Reaction-diffusion kinetics on lattice at the microscopic scale

• Main Authors: Chew, Wei-Xiang, Kaizu, Kazunari, Watabe, Masaki, Muniandy, Sithi V, Takahashi, Koichi, Arjunan, Satya N. V
• Format: Journal Article
• Language: English
• Published: 01-09-2018
• Subjects: Quantitative Biology - Biomolecules; Quantitative Biology - Quantitative Methods; Quantitative Biology - Subcellular Processes
• DOI: 10.48550/arxiv.1805.12311

Phys. Rev. E 98, 032418 (2018) Lattice-based stochastic simulators are commonly used to study biological
reaction-diffusion processes. Some of these schemes that are based on the
reaction-diffusion master equation (RDME), can simulate for extended spatial
and temporal scales but cannot directly account for the microscopic effects in
the cell such as volume exclusion and diffusion-influenced reactions.
Nonetheless, schemes based on the high-resolution microscopic lattice method
(MLM) can directly simulate these effects by representing each finite-sized
molecule explicitly as a random walker on fine lattice voxels. The theory and
consistency of MLM in simulating diffusion-influenced reactions have not been
clarified in detail. Here, we examine MLM in solving diffusion-influenced
reactions in 3D space by employing the Spatiocyte simulation scheme. Applying
the random walk theory, we construct the general theoretical framework
underlying the method and obtain analytical expressions for the total rebinding
probability and the effective reaction rate. By matching Collins-Kimball and
lattice-based rate constants, we obtained the exact expressions to determine
the reaction acceptance probability and voxel size. We found that the size of
voxel should be about 2% larger than the molecule. MLM is validated by
numerical simulations, showing good agreement with the off-lattice
particle-based method, eGFRD. MLM run time is more than an order of magnitude
faster than eGFRD when diffusing macromolecules with typical concentrations in
the cell. MLM also showed good agreements with eGFRD and mean-field models in
case studies of two basic motifs of intracellular signaling, the protein
production-degradation process and the dual phosphorylation cycle. Moreover,
when a reaction compartment is populated with volume-excluding obstacles, MLM
captures the non-classical reaction kinetics caused by anomalous diffusion of
reacting molecules.