From species to pathway and tissue as process

• Authors: Muffy Calder;Oana Andrei;Andrea Degasperi;Robin Donaldson
• Venue: Proceedings of the 8th International Conference on Computational Methods in Systems Biology
• Year: 2010

Process algebras were originally designed for modelling concurrent computations. Over the last decade, computer scientists have explored their application to modelling bio-molecular processes, with considerable success. A predominant abstraction is molecule-as-process [RSS01, Car08], where each process represents a molecule. Analysis is by simulation and in a stochastic setting, there is a clear correspondence with stochastic simulation as proposed by Gillespie [Gil77]. An alternative abstraction is species-as-process [CGH06, CH09b], based on models that are continuous time Markov chains (CTMC) with levels of concentration. This population-based abstraction allows control of the granularity of representation, at one end of the spectrum corresponding to Gillespie simulation and at the other end, ordinary differential equations. A key feature of this style is it permits a range of analysis techniques in addition to simulation, namely relations (e.g. bisimulation) and model-checking properties expressed in qualitative and quantitative logics. Within the species-as-process paradigm, a useful style has been reagent-centric models[CH09a], where all reagents in a reaction map to processes, whose variation reflect decrease through consumption and increase through product formation (consumers and producers). The reagent-centric style of modelling provides a distributed view of a system and is easily represented in a state-based formalism where state variables represent levels of concentration. An example is the language of reactive modules used in the PRISM model-checker [KNP02]. Whilst this language is not strictly a process algebra: processes are represented by modules, there is process algebraic synchronisation between modules. Moreover, modules can be generic. This talk gives an overview of recent advances and applications of the reagent-centric modelling paradigm, extending basic reasoning about concentration levels and then developing higher level concepts such as pathway-as-process and tissue-as-process. We consider how to extend basic reasoning about concentration levels by the addition of trend formulas, state formulas that represent ascending or descending trends of concentration [AC10]. These are similar to the sign of a first-order derivative, but in a stochastic setting. We then consider extending the species-as-process paradigm to pathway-as-process. While still adopting the reagent-centric style, we model a signalling pathway as a (synchronising) parallel composition (with renaming) of instances of generic modules, which have both internal and external reactions. The motivation is to investigate pathway interactions, known as crosstalk, and so pathways are themselves composed. We show how we can use a quantitative logic to detect cross-talk, and a qualitative logic to characterise the type of crosstalk [DC10b]. Finally, we describe a new stochastic process algebra for modelling different levels of abstraction, specifically biochemistry and tissue. The algebra is motivated by modelling pattern formation based on reaction-diffusion equations. Processes represent both biochemical species and tissues at certain locations; an explicit notion of geometrical space is embedded in the algebra. Synchronisation between the two levels is through special actions called hooks [DC10a]. The ultimate goal is to be able to compare models of similar tissue formation, but with different underlying biochemistry.