Hodgkin, membrane potential

The voltage sensor is the part of a channel protein responsible for detection of the membrane potential. A voltage sensor of the voltage-dependent Na+ channel was predicted by Hodgkin and Huxley in 1952. Positively charged amino acid residues in S4 of each repeat play an essential role as the voltage sensor. 

A breakthrough in cell modelling occurred with the work of the British scientists. Sir Alan L. Hodgkin and Sir Andrew F. Huxley, for which they were in 1963 (jointly with Sir John C. Eccles) awarded the Nobel prize. Their new electrical models calculated the changes in membrane potential on the basis of the underlying ionic currents. 

Equation (3) suggests that the membrane potential in the presence of sufficient electrolytes in Wl, W2, and LM is primarily determined by the potential differences at two interfaces which depend on charge transfer reactions at the interfaces, though the potential differences at interfaces are not apparently taken into account in theoretical equations such as Nernst-Planck, Henderson, and Goldman-Hodgkin-Katz equations which have often been adopted in the discussion of the membrane potential. 

The relationship between the electrical excitation of the axon and the membrane potential was clarified by A. L. Hodgkin and A. P. Huxley in... 

This Goldman-Hodgkin-Katz voltage equation is often used to determine the relative permeabilities of ions from experiments where the bathing ion concentrations are varied and changes in the membrane potential are recorded [5],... 

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]. 

As indicated above, theoretical models for biological rhythms were first used in ecology to study the oscillations resulting from interactions between populations of predators and preys [6]. Neural rhythms represent another field where such models were used at an early stage The formalism developed by Hodgkin and Huxley [7] stiU forms the core of most models for oscillations of the membrane potential in nerve and cardiac cells [33-35]. Models were subsequently proposed for oscillations that arise at the cellular level from regulation of enzyme, receptor, or gene activity (see Ref. 31 for a detailed fist of references). 

An equation (also referred to as the constant field equation, the Goldman-Hodgkin-Katz equation, and the GHK equation) which relates the membrane potential (Ai/r) to the individual permeabilities of the ions (and their concentrations) on both sides of the membrane. Thus,... 

To establish the chemical basis of the action potential, A. L. Hodgkin and A. F. Huxley in the 1950s devised the voltage clamp, a sophisticated device by which the transmembrane current can be measured while using a feedback mechanism to fix the membrane potential at a preselected value.413-417 Using the voltage clamp the membrane conductance could be measured as a function of the membrane potential... 

If the permeability is significant for both potassium and sodium, the Nernst equation is not a good predictor of membrane potential, but the Goldman-Hodgkin-Katz equation may be used. 

Modified Hodgkin-Huxley Model. In the HH model, the membrane current I, written as a function of V is expressed by the system of coupled equations given in Table I. In these equations V is the displacement of membrane potential from the resting value (depolarization negative). Constants Cm, g, gjga, 8i VK VNa and V] are explained in detail in ( 1). In Table I, l n and g m h are the potassium and sodium conductances, respectively. The dimensionless dynamical quantities m, n, and h are solutions of the given first order differential equations and vary between zero and unity after a change in membrane potential. The a and 3 rate constants are assumed to depend only on the instantaneous value of membrane potential. 

These equations offer an adequate basis for the development of the negative membrane potential of 70 to 90 mV. Excitation as a process characterizing nerve and muscle cells is associated with a transient reduction or abolition of this membrane potential, and in some cases with a temporary "overshoot" or reversal of its polarity. Just as for the membrane potential, these major but transient perturbations in the production of action potentials have been adequately modeled in dynamics of ionic equilibria by Hodgkin and Huxley (2). 

This theory of an equilibrium of one species between each side of the membrane was formulated by Donnan in 1925 and from then until 1955, it reigned as the theory of membrane potentials. Its demise came when radiotracer measurements showed that all relevant ions (e.g., K+, Na+, and Cl ) permeated more than a dozen actual biological membranes, although each ion had a characteristic permeability coefficient in each membrane (Hodgkin and Keynes, 1953). 

Thus, one can artificially change the concentrations of Na+, K+, and Cl on either side of the membrane. Then, one can go back to the Hodgkin-Katz equation (14.5) and ask what change in potential these artificial changes of ionic concentrations should bring about. There is found (Jahn, 1962) to be a poor match between theory and experiment. Ionic concentration differences alone, then, do not completely determine membrane potentials in living systems. 

Fig. 14.15. Stimulating current in membrane potential experiment Hodgkin and Huxley (Reprinted from J. Koryta, Ions, Electrodes and Membranes, p. 174, Copyright J. Wiley Sons, Ltd. 1991. Reproduced with permission of J. Wiley Sons, Ltd.).

The voltage v in the Hodgkin-Huxley model is the membrane potential measured relative to the equilibrium voltage Veq v = AT — Veq, where Veq is the potential when no current is applied. The experimentally determined equilibrium potentials (which depend on the ion gradients across the membrane) for the model are... 

A. L. Hodgkin and A. F. Huxley. The dual effect of membrane potential on sodium conductance in the giant axon of Loligo. J. Physiol., 116 497-506, 1952. 

Voltage-dependent channels, such as the classical sodium or potassium channels in nerve tissue, change their conductance with membrane potential. The changes in conductance are a very steep function of membrane voltage conductance values can increase as much as 150 times for an increment of 10 mV in membrane potential (Hodgkin and Huxley, 1952). 

---