Barrier crossing with concentration boundary conditions in biological channels and chemical reactions

Victor Barcilon*, Duanpin Chen, Robert S. Eisenberg, Mark A. Ratner

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

24 Scopus citations


Ions move into biological cells through pores in proteins called ionic channels, driven by gradients of potential and concentration imposed across the channel, impeded by potential barriers and friction within the pore. It is tempting to apply to channels the chemical theory of barrier crossing, but important issues must first be solved: Concentration boundary conditions must be used and flux must be predicted for applied potentials of all sizes and for barriers of all shapes, in particular, for low barriers. We use a macroscopic analysis to describe the flux as a convolution integral of a mathematically defined adjoint function, a Green's function. It so happens that the adjoint function also describes the first-passage time of a single particle moving between boundary conditions independent of concentration. The (experimentally observable) flux is computed from analytical formulas, from simulations of discrete random walks, and from simulations of the Langevin or reduced Langevin equations, with indistinguishable results. If the potential barrier has a single, large, parabolic peak, away from either boundary, an approximate expression reminiscent of Kramers' formula can be used to determine the flux. The fluxes predicted can be compared with measurements of current through single channels under a wide range of experimental conditions.

Original languageEnglish (US)
Pages (from-to)1193-1212
Number of pages20
JournalThe Journal of Chemical Physics
Issue number2
StatePublished - 1993

ASJC Scopus subject areas

  • Physics and Astronomy(all)
  • Physical and Theoretical Chemistry


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