Hostname: page-component-5c6d5d7d68-wbk2r Total loading time: 0 Render date: 2024-08-18T13:45:17.009Z Has data issue: false hasContentIssue false

Surmounting barriers in ionic channels

Published online by Cambridge University Press:  17 March 2009

K. E. Cooper
Affiliation:
Department of Physiology, Rush Medical College, 1750 W. Harrison, Chicago IL 60612, U.S.A.
P. Y. Gates
Affiliation:
Department of Physiology, Rush Medical College, 1750 W. Harrison, Chicago IL 60612, U.S.A.
R. S. Eisenberg
Affiliation:
Department of Physiology, Rush Medical College, 1750 W. Harrison, Chicago IL 60612, U.S.A.

Extract

Biological cells are defined by the membrane that shields their vital molecules from the environment. The lipid bilayer of the membrane is an effective dielectric shield (Parsegian, 1969; Andersen, 1978; Honig et al. 1986), preventing penetration by charged molecules: the lipid presents a large electrostatic energy barrier because it cannot neutralize the charge of solute molecules nearly as well as water. This energy barrier inhibits the permeation of solutes with local charge, even metabolites. Of course, metabolites do enter cells, and so physiologists have suspected (for a very long time, Hille, 1984, ch. 8) that the membrane shield is pierced by aqueous channels, through which solutes diffuse (with their local charge substantially neutralized) as they cross the membrane. These aqueous pores now have molecular reality (e.g. Noda et al. 1984; Miller, 1986). Each is formed by a specialized protein, integral to membranes, perhaps shaped like a thick-walled pipe, called ionic channels. Channels control the movement of many important molecules in and out of cells by the ‘gating’ mechanism that controls their opening and closing and by the selective properties of their open channel.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1988

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Andersen, E. S. (1953). On the fluctuations of sums of random variables. Math. Scand. 2, 263285.CrossRefGoogle Scholar
Andersen, E. S. (1974). Survey of fluctuation theory. Adv. appl. Prob. 6, 188259.CrossRefGoogle Scholar
Andersen, O. S. (1978). Permeability properties of unmodified lipid blayer membranes. In ‘Membrane Transport in Biology’, ch. 11, pp. 369–446. In: Membrane Transport in Biology: Concepts and Models, vol. 1 (ed. Tosteson, D. C.), pp. 5113. New York: Springer-Verlag.Google Scholar
Apostol, T. M. (1967). Calculus: One-Variable Calculus, with an Introduction to Linear Algebra, vol. 1 (2nd edn). New York: John Wiley.Google Scholar
Attwell, D. & Jack, J. (1978). The interpretation of membrane current voltage relations. A Nernst–Planck analysis. Prog. Biophys. molec. Biol. 34, 81107.CrossRefGoogle ScholarPubMed
Baer, M. (1985). Theory of Chemical Reaction Dynamics. CRC Press, Boca Raton, Florida.Google Scholar
Barcilon, V. (1986). Inverse eigenvalue problems. In Inverse Problems (ed. Dold, A. and Eckman, B.), New York: Springer-Verlag.Google Scholar
Bass, L., Bracken, A. & Hilden, J. (1986). Flux ratio theorems for nonstationary membrane transport with temporary capture of tracer. J. theor. Biol. 118, 327338.Google Scholar
Berg, H. C. (1983). Random Walks in Biology. Princeton, N.J.: Princeton University Press.Google Scholar
Berne, B. J. (1985). Molecular dynamics and Monte Carlo simulations of rare events. In: Multiple Time Scales, (ed. Brackbill, J. U. and Cohen, B. I.), pp. 419436. Academic Press.Google Scholar
Berry, S. R., Rice, S. A. & Ross, J. (1980). Physical Chemistry. New York: John Wiley.Google Scholar
Bitsanis, I., Magda, J. J., Tirrell, M. & Davis, H. T. (1987). Molecular dynamics of flow in micropores. J. chem. Phys. 87, 1733.CrossRefGoogle Scholar
Blake, I. F. & Lindsey, W. C. (1973). Level-crossing problems for random processes. IEEE Trans. Info. Theory, pp. 295315.CrossRefGoogle Scholar
Bockris, J. O'M. & Reddy, A. K. N. (1970). Modern Electrochemistry, vol. 1. New York: Plenum Press.Google Scholar
Buffham, B. A. (1985). Residence–time distributions in regions of steady-flow systems. Nature 314, 606608.CrossRefGoogle Scholar
Carrier, G. F. & Pearson, C. E. (1976). Partial Differential Equations: Theory and Technique. New York: Academic Press.Google Scholar
Chandrasekhar, S. (1943). Stochastic problems in physics and astronomy. Rev. mod. Phys. 15, 189.CrossRefGoogle Scholar
Coddington, E. A. & Levinson, N. (1955). Theory of Ordinary Differential Equations. New York: McGraw-Hill.Google Scholar
Cooper, K. E., Jakobsson, E. & Wolynes, P. (1985). The theory of ion transport through membrane channels. Prog. Biophys. molec. Biol. 46, 5196.CrossRefGoogle ScholarPubMed
Courant, R. (1936). Differential and Integral Calculus, vol. 2. New York: Interscience.Google Scholar
Cox, D. R. & Miller, H. D. (1965). The Theory of Stochastic Processes. New York: Chapman and Hall.Google Scholar
Dani, J. A. & Levitt, D. G. (1981). Water transport and ion–water interaction in the gramicidin channel. Biophys. J. 35, 501508.CrossRefGoogle ScholarPubMed
Drake, A. W. (1967). Fundamentals of Applied Probability Theory. New York: McGraw-Hill.Google Scholar
Dygas, M. M., Matkowsky, B. J. & Schuss, Z. (1986). A singular perturbation approach to non-Markovian escape rate problems. SIAM Jl appl. Math. 46, 265298.CrossRefGoogle Scholar
Elsenberg, D. & Crothers, D. (1979). Physical Chemistry with Applications to the Life Sciences. Menlo Park, California: Benjamin/Cummings Publishing Co.Google Scholar
Fatt, P. & Katz, B. (1951). An analysis of the end-plate potential recorded with an intracellular electrode. J. Physiol. Lond. 115, 320370.CrossRefGoogle ScholarPubMed
Feller, W. (1950). An Introduction to Probability Theory and Its Applications, vol. 1. New York: John Wiley.Google Scholar
Feynman, R. P., Leighton, R. B. & Sands, M. (1963). The Feynman Lectures on Physics, vol. 1. New York: Addison-Wesley.Google Scholar
Fleming, G. R., Courtney, S. H. & Balk, M. W. (1986). Activated barrier crossing: comparison of experiment and theory. J. statist. Phys. 42, 83104.CrossRefGoogle Scholar
Frauenfelder, H. & Wolynes, P. G. (1985). Rate theories and puzzles of hemeprotein kinetics. Science 229, 337346.CrossRefGoogle ScholarPubMed
Frehland, E. (1982). Stochastic Transport Processes in Discrete Biological Systems. Lecture Notes in Biomathematics vol. 47. New York: Springer-Verlag.CrossRefGoogle Scholar
Gardiner, G. W. (1983). Handbook of Stochastic Methods. New York: Springer-Verlag.CrossRefGoogle Scholar
Gladwell, G. M. L. (1986). Inverse Problems in Vibration. Boston: Martinus Nijhoff.CrossRefGoogle Scholar
Goel, N. S. & Richter-Dyn, N. (1974). Stochastic Models in Biology. New York: Academic Press.Google Scholar
Gumbel, E. J. (1958). Statistics of Extremes. New York: Columbia University Press.CrossRefGoogle Scholar
Hänggi, P. (1986). Escape from a metastable state. J. statist. Phys. 42, 105148.CrossRefGoogle Scholar
Hardt, S. L. (1979). Pace of diffusion through membranes. J.memb. Biol. 48, 299323.CrossRefGoogle Scholar
Hardt, S. L. (1981). The diffusion transit time. A simple derivation. Bull. Math. Biol. 43. 8999.CrossRefGoogle Scholar
Hill, T. L. (1960). An Introduction to Statistical Thermodynamics (ed. Bonner, F. T. and Pimentel, G. C.), Reading, Mass.: Addison-Wesley Publishing Co.Google Scholar
Hill, T. L. (1977). Free Energy Transduction in Biology. New York: Academic Press.Google Scholar
Hill, T. L. (1985). Cooperativity Theory in Biochemistry. New York: Springer-Verlag.CrossRefGoogle Scholar
Hille, B. (1984). Ionic Channels of Excitable Membranes. Sunderland, Mass.: Sinauer Associates.Google Scholar
Hille, E. & Phillips, R. S. (1957). Functional Analysis and Semi-Groups. Providence, Rhode Island: American Mathematical Society.Google Scholar
Hille, E. & Schwarz, W. (1978). Potassium channels as multi-ion single-file pores. J. gen. Physiol. 72, 409442.CrossRefGoogle ScholarPubMed
Hladky, S. B. (1986). Models for ion transport in gramicidin channels: how many sites? In: Proceedings of the International Symposium on Ion Transport through Membraes (ed. Yagi, K. and Pullman, B.). New York: Academic Press (in the press).Google Scholar
Hladky, S. B. & Haydon, D. A. (1984). Ion movements in gramicidin channels. Curr. Top. Membr. & Transport 21, 327368.CrossRefGoogle Scholar
Hoare, M. R. (1971). The linear gas. Adv. chem. Phys. 20, 135214.Google Scholar
Hodgkin, A. L. & Huxley, A. F. (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. Lond. 117, 500544.CrossRefGoogle ScholarPubMed
Hodgkin, A. L., Huxley, A. F. & Katz, B. (1952). Measurements of current-voltage relations in the membrane of the giant axon of Loligo. J. Physiol. Lond. 116, 424448.CrossRefGoogle ScholarPubMed
Honig, B. H., Hubbel, W. L. & Flewelling, R. F. (1986). Electrostatic interactions in membranes and proteins. A. Rev. Biophys. Biophys. Chem. 15, 163193.CrossRefGoogle ScholarPubMed
Hynes, J. T. (1985). Chemical reaction dynamics in solution. A. Rev. phys. Chem. 36, 573597.CrossRefGoogle Scholar
Jacquez, J. A. (1985). Compartmental Analysis in Biology and Medicine, 1985. Ann Arbor, MI: University of Michigan Press.Google Scholar
Jakobsson, E. & Chiu, S. (1987). Stochastic theory of ion movement in channels with single-ion occupancy: application to sodium permeation of gramicidin channels. Biophys. J. 52, 3345.CrossRefGoogle ScholarPubMed
Karlin, S. & Taylor, H. M. (1975). A First Course in Stochastic Processes. New York: Academic Press.Google Scholar
Karlin, S. & Taylor, H. M. (1981). A Second Course in Stochastic Processes. New York: Academic Press.Google Scholar
Kramers, H. A. (1940). Brownian motion in a field of force and the diffusion model of chemical reactions. Physica VII, 4, 284304.CrossRefGoogle Scholar
Lapidus, L. & Pinder, G. F. (1982). Numerical Solution of Partial Differential Equations in Science and Engineering. New York: John Wiley.Google Scholar
Läuger, Z. (1973). Ion transport through pores: a rate-theory analysis. Biochim. biophys. Acta 311, 423441.CrossRefGoogle Scholar
Levitt, D. G. (1982). Comparison of Nernst–Planck and reaction-rate models for multiply occupied channels. Biophys. J. 37, 575587.CrossRefGoogle ScholarPubMed
Levitt, D. G. (1986). Interpretation of biological ion channel flux data. Reaction rate versus continuum theory. A. Rev. biophys. Biophys. Chem. 15, 2957.CrossRefGoogle ScholarPubMed
Lindenberg, K. & West, B. J. (1986). The first, the biggest, and other such considerations. J. statist. Phys. 42, 201243.CrossRefGoogle Scholar
Mandl, P. (1968). Analytical Treatment of One-dimensional Markov Processes. New York: Springer-Verlag.Google Scholar
Matkowsky, B. J., Schuss, Z. & Tier, C. (1984). Uniform expansion of the transition rate in Kramer's problem. J. statist. Phys. 35, 443456.CrossRefGoogle Scholar
McQuarrie, D. A. (1976). Statistical Mechanics. New York: Harper and Row.Google Scholar
Mel'nikov, V. I. & Meshkov, S. V. (1986). Theory of activated rate processes: exact solution of the Kramers problem. J. chem. Phys. 85, 10181027.CrossRefGoogle Scholar
Miller, C. (1986). Ion Channel Reconstitution. New York: Plenum Press.CrossRefGoogle Scholar
Miller, W. H. (1976). Dynamics of Molecular Collisions. Part B. New York: Plenum Press.Google Scholar
Murthy, C. S. & Singer, K. (1987). Description of the molecular trajectories in simple liquids. J. phys. Chem. 91, 2130.CrossRefGoogle Scholar
Nauman, E. B. & Buffham, B. A. (1983). Mixing in Continuous Flow Systems. New York: John Wiley & Sons.Google Scholar
Nitzan, A. (1987). Non-markovian theory of activated rate processes. VI. Unimolecular reactions in condensed phases. J. chem. Phys. 86, 27342748.CrossRefGoogle Scholar
Noda, M., Shimizu, S., Tanabe, T., Takai, T., Kayano, T., Ikeda, T., Takahashi, H., Nakayama, H., Kanaoka, Y., Minamino, N., Kangawa, K., Matsuo, H., Raftery, M. A., Hirose, T., Inayama, , Seiichi, , Hayashida, H., Miyata, T. & Numa, S. (1984). Primary structure of electrophorus electricus sodium channel deduced from cDNA sequence. Nature 312, 121127.CrossRefGoogle ScholarPubMed
Northrup, S. H. & Hynes, J. T. (1980). The stable states picture of chemical reactions. I. Formulation for rate constants and initial condition effects. J. chem. Phys. 73, 27002714.CrossRefGoogle Scholar
Papoulis, A. (1962). The Fourier Integral and Its Applications. New York: McGraw-Hill.Google Scholar
Papoulis, A. (1984). Probability, Random Variables, and Stochastic Processes, 2nd edn. New York: McGraw-Hill.Google Scholar
Parsegian, A. (1969). Energy of an ion crossing a low dielectric membrane: solutions to four relevant electrostatic problems. Nature 221, 844846.CrossRefGoogle Scholar
Parzen, E. (1960). Modern Probability Theory and Its Applications. New York: John Wiley.CrossRefGoogle Scholar
Parzen, E. (1962). Stochastic Processes. San Francisco: Holden-Day.Google Scholar
Pawula, R. F. (1967). Approximation of the linear Boltzmann equation by the Fokker–Planck equation. Phys. Rev. 162, 186188.CrossRefGoogle Scholar
Protter, M. H. & Weinberger, H. F. (1984). Maximum Principles in Differential Equations. New York: Springer-Verlag.CrossRefGoogle Scholar
Purcell, E. M. (1985). Electricity and Magnetism. New York: McGraw-Hill.Google Scholar
Ricciardi, L. M. (1977). Diffusion Processes and Related Topics in Biology. New York: Springer-Verlag.CrossRefGoogle Scholar
Risken, H. (1984). The Fokker–Planck Equation : Methods of Solution and Applications. New York: Springer-Verlag.CrossRefGoogle Scholar
Sakmann, B. & Neher, E. (1983). Single-Channel Recording. New York: Plenum Press.Google Scholar
Sandblom, J., Ring, A. & Eisenman, G. (1982). Linear network representation of multistate models of transport. Biophys. J. 38, 93104.CrossRefGoogle ScholarPubMed
Schulten, K., Schulten, Z. & Szabo, A. (1981). Dynamics of reactions involving diffusive barrier crossing. J. chem. Phys. 74, 44264432.CrossRefGoogle Scholar
Sheppard, C. W. (1962). Basic Principles of the Tracer Method: Introduction to Mathematical Tracer Kinetics. New York: John Wiley.Google Scholar
Siegert, A. J. F. (1951). On the first passage time probability problem. Phys. Rev. 81, 617623.CrossRefGoogle Scholar
Skinner, J. L. & Wolynes, P. G. (1978). Relaxation processes and chemical kinetics. J. chem. Phys. 69, 21432150.CrossRefGoogle Scholar
Skinner, J. L. & Wolynes, P. G. (1979). Derivation of Smoluchowski equations with corrections for Fokker–Planck and BKG collision models. Physica 96a, 561572.CrossRefGoogle Scholar
Skinner, J. L. & Wolynes, P. G. (1980). General kinetic models of activated processes in condensed phases. J. chem. Phys. 72, 49134927.CrossRefGoogle Scholar
Sten-Knudsen, O. (1978). Passive transport processes. In: Membrane Transport in Biology: Concepts and Models, vol. 1 (ed. Tosteson, D. C.), pp. 5113. New York: Springer-Verlag.Google Scholar
Stimers, J. R., Bezanilla, F. & Taylor, R. E. (1987). Sodium channel gating currents. Origin of the rising phase. J. gen. Physiol. 89, 521540.CrossRefGoogle ScholarPubMed
Stratonovich, R. L. (1963). Topics in the Theory of Radom Noise, vol. 1. New York: Gordon and Breach.Google Scholar
Straub, J. E. & Berne, B. J. (1986). Energy diffusion in many-dimensional Markovian systems: The consequences of competition between inter- and intramolecular vibrational energy transfer. J. chem. Phys. 84, 29993006.CrossRefGoogle Scholar
Straub, J. E., BOrkovec, M. & Berne, B. (1986). Non-Markovian activated rate process: Comparison of current theories with numerical simulation data. J. chem. Phys. 84, 17881794.CrossRefGoogle Scholar
Szabo, A., Schulten, K. & Schulten, Z. (1980). First passage time approach to diffusion controlled reactions. J. chem. Phys. 72, 43504357.CrossRefGoogle Scholar
Tyrrell, H. J. V. & Harris, K. R. (1984). Diffusion in Liquids. Butterworths Monographs in Chemistry. Boston: Butterworths.Google Scholar
van Kampen, N. G. (1981). Stochastic Processes in Physics and Chemistry. New York: North-Holland.Google Scholar
van Kampen, N. G. (1983). The diffusion approximation for Markov processes. In: Thermodynamics and Kinetics of Biological Processes (ed. Lamprecht, I. and Zotin, A. I.), New York: Walter de Gruyter.Google Scholar
Weiss, G. H. (1966). First passage time problems in chemical physics. Adv. Chem. Phys. 13 118.Google Scholar
Weiss, G. H. (1986). Overview of theoretical models for reaction rates. J. Stat. Phys. 42, 336.CrossRefGoogle Scholar
Williams, M. M. R. (1966). The Slowing Down and Thermalization of Neutrons. New York: American Elsevier Publishing Co.Google Scholar
Zauderer, E. (1983). Partial Differential Equations of Applied Mathematics. New York: John Wiley.Google Scholar