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The Davson-Danielli model threw new light on the understanding of cell membranes, by stressing the important role played by proteins in biological membranes. By the 1950s, cell biologists verified the existence of plasma membranes through the use of electron microscopy (which accounted for higher resolutions).
Electrical input–output membrane voltage models – These models produce a prediction for membrane output voltage as a function of electrical stimulation given as current or voltage input. The various models in this category differ in the exact functional relationship between the input current and the output voltage and in the level of detail.
The membrane model is for a small section of the cell membrane; for larger sections it can be extended by adding similar sections, called compartments, with the parameter values being the same or different. The compartments are cascaded by a resistance, called axial resistance. Figure 6 shows a compartmental model of a neuron that is developed ...
The response of whole neuron model i.e. soma and dendrites, can be written in closed form. The response of the spatially extended model to periodic forcing is described by stroboscopic map. A Arnol'd tongue quasi-active model can be constructed with a linear stability analysis of the map with carefully treating the non-differentiability of soma ...
One of the earliest models of the neuron was based on mathematical and physical modelling: the integrate-and-fire model, which was developed in 1907. Decades later, the discovery of the squid giant axon led Alan Hodgkin and Andrew Huxley (half-brother to Aldous Huxley) to develop the Hodgkin–Huxley model of the neuron in 1952. [8]
The Hodgkin–Huxley model, or conductance-based model, is a mathematical model that describes how action potentials in neurons are initiated and propagated. It is a set of nonlinear differential equations that approximates the electrical engineering characteristics of excitable cells such as neurons and muscle cells .
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