  In this article we address the three-dimensional modeling and simulation of
biological ion channels using a continuum-based approach. Our multi-physics
formulation self-consistently combines, to the best of our knowledge for the
first time, ion electrodiffusion, channel fluid motion, thermal self-heating
and mechanical deformation. The resulting system of nonlinearly coupled partial
differential equations in conservation form is discretized using the Galerkin
Finite Element Method. The validation of the proposed computational model is
carried out with the simulation of a cylindrical voltage operated ion
nanochannel with K+ and Na+ ions. We first investigate the coupling between
electrochemical and fluid-dynamical effects. Then, we enrich the modeling
picture by investigating the influence of a thermal gradient. Finally, we add a
mechanical stress responsible for channel deformation and investigate its
effect on the functional response of the channel. Results show that fluid and
thermal fields have no influence in absence of mechanical deformation whereas
ion distributions and channel functional response are significantly modified if
mechanical stress is included in the model. These predictions agree with
biophysical conjectures on the importance of protein conformation in the
modulation of channel electrochemical properties.
