Rule-based spatial modeling with diffusing, geometrically constrained molecules.

Area of Science:

• Computational Chemistry
• Biophysics
• Chemical Engineering

Background:

• Current coarse-grained, particle-based spatial simulation methods struggle with combinatorially complex chemical reaction systems.
• Existing models often lack detailed spatial representation (location, orientation, geometry) for molecules.
• Implicit reaction rule formalisms can define complex or infinite reaction networks.

Purpose of the Study:

• To develop a new modeling approach for spatial simulations of complex chemical reaction systems.
• To integrate molecular geometry and orientation into particle-based simulations.
• To bridge the gap between abstract reaction models and detailed spatial simulations.

Main Methods:

• A coarse-grained, particle-based spatial simulation approach was developed.
• Molecules were assigned location, orientation, and geometry within the reactor.
• The BioNetGen formalism was used for implicit specification of reaction networks, compatible with LAMMPS.
• Additional geometry data files were required for model implementation.

Main Results:

• Simulations demonstrated dynamics fundamentally different from classical reaction-diffusion (e.g., PDE, Gillespie).
• Combinatorial complexity and geometric effects led to faster-than-diffusion transport and self-assembly (e.g., molecular walkers on microtubules).
• Geometric information was shown to alter the organizational structure and stability of reaction systems, impacting stationary states.

Conclusions:

• The developed approach offers a new general framework for spatial simulations.
• It fills a gap between models with no/rigid spatial representation (PDEs) and specialized coarse-grained systems.
• This method enables the observation of emergent phenomena driven by combinatorial complexity and geometry.