Hodgkin-Huxley channels

Derived from Hodgkin-Huxley s celebrated theory and inspired by the experimental observations, cellular calcium dynamics, either stimulated via inositol 1,4,5-trisphosphate (IP3) receptor in many non-muscle cells [69,139], or via the ryanodine receptor in muscle cells [108], is another extensively studied oscillatory system. Both receptors are themselves Ca2+ channels, and both can be activated by Ca2+, leading to calcium-induced calcium release from endoplasmic reticulum. 

The psychologist Maslow wrote that if the only tool you have is a hammer, you tend to treat everything as if it were a nail (4). Markov processes based on the Hodgkin-Huxley model had been widely used to describe ionic currents measured in many different experiments. However, in 1986, we began to use a new tool to analyze the patch clamp data. The insight gained from this new analysis has changed our ideas about the processes that open and close the ion channel. The new tool is based on fractals. 

The Markov description of ion channel kinetics, originally derived from the Hodgkin-Huxley model, implies that the ion channel protein has certain physical properties. 

Thanks to the studies of Hodgkin Huxley, which culminated in 1952 with the publication of a series of articles, of which the last was of theoretical nature, the physicochemical bases of neuronal excitability giving rise to the action potential were elucidated. Soon after, Huxley (1959) showed how a nerve cell can generate a train of action potentials in a periodic manner (see also Connor, Walter McKown, 1977 Aihara Matsumoto, 1982 Rinzel Ermentrout, 1989). Even if the properties of the ionic channels involved have not yet been fully elucidated, cardiac oscillations originate in a similar manner from the pacemaker properties of the specialized, electrically excitable tissues of the heart (Noble, 1979,1984 Noble Powell, 1987 Noble, DiFrancesco Denyer, 1989 DiFrancesco, 1993). These examples remained the only biological rhythms whose molecular mechanism was known to some extent, until the discovery of biochemical oscillations. 

The nonlinearity of kinetic equations of the Hodgkin-Huxley type might also result, at least in part, from the cooperative allosteric properties of ion channels. The crystallographic study of these channels indeed reveals that they are often formed by multiple interacting subunits (Noda et al, 1984). 

In 1952, Alan Hodgkin and Andrew Huxley pubHshed a paper showing how a nonlinear empirical model of the membrane processes could be constructed [Hodgkin and Huxley, 1952]. In the five decades since their work, the Hodgkin-Huxley (abbreviated HH) paradigm of modeling cell membranes has been enormously successful. While the concept of ion channels was not estabhshed when they performed their work, one of their main contributions was the idea that ion-selective processes existed in the membrane. It is now known that most of the passive transport of ions across cell membranes is accompHshed by ion-selective channels. In addition to constructing a nonhnear model, they also estabhshed a method to incorporate experimental data into a nonlinear mathematical membrane model. 

Electrical noise in biological membrane systems is explained in terms of opening and closing of ionic channels (for two useful review see De Felice (1981) and Frehland (1982)). The qualitative behaviour of membrane activity strongly depends on the density of membrane channels (Holden, 1981 Holden Yoda 1981). Integrating numerically the celebrated Hodgkin-Huxley equations (Hodgkin Huxley, 1952) it was demonstrated that the number of channels is a bifurcation parameter. The fact that channel... 

A concrete example of a model for neuronal bursting (Plant, 1981) has been analyzed in considerable detail by Rinzel and Lee (1987). The model utihzes the Hodgkin-Huxley model, eqs. (13.3) and (13.4), as the mechanism for action-potential generation and introduces two additional conductances, a calcium channel and a calcium-activated potassium channel, to produce the bursting behavior. The membrane potential is given by... 

Activation Atrial preparation Biophysics Calcium channel Cardiac action potential Channel kinetics Comprehensive in vitro proarrhythmia assay Delayed rectifier Early afterdepolarisation ECG Hodgkin-Huxley ICHS7A ICHS7B In silico modelling Inactivation Inward rectifier Langendorff heart Purkinje fibre Safety assessment Sodium channel Stem cells... 

The spectral analysis of fluctuations yields also valuable information, and it can be used to test the validity of kinetic schemes describing the transitions between different channel states. In Ranvier nodes the component of the sodium current fluctuations which corresponds to the sodium inactivation process observed in voltage-clamp experiments is much larger than expected from a simple Hodgkin-Huxley scheme with statistically independent activation and inactivation processes. This finding provides a strong argument in favour of the hypothesis that the inactivation process is at least partially sequential to the activation process. 

Several attempts will be done to fit the gj (t) records with models having different reaction-schemes from the classical Hodgkin-Huxley one. To answer the second question we can anticipate that (although the data on our hands are still widely incomplete) similar effects are observed for the opening and closing rates of the sodium channel. 

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