Joseph W. Jerome

Riccardo Sacco, Paolo Airoldi, Aurelio G. Mauri et al.

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.

Riccardo Sacco, Fabio Manganini, Joseph W. Jerome

In this article we address the study of ion charge transport in the biological channels separating the intra and extracellular regions of a cell. The focus of the investigation is devoted to including thermal driving forces in the well-known velocity-extended Poisson-Nernst-Planck (vPNP) electrodiffusion model. Two extensions of the vPNP system are proposed: the velocity-extended Thermo-Hydrodynamic model (vTHD) and the velocity-extended Electro-Thermal model (vET). Both formulations are based on the principles of conservation of mass, momentum and energy, and collapse into the vPNP model under thermodynamical equilibrium conditions. Upon introducing a suitable one-dimensional geometrical representation of the channel, we discuss appropriate boundary conditions that depend only on effectively accessible measurable quantities. Then, we describe the novel models, the solution map used to iteratively solve them, and the mixed-hybrid flux-conservative stabilized finite element scheme used to discretize the linearized equations. Finally, we successfully apply our computational algorithms to the simulation of two different realistic biological channels: 1) the Gramicidin-A channel considered in~\cite{JeromeBPJ}; and 2) the bipolar nanofluidic diode considered in~\cite{Siwy7}.