Abstract
Ion channels are proteins in the lipid cell membrane. They spontaneously fluctuate between conformational shapes that are open or closed to the passage of ions. The ionic currents through an individual channel can be resolved by the patch clamp technique. Thus, the time sequence of open and closed conformational states can be measured in one channel molecule. The probability density function of the dwell times in the open and closed states displays scaling functions that may arise from: (1) a large number of conformational substates having a continuous distribution of activation energy barriers, (2) time-dependent changes in the energy barriers between states, or (3) local interactions that constrain local structures which interact hierarchically to form global structure.
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References
B. Hille,Ionic Channels of Excitable Membranes (Sinauer, Sunderland, Massachusetts, 1984).
B. Sakmann and E. Neher,Single-Channel Recording (Plenum Press, New York, 1983).
L. S. Liebovitch, J. Fischbarg, and J. P. Koniarek, Ion channel kinetics: A model based on fractal scaling rather than multistate Markov processes,Math. Biosci. 84:37–68 (1987).
L. S. Liebovitch and S. Weinbaum, A model of epithelial water transport,Biophys. J. 35:315–338 (1981).
L. S. Liebovitch and J. M. Sullivan, Fractal analysis of a voltage-dependent potassium channel from cultured mouse hippocampal neurons,Biophys. J. 52:979–988 (1987).
L. S. Liebovitch and T. I. Toth, Fractal activity in cell membrane ion channels,Ann. N. Y. Acad. Sci. 591:375–391 (1990).
J. R. Alcala, E. Gratton, and F. G. Prendergast, Interpretation of fluorescent decays in proteins using continuous lifetime distributions,Biophys. J. 51:925–936 (1987).
R. H. Austin, K. W. Beeson, L. Eisentstein, H. Frauenfelder, and I. C. Gunsalus, Dynamics of ligand binding to myoglobin,Biochemistry 14:5355–5373 (1975).
T. G. Dewey and D. B. Spencer, Are protein dynamics fractal ?Comm. Mol. Cell. Biophys. 7:155–171 (1991).
G. M. Barrow,Physical Chemistry, 4th ed. (McGraw-Hill, New York, 1961).
L. S. Liebovitch and T. I. Tóth, Distributions of activation energy barriers that produce stretched exponential probability distributions for the time spent in each state of the two state reaction A⇌B,Bull. Math. Biol. 53:443–55 (1991).
R. McGee, Jr., M. S. P. Sansom, and P. N. R. Usherwood, Characterization of a delayed rectifier K+ channel in NG108-15 neuroblastoma × glioma cells: Gating kinetics and the effects of enrichment of membrane phospholipids with arachidonic acid,J. Membrane Biol. 102:21–34 (1988).
G. Careri, P. Fasella, and E. Gratton, Statistical time events in enzymes: A physical assessment,CRC Crit. Rev. Biochem. 3:141–164 (1975).
M. Karplus and J. A. McCammon, Dynamics of proteins: Elements and function,Annu. Rev. Biochem. 52:263–300 (1983).
J. A. McCammon and S. C. Harvey,Dynamics of Proteins and Nucleic Acids (Cambridge University Press, Cambridge, 1987).
W. D. Tian, J. T. Sage, V. Srajer, and P. M. Champion, Relaxation dynamics of myoglobin in solution,Phys. Rev. Lett. 68:408–411 (1992).
L. S. Liebovitch and T. I. Toth, A model of ion channel kinetics using deterministic chaotic rather than stochastic processes,J. Theor. Biol. 148:243–267 (1991).
L. S. Liebovitch and F. P. Czegledy, A model of ion channel kinetics based on deterministic chaotic motion in a potential with two local minima,Ann. Biomed. Eng. 20:517–531 (1992).
K. Y. Billah and R. H. Scanlan, Resonance, Tacoma Narrows bridge failure, and undergraduate physics textbooks,Am. J. Phys. 59:118–124 (1991).
H. Frauenfelder, Proteins and glasses, inStructure and Dynamics of Nucleic Acids, Proteins, and Membranes, E. Clementi and S. Chin, eds. (Plenum Press, New York, 1986), pp. 169–177.
D. L. Stein, Condensed matter biophysics: Structure and dynamics of large biomolecules, inStructure, Dynamics and Function of Biomolecules, A. Ehrenberg, R. Rigler, A. Graslund, and L. Nilsson, eds. (Springer-Verlag, New York, 1987), pp. 70–74.
P. Leopold, Mult-scale Ising model for protein denaturation,Biophys. J. 57:82a (1990).
M. Sasai and P. G. Wolynes, Molecular theory of associative memory Hamiltonian models of protein folding,Phys. Rev. Lett. 65:2740–2743 (1990).
J. L. McClelland and D. E. Rumelhart,Explorations in Parallel Distributed Processing (MIT Press, Cambridge, Massachusetts, 1989).
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Liebovitch, L.S. Interpretation of protein structure and dynamics from the statistics of the open and closed times measured in a single ion-channel protein. J Stat Phys 70, 329–337 (1993). https://doi.org/10.1007/BF01053971
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DOI: https://doi.org/10.1007/BF01053971