Abstract
In this chapter, we discuss elementary concepts from neurophysiology. We treat the generation of the membrane potential, the role and dynamics of voltage-gated channels and the Hodgkin-Huxley equations. We present experimental techniques, in particular the voltage and patch-clamp technique, that have been essential in elucidating fundamental processes of neuronal dynamics. Several concepts are illustrated with clinical examples. At the end of this chapter, you will understand the critical role of ion concentration gradients for establishing the resting membrane potential and the role of the voltage-gated sodium and potassium channels in the generation of action potentials. You understand how Hodgkin and Huxley were able to formulate the Hodgkin-Huxley equations and you can perform essential simulations using these equations to explore the effects of changes in ion homeostasis or abnormal channel gating.
The human brain has 100 billion neurons, each neuron connected to 10 thousand other neurons. Sitting on your shoulders is the most complicated object in the known universe. Â
— Michio Kaku
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Notes
- 1.
Here, we take the approach using conductances after introducing the electrical equivalent circuit. A similar approach is to use the Goldman-Hodgkin-Katz voltage equation that is based on ion concentrations and permeabilities. See e.g. [130].
- 2.
The pump also has a small contribution to the membrane potential, as the net current is not zero (three sodium ions are pumped out while two potassium ions are pumped in). The effect is small, however, approximately −2 to −5 mV.
- 3.
We are dealing with average properties. At a later instance, we discuss the behaviour of individual ion channels.
- 4.
We discuss general aspects of differential equations in Chap. 3.
- 5.
This is the standard form of the activation and inactivation variables.
- 6.
Historically, Hodgkin and Huxley used different expressions for the activation and inactivation variables, using
$$\begin{aligned} \begin{array}{l} \dot{n}=\alpha _n(V) (1-n)-\beta _n(V)n,\\ \dot{m}=\alpha _m(V) (1-m)-\beta _m(V)m,\\ \dot{h}=\alpha _h(V) (1-h)-\beta _h(V)h, \end{array} \end{aligned}$$where the functions \(\alpha _j(V)\) and \(\beta _j(V)\), with \(j\in {n,m,h}\) describe the transition rates between open and closed states of the channels.
- 7.
Remember that it then holds that \(I_\mathrm{Na}=g_\mathrm{Na}(E_\mathrm{Na}-V_m)=g_\mathrm{Na}\times 0\) as the Nernst potential of sodium is experimentally set to equal the membrane voltage set by the voltage clamp.
- 8.
Tasaki et al. Biophysical Journal, 1989.
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van Putten, M.J.A.M. (2020). Electrophysiology of the Neuron. In: Dynamics of Neural Networks. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-61184-5_1
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