Effect of Gradient Magnetic Fields on Molecular Diffusion Through Cell Membranes: A Theoretical and Numerical Study

Abstract

The diffusion of biologically active molecules is a fundamental and ubiquitous process that governs numerous mechanisms and defines the characteristic time scales of essential cellular activities. In this work, we investigate how a strong static magnetic field (MF) influences the diffusion behaviour of both paramagnetic and diamagnetic species within a human cell. We first describe the influence of a homogeneous static magnetic field on molecular diffusion, and subsequently, for the first time, derive an analytical expression that includes the effects of a non-uniform magnetic field. Both equations were solved numerically, revealing that the influence of magnetic field non-uniformity becomes significant only in the presence of high gradinet magnetic fields. In contrast, for weak gradient magnetic fields, their effect on the diffusion of biologically active molecules is smaller, yet it cannot be neglected compared to a homogeneous field.