The Goldman-Hodgkin-Katz equation and graphical 'load-line' analysis of ionic flow through outer hair cells

While the 'membrane potential' of a cell which has a homogeneous membrane and surrounding environment, and which is not pumping ions electrogenically (passing no net current through its membranes), can be estimated from the Goldman voltage equation, this equation is inappropriate for other cells. In the mammalian cochlea such problematic cells include the cells of stria vascularis and the sensory hair cells of the organ of Corti. Not only is the Goldman voltage equation inappropriate, but in asymmetric cells the concept of a single 'membrane potential' is misleading: a different transmembrane voltage is required to define the electrical state of each section of the cell's heterogeneous membrane. This paper presents a graphical 'load-line analysis' of currents through one such asymmetric cell, the outer hair cells of the organ of Corti. The approach is extremely useful in discussing the effects of various cochlear manipulations on the electrical potential within hair cells, even without a detailed knowledge of their membrane conductance. The paper discusses how modified Goldman-Hodgkin-Katz equations can be used to describe stretch-activated channels, voltage-controlled channels, ligand-mediated channels, and how the combination of these channels and the extracellular ionic concentrations should affect the hair cell's resting intracellular potential and resting transcellular current, its receptor current and receptor potential, and the extracellular microphonic potential around these cells. Two other issues discussed are the role of voltage-controlled channels in genetically determining membrane potential, and the insensitivity of hair cells to changes of extracellular potassium concentration under some conditions.