Schrodinger equation, Maxwell-Bolzmann distribution and a single channel current

K. Cheng, P. P. Tarjan, C. Zou -h.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Scopus citations

Abstract

The dual nature, wave and particle, of ions in the biological system was considered. A theoretical model, based on the steady state Schrodinger equation and Maxwell-Bolzmann distribution of energy, is proposed to describe passive transport of ions through a biological membrane channel in a time independent field. Constant height (V2) and length( L) of the potential energy barrier and effective mass of ions are used in the model. This model shows that an ion may go through or be reflected from a channel whether its energy is lower or higher than the barrier. This is a departure from classical theory. Based on a published I - V(m) (channel current - transmembrane voltage) curve from an activated K+ channel in a human erythrocyte membrane, calculations with our model show that more than 99% of the channel current is contributed by ions with higher energy than the potential barrier. The current can be amplified 10,000 times while V2 is reduced from 0.45 eV (channel closed) to 0.20 eV (channel opened) at V(m) = 0.07 V. In contrast, the current changes only 1.5% while L is narrowed from 90 Å to 30 Å at V(m) = 0.07 V, V2 = 0.20 eV. The energy barrier: V2 = 0.16 + 0.43 V(m) (eV), at r = 0.99, for 0.02 V ≤ V(m) ≤ 0.12 V.

Original languageEnglish (US)
Title of host publicationBiomedical Sciences Instrumentation
PublisherPubl by ISA Services Inc
Pages361-367
Number of pages7
Volume29
ISBN (Print)1556174578, 9781556174575
StatePublished - Sep 6 1993
EventProceedings of the 30th Annual Rocky Mountain Bioengineering Symposium and the 30th International ISA Biomedical Sciences Instrumentation Symposium - San Antonio, TX, USA
Duration: Apr 2 1993Apr 3 1993

Other

OtherProceedings of the 30th Annual Rocky Mountain Bioengineering Symposium and the 30th International ISA Biomedical Sciences Instrumentation Symposium
CitySan Antonio, TX, USA
Period4/2/934/3/93

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Keywords

  • Effective constant height of potential energy barrier(ECHPEB)
  • Single channel current

ASJC Scopus subject areas

  • Hardware and Architecture

Cite this

Cheng, K., Tarjan, P. P., & Zou -h., C. (1993). Schrodinger equation, Maxwell-Bolzmann distribution and a single channel current. In Biomedical Sciences Instrumentation (Vol. 29, pp. 361-367). Publ by ISA Services Inc.