Multiple channels and calcium dynamics

Abstract

This chapter will focus on modeling the electrical properties of one particular neuron type whose various macroscopic currents have been described in detail, the bullfrog sympathetic ganglion "B"-type cell (see figure 4.1). Cells of this type are the largest in the ganglion, having a mean diameter of 35 μm (Honma 1984; for a scanning electron microscope study of the bullfrog sympathetic ganglion, see Baluk 1986). They receive inputs from rapidly conducting presynaptic axons, the terminals of which engulf the soma and axon hillock. There are several reasons why these cells have proven to be unusually favorable objects for research. They are indubitably neuronal. They can be studied in their fully mature form at various levels of simplification (within the intact ganglion, in explant cultures, or after complete dissociation) and using a variety of different techniques (two-electrode voltage clamp, single-electrode voltage clamp, whole-cell and single-channel patch recording, and intracellular injection). Because dendrites are absent and all synapses are formed on or near the cell body, these cells present few space clamp problems. Thus, the soma of these cells can be modeled accurately by a single spherical compartment. Finally, the voltage-dependent conductances of the cells are targets for various types of unusual "modulating" slow synaptic actions that are far more prevalent in the nervous system than originally suspected (Adams and Brown 1982; Kuffier and Sejnowski 1983; Nicoll 1988). Thus the bullfrog sympathetic ganglion cells provide an ideal environment for studying cellular adaptation, slow synaptic transmission, and other such phenomena crucial for understanding information-processing operations that occur on time scales from miliiseconds to many minutes. Our aim in this chapter is to provide the reader with a complete model for these typical vertebrate cells, which are geometrically rather simple but electrically quite complex, and to describe the relevant numerical algorithms. Our approach is by now a common one: we attempt to dissect out or hold constant as many of the features of the system under study as possible and to describe the remaining features with empirical equations of sufficient detail to determine how they affect the behavior of the system as a whole. By allowing subsystems observed in isolation (e.g., channels recorded under patch clamp or currents measured in isolation by pharmacologically blocking other currents) to interact with the other components of the system, simulations serve not merely to display a system already described in detail but also to test the modelers' understanding of that system's integrative aspects. Furthermore, features of the system that are experimentally inaccessible or not easily controlled (e.g., the activation state of a given current) can easily be visualized with the aid of the computer.

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