DNA capture into the ClyA nanopore: diffusion-limited versus reaction-limited processes

A Diffusion-Limited Reaction

Fluctuations in diffusion-controlled reactions lack the necessary features for a mesoscopic description. We show how the correlations dominate the dynamics by juxtaposing the macroscopic dynamics of a cellular automaton model for the diffusion-controlled limit to the deterministic diffusion-reaction rate equation for the same reaction. A more detailed N-body master equation is then presented in...

Simulation of chemical reaction via particle tracking: diffusion-limited versus thermodynamic rate-limited regimes

Chemical reactions may be simulated without regard to local concentrations by applying simple probabilistic rules of particle interaction and combination. The forward reaction A+B → C is coded by calculating the probability that any A and B particles will occupy the same volume over some time interval. This becomes a convolution of the location densities of the two particles. The backward react...

Diffusion-limited reaction in one dimension

Reaction rates that are controlled by collisions between diffusing particles depend on the distribution of distances between particles as well as on the concentration of particles. Classical treatment of reaction rates thus produces a hierarchy of particle correlation functions. However, when collision between particles results in annihilation, it is possible to sidestep this hierarchy and find...

A Mathematical Interpretation of Limited Diffusion Processes

Reaction-diffusion master equation, diffusion-limited reactions, and singular potentials.

To model biochemical systems in which both noise in the chemical reaction process and spatial movement of molecules is important, both the reaction-diffusion master equation (RDME) and Smoluchowski diffusion-limited reaction (SDLR) partial differential equation (PDE) models have been used. In previous work we showed that the solution to the RDME may be interpreted as an asymptotic approximation...