Contexte
In models of biological systems on chemical level, it is often assumed that the chemical solution in the compartment (e.g. a cell) is well mixed. The diffusion within compartment is assumed to be fast compared to the speed of chemical reactions. This allows disregarding spatial configuration of the compartment in the model and simplifies it greatly. They are simulated using ordinary differential equations (ODEs).
However, this assumption cannot always be made. For example, within the cell the diffusion can be obstructed and slowed down by large molecular complexes (DNA, cytoskeleton parts), which gives rise to a non-homogeneous distribution of chemicals within the compartment. In this case, a spatial model must be used. One such model is a reaction-diffusion system.
Typically reaction-diffusion systems are formalized as systems of partial differential equations (PDEs). To simulate them, a PDE solver is used, which discretizes the space into small volumes (or triangles in 2D) and makes an ODE system for every volume, which are then simulated together.
Problématique
In BioComputing we have developed a flexible rule-based language for modeling chemical systems, React(C). It allows specifying complex biochemical systems with a concise set of rules. However, it currently lacks the possibility of defining reaction-diffusion systems in the general way, because it only allows writing discrete systems.
Travail à réaliser
Building upon our React(C) code (written in Scala programming language), add the possibility of annotating React(C) models with the spatial (geometry) information. The geometries could be defined by e.g. a vector format image.
Make a tool which, using the spatial annotations, will discretize given React(C) model automatically and write its discrete version as another React(C) model. This step can use the space discretization (triangulation) procedure already implemented in many PDE solvers, e.g. in Matlab.
Make a visualization tool which will show the result of the spatial simulation as a movie.
Bibliographie
1. Johan Hattne, David Fange and Johan Elf (2005). Stochastic reaction-diffusion simulation with MesoRD. Bioinfomatics.
2. Mathias John; Cédric Lhoussaine; Joachim Niehren; Cristian Versari (2011). Biochemical Reaction Rules with Constraints. 20th European Symposium on Programming Languages.
3. Scala programming language: http://www.scala-lang.org/
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