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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
"... Abstract. 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 syste ..."
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Cited by 70 (18 self)
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Abstract. 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. 1
Scalable simulation of cellular signaling networks
 In Proceedings of APLAS 2007
, 2007
"... Abstract. 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 ..."
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Cited by 33 (11 self)
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Abstract. 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. 1
Abstract interpretation of cellular signalling networks
 4905 of LNCS
, 2008
"... Abstract. 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 repr ..."
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Cited by 23 (7 self)
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Abstract. 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. 1
On the computational power of biochemistry
 In AB’08, volume 5147 of LNCS
, 2008
"... Abstract. We explore the computational power of biochemistry with respect to basic chemistry, identifying complexation as the basic mechanism that distinguishes the former from the latter. We use two process algebras, the Chemical Ground Form (CGF) which is equivalent to basic chemistry, and the Bio ..."
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Cited by 21 (8 self)
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Abstract. We explore the computational power of biochemistry with respect to basic chemistry, identifying complexation as the basic mechanism that distinguishes the former from the latter. We use two process algebras, the Chemical Ground Form (CGF) which is equivalent to basic chemistry, and the Biochemical Ground Form (BGF) which is a minimalistic extension of CGF with primitives for complexation. We characterize an expressiveness gap: CGF is not Turing complete while BGF supports a finite precise encoding of Random Access Machines, a wellknown Turing powerful formalism. 1
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 15 (5 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.
Stochastic Calculus of Looping Sequences for the Modelling and Simulation of Cellular Pathways
"... 1 ..."
Bisimulation Congruences in the Calculus of Looping Sequences
 Int. Colloquium on Theoretical Aspects of Computing (ICTAC’06), LNCS 4281
, 2006
"... Abstract. The Calculus of Looping Sequences (CLS) is a calculus suitable to describe biological systems and their evolution. CLS terms are constructed by starting from basic constituents and composing them by means of operators of concatenation, looping, containment and parallel composition. CLS ter ..."
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Cited by 13 (12 self)
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Abstract. The Calculus of Looping Sequences (CLS) is a calculus suitable to describe biological systems and their evolution. CLS terms are constructed by starting from basic constituents and composing them by means of operators of concatenation, looping, containment and parallel composition. CLS terms can be transformed by applying rewrite rules. We give a labeled transition semantics for CLS by using, as labels, contexts in which rules can be applied. We define bisimulation relations that are congruences with respect to the operators on terms, and we show an application of CLS to the modeling of a biological system and we use bisimulations to reason about properties of the described system. 1 Introduction In the last few years many formalisms originally developed by computer scientiststo model systems of interacting components have been applied to Biology. Among these, there are Petri Nets [9], Hybrid Systems [1], and the sscalculus [6, 12].Moreover, some new formalisms have been proposed to describe biomolecular and membrane interactions [2, 4, 5, 7, 10, 11]. The formal modeling of biologicalsystems allows the development of simulators and the verification of properties of the described systems.The sscalculus and new calculi based on it [10, 11] have been particularlysuccessful in the description of biological systems. Interactions of biological components are modeled as communications on channels whose names can be passed.Sharing names of private channels allows describing biological compartments, such as membranes. Calculi such as those proposed in [4, 5, 7] give an abstractdescription of systems and offer special biologically motivated operators.
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 8 (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
The Calculus of Looping Sequences for Modeling Biological Membranes
 8th Workshop on Membrane Computing (WMC8), LNCS 4860
, 2007
"... We survey the formalism Calculus of Looping Sequences (CLS) and a number of its variants from the point of view of their use for describing biological membranes. The formalism CLS is based on term rewriting and allows describing biomolecular systems. A first variant of CLS, called Stochastic CLS, ex ..."
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Cited by 7 (6 self)
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We survey the formalism Calculus of Looping Sequences (CLS) and a number of its variants from the point of view of their use for describing biological membranes. The formalism CLS is based on term rewriting and allows describing biomolecular systems. A first variant of CLS, called Stochastic CLS, extends the formalism with stochastic time, another variant, called LCLS (CLS with links), allows describing proteins interaction at the domain level. A third variant is introduced for easier description of biological membranes. This extension can be encoded into CLS as well as other formalisms capable of membrane description such as Brane Calculi and P Systems. Such encodings allow verifying and simulating descriptions in Brane Calculi and P Systems by means of verifiers and simulators developed for CLS. 1