Models and Analogues in Biology

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ELECTRICAL ANALOGUES IN BIOLOGY

BY J. DAINTY Department of Biophysics, University of Edinburgh

It should not be surprising that analogues have an important place in biology because one of the chief uses of an analogue is to 'explain' an unfamiliar, difficult or complex phenomenon in terms of a better known or simpler one; and biology is indeed very difficult and complex. An analogue--a model based on analogy--involves 'a simplification of the actual subject for analysis into sufficiently few elements that a mathematical (or experimental) treatment of its behaviour under any desired conditions may be possible' ( MacDonald & Wyndham, 1950); and it 'crystallizes in one diagram (or piece of apparatus) the characteristics of a system which otherwise requires much apparently complex mathematical or verbal explanation' ( MacDonald & Wyndham, 1950). Thus an analogue both simplifies and puts into familiar terms a complicated phenomenon and hence enables one to think much more clearly about the subject--things are much more 'intuitively' obvious.

The use of analogy can be defined as follows: 'if two different . . . phenomena A and B are described by the same mathematical formulism, quantitative conclusions can be drawn about the phenomenon A by studying the phenomenon B' ( Liebmann, 1953). A might be a mechanical, hydrodynamic, chemical or even more complicated, phenomenon and we are here concerned with choosing B to be electrical. The apparatus, model, etc., of B designed to investigate A by analogy is the analogue.

There are many possible types of analogue--electrical, hydraulic, mechanical, etc.--but electrical analogues are probably the most popular and useful. This is due, in the first place, to the fact that simple electrical expressions, phenomena, ways of thinking, are becoming increasingly well known; more and more biologists can, automatically and intuitively think in electrical terms. Words and concepts like current, resistance, shunt, series, feedback, etc., are becoming part of the biologist's accepted background knowledge. (This of course is a sine qua non for any analogue: it must be easily and immediately understood by the user; no one should use an electrical analogue who is not very familiar with electricity.) Another reason for the importance of electrical analogues is that if one wants to use an analogue experimentally, i.e. not just do arithmetic from a simple diagram, then electrical measurements are probably the easiest and most accurate to make and results can be displayed on cathode-ray tubes or automatically recorded on charts.

In this paper I shall be chiefly concerned with a few physico-chemical aspects of biological systems and will show how the problems involved have

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