2.3 Why do not we use an exact model of a biological
neuron?
(translation by Agata Barabasz agata.barabasz@op.pl)
All artificial neurons, sigmoid and radial, described in this chapter, as well as used in
further parts of this book, are simplified models of real biological neurons. This statement
has already appeared, however now I want to show you, how far simplified artificial neurons
are. To achieve this purpose I will use the example of researches conducted by de Schutter.
For many years this researcher dealt with that, to maximally faithfully and maximally exactly
reconstruct in the computer model, all that we know about the structure and working (in the
smallest details) of the only one neuron - specifically so called Purkinji cell. His model
referred to electric systems, which according to Hodgkin’s and Huxley’s (the Nobel Prize in
1963) researches model a bioelectrical activity of individual fibres (dendrites and axon) and a
cell membrane of neuron’s soma. In the researches with the extraordinary accuracy a shape
of the real Purkinji cell was reconstructed and Neher’s and Sakamann’s researches (the Nobel
Prize in 1991) about functioning of so called ion channels were taken into consideration. A
structure of the modelled cell and replacement circuit diagram, used in de Schutter model are
shown in a picture 2.16.
Picture 2.16 The Model of the neuron maximally faithful to a biological original, used in de Schutter’s
researches
The model built by de Schutter, turned out to be extremely complicated and costly in
calculations. It is enough to say, that for building the model were used:
 1600 so-called compartments (fragments of the cell treated as homogeneous parts
containing determined substances in determined concentrations),
 8021 models of ion channels,
 10 types of different complicated mathematical descriptions of ion channels
dependent on voltage,
 32000 differential equations (!)
 19200 parameters necessary to estimate at tuning the model up,
 a precise description of the morphology of a cell reconstructed on the basis of
precise microscopic images
Picture 2.17 Some of results obtained in de Schutter researches. At the top - electric activity of the
simulated cell, at the bottom - the biochemical phenomenon (flow of ions of calcium)
Nothing strange, that for simulating several seconds of "life" of such a nerve cell was
necessary to use a large supercomputer , yet it required many hours of his continuous work.
It has to be admitted, that results of this modelling are very impressive. Some of them are
presented in picture 2.17.
However results of this experiments are unambiguous: The attempt of faithful modelling the
structure and action of a real biological neuron turned out to be successful but it is too
expensive way in order to try to create practically useful neural networks this way.
Therefore, from now on we will be using only simplified models, and we will be expecting,
that in spite of these applied simplifications the neural network will be able to not only
effectively solve different tasks, but additionally it will also be able to the fact, that it’s
behaviour can bring us interesting conclusions about the behaviour of human ( for example
your!) brain. Soon you will convince yourself about it!