Study Of Diffusional Properties Of Suspended Systems Using Monte Carlo Simulation

Diffusional properties of a system which consists of a composite of straight conducting wires, suspended isotropically in a poorly conducting medium, and the random walk of proteins inside a nucleus filled with Gaussian DNA chains is studied using Monte-Carlo simulations. The diffusion process is modeled using a random walker which moves in a continuous space with wires or chains as obstacles. The conductivity of the composite containing straight conducting wires and the macroscopic diffusion coefficient inside a matrix of Gaussian DNA chains are discussed and compared with recent theoretical scaling predictions through the analysis of the macroscopic diffusion coefficient. In the wires model, the macroscopic diffusion coefficient is closely related to the macroscopic conductivity of the suspension, which is shown to increase approximately linear with the wire conductivity at low-to moderate wire conductivities, and approaching a plateau at very high wire conductivities, additionally being a function of the volume fraction of wires. A deviation from simple theoretical scaling predictions is observed and discussed in the paper. In the Gaussian chain model, the simulations show that the macroscopic diffusion coefficient of the protein is dropping with the increase of the DNA volume fraction and with increasing protein-chain affinity. The results are shown to be consistent with those recently obtained by another group using a lattice model.