloquial concept of pathway and, perhaps more surprisingly, how conflict can be used to dissect the signalling dynamics to obtain a qualitative handle on the range of system behaviours. By taming the combinatorial explosion, and exposing the causal structures and key kinetic junctures in a model, agent and rulebased representations hold promise for making modelling more powerful, more perspicuous, and of appeal to a wider audience.
Scalable simulation of cellular signaling networks
 IN PROCEEDINGS OF APLAS 2007
, 2007
"... Given the combinatorial nature of cellular signalling pathways, where biological agents can bind and modify each other in a large number of ways, concurrent or agentbased languages seem particularly suitable for their representation and simulation [1–4]. Graphical modelling languages such as κ [5– ..."
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Cited by 59 (13 self)
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Given the combinatorial nature of cellular signalling pathways, where biological agents can bind and modify each other in a large number of ways, concurrent or agentbased languages seem particularly suitable for their representation and simulation [1–4]. Graphical modelling languages such as κ [5–8], or the closely related BNG language [9– 14], seem to afford particular ease of expression. It is unclear however how such models can be implemented. 6 Even a simple model of the EGF receptor signalling network can generate more than 10 23 nonisomorphic species [5], and therefore no approach to simulation based on enumerating species (beforehand, or even onthefly) can handle such models without sampling down the number of potential generated species. We present in this paper a radically different method which does not attempt to count species. The proposed algorothm uses a representation of the system together with a superapproximation of its ‘event horizon ’ (all events that may happen next), and a specific correction scheme to obtain exact timings. Being completely local and not based on any kind of enumeration, this algorithm has a per event time cost which is independent of (i) the size of the set of generable species (which can even be infinite), and (ii) independent of the size of the system (ie, the number of agent instances). We show how to refine this algorithm, using concepts derived from the classical notion of causality, so that in addition to the above one also has that the even cost is depending (iii) only logarithmically on the size of the model (ie, the number of rules). Such complexity properties reflect in our implementation which, on a current computer, generates about 10 6 events per minute in the case of the simple EGF receptor model mentioned above, using a system with 10 5 agents.
Rulebased modeling of biochemical systems with BioNetGen
 IN METHODS IN MOLECULAR BIOLOGY: SYSTEMS BIOLOGY
, 2009
"... Rulebased modeling involves the representation of molecules as structured objects and molecular interactions as rules for transforming the attributes of these objects. The approach is notable in that it allows one to systematically incorporate sitespecific details about proteinprotein interactio ..."
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Cited by 43 (10 self)
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Rulebased modeling involves the representation of molecules as structured objects and molecular interactions as rules for transforming the attributes of these objects. The approach is notable in that it allows one to systematically incorporate sitespecific details about proteinprotein interactions into a model for the dynamics of a signaltransduction system, but the method has other applications as well, such as following the fates of individual carbon atoms in metabolic reactions. The consequences of proteinprotein interactions are difficult to specify and track with a conventional modeling approach because of the large number of protein phosphoforms and protein complexes that these interactions potentially generate. Here, we focus on how a rulebased model is specified in the BioNetGen language (BNGL) and how a model specification is analyzed using the BioNetGen software tool. We also discuss new developments in rulebased modeling that should enable the construction and analyses of comprehensive models for signal transduction pathways and similarly largescale models for other biochemical systems.
Abstract interpretation of cellular signalling networks
 4905 OF LNCS
, 2008
"... Cellular signalling pathways, where proteins can form complexes and undergo a large array of post translational modifications are highly combinatorial systems sending and receiving extracellular signals and triggering appropriate responses. Processcentric languages seem apt to their representatio ..."
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Cited by 33 (8 self)
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Cellular signalling pathways, where proteins can form complexes and undergo a large array of post translational modifications are highly combinatorial systems sending and receiving extracellular signals and triggering appropriate responses. Processcentric languages seem apt to their representation and simulation [1–3]. Rulecentric languages such as κ [4–8] and BNG [9, 10] bring in additional ease of expression. We propose in this paper a method to enumerate a superset of the reachable complexes that a κ rule set can generate. This is done via the construction of a finite abstract interpretation. We find a simple criterion for this superset to be the exact set of reachable complexes, namely that the superset is closed under swap, an operation whereby pairs of edges of the same type can permute their ends. We also show that a simple syntactic restriction on rules is sufficient to ensure the generation of a swapclosed set of complexes. We conclude by showing that a substantial rule set (presented in Ref. [4]) modelling the EGF receptor pathway verifies that syntactic condition (up to suitable transformations), and therefore despite its apparent complexity has a rather simple set of reachables.
Abstract interpretation and types for systems biology
 IN: THEORETICAL COMPUTER SCIENCE
, 2008
"... Abstract interpretation is a theory of abstraction that has been introduced for the analysis of programs. In particular, it has proved useful for organizing the multiple semantics of a given programming language in a hierarchy corresponding to different detail levels, and for defining type systems f ..."
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Cited by 26 (8 self)
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Abstract interpretation is a theory of abstraction that has been introduced for the analysis of programs. In particular, it has proved useful for organizing the multiple semantics of a given programming language in a hierarchy corresponding to different detail levels, and for defining type systems for programming languages and program analyzers in software engineering. In this paper, we investigate the application of these concepts to systems biology formalisms. More specifically, we consider the Systems Biology Markup Language SBML, and the Biochemical Abstract Machine BIOCHAM with its differential, stochastic, discrete and boolean semantics. We first show how all of these different semantics, except the differential one, can be formally related by simple Galois connections. Then we define 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 further abstractions, and to the implementation of linear or quadratic time type checking as well as type inference algorithms. Furthermore, we show a theorem of independence of the graph of activation and inhibition effects from the kinetic expressions in the reaction model, under general conditions. 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 commonly used in systems biology already provides some guidelines for the extensions of biochemical reaction rule languages.
Statistical model checking in BioLab: applications to the automated analysis of TCell receptor signaling pathway
 In CMSB’08
, 2008
"... 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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Cited by 25 (7 self)
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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.
Rulebased modelling, symmetries, refinements
"... Abstract. Rulebased modelling is particularly effective for handling the highly combinatorial aspects of cellular signalling. The dynamics is described in terms of interactions between partial complexes, and the ability to write rules with such partial complexesi.e., not to have to specify all the ..."
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Cited by 20 (9 self)
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Abstract. Rulebased modelling is particularly effective for handling the highly combinatorial aspects of cellular signalling. The dynamics is described in terms of interactions between partial complexes, and the ability to write rules with such partial complexesi.e., not to have to specify all the traits of the entitities partaking in a reaction but just those that matter is the key to obtaining compact descriptions of what otherwise could be nearly infinite dimensional dynamical systems. This also makes these descriptions easier to read, write and modify. In the course of modelling a particular signalling system it will often happen that more traits matter in a given interaction than previously thought, and one will need to strengthen the conditions under which that interaction may happen. This is a process that we call rule refinement and which we set out in this paper to study. Specifically we present a method to refine rule sets in a way that preserves the implied stochastic semantics.
Formal Cell Biology in Biocham
"... Abstract. Biologists use diagrams to represent interactions between molecular species, and on the computer, diagrammatic notations are also employed in interactive maps. These diagrams are fundamentally of two types: reaction graphs and activation/inhibition graphs. In this tutorial, we study these ..."
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Cited by 16 (6 self)
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Abstract. Biologists use diagrams to represent interactions between molecular species, and on the computer, diagrammatic notations are also employed in interactive maps. These diagrams are fundamentally of two types: reaction graphs and activation/inhibition graphs. In this tutorial, we study these graphs with formal methods originating from programming theory. We consider systems of biochemical reactions with kinetic expressions, as written in the Systems Biology Markup Language (SBML), and interpreted in the Biochemical Abstract Machine (Biocham) at different levels of abstraction, by either an asynchronous boolean transition system, a continuous time Markov chain, or a system of Ordinary Differential Equations over molecular concentrations. We show that under general conditions satisfied in practice, the activation/inhibition graph is independent of the precise kinetic expressions, and is computable in linear time in the number of reactions. Then we consider the formalization of the biological properties of systems, as observed in experiments, in temporal logics. We show that these logics are expressive enough to capture semiqualitative semiquantitative properties of the boolean and differential semantics of reaction models, and that modelchecking techniques can be used to validate a model w.r.t. its temporal specification, complete it, and search for kinetic parameter values. We illustrate this modelling method with examples on the MAPK signalling cascade, and on Kohn’s map of the mammalian cell cycle. 1
Graph Rewriting and Strategies for Modeling Biochemical Networks
 in "International Workshop on Natural Computing and Applications  NCA 2007, Timisoara, Roumanie", IEEE Computer Society
"... Abstract. In this paper, we present a rewriting framework for modeling molecular complexes, biochemical reaction rules, and generation of biochemical networks based on the representation of molecular complexes as a particular type of multigraphs with ports called molecular graphs. The advantage of t ..."
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Cited by 12 (4 self)
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Abstract. In this paper, we present a rewriting framework for modeling molecular complexes, biochemical reaction rules, and generation of biochemical networks based on the representation of molecular complexes as a particular type of multigraphs with ports called molecular graphs. The advantage of this approach is to obtain for free a rewriting calculus which allows defining at the same level transformation rules and strategies for modeling rule selection and application, in order to prototype network generation. 1
Crossing the Mesoscale NoMan’s Land via Parallel Kinetic Monte Carlo
, 2009
"... The kinetic Monte Carlo method and its variants are powerful tools for modeling materials at the mesoscale, meaning at length and time scales in between the atomic and continuum. We have completed a 3 year LDRD project with the goal of developing a parallel kinetic Monte Carlo capability and applyin ..."
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Cited by 11 (0 self)
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The kinetic Monte Carlo method and its variants are powerful tools for modeling materials at the mesoscale, meaning at length and time scales in between the atomic and continuum. We have completed a 3 year LDRD project with the goal of developing a parallel kinetic Monte Carlo capability and applying it to materials modeling problems of interest to Sandia. In this report we give an overview of the methods and algorithms developed, and describe our new opensource code called SPPARKS, for Stochastic Parallel PARticle Kinetic Simulator. We also highlight the development of several Monte Carlo models in SPPARKS for specific materials modeling applications, including grain growth, bubble formation, diffusion in nanoporous materials, defect formation in erbium hydrides, and surface growth