Modeling and simulation of transmembrane ionic transport of cells exposed to magnetic field using the Monte Carlo method

Abstract

This work presents a model for the simulation of plasmatic transmembrane ionic transport that may be exposed to a static gradient magnetic field. The simulation was carried out using the Monte Carlo method to simulate the transmembrane cell transport of five types of ions and obtain observables such as membrane potential, ionic current, and osmotic pressure. To implement the Monte Carlo method, a Hamiltonian was used that includes the contributions of the energy due to the cellular electric field, the electrostatic interaction between the ions, the friction force generated by moving the ion in the center and the contribution given by subduing a cell to a magnetic field gradient. The input parameters to carry out a simulation are the intra and extracellular concentrations of each ionic species, the length of the extracellular medium, the number of Monte Carlo steps (MCS) and the value of the magnetic gradient. The model was validated contrasting it with Gillespie’s algorithm to obtain variations less than 3 % in terms of membrane potential. The Monte Carlo Method combined with the Metropolis algorithm were considered for recreating the stochastic behavior of ion movement.