Hodgkin-Huxley theory

The P s are now permeability coefficients and are related to the mobilities of the ions as in the original Nernst theory. The subscripts in and out refer to the concentrations of the ions inside and outside the membrane and the P s describe diffusion coefficients, mobilities, and the membrane thickness, but, in the Hodgkin-Huxley theory, were used as adjustable parameters. 

The demise of the famous Hodgkin-Huxley theory of nerve conductance brings to mind other Nobel prizes in electrochemically related areas. In 1959 Heyrovsky was recognized for a new analytical method, and this polarography has been the origin of many modem methods of electroanalysis. The award for Nobel Prize to Mitchell in 1978 (for a chemiosmotic model of membrane function) and metabolism seems to have been based on a lack of awareness of a simpler, clearer (prior) model by Williams for interpreting the same functions. The award to Marcus in 1992 for the theory of redox reactions (1956) seems to have lacked awareness of an earlier publication by Weiss that described similar ideas. 

The widespread evidence that Planck s steady state liquid junction potential is not a sufficient basis to the interpretation of membrane potentials in living systems raises as a question the real origin of potentials in living systems. Correspondingly, it makes questionable the basis of the Hodgkin-Huxley theory. 

The best-known theory of the spike potential produced in an impulse down a nerve is that due to Hodgkin, Huxley, and Katz (1952). Although this theory is still current among electrophysiologists, it is now regarded with skepticism by a number of physical scientists who have examined it in the light of modem... 

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. 

Jane Cronin Mathematical aspects of Hodgkin-Huxley neural theory... 

The Ionic Theory of Cell Potential by Hodgkin, Huxley, and Katz... 

The membrane potential in biology came to prominence in the days in which electrode phenomena were treated exclusively in terms of equilibrium thermodynamics. Between 1892 (Nernst ) and 1911 (Donnan " ), three treatments were given of membrane potentials. They form such a durable part of electrochemistry, not because of their importance per se, or even of their direct relevance to biological phenomena, but because one of them was the origin of the best-known of bioelectrochemical theories, the Hodgkin-Huxley-Katz mechanism for the passage of electricity through nerves. 

Although there now exists considerably more knowledge concerning membrane structure, and correlations between membrane structure and ionic permeability changes under a host of different conditions have been documented, there still does not exist a molecular theory explaining excitable membrane phenomena in the usual sense where the application of statistical mechanics yields empirically observed and derived thermodynamic relationships, e.g., the Hodgkin-Huxley equations. 

It should be mentioned, that the incorporation of the intercalated discs in the model completely changes classical relationships obtained from continuous ( Hodgkin-Huxley ) cable theory. For example, the inverse square root relationship between velocity and axial resistance does not hold, and an increase in accompanies slow conduction caused by high disc resistance. These deviations from classical continuous cable theory are further discussed elsewhere (Diaz et al., 1983 Rudy et al., 1983). 

The proposed model for the so-called sodium-potassium pump should be regarded as a first tentative attempt to stimulate the well-informed specialists in that field to investigate the details, i.e., the exact form of the sodium and potassium current-voltage curves at the inner and outer membrane surfaces to demonstrate the excitability (e.g. N, S or Z shaped) connected with changes in the conductance and ion fluxes with this model. To date, the latter is explained by the theory of Hodgkin and Huxley U1) which does not take into account the possibility of solid-state conduction and the fact that a fraction of Na+ in nerves is complexed as indicated by NMR-studies 124). As shown by Iljuschenko and Mirkin 106), the stationary-state approach also considers electron transfer reactions at semiconductors like those of ionselective membranes. It is hoped that this article may facilitate the translation of concepts from the domain of electrodes in corrosion research to membrane research. 

Until the 1950s, the rare periodic phenomena known in chemistry, such as the reaction of Bray [1], represented laboratory curiosities. Some oscillatory reactions were also known in electrochemistry. The link was made between the cardiac rhythm and electrical oscillators [2]. New examples of oscillatory chemical reactions were later discovered [3, 4]. From a theoretical point of view, the first kinetic model for oscillatory reactions was analyzed by Lotka [5], while similar equations were proposed soon after by Volterra [6] to account for oscillations in predator-prey systems in ecology. The next important advance on biological oscillations came from the experimental and theoretical studies of Hodgkin and Huxley [7], which clarified the physicochemical bases of the action potential in electrically excitable cells. The theory that they developed was later applied [8] to account for sustained oscillations of the membrane potential in these cells. Remarkably, the classic study by Hodgkin and Huxley appeared in the same year as Turing s pioneering analysis of spatial patterns in chemical systems [9]. 

Equation (3.12) is an identity that does not depend on the details of the kinetic reaction mechanism that is operating in a particular system [19], We [19] have shown that Equation (3.12) is intimately related to the Crooks fluctuation theorem [41] - an important result in non-equilibrium statistical thermodynamics - as well as to theories developed by Hill [87, 90], Ussing [201], and Hodgkin and Huxley [95],... 

---