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The Axon model simulates the equations and parameters derived from experiments by Hodgkin and Huxley on the squid giant axon. Because of the exact correspondence between the equations incorporated into this model and the equations developed in the studies of Hodgkin and Huxley, this model generates graphs that mirror precisely the theoretical curves depicted in the Hodgkin-Huxley papers on the squid axon. Three similar models are included in this chapter: the single space-clamped axon, simultaneous simulations of several spaced-clamped axons to compare model output when parameters are altered, and a simulation of the spatially extended axon to illustrate impulse propagation.

The rapid conduction of signals by neurons over distances greater than about 1 mm occurs almost exclusively by electrical impulses. This chapter presents the fundamental concepts that underlie the generation and propagation of these nerve impulses. After a brief historical summary, the remainder of the chapter describes the voltage-clamp experiments of A. L. Hodgkin and A. F. Huxley on the giant axon of the squid. The results and the conclusions furnished by these seminal experiments provide the bases for the current understanding of the electrical nature of neuronal signaling. The Hodgkin-Huxley experiments, together with the equations that encapsulate the experimental results, are presented here in detail to emphasize their central importance for neurophysiology and to present an exemplar of science at its best.

Nerve impulses traversing the brain were likened by Sherrington to points of light in an enchanted loom. The electrochemical nature of the nerve impulse was largely elucidated by Hodgkin and Huxley in their studies of the squid giant axon in the years immediately before and after the 1939–45 war. Although the impact of this work within the neuroscience community was immense, it was overshadowed elsewhere by the discovery of the helical structure of DNA by Watson and Crick at about the same time. Both types of work had involved complex mathematics and deep insights, but the Hodgkin-Huxley studies had included a series of brilliant experiments and had been the climax of almost two centuries of nerve impulse research.

Now in Chicago, Kenneth Cole employs a negative feedback circuit, devised by a colleague, to clamp the voltage across the membrane of the squid giant axon. He shows that during the action potential there is an initial inward current followed by an outward current, and he attributes the latter to potassium ions. Hodgkin visits Cole who shows him the new technique and loans him some of the apparatus needed for voltage-clamp work. Within a few months Hodgkin has his own voltage-clamp system built and resumes work with Huxley on the squid giant axon at Plymouth, initially with Katz as well. By replacing sodium in the bathing fluid with choline, they are able to show that the early inward current during the action potential is indeed a sodium one, and that the later, outward, current is carried by potassium ions. On the basis of the experimental data Huxley is able to derive an equation describing the flow of current through the nerve membrane at any instant. He and Hodgkin introduce special terms which they interpret as the effects of mobile particles within the membrane. From their equations, Huxley is able to compute the form and conduction velocity of the action potential. The British voltage-clamp work is published in five papers and creates a stir; however, Cole’s assistance is not acknowledged. Hodgkin and Huxley share the 1963 Nobel Prize with Eccles.

This chapter describes the voltage clamp device, the experiments of Hodgkin and Huxley, the mathematical model into which their data were fitted, and the resulting simulation of a wide variety of recognized electrophysiological phenomena (activation, propagation, etc.). The voltage clamp procedure was developed in 1949. Because of its importance, this chapter first discusses the principle of the voltage clamp method in detail. The Hodgkin and Huxley work is important not only for its ability to describe quantitatively both the active and the passive membrane, but for its contribution to a deeper understanding of the membrane mechanisms that underlie its electrophysiological behavior.

This chapter focuses on various electrophysiological techniques. The voltage-clamp technique has been a powerful tool in the development of membrane biophysics. Applied to large cells, such as squid axons or giant snail neurones, this technique allows for the reconstruction of an action potential by means of separate Na⁺ and K⁺ conductances. However, the need to penetrate cells with two micro-electrodes restricts its use only to large cells. This limitation can be partly overcome by the introduction of a voltage-clamp circuit, which only needs one micro-electrode; this has been useful for describing ion currents in small cells. At the same time, the patch-clamp technique for measuring single currents was developed by Neher and Sakmann (1976). When the improved patch-clamp technique for single-channel and whole-cell recordings was described in detail it quickly became the technique for investigating the electrical properties of cell membranes. This method represents a major advance in the ability to monitor cell membrane function.

Ion channels are cellular proteins that conduct the movement of ions from one side of a membrane to the other. The resultant changes in local ion concentrations and electrical field play pivotal roles in physiological processes, as wide ranging as cell to cell communication, cell proliferation and secretion. This chapter provides a brief historical perspective then introduces the basic theory, terminology, and generic structural and functional features of ion channels. In addition, an overview of relevant ion channel methodologies is provided. The chapter aims to set the scene and to equip the non-specialist reader with sufficient background and understanding to comprehend and enjoy subsequent chapters which provide a more detailed analysis of channel families and individual channels.

This chapter deals with three aspects of cylindrical voltage-clamp designs, namely, dynamic response, noise performance, and system linearity. The clamp dynamic performance affects both the speed and accuracy of membrane potential control. Also, because the membrane potential may be treated as an electrical driving function that initiates the membrane-bound gating charge movements, the clamp dynamic characteristics influence the accuracy and intrinsic bandwidth of the recorded gating currents. A random noise, superimposed on the gating current signal at the current-to-voltage converter output, arises from two sources: intrinsic—from the preparation itself, specifically resistor (R _s); and extrinsic—from the voltage clamp, recording chamber, and electrodes. Based on equivalent noise resistances, an evaluation of the clamp noise performance can then be made to identify which components contribute significantly to the overall noise. The linearity of the complete signal pathway between electrodes and data acquisition hardware is necessary for accurate registration of gating currents, particularly during their early time course. Since the currents of interest result from the subtraction of two signals that can be up to 1000 times larger, any instrumentation non-linearities will not be readily distinguished from the gating currents themselves. The results of the dynamic and noise analyses have facilitated the realization of a cylindrical axon voltage clamp having a predictable performance compatible with the requirements for high-resolution gating current measurements. These improvements to the clamp design and realization have enabled high-resolution recordings of fast intermediate, and slow, charge movements associated with voltage-dependent processes in the squid giant axon.

This chapter explores the capacitative properties of biological membranes and provides ways to measure the membrane capacitance in striated muscle. The capacitance of a bilayer is inversely related to the chain length of its constituent hydrocarbons, and the latter is in turn proportional to bilayer thickness. The nature of the polar head groups does not greatly affect membrane capacitance. Skeletal muscle membranes form a network of 50-nm diameter branching tubules penetrating into the fibre whose lumina are continuous with extracellular fluid. Such a system would intrinsically have particular capacitative properties. Using the Laplace transform, a square-root relationship between membrane impedance properties and the input parameters is found. The ‘lumped’ four-component model offers the simplest available electrical description of striated muscle membrane geometry. In contrast, distributed models represent the transverse tubules as a cable system that allows radial voltage differences. Lattice models have proven useful in both the interpretation of the measurements of linear capacitances and the localization of non-linear charge to different regions of membrane. The chapter also discusses voltage-clamp methods for studying the dielectric properties of skeletal muscle. Each voltage-clamp method has characteristic advantages and limitations. The most appropriate equivalent circuit to represent the transverse tubular system remains incompletely resolved. The cable properties of tubular membrane necessitate an operational definition of measured effective capacitance arising from an application of the properties of the Laplace transform to a general circuit network. The studies suggest that, at least through the frequency range over which charge movements have been measured, the effective capacitance accurately reflects the properties of the actual electrical elements of surface or tubular membrane, given appropriate bathing solutions and voltage-clamp geometry.

This chapter describes the voltage-gated ion channels. It considers the different types of formalisms in modeling ionic currents as the action potential and voltage-clamp recordings of the T-type calcium current in thalamic neurons. The chapter specifically reviews the voltage-clamp behavior of the sodium channel and the genesis of action potentials, as well as the characteristics of the T-type calcium current and the genesis of bursts of action potentials by the T-current in thalamic neurons. It shows that nonlinear thermodynamic models offer fits of a quality comparable to empirical Hodgkin-Huxley models, but that their form is physically more plausible.

Based on a language largely accessible to a non-specialized readership, this chapter presents some of the fundamental aspects of the modern understanding on the way electricity is involved in nerve conduction. It appears how, in their evolutionary endeavor to develop electric conduction along thin nerve fibers, living organisms had to face extremely difficult physical constraints due to the exceedingly high electric resistance of nerve fibers. The result has been the development of an impulsive form of electric signal which is progressively re-generated during its progression along the fiber, at the expense of a local electrochemical energy, somewhat corresponding to the animal electricity invoked by Luigi Galvani more than two centuries ago.

“Channels and electrical signals” is the third chapter of the book Sensory Transduction and reviews the structure and function of ion channels, the structure of channel pores, and mechanisms of gating. It introduces ionotropic receptor molecules, which are proteins that function as sensory receptors but are also ion channels, whose gating can produce changes in membrane conductance directly. It then uses the hair cell of the inner ear as an example to introduce the concepts of membrane potentials, the Nernst equation, ion homeostasis, the Goldman voltage equation, and driving force. A description of the technique of voltage clamping follows, together with the application of this technique to the hair cell to explain the method of measuring changes in channel gating and the ion selectivity of channel pores.