Some studies on the ionic basis of the current-voltage relations in cardiac muscle

Thesis

Measurements of the electrical properties of the cardiac Purkinje fibre membrane have been made with intracellular electrodes; and in a separate study, computations based on a mathematical model of the membrane have been performed.

Evidence has been found that the instantaneous potassium permeability of the membrane varies as a function of the difference between the K equilibrium potential and the membrane potential, rather than of the latter alone. Superimposed upon this, there is a time-dependent slow increase in K conductance on depolarization, corresponding to the delayed rectification described by the Hodgkin-Huxley relation when n² is used in place of n⁴. The time constant is voltage dependent and may be up to hundreds of msec. This increase and its subsequent decline can account for repolarization from the plateau of the action potential, and for pacemaker activity. During long-lasting outward currents applied across the membrane there is a gradual depolarization of the K equilibrium potential; evidence suggests that K ions accumulate transiently in an extracellular space adjacent to the membrane.

Solutions to Noble's (1962) modified Hodgkin-Huxley equations have been computed for a membrane with part of its capacitance in series with a constant resistance. Rates of depolarization and repolarization have thereby been increased to experimentally-observed values; also, a possible explanation for the pre-plateau notch in some action potentials has resulted. An evaluation of the ramp-shaped voltage clamp as an analytical tool has been attempted, by computing solutions of the same equations under such conditions. The equations have also been solved when is a function of n².

Authors: McAllister, R

• Peer review status: Peer reviewed
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford