Rule-based spatial modeling with diffusing, geometrically constrained molecules
1 Friedrich Schiller University Jena, Bio Systems Analysis Group, Ernst-Abbe-Platz 1-4, 07743 Jena, Germany
2 German Cancer Research Center, Im Neuenheimer Feld 581, 69120 Heidelberg, Germany
3 Jena Centre for Bioinformatics (JCB), Jena, Germany
4 Friedrich Schiller University Jena, School of Biology and Pharmacy, Department of Bioinformatics, Ernst-Abbe-Platz 1-4, 07743 Jena, Germany
BMC Bioinformatics 2010, 11:307 doi:10.1186/1471-2105-11-307Published: 7 June 2010
We suggest a new type of modeling approach for the coarse grained, particle-based spatial simulation of combinatorially complex chemical reaction systems. In our approach molecules possess a location in the reactor as well as an orientation and geometry, while the reactions are carried out according to a list of implicitly specified reaction rules. Because the reaction rules can contain patterns for molecules, a combinatorially complex or even infinitely sized reaction network can be defined.
For our implementation (based on LAMMPS), we have chosen an already existing formalism (BioNetGen) for the implicit specification of the reaction network. This compatibility allows to import existing models easily, i.e., only additional geometry data files have to be provided.
Our simulations show that the obtained dynamics can be fundamentally different from those simulations that use classical reaction-diffusion approaches like Partial Differential Equations or Gillespie-type spatial stochastic simulation. We show, for example, that the combination of combinatorial complexity and geometric effects leads to the emergence of complex self-assemblies and transportation phenomena happening faster than diffusion (using a model of molecular walkers on microtubules). When the mentioned classical simulation approaches are applied, these aspects of modeled systems cannot be observed without very special treatment. Further more, we show that the geometric information can even change the organizational structure of the reaction system. That is, a set of chemical species that can in principle form a stationary state in a Differential Equation formalism, is potentially unstable when geometry is considered, and vice versa.
We conclude that our approach provides a new general framework filling a gap in between approaches with no or rigid spatial representation like Partial Differential Equations and specialized coarse-grained spatial simulation systems like those for DNA or virus capsid self-assembly.