A FOKKER–PLANCK APPROACH TO THE RECONSTRUCTION OF A CELL MEMBRANE POTENTIAL

A new method to reconstruct the structure of a cell membrane potential based on observation of the stochastic motion of particles on the membrane is presented. This inverse problem is formulated as an optimization problem governed by a mean-field Fokker–Planck equation, which allows a nonparametric reconstruction. The functional to be minimized includes a least-squares error term of the computed and observed particles’ densities and a Tikhonov regularization term. The resulting optimization problem is solved on a sequence of time windows to determine the potential together with an estimate of uncertainty of its reconstruction. Results of numerical experiments are presented that successfully validate the proposed reconstruction procedure and demonstrate its applicability in a superresolution microscopy framework.