Application of finite-difference methods to membrane-mediated protein interactions and to heat and magnetic field diffusion in plasmas

A robust finite-difference approach for solving physically distinct cross-disciplinary problems such as membrane-mediated protein–protein interactions and heat and magnetic field diffusion in plasmas is described for rectangular grids. Mathematical models representing these physical phenomena are fourth- and second-order partial differential equations with variable coefficients. The finite-difference coupled harmonic oscillators technique was developed to treat arbitrary aggregates of inclusions in membranes automatically accounting for their non-pairwise interactions. The method was applied to study the stabilization of ion channels in a cluster due to membrane-mediated interactions and to examine the effects of anisotropic membrane slope relaxation on the elastic free energy. To obtain contributions from heat and magnetic field diffusion, the splitting method for the physical processes has been used in the numerical solution of resistive magnetohydrodynamic equations. The fully implicit scheme is outlined, tested and applied to problems of the diffusive redistribution of magnetic field and heat in the plasma.