The Neuronal Electrical Response to Current Stimuli as a Mechanism for Information Coding
Abstract: The Hodgkin Huxley model which was published in 1952, describes the mechanism and principles of electrical conduction of neuronal membranes. This model revolutionized our understanding of how the nervous system processes information. The model provides a mathematical depiction of the formation of the action potential, and its propagation along the neuronal axon. The model is described by four nonlinear differential equations, based on the nonlinear conductance of the ion channels. Using the Hodgkin Huxley model, we explore the axonal response to external current stimuli. We investigate the space clamp and cable models and present a novel detailed bifurcation analysis.
According to this model, weak current stimuli that are slightly above the threshold lead to the generation of a single action potential. Higher current stimuli lead to the generation of an infinite train of action potentials. Further increases in the current stimuli produce a single action potential resembling the weak stimuli.
In this study we focus on two borderline cases between these regimes. In the first regime, a finite number of spikes are generated followed by constant voltage. We demonstrate that the number of action potentials is controllable and can be adjusted to any finite number. In the second regime, spike series followed by failures are generated. We demonstrate the ability to control the number of action potentials before a failure. For specific current stimulus regimes, chaotic behavior was observed.
In addition, we examine the remarkable influence of the axonal morphology, namely the axon radius and branching points, and the influence of the temperature on activity patterns.
These two borderline phenomena and the effect of morphology on the electrical response illustrate ways in which the pattern of axonal activity can be controlled, and suggest that this behavior may be instrumental in information coding.
The study of the non-linear behavior of the neuronal electrical response may thus contribute to a better understanding of dynamical neuronal diseases such as epilepsy and Parkinson's.
* Research was carried out towards the M.Sc. degree in Electrical Engineering, advised by Dr. Orit Shefi, Faculty of Engineering, Bar-Ilan University.