Abstract
The present study proposes a stochastic simulation scheme to model reactive boundaries through a position jump process which can be readily implemented into the Inhomogeneous Stochastic Simulation Algorithm by modifying the propensity of the diffusive jump over the reactive boundary. As compared to the literature, the present approach does not require any correction factors for the propensity. Also, the current expression relaxes the constraint on the compartment size allowing the problem to be solved with a coarser grid and therefore saves considerable computational cost. The modified algorithm is then applied to simulate three reaction-diffusion systems with reactive boundaries.
Highlights
Two of the most important events taking place in biochemical systems are diffusion and reactions
The present study proposes a stochastic simulation scheme to model reactive boundaries through a position jump process which can be readily implemented into the Inhomogeneous Stochastic Simulation Algorithm by modifying the propensity of the diffusive jump over the reactive boundary
Motivated by the existence of partially permeable boundaries in cell biology, the present paper proposed a modified position jump process leading to an expression for the propensity of a diffusion jump over a partially adsorbing boundary, which can be readily implemented into the Inhomogeneous Stochastic Simulation Algorithm (ISSA)
Summary
Two of the most important events taking place in biochemical systems are diffusion and reactions. Particles constantly diffuse throughout the system as a result of their thermal energy. Particles have collisions with one another, some of which may lead to chemical reactions. As long as there are a large number of reactive particles, the behavior of the system may be modeled using reaction-diffusion partial differential equations. A deterministic model may be inaccurate or even inapplicable for systems with a small abundance of particles [1].
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