Abstract
Microscopic models of reaction-diffusion processes on the cell membrane can link local spatiotemporal effects to macroscopic self-organized patterns often observed on the membrane. Simulation schemes based on the microscopic lattice method (MLM) can model these processes at the microscopic scale by tracking individual molecules, represented as hard spheres, on fine lattice voxels. Although MLM is simple to implement and is generally less computationally demanding than off-lattice approaches, its accuracy and consistency in modeling surface reactions have not been fully verified. Using the Spatiocyte scheme, we study the accuracy of MLM in diffusion-influenced surface reactions. We derive the lattice-based bimolecular association rates for two-dimensional (2D) surface-surface reaction and one-dimensional (1D) volume-surface adsorption according to the Smoluchowski-Collins-Kimball model and random walk theory. We match the time-dependent rates on lattice with off-lattice counterparts to obtain the correct expressions for MLM parameters in terms of physical constants. The expressions indicate that the voxel size needs to be at least 0.6% larger than the molecule to accurately simulate surface reactions on triangular lattice. On square lattice, the minimum voxel size should be even larger, at 5%. We also demonstrate the ability of MLM-based schemes such as Spatiocyte to simulate a reaction-diffusion model that involves all dimensions: three-dimensional (3D) diffusion in the cytoplasm, 2D diffusion on the cell membrane, and 1D cytoplasm-membrane adsorption. With the model, we examine the contribution of the 2D reaction pathway to the overall reaction rate at different reactant diffusivity, reactivity, and concentrations.
Highlights
Many essential and intriguing intracellular biochemical systems are mediated by the cell membrane
Since reactions in microscopic lattice method (MLM) take place stochastically, we examine the steady-state distribution of molecule number in the reversible homodimerization reaction, A + A ka2D B, with kd 2D
MLM surface reactions have not been verified in terms of their consistency with continuum-based theory
Summary
Many essential and intriguing intracellular biochemical systems are mediated by the cell membrane. The SCK model was used together with the Spatiocyte scheme to construct a general theoretical framework of MLM for simulating reaction and diffusion processes in three-dimensional (3D) space [56]. Within this framework, the expressions for on-lattice reaction rate constant, reaction and rebinding probabilities, and voxel size were derived to reproduce off-lattice reaction kinetics consistently. We employ the SCK model to derive on-lattice time-dependent rate coefficients for the surface reactions.
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