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- A Quantitative Approximation Scheme for the Traveling Wave S...A Quantitative Approximation Scheme for the Traveling Wave Solutions in the Hodgkin–Huxley Model
Biophysical Journal, Volume 79, Issue 6, 1 December 2000, Pages 2893-2901
C.B. Muratov
AbstractWe introduce an approximation scheme for the Hodgkin–Huxley model of nerve conductance that allows calculation of both the speed and shape of the traveling pulses, in quantitative agreement with the solutions of the model. We demonstrate that the reduced problem for the front of the traveling pulse admits a unique solution. We obtain an explicit analytical expression for the speed of the pulses that is valid with good accuracy in a wide range of the parameters.
Abstract | Full Text | PDF (143 kb) - Real-Time Kinetic Modeling of Voltage-Gated Ion Channels Usi...Real-Time Kinetic Modeling of Voltage-Gated Ion Channels Using Dynamic Clamp
Biophysical Journal, Volume 95, Issue 1, 1 July 2008, Pages 66-87
Lorin S. Milescu, Tadashi Yamanishi, Krzysztof Ptak, Murtaza Z. Mogri and Jeffrey C. Smith
AbstractWe propose what to our knowledge is a new technique for modeling the kinetics of voltage-gated ion channels in a functional context, in neurons or other excitable cells. The principle is to pharmacologically block the studied channel type, and to functionally replace it with dynamic clamp, on the basis of a computational model. Then, the parameters of the model are modified in real time (manually or automatically), with the objective of matching the dynamical behavior of the cell (e.g., action potential shape and spiking frequency), but also the transient and steady-state properties of the model (e.g., those derived from voltage-clamp recordings). Through this approach, one may find a model and parameter values that explain both the observed cellular dynamics and the biophysical properties of the channel. We extensively tested the method, focusing on Na models. Complex Markov models (10–12 states or more) could be accurately integrated in real time at >50kHz using the transition probability matrix, but not the explicit Euler method. The practicality of the technique was tested with experiments in raphe pacemaker neurons. Through automated real-time fitting, a Hodgkin-Huxley model could be found that reproduced well the action potential shape and the spiking frequency. Adding a virtual axonal compartment with a high density of Na channels further improved the action potential shape. The computational procedure was implemented in the free QuB software, running under Microsoft Windows and featuring a friendly graphical user interface.
Abstract | Full Text | PDF (3005 kb) - Nonequilibrium Response Spectroscopy of Voltage-Sensitive Io...Nonequilibrium Response Spectroscopy of Voltage-Sensitive Ion Channel Gating
Biophysical Journal, Volume 74, Issue 1, 1 January 1998, Pages 210-229
Mark M. Millonas and Dorothy A. Hanck
AbstractWe describe a new electrophysiological technique called , which involves application of rapidly fluctuating (as high as 14kHz) 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.
Abstract | Full Text | PDF (304 kb) - …more
Copyright © 1972 The Biophysical Society. All rights reserved.
Biophysical Journal, Volume 12, Issue 8, 948-959, 1 August 1972
doi:10.1016/S0006-3495(72)86136-8
Articles
On the Theory of Ion Transport across the Nerve Membrane
Terrell L. Hill and Yi-Der Chen
Abstract
The theoretical power density spectrum G(f) of fluctuations in the steady-state squid axon K+ current in the 103 Hz region has been derived assuming that these are fluctuations in the number of open K+ channels in the Hodgkin-Huxley (HH) model. Various modifications of the HH model were also studied. The results were negative in all cases when compared with experiment. This confirms the generally held view that the observed G(f) ∼ 1/f is associated primarily with K+ current through open K+ channels and not with the open-close kinetics of these channels.
