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Multilevel modelling via stochastic multilevel multiset rewriting
 MATHEMATICAL STRUCTURES IN COMPUTER SCIENCE
, 2011
"... We present a simple stochastic rulebased approach to multilevel modelling for computational systems biology. Populations are modelled using multilevel multisets; these contain both species and agents, with the latter possibly containing further such multisets. Rules are pairs of such multisets, bu ..."
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We present a simple stochastic rulebased approach to multilevel modelling for computational systems biology. Populations are modelled using multilevel multisets; these contain both species and agents, with the latter possibly containing further such multisets. Rules are pairs of such multisets, but now allowing variables to occur (as well as species and agents), together with an associated stochastic rate. We give two illustrative examples. The first is an extracellular model of virus infection, coupled with an intracellular model of viral reproduction; this model can demonstrate successive waves of infection. The second is a model of cell division in which a repressor protein is diluted in successive generations, when repression no longer occurs. The multilevel multiset approach can also be seen in terms of stochastic term rewriting for the theory of a commutative monoid, equipped with extra constants (for the species) and unary operations (for the agents). We further discuss the relationship of this approach with two others: Krivine et al.’s stochastic bigraphs, restricted to Milner’s place graphs, and Coppo et al.’s Stochastic Calculus of Wrapped Compartments. These various relationships provide evidence for the fundamental nature of the approach.
Coloured Stochastic Multilevel Multiset Rewriting
"... From the phosphorylation state of a molecule to the volume of a cell, parameters are ubiquitous in systems biology. At the same time, most models involve static or dynamic compartments, for example to separate cells from their environment. We introduce coloured stochastic multilevel multiset rewriti ..."
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From the phosphorylation state of a molecule to the volume of a cell, parameters are ubiquitous in systems biology. At the same time, most models involve static or dynamic compartments, for example to separate cells from their environment. We introduce coloured stochastic multilevel multiset rewriting, an expressive formalism for modelling systems with parameters and complex dynamic, multilevel compartment structures, and an extension of both multilevel multiset rewriting and coloured Petri nets. While being very expressive, it allows the direct and natural expression of biological ideas. We give some illustrative examples, demonstrating the use of parameters to handle cell states, position and volume, and variable rates. We further demonstrate the use of rules with complex righthand sides for reproduction. We regard these examples as paving the way for more biologically relevant models.
A CALCULUS OF CHEMICAL SYSTEMS
"... In recent years various calculi have been proposed for modelling biological systems, typically intracellular pathways. These calculi generally fall into one of two camps: ones based on process calculi, such as Milner’s picalculus [24], and rulebased ones. Examples of the former include [31, 32, 30 ..."
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In recent years various calculi have been proposed for modelling biological systems, typically intracellular pathways. These calculi generally fall into one of two camps: ones based on process calculi, such as Milner’s picalculus [24], and rulebased ones. Examples of the former include [31, 32, 30]; examples of the latter include BIOCHAM, κ, BioNet
Modeling biological systems with delays in BioPEPA
 Electronic Proceedings in Theoretical Computer Science
, 2010
"... Delays in biological systems may be used to model events for which the underlying dynamics cannot be precisely observed, or to provide abstraction of some behavior of the system resulting more compact models. In this paper we enrich the stochastic process algebra BioPEPA, with the possibility of a ..."
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Delays in biological systems may be used to model events for which the underlying dynamics cannot be precisely observed, or to provide abstraction of some behavior of the system resulting more compact models. In this paper we enrich the stochastic process algebra BioPEPA, with the possibility of assigning delays to actions, yielding a new nonMarkovian process algebra: BioPEPAd. This is a conservative extension meaning that the original syntax of BioPEPA is retained and the delay specification which can now be associated with actions may be added to existing BioPEPA models. The semantics of the firing of the actions with delays is the delayasduration approach, earlier presented in papers on the stochastic simulation of biological systems with delays. These semantics of the algebra are given in the StartingTerminating style, meaning that the state and the completion of an action are observed as two separate events, as required by delays. Furthermore we outline how to perform stochastic simulation of BioPEPAd systems and how to automatically translate a BioPEPAd system into a set of Delay Differential Equations, the deterministic framework for modeling of biological systems with delays. We end the paper with two example models of biological systems with delays to illustrate the approach. 1
A Minimal OO Calculus for Modelling Biological Systems
 Computational Models for Cell Processes (CompMod) 2011, EPTCS 67:50–64
, 2011
"... In this paper we present a minimal object oriented core calculus for modelling the biological notion of type that arises from biological ontologies in formalisms based on term rewriting. This calculus implements encapsulation, method invocation, subtyping and a simple form of overriding inheritance, ..."
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In this paper we present a minimal object oriented core calculus for modelling the biological notion of type that arises from biological ontologies in formalisms based on term rewriting. This calculus implements encapsulation, method invocation, subtyping and a simple form of overriding inheritance, and it is applicable to models designed in the most popular termrewriting formalisms. The classes implemented in a formalism can be used in several models, like programming libraries. 1
SPATIAL MODELING IN CELL BIOLOGY AT MULTIPLE LEVELS
"... Most modeling and simulation approaches applied in cell biology assume a homogeneous distribution of particles in space, although experimental studies reveal the importance of space to understand the dynamics of cells. There are already numerous spatial approaches focusing on the simulation of cells ..."
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Most modeling and simulation approaches applied in cell biology assume a homogeneous distribution of particles in space, although experimental studies reveal the importance of space to understand the dynamics of cells. There are already numerous spatial approaches focusing on the simulation of cells. Recently, they have been complemented by a set of spatial modeling languages whose operational semantics are tied partly to existing simulation algorithms. These modeling languages allow an explicit description of spatial phenomena, and facilitate analysis of the temporal spatial dynamics of cells by a clear separation between model, semantics, and simulator. With the supported level of abstraction, each of those offers a different perception of the spatial phenomena under study. In this paper, we give an overview of existing modeling formalisms and discuss some ways of combining approaches to tackle the problem the computational costs induced by spatial dynamics. 1
G.Ciobanu, M.Koutny (Eds.): Membrane Computing and Biologically Inspired Process Calculi 2010 (MeCBIC 2010)
"... c © Barbuti et al. This work is licensed under the Creative Commons Attribution License. Aspects of multiscale modelling in a process algebra for biological systems ..."
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c © Barbuti et al. This work is licensed under the Creative Commons Attribution License. Aspects of multiscale modelling in a process algebra for biological systems
SelfReplicating DNA Nanostructures: Autocatalytic Nanodevices derived from Catalytic Nanodevices
"... This paper describes some general techniques for transforming the design of a class of catalytic DNA nanodevices into the design for autocatalytic DNA nanodevices. Our techniques are particularly applicable to catalytic DNA nanodevices that act as detectors, where we would like their response to be ..."
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This paper describes some general techniques for transforming the design of a class of catalytic DNA nanodevices into the design for autocatalytic DNA nanodevices. Our techniques are particularly applicable to catalytic DNA nanodevices that act as detectors, where we would like their response to be sped up via autocatalytic behavior. We provide an example of this general scheme for design of autocatalytic DNA nanodevices from catalytic DNA nanodevices via design and demonstration of a autocatalytic selfreplicating DNA 3arm junction system, derived from a catalytic DNA 3arm junction system previously devised by Pierce et al [18]. 1