Efficient kinetic Monte Carlo method for reaction–diffusion problems with spatially varying annihilation rates

Abstract

We present an efficient Monte Carlo method to simulate reaction-diffusion processes with spatially varying particle annihilation or transformation rates as it occurs for instance in the context of motor-driven intracellular transport. Like Green's function reaction dynamics and first-passage time methods, our algorithm avoids small diffusive hops by propagating sufficiently distant particles in large hops to the boundaries of protective domains. Since for spatially varying annihilation or transformation rates the single particle diffusion propagator is not known analytically, we present an algorithm that generates efficiently either particle displacements or annihilations with the correct statistics, as we prove rigorously. The numerical efficiency of the algorithm is demonstrated with an illustrative example.

Bystander cells enhance NK cytotoxic efficiency by reducing search time

“…A kinetic Monte Carlo scheme was implemented to generate the Brownian motion of disk-like particles in a square geometry; disks represent targets, obstacles, and bystanders. A very efficient First Passage Kinetic Monte Carlo algorithm (FPKMC) was used as documented in the literature 48 49 50 , also denoted as GFRD MC (Greens function reaction diffusion Monte Carlo). For each parameter set 40.000 samples of the random trajectories and the random times were generated when targets were hit and removed.…”

Microscopic modeling of confined crystal growth and dissolution

“…This is referred to as the maximum distance method, and is thoroughly analyzed in Ref. [21], where it is stated that √ 6r max ∈ [7,9] is safe for all practical purposes (3 √ 6 7.35 in our case). This also means that particle with a vertical position greater than the maximum surface height plus r max has a deposition rate equal to 0.…”

On the Green's function of the partially diffusion-controlled reversible ABCD reaction for radiation chemistry codes

“…Table methods usually necessitate an extensive set-up to calculate and hold the pre-calculated data, which may be very time and memory consuming, especially when the table has more than one dimension [33] and, as it will be the case in our future work, when large systems comprising many types of particles with different reaction channels are simulated. This method might be useful for particle-based event-driven simulation schemes of the FPKMC (first-passage kinetic Monte Carlo) [13] and GFRD (Green's functions reaction dynamics) [8]. For example, in the GFRD method, simple geometric domains such as spheres are put around at most two particles to shield them from the influence of other particles.…”

“…Simulations based on the Green's functions of the diffusion equation (GFDE) have been widely used to study chemical reactions in solutions [1][2][3][4][5][6][7][8][9][10][11][12][13]. More recently, this approach has been used in radiation chemistry codes to simulate the radiolysis of water and aqueous solutions [14,15], chemical dosimeters [16] and to study of interaction of ligand molecules with receptors [17].…”