A mathematical model of the nerve impulse at the molecular level.

McIlroy, Douglas Kenneth (1970). A mathematical model of the nerve impulse at the molecular level. PhD Thesis, School of Physical Sciences, The University of Queensland.

       
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Author McIlroy, Douglas Kenneth
Thesis Title A mathematical model of the nerve impulse at the molecular level.
School, Centre or Institute School of Physical Sciences
Institution The University of Queensland
Publication date 1970
Thesis type PhD Thesis
Supervisor Prof L. Bass
Total pages 220
Language eng
Subjects 02 Physical Sciences
Formatted abstract More than one hundred years of research into nerve fibres and closely related subjects have seen little more than the development of a macroscopic theory of nervous conduction. The culmination of this phenomenological stage was essentially reached in 1952 with the publication of the great work of Hodgkin and Huxley which, however, does not penetrate at all to the underlying microscopic mechanism responsible for the permeability changes which control the electric impulse in nerves. The present thesis has, therefore, as its basic aim the development of mathematical models of the nerve, at the molecular level, with the object of deducing the main features of the nervous impulse.

To begin this task, a thorough examination of the tenets of the two main schools of thought on nerve research is undertaken: on the one hand, there is the widely esteemed physical school lead by Hodgkin and Huxley, whose great success at the macroscopic level has created the general feeling that the most fruitful lines of attack on the problem of investigating nervous conduction, might be along those of a physical theory; and on the other hand, there is the biochemical school lead by Nachmansohn, which has accumulated an impressive body of experimental evidence to support its thesis set at the structural level.

We, therefore, attempt the programme of first extending and then uniting the general Ideas of these two schools under a quantitative theory. As a starting point in this Integration process, we search for the mechanism responsible for triggering the permeability changes following a depolarization of the axonal membrane. The trigger mechanism must involve a physicochemical parameter of the membrane state which is sufficiently immune to thermal fluctuations in the membrane (in accordance with the remarkable stability of the axon) and which must have a strong effect on some component of the membrane likely to be involved in the control of permeability. Bass and Moore (1968) suggest that such a parameter is the (buffered) pH of the membrane and Bass and MclLroy (1968) demonstrate that the activities of enzymes with suitable properties are radically affected by a critical increment in membrane pH.

We next proceed with the construction of a quantitative model of the axonal membrane based on this mechanism and on our extension of the ideas of the biochemical school, and we are able to show that this (enzyme) model of the nerve is indeed capable of reproducing a satisfactory action potential. SOTO points of our theoretical results are somewhat unsatisfactory, but we show that by including in a natural way the effect of extracellular calcium in the model, these defects are largely reduced. The results of the theory are subjected to searching criticism but no serious flaws are discovered though some further interesting deductions and predictions from the model are made: in particular we deduce from the model that in aqueous solution, the activity maximum of the long-postulated and as yet unidentified receptor enzyme of the biochemical school, is located at pH 9.9.

Thus, for the first time, the properties of excitable membranes are deduced from a very likely and identifiable molecular structure.
Keyword Nervous system -- Mathematical models

 
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Created: Mon, 11 Jul 2011, 13:07:00 EST by Ning Jing on behalf of The University of Queensland Library