Modeling and Simulation of Thermo-Fluid-Electrochemical Ion Flow in Biological Channels
This work provides a more comprehensive modeling framework for ion transport in biological channels, but the improvements are incremental as it builds on existing models and demonstrates only qualitative agreement with prior studies.
The authors extended the velocity-extended Poisson-Nernst-Planck (vPNP) model to include thermal driving forces, proposing two new models (vTHD and vET) and validated them through simulations of Gramicidin-A and a bipolar nanofluidic diode, showing consistency with prior results.
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}.