Hydrodynamic model of temperature change in open ionic channels

Biophysical Journal
D P ChenC W Shu

Abstract

Most theories of open ionic channels ignore heat generated by current flow, but that heat is known to be significant when analogous currents flow in semiconductors, so a generalization of the Poisson-Nernst-Planck theory of channels, called the hydrodynamic model, is needed. The hydrodynamic theory is a combination of the Poisson and Euler field equations of electrostatics and fluid dynamics, conservation laws that describe diffusive and convective flow of mass, heat, and charge (i.e., current), and their coupling. That is to say, it is a kinetic theory of solute and solvent flow, allowing heat and current flow as well, taking into account density changes, temperature changes, and electrical potential gradients. We integrate the equations with an essentially nonoscillatory shock-capturing numerical scheme previously shown to be stable and accurate. Our calculations show that 1) a significant amount of electrical energy is exchanged with the permeating ions; 2) the local temperature of the ions rises some tens of degrees, and this temperature rise significantly alters for ionic flux in a channel 25 A long, such as gramicidin-A; and 3) a critical parameter, called the saturation velocity, determines whether ionic motion is overda...Continue Reading

Citations

Feb 20, 2010·Bulletin of Mathematical Biology·Guo-Wei Wei
Nov 11, 2014·Journal of Theoretical & Computational Chemistry·Guo-Wei Wei
May 15, 2013·Biophysical Journal·Bob Eisenberg
Jan 24, 2007·Biophysical Journal·Madoka SuzukiShin'ichi Ishiwata
Nov 23, 2012·SIAM Review·Guo-Wei WeiKelin Xia
Nov 8, 2017·ACS Nano·David A SimpsonLloyd C L Hollenberg
Aug 21, 2012·The Journal of Physical Chemistry. B·Tzyy-Leng HorngBob Eisenberg

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