It is not well understood when during embryonic development the elements of a cell's responsiveness first appear, nor the factors controlling their appearance. A strategy to approach this issue is to determine which aspects of neuronal development are highly stereotyped in presence, timing, or pattern across a variety of cell types, and which are more diversified by cell type, region, or other parameters. We have used a fluorescent potentiometric oxonol dye in conjunction with a digital video imaging system to record the emergence and distribution of specific forms of excitability in dissociated embryonic rat spinal cord cells. We studied the expression of responses to veratridine, a sodium channel activator; muscimol, a GABAA receptor agonist; and kainic acid, an agonist at a class of glutamate receptors. Responses were consistently detectable in a percentage of cells dissociated from the earliest age examined, embryonic day 13, and increased progressively in later ages. Cells were examined from four regions, with cervical-lumbosacral and ventrodorsal distinctions. In the population of cells from each region, functional sodium channels appeared prior to GABAA receptors, which in turn emerged prior to kainate-activated glutamate receptors. This pattern was common to all spinal cord regions and revealed ventrodorsal and rostrocaudal gradients reflecting the known pattern of spinal cord neurogenesis. Analysis of the individual cell responses indicated that the stereotypical pattern of sequential channel development occurs individually on most cells in each region.

The inward sodium current in cardiac muscle is difficult to study by voltage clamp methods, so various indirect experimental measures have been used to obtain insight into its characteristics. These methods depend on the relationship between maximal upstroke velocity of the action potential (Vmax) and the sodium current (INa), usually defined in terms of the Hodgkin-Huxley model. These relationships were explored using an adaptation of this model to cardiac Purkinje fibers. In general Vmax corresponded to INa, and it could be used to determine the relationship of membrane potential to GNa, and h infinity. The results, however, depended on the method of stimulation of the action potential, and an optimal stimulation method was determined. A commonly used experimental technique called "membrane responsiveness" was shown to distort seriously the properties of steady-state gating inactivation that is supposed to measure. Estimation of the changes in maximal sodium conductance, such as those produced by tetrodotoxin (TTX), would be accurately measured. Some experimental results have indicated a voltage-dependent effect of TTX. Characteristics of the measures of TTX effect under those conditions were illustrated. In summary, calculations with a model of the cardiac Purkinje fiber action potential provide insight into the accuracy of certain experimental methods using maximal upstroke velocity as a measure of INa, and cast doubt on other experimental methods, such as membrane responsiveness.

Propagation of the action potential is a complex process, and the relationships among the various factors involved in conduction have not been clear. We use three mathematical models of uniform conduction in a cable to clarify some of these relationships. One model is newly derived here, and two have been previously derived by Hunter et al. (1975, Prog. Biophys. Mol. Biol., 30:99-144). These models were able to simulate individual experimental action potential upstrokes previously obtained (Walton and Fozzard, 1983, Biophys. J., 44:1-8). The models were then utilized to provide relationships between measures of conduction. Among these were that maximal upstroke velocity (Vmax) is directly proportional to peak inward ionic current normalized by capacitance that is filled during the upstroke (I/Cf), and that conduction velocity was directly related to the square root of either Vmax or I/Cf. These relationships were shown to be model independent and to predict the experimental results, thus providing validated quantitative relationships that were not discernible through use of experimental data alone. The concept of safety factor was considered and a parameter was proposed that may be related to safety factor.

Conduction velocity is a complex physiological process that integrates the active and passive properties of the excitable cell. The relations between these properties in determining the conduction velocity are not intuitively obvious, and models have been used frequently to illustrate important relationships. To study the relationships of important parameters and to evaluate commonly used models, we changed conduction velocity experimentally in sheep cardiac Purkinje strands by reducing extracellular Na systematically. Cable analyses were also performed to obtain passive membrane and cable properties. Resting membrane resistance and capacitance did not change, nor did core resistance. Active properties measured in addition to conduction velocity included maximal upstroke velocity, action potential height, time constant of the foot, peak inward current, and upstroke power. With reduction in extracellular Na, all of these parameters of the action potential changed nonlinearly and not in direct proportion to the change in conduction velocity. The only simple relation found was a linear relationship between maximal upstroke velocity and peak inward current, normalized by the capacity of the foot. Models based on the cable equation and the wave equation offer a basis for quantitative analysis of conduction, and these data can be used to test the models.