Chirality

Leonardo, Vol. 8, pp. 245-248. Pergamon Press 1975. Printed in Great Britain CHIRALITY* Lancelot Law Whyte** In his Boyle Lecture at Oxford in 1893 on molecular arrangements in crystals, Kelvin introduced the term ‘chirality’ from ( p i p , hand). ‘I call any geometrical figure or group of points “chiral”, and say it has “chirality”, if its image in a plane mirror, ideally realized, cannot be brought into coincidence with itself’ [l]. He called forms of the same sense (e.g. all L-handed) ‘homochiral‘ and equal forms of opposite sense ‘heterochiral’. J. Larmor and A. S. Eddington used ‘chiral’ and the writer [2] analyzed the concept, listed the main chiral forms and gave a more explicit definition: ‘Three-dimensional forms (point arrangements, structures, displacements , and other processes) which possess non-superposable mirror images are called “chiral”.’ This presupposes that the mirror image of the phenomenon, e.g. of a magnetic vector, is either known from observation or established by an acceptable convention. ‘Chirality’ is used in preference to similar but ambiguous terms (e.g. asymmetry, dissymetry) with associations which can mislead [2] when it is desired to refer to a general property defined in terms of spatial relations only (e.g. Cahn, 1966 [3]), not of particular physical or chemical effects (e.g. optical rotation, since some non-chiral structures can display optical activity, Wooster, 1946). The property of chirality is dual (L, left, or R, right, laevo or dextro), global, geometrical, three-dimensional , Euclidean and non-relativistic, spatial relations being separated from temporal. Moreover it refers to a structure at some specified level (or set of levels) in the structural hierarchies of the physical universe or of organisms. There is no necessary correlation between chirality at one level and its presence or absence at a neighbouring level. A chiral process is one, successive states of which are chiral. Chiral forms fall into two main classes: screws (conical or helical) ordered with respect to a line, and skews, ordered around a centre. Thus a chiral chemical group or molecule may be skew * This unpublished manuscript was written between 1969-1970 and is published with the permission of Mrs. Eve Whyte, 93 Redington Road, London, N.W.3, England. ** Lancelot Law Whyte (1896-1972), philosopher, scientist and investment banker, was a Leonardo Honorary Editorial Advisor. (around an asymmetrical centre) or screw (arranged as a helix) and the two chiral forms are called enantiomers. A chiral form is (theoretically) converted into its mirror image by a rotation in fourdimensional space. We cannot consider here the psychological and social connotations that left and right (or equivalents ) possess in different cultures [4, 5 1 and turn to the history of chirality in physics and biophysics . Interest in L- or R-handed arrangements of points or atoms and in chiral organic forms long preceded their scientific analysis. Plato considered the properties of mirror images;Aristotle discussed chiral forms; Lucretius devoted 100lines of On the Nature o f Things [6]to images in mirrors; Leonardo da Vinci used mirror writing; Kant found in the existence of chiral forms support for his theory of space; Goethe wrote an essay ‘On The Spiral Tendency in Vegetation’ and many early scientists were interested in the screw forms of plants and shells (cf. Figure). Edith Sitwell’s hand holding a helical shell. (From 1958 Christmas card of Eve and Lance Whyte.) 245 246 Lancelot Law Whyte The scientific mind looks for symmetry, so it is scarcely surprising that it was not until the 19th and 20th centuries that quantitative science came to grips with the chiral aspects of nature, which we now know to be of great importance. On six occasions from 1810 to 1957, chiral phenomena were unexpectedly discovered that involved a revision of previous theoretical assumptions. The bias in favour of symmetry has meant that the systematic study of skew and screw effects has only been taken up when the experimental facts compelled it. A primary aim of science is the elimination of arbitrariness by the discovery of intelligible reason for everything being as it is and not otherwise. But no-one has yet conceived ,a sufficient reason for a fundamental or general chiral bias, say in...