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Biophys J. Jan 1998; 74(1): 210–229.
PMCID: PMC1299376

Nonequilibrium response spectroscopy of voltage-sensitive ion channel gating.


We describe a new electrophysiological technique called nonequilibrium response spectroscopy, which involves application of rapidly fluctuating (as high as 14 kHz) large-amplitude voltage clamp waveforms to ion channels. As a consequence of the irreversible (in the sense of Carnot) exchange of energy between the fluctuating field and the channel protein, the gating response is exquisitely sensitive to features of the kinetics that are difficult or impossible to adequately resolve by means of traditional stepped potential protocols. Here we focus on the application of dichotomous (telegraph) noise voltage fluctuations, a broadband Markovian colored noise that fluctuates between two values. Because Markov kinetic models of channel gating can be embedded within higher-dimensional Markov models that take into account the effects of the voltage fluctuations, many features of the response of the channels can be calculated algebraically. This makes dichotomous noise and its generalizations uniquely suitable for model selection and kinetic analysis. Although we describe its application to macroscopic ionic current measurements, the nonequilibrium response method can also be applied to gating and single channel current recording techniques. We show how data from the human cardiac isoform (hH1a) of the Na+ channel expressed in mammalian cells can be acquired and analyzed, and how these data reveal hidden aspects of the molecular kinetics that are not revealed by conventional methods.

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Selected References

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  • Armstrong CM. Sodium channels and gating currents. Physiol Rev. 1981 Jul;61(3):644–683. [PubMed]
  • Armstrong CM, Bezanilla F. Currents related to movement of the gating particles of the sodium channels. Nature. 1973 Apr 13;242(5398):459–461. [PubMed]
  • Armstrong CM, Bezanilla F. Charge movement associated with the opening and closing of the activation gates of the Na channels. J Gen Physiol. 1974 May;63(5):533–552. [PMC free article] [PubMed]
  • Armstrong CM, Bezanilla F. Inactivation of the sodium channel. II. Gating current experiments. J Gen Physiol. 1977 Nov;70(5):567–590. [PMC free article] [PubMed]
  • Colquhoun D, Hawkes AG. On the stochastic properties of single ion channels. Proc R Soc Lond B Biol Sci. 1981 Mar 6;211(1183):205–235. [PubMed]
  • Conti F, Hille B, Nonner W. Non-stationary fluctuations of the potassium conductance at the node of ranvier of the frog. J Physiol. 1984 Aug;353:199–230. [PMC free article] [PubMed]
  • Conti F, Wanke E. Channel noise in nerve membranes and lipid bilayers. Q Rev Biophys. 1975 Nov;8(4):451–506. [PubMed]
  • Fernández JM, Bezanilla F, Taylor RE. Distribution and kinetics of membrane dielectric polarization. II. Frequency domain studies of gating currents. J Gen Physiol. 1982 Jan;79(1):41–67. [PMC free article] [PubMed]
  • Fohlmeister JF, Adelman WJ., Jr Gating current harmonics. I. Sodium channel activation gating in dynamic steady states. Biophys J. 1985 Sep;48(3):375–390. [PMC free article] [PubMed]
  • Fohlmeister JF, Adelman WJ., Jr Gating current harmonics. II. Model simulations of axonal gating currents. Biophys J. 1985 Sep;48(3):391–400. [PMC free article] [PubMed]
  • Fohlmeister JF, Adelman WJ., Jr Gating current harmonics. III. Dynamic transients and steady states with intact sodium inactivation gating. Biophys J. 1986 Sep;50(3):489–502. [PMC free article] [PubMed]
  • Fohlmeister JF, Adelman WJ., Jr Gating current harmonics. I. Sodium channel activation gating in dynamic steady states. Biophys J. 1985 Sep;48(3):375–390. [PMC free article] [PubMed]
  • Hanck DA, Sheets MF. Time-dependent changes in kinetics of Na+ current in single canine cardiac Purkinje cells. Am J Physiol. 1992 Apr;262(4 Pt 2):H1197–H1207. [PubMed]
  • Hanck DA, Sheets MF. Extracellular divalent and trivalent cation effects on sodium current kinetics in single canine cardiac Purkinje cells. J Physiol. 1992 Aug;454:267–298. [PMC free article] [PubMed]
  • Hartmann HA, Tiedeman AA, Chen SF, Brown AM, Kirsch GE. Effects of III-IV linker mutations on human heart Na+ channel inactivation gating. Circ Res. 1994 Jul;75(1):114–122. [PubMed]
  • HODGKIN AL, HUXLEY AF. A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol. 1952 Aug;117(4):500–544. [PMC free article] [PubMed]
  • HODGKIN AL, HUXLEY AF, KATZ B. Measurement of current-voltage relations in the membrane of the giant axon of Loligo. J Physiol. 1952 Apr;116(4):424–448. [PMC free article] [PubMed]
  • Horn R, Korn SJ. Model selection: reliability and bias. Biophys J. 1989 Feb;55(2):379–381. [PMC free article] [PubMed]
  • Horsthemke W, Lefever R. Voltage-noise-induced transitions in electrically excitable membranes. Biophys J. 1981 Aug;35(2):415–432. [PMC free article] [PubMed]
  • Katz B, Miledi R. Membrane noise produced by acetylcholine. Nature. 1970 Jun 6;226(5249):962–963. [PubMed]
  • Katz B, Miledi R. The statistical nature of the acetycholine potential and its molecular components. J Physiol. 1972 Aug;224(3):665–699. [PMC free article] [PubMed]
  • Keynes RD, Rojas E. Kinetics and steady-state properties of the charged system controlling sodium conductance in the squid giant axon. J Physiol. 1974 Jun;239(2):393–434. [PMC free article] [PubMed]
  • Kirkpatrick S, Gelatt CD, Jr, Vecchi MP. Optimization by simulated annealing. Science. 1983 May 13;220(4598):671–680. [PubMed]
  • Läuger P, Stephan W, Frehland E. Fluctuations of barrier structure in ionic channels. Biochim Biophys Acta. 1980 Oct 16;602(1):167–180. [PubMed]
  • Makielski JC, Sheets MF, Hanck DA, January CT, Fozzard HA. Sodium current in voltage clamped internally perfused canine cardiac Purkinje cells. Biophys J. 1987 Jul;52(1):1–11. [PMC free article] [PubMed]
  • Mannuzzu LM, Moronne MM, Isacoff EY. Direct physical measure of conformational rearrangement underlying potassium channel gating. Science. 1996 Jan 12;271(5246):213–216. [PubMed]
  • Marmarelis PZ, Naka K. White-noise analysis of a neuron chain: an application of the Wiener theory. Science. 1972 Mar 17;175(4027):1276–1278. [PubMed]
  • Marmarelis PZ, Naka K. Experimental analysis of a neural system: two modeling approaches. Kybernetik. 1974 May 31;15(1):11–26. [PubMed]
  • MARMONT G. Studies on the axon membrane; a new method. J Cell Physiol. 1949 Dec;34(3):351–382. [PubMed]
  • Millonas MM, Chialvo DR. Control of voltage-dependent biomolecules via nonequilibrium kinetic focusing. Phys Rev Lett. 1996 Jan 15;76(3):550–553. [PubMed]
  • Millonas MM, Chialvo DR. Nonequilibrium fluctuation-induced phenomena in Josephson junctions. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1996 Mar;53(3):2239–2242. [PubMed]
  • Sheets MF, Kyle JW, Krueger S, Hanck DA. Optimization of a mammalian expression system for the measurement of sodium channel gating currents. Am J Physiol. 1996 Sep;271(3 Pt 1):C1001–C1006. [PubMed]
  • Stimers JR, Bezanilla F, Taylor RE. Sodium channel gating currents. Origin of the rising phase. J Gen Physiol. 1987 Apr;89(4):521–540. [PMC free article] [PubMed]
  • Stühmer W, Conti F, Suzuki H, Wang XD, Noda M, Yahagi N, Kubo H, Numa S. Structural parts involved in activation and inactivation of the sodium channel. Nature. 1989 Jun 22;339(6226):597–603. [PubMed]
  • Takashima S. Frequency domain analysis of asymmetry current in squid axon membrane. Biophys J. 1978 Apr;22(1):115–119. [PMC free article] [PubMed]
  • Taylor RE, Bezanilla F. Comments on the measurement of gating currents in the frequency domain. Biophys J. 1979 May;26(2):338–340. [PMC free article] [PubMed]
  • Taylor RE, Bezanilla F. Sodium and gating current time shifts resulting from changes in initial conditions. J Gen Physiol. 1983 Jun;81(6):773–784. [PMC free article] [PubMed]
  • Ukomadu C, Zhou J, Sigworth FJ, Agnew WS. muI Na+ channels expressed transiently in human embryonic kidney cells: biochemical and biophysical properties. Neuron. 1992 Apr;8(4):663–676. [PubMed]
  • Vandenberg CA, Bezanilla F. Single-channel, macroscopic, and gating currents from sodium channels in the squid giant axon. Biophys J. 1991 Dec;60(6):1499–1510. [PMC free article] [PubMed]
  • Vandenberg CA, Bezanilla F. A sodium channel gating model based on single channel, macroscopic ionic, and gating currents in the squid giant axon. Biophys J. 1991 Dec;60(6):1511–1533. [PMC free article] [PubMed]
  • Yang N, George AL, Jr, Horn R. Molecular basis of charge movement in voltage-gated sodium channels. Neuron. 1996 Jan;16(1):113–122. [PubMed]
  • Yang N, George AL, Jr, Horn R. Probing the outer vestibule of a sodium channel voltage sensor. Biophys J. 1997 Nov;73(5):2260–2268. [PMC free article] [PubMed]
  • Yang N, Horn R. Evidence for voltage-dependent S4 movement in sodium channels. Neuron. 1995 Jul;15(1):213–218. [PubMed]

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