TY - JOUR

T1 - Hydrodynamic model of temperature change in open ionic channels

AU - Chen, D. P.

AU - Eisenberg, R. S.

AU - Jerome, J. W.

AU - Shu, C. W.

N1 - Funding Information:
Olaf Andersen made many useful criticisms and suggestions for which we are grateful. DPC would like to thank Prof. Fred Cohen for careful proofreading of this manuscript, to thank Prof. V. Barcilon for useful discussions, and to thank Prof. M. Sokabe for his encouragement of this work. DPC and RSE are supported by National Science Foundation grant BIR-9205688. JWJ, supported by National Science Foundation grant DMS-9123208, is also a visiting professor at the Department of Molecular Biophysics and Physiology of Rush Medical College. CWS is supported by National Science Foundation grant ECS-9214488 and U.S. Army Research Office grant DAAH04-94-G-0205.

PY - 1995

Y1 - 1995

N2 - 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 overdamped (Poisson-Nernst-Planck theory), is an intermediate regime (called the adiabatic approximation in semiconductor theory), or is altogether unrestricted (requiring the full hydrodynamic model). It seems that significant temperature changes are likely to accompany current flow in the open ionic channel.

AB - 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 overdamped (Poisson-Nernst-Planck theory), is an intermediate regime (called the adiabatic approximation in semiconductor theory), or is altogether unrestricted (requiring the full hydrodynamic model). It seems that significant temperature changes are likely to accompany current flow in the open ionic channel.

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U2 - 10.1016/S0006-3495(95)80101-3

DO - 10.1016/S0006-3495(95)80101-3

M3 - Article

C2 - 8599638

AN - SCOPUS:0028847318

VL - 69

SP - 2304

EP - 2322

JO - Biophysical Journal

JF - Biophysical Journal

SN - 0006-3495

IS - 6

ER -