Historical Aspects of the Origin Of Diffusion Theory in 19th-Century Mechanistic Materialism

HISTORICAL ASPECTS OF THE ORIGIN OF DIFFUSION THEORY IN 19TH-CENTURY MECHANISTIC MATERIALISM DENYS N. WHEATLEY* and PAUL S. AGUTTERf Introduction DIFFUSION AS A PHENOMENON Diffusion is a familiar everyday phenomenon, uncontentiously connoting the spreading of material in all directions from a source. As a scientific term, it describes more precisely the net flow of matter resulting from random movements of molecules from a region of high concentration to one oflower concentration. A mathematical relationship exists between the rate at which a substance travels through a medium and the concentration gradient of that substance, known as Fick's Law of Diffusion [I]: ^ = -D(cx - C0). dt D, the proportionality constant, is the diffusion coefficient or diffusivity of the medium. A more precise mathematical formulation shows that at any point along an axis ? from the starting-point of diffusion: dc _ _ d2c dtdx2' Diffusion theory has played a highly significant role in the emergence of modern scientific thought. Early this century, Einstein and von SmoluchowThe authors are indebted to a number of colleagues with whom they have discussed this work, especially Christopher Lawrence and D.E. Allen. This study was financed by a project grant from The Wellcome Trust. *Cell Pathology Unit, University Medical School, Aberdeen AB25 2ZD, United Kingdom. fDept. of Biological Sciences, Napier University, Edinburgh.© 1996 by The University of Chicago. All rights reserved. 0031-5982/96/3904-0962$01.00 •ectives in Biology and Medicine, 40, 1 ¦ Autumn 1996 | 139 ski independently found an explanation for Fick's law in Brownian motion [2-4] . It assisted in the development of the stochastic theory [5] , which in turn was instrumental in the development of quantum mechanics (e.g., Feynman's path integral method) , and hence to connections between functional analysis, differential equations, and probability theory in mathematics [6]. Many solutes important in cell functioning are transported by active processes , otherwise diffusion is held responsible in the vast majority of cases, especially where no specific machinery appears to exist. Increasingly abundant evidence shows the inadequacy of diffusion theory to account for much of the intracellular movements of substances [7-10], especially as the extraordinary complexity of the cell internum is revealed. Diffusion theory, however, has been a cornerstone of modern biology. Although simple in concept, it may now need be abandoned in favor of more realistic, albeit far more sophisticated models. In the absence of consensus on the organization of the intracellular state, including the water [11], this is unlikely to be achieved in the near future; and the sheer mathematics of the task is itself awesome. Diffusion theory as applied to a simple aqueous solution is a very inadequate representation of solute movement in living organisms, at best only the roughest approximation, at worst seriously flawed, and usually irrelevant in much ofbiology [12] . This ' 'challenge" to its validity and applicability probably would not have occurred if physicists had not themselves emphasized its shortcomings [see 13, 14]. We therefore examined the theory from this more theoretical viewpoint [15] , before studying the implications and consequences of its inception as a basic concept in biology for over 150 years. The latter has principally been undertaken from a historical perspective , and suggests that many ofthe difficulties stem from diffusion theory 's origins in the mechanistic materialist philosophy of the mid-19th century . DIFFUSION THEORY AND ITS APPLICABILITY Having satisfactorily accounted for diffusion from the kinetic theory of gases, Einstein reasoned that the mathematical formulae were adequate descriptions of liquid solutions, and of suspensions of solid particles in liquid media, provided they are sufficiently "gas-like, " which rests on certain assumptions , the physical requirements of which are briefly outlined here [see 15 for a detailed treatment]. Particles, including those of the solvent molecules, must move independently and in response to single collisions; multiple collisions must be rare. The model is only approximately valid when the solution/suspension is sufficiently dilute for the particles to be (ideally) non-interacting spheres. Non-spherical geometry does not seriously affect the application of the Stokes-Einstein equation [2], but if the 140 Denys N. Wheatley and Paul S. Agutter ¦ Origin ofDiffusion Theory particles are deformable then translational kinetic energy is not conserved at collision. Furthermore, the gas...