Markov, fractal, diffusion, and related models of ion channel gating. A comparison with experimental data from two ion channels. 1989

M S Sansom, and F G Ball, and C J Kerry, and R McGee, and R L Ramsey, and P N Usherwood
Department of Zoology, University of Nottingham, University Park, United Kingdom.

The gating kinetics of single-ion channels are generally modeled in terms of Markov processes with relatively small numbers of channel states. More recently, fractal (Liebovitch et al. 1987. Math. Biosci. 84:37-68) and diffusion (Millhauser et al. 1988. Proc. Natl. Acad. Sci. USA. 85:1502-1507) models of channel gating have been proposed. These models propose the existence of many similar conformational substrates of the channel protein, all of which contribute to the observed gating kinetics. It is important to determine whether or not Markov models provide the most accurate description of channel kinetics if progress is to be made in understanding the molecular events of channel gating. In this study six alternative classes of gating model are tested against experimental single-channel data. The single-channel data employed are from (a) delayed rectifier K+ channels of NG 108-15 cells and (b) locust muscle glutamate receptor channels. The models tested are (a) Markov, (b) fractal, (c) one-dimensional diffusion, (d) three-dimensional diffusion, (e) stretched exponential, and (f) expo-exponential. The models are compared by fitting the predicted distributions of channel open and closed times to those observed experimentally. The models are ranked in order of goodness-of-fit using a boot-strap resampling procedure. The results suggest that Markov models provide a markedly better description of the observed open and closed time distributions for both types of channel. This provides justification for the continued use of Markov models to explore channel gating mechanisms.

UI MeSH Term Description Entries
D007473 Ion Channels Gated, ion-selective glycoproteins that traverse membranes. The stimulus for ION CHANNEL GATING can be due to a variety of stimuli such as LIGANDS, a TRANSMEMBRANE POTENTIAL DIFFERENCE, mechanical deformation or through INTRACELLULAR SIGNALING PEPTIDES AND PROTEINS. Membrane Channels,Ion Channel,Ionic Channel,Ionic Channels,Membrane Channel,Channel, Ion,Channel, Ionic,Channel, Membrane,Channels, Ion,Channels, Ionic,Channels, Membrane
D008433 Mathematics The deductive study of shape, quantity, and dependence. (From McGraw-Hill Dictionary of Scientific and Technical Terms, 6th ed) Mathematic
D008564 Membrane Potentials The voltage differences across a membrane. For cellular membranes they are computed by subtracting the voltage measured outside the membrane from the voltage measured inside the membrane. They result from differences of inside versus outside concentration of potassium, sodium, chloride, and other ions across cells' or ORGANELLES membranes. For excitable cells, the resting membrane potentials range between -30 and -100 millivolts. Physical, chemical, or electrical stimuli can make a membrane potential more negative (hyperpolarization), or less negative (depolarization). Resting Potentials,Transmembrane Potentials,Delta Psi,Resting Membrane Potential,Transmembrane Electrical Potential Difference,Transmembrane Potential Difference,Difference, Transmembrane Potential,Differences, Transmembrane Potential,Membrane Potential,Membrane Potential, Resting,Membrane Potentials, Resting,Potential Difference, Transmembrane,Potential Differences, Transmembrane,Potential, Membrane,Potential, Resting,Potential, Transmembrane,Potentials, Membrane,Potentials, Resting,Potentials, Transmembrane,Resting Membrane Potentials,Resting Potential,Transmembrane Potential,Transmembrane Potential Differences
D008954 Models, Biological Theoretical representations that simulate the behavior or activity of biological processes or diseases. For disease models in living animals, DISEASE MODELS, ANIMAL is available. Biological models include the use of mathematical equations, computers, and other electronic equipment. Biological Model,Biological Models,Model, Biological,Models, Biologic,Biologic Model,Biologic Models,Model, Biologic
D002460 Cell Line Established cell cultures that have the potential to propagate indefinitely. Cell Lines,Line, Cell,Lines, Cell
D004058 Diffusion The tendency of a gas or solute to pass from a point of higher pressure or concentration to a point of lower pressure or concentration and to distribute itself throughout the available space. Diffusion, especially FACILITATED DIFFUSION, is a major mechanism of BIOLOGICAL TRANSPORT. Diffusions
D005971 Glutamates Derivatives of GLUTAMIC ACID. Included under this heading are a broad variety of acid forms, salts, esters, and amides that contain the 2-aminopentanedioic acid structure. Glutamic Acid Derivatives,Glutamic Acids,Glutaminic Acids
D000818 Animals Unicellular or multicellular, heterotrophic organisms, that have sensation and the power of voluntary movement. Under the older five kingdom paradigm, Animalia was one of the kingdoms. Under the modern three domain model, Animalia represents one of the many groups in the domain EUKARYOTA. Animal,Metazoa,Animalia
D015221 Potassium Channels Cell membrane glycoproteins that are selectively permeable to potassium ions. At least eight major groups of K channels exist and they are made up of dozens of different subunits. Ion Channels, Potassium,Ion Channel, Potassium,Potassium Channel,Potassium Ion Channels,Channel, Potassium,Channel, Potassium Ion,Channels, Potassium,Channels, Potassium Ion,Potassium Ion Channel
D017470 Receptors, Glutamate Cell-surface proteins that bind glutamate and trigger changes which influence the behavior of cells. Glutamate receptors include ionotropic receptors (AMPA, kainate, and N-methyl-D-aspartate receptors), which directly control ion channels, and metabotropic receptors which act through second messenger systems. Glutamate receptors are the most common mediators of fast excitatory synaptic transmission in the central nervous system. They have also been implicated in the mechanisms of memory and of many diseases. Excitatory Amino Acid Receptors,Glutamate Receptors,Receptors, Excitatory Amino Acid,Excitatory Amino Acid Receptor,Glutamate Receptor,Receptor, Glutamate

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