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6 Theory of Thansport <strong>in</strong> Ion Channels 167[22] Dani, J. A., Levitt, D., Biophys. J. 1981, 35, 501-508.[23] Rosenberg, P. A., F<strong>in</strong>kelste<strong>in</strong>, A., J. Gen. Physiol. 1978, 72, 327-340.[24] F<strong>in</strong>kelste<strong>in</strong>, A., Andersen, 0. S., J. Membr. Biol. 1981, 59, 155-171.[25] Andersen, 0. S., Annu. Rev. Physiol. 1984, 46, 531-548.[26] Andersen, 0. S., Procopio, J., Acta Physiol. Suppl. 1980, 481, 27-35.[27] Becker, M. D., Koeppe 11, R. E., Andersen, 0. S., Biophys. J. 1992, 62, 25-27.[28] Mackay, D. H., Berens, P. H., Wilson, K. R., Biophys. J. 1983, 46, 229-248.[29] Kim, K. S., Clementi, E., J Am. Chem. SOC. 1985, 107, 5504-5513.[30] Urry, D. W., Venkatachalam, C. M., J. Comp. Chem. 1983, 4, 461-469.[31] Chiu, S. W., Subramaniam, S., Jakobsson, E., McCammon, J. A., Biophys. J. 1989, 56,253 -261.[32] Chiu, S. W., Jakobsson, E., Subramaniam, S., McCammon, J. A., Biophys. J. 1991, 60,273-285.[33] Etchebest, C., Pullman, A., J. Biomol. Struct. &Dun. 1986, 3, 805-825.[34] Pullman, A., Q. Rev. Biophys. 1987, 20, 173-200.[35] Jordan, P. C., Transport through membranes: Carriers, channels andpumps, A. Pullmanet al. (eds.), Kluwer Academic Publisher, 1988, pp. 237-251.[36] Aqvist, J., Warshel, A., Biophys. J. 1989, 56, 171-182.[37] Roux, B., Karplus, M., Biophys. J. 1988, 53, 297-309.[38] Roux, B., Karplus, M., Biophys. .I 1991, 59, 961-981.[39] Roux, B., Karplus, M., J. Phys. Chem. 1991, 95, 4856-4868.[40] Roux, B., Karplus, M., J. Am. Chem. SOC. 1993, 115, 3250-3262.[41] Urry, D. W., Proc. Natl. Acad. Sci. USA 1971, 68, 672-676.[42] Urry, D. W., Walker, J. T., Trapane, T. L., L Membr. Biol. 1982, 69, 225-231.[43] Urry, D. W., Prasad, K. U., Trapane, T. L., Proc. Natl. Acad. Sci. USA 1982, 79,390- 394.[44] Urry, D. W., Trapane, T. L., Prasad, K. U., Science 1983, 221, 1064-1067.[45] Arseniev, A. S., Bystrov, V. F., Ivanov, T. V., Ovch<strong>in</strong>nikov, Y. A., FEBS Lett. 1985, 186,168- 174.[46] Bystrov, V. F., Arseniev, A. S., Tetrahedron 1988, 44, 925-940.[47] Cornell, B. A., Separovic, F., Baldassi, A. J., Smith, R., Biophys. J. 1988, 53, 67-76.[48] Smith, R., Thomas, D. E., Separovic, F., Atk<strong>in</strong>s, A. R., Cornell, B. A., Biophys. J; 1989,56, 307-314.[49] Nicholson, L. K., LoGrasso, P. V., Cross T, A., J. Am. Chem SOC. 1989, Ill, 400-401.[50] Nicholson, L. K., Cross, T. A., Biochem. 1989, 28, 9379-9385.[51] Wooley, G. A., Wallace, B. A., J. Membr. Biol. 1992, 129, 109-136.[52] Lauger, P., Biochim. Biophys. Acta 1973, 311, 423-441.[53] Levitt, D. G., Ann. Rev. Biophys. Chem. 1987, IS, 29-57.[54] Furois-Corb<strong>in</strong> S., Pullman, A., Biochim. Biophys. Acta 1989, 984, 339-350.[55] Furois-Corb<strong>in</strong>, S., Pullman, A., Biophys. Chem. 1991, 39, 153 - 159.[56] Brooks 111, C. L., Karplus, M., Pettitt, B. M., Advances <strong>in</strong> Chemical Physics Vol. LXXI,Prigog<strong>in</strong>e, J., Rice, S. A. (eds.), John Wiley & Sons, New York, 1988.[57] Helfand, E., Phys. Rev. 1960, 119, 1-9.[58] Cooper, K. E., Jakobsson, E., Wolynes, P. G., Prog. Biophys. Mol. Biol. 1985,46, 51-96.[59] The net charge per unit area, Qhet, necessary to generate the transmembrane potential isAIJ/E~/M, where cM and AX are the dielectric constant and the thickness of thehydrocarbon region. For a typical potential of 100 millivolts the net charge per area isapproximately one unit charge per square of (25 nm)2. The charge imbalance is distributedwith<strong>in</strong> a distance comparable to the Debye length from the membrane, i. e., on theorder of (- 0.9 nm). S<strong>in</strong>ce a physiological concentration of KC1 (150 mM) represents ap-

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