GENERAL INTRODUCTION STRUCTURE ARRANGEMENTS OF MACROMOLECULES BY J. D. BERNAL Dept. of Physics, Birkbeck College, Malet St., London, W.C. 1 Received 1 1 th February, 1958 The printed title of this discussion is necessarily an abbreviated one and does not give a sharp enough idea of the range and limitations of the subject to be covered. A more correct title would be The Configurations and Close Znteractions of Macromolecules and their Expressions : in solutions, in liquid crystals and in the solid state. The papers will deal with one or the other aspects of this field and will, for the most part, not go beyond it. In this introductory contribution I have chosen what is the easiest part of the subject namely the discussion of the actual spatial arrangement of atoms inside macromolecules under the various conditions in which we study them.First, I try to define what is meant by macromolecules for the purposes of this discussion. The simplest definition is included in the word itself-a macro- molecule is simply a big molecule-but the question is how big, and here we have to draw what appears at first to be a somewhat arbitrary line, let us say a molec- ular weight of not less than 5000. An upper limit however will be much more difficult to formulate. If we take this as the size of a medium virus particle at 4 x 107, this gives a range of 8000 between them or a 20-fold difference in linear scale corresponding to the range between a cube of side 20A to one of 400A. But though this definition may not be precise, for we can probably go beyond it on both sides for special macromolecules, it corresponds to more than an arbitrary blocking-out of a certain size of particle.It really represents a range of structures which have something in common. In the old days they would have been called colloidal particles and they would have been defined by their external properties, that is, their possibilities of remaining in the state of a sol or of being coagulated in different ways. Here, with our greater knowledge, we are more concerned with their internal structure. This is a deliberate restriction for the purpose of this discussion. A general discussion on the configurations and interactions of macromolecules should go beyond the close interactions which we will discuss here to consider those between these colloidal particles in solution and in a more condensed gel state-the discussion of the long-range forces.But this it was thought would take us too far afield and necessitate a conference of at least twice the length so we had to confine ourselves to a discussion of the conditions which fix the internal structure of the larger types of macromolecules and the relations of macromolecules of all sizes to each other when they are in close contact, that is, when they are in the form of dense solids or fibres. This reduces the physical part of the discussion to that of interactions at normal chemical interatomic distances-those dealt with in the decreasing hierarchy of interaction energies from homopolar through ionic and hydrogen bonds to van der Waals’ bonds.We will not, in general, be considering macro- molecules as a whole but only in part-where they touch each other-and deter- mining what fixes their internal configurations. Now the peculiar complexity of macromolecules as well as their main interest -both in themselves and on account of their biological and industrial importance 78 STRUCTURE ARRANGEMENTS OF MACROMOLECULES -depends fundamentally on the fact that they are composed of atoms held together by forces of very different strengths. I speak here of forces although it is a very old-fashioned analogy because a force is the shortest word to refer to the shapes of mutual potential energy curves containing minima of different depths. When I say a strong force I usually mean one with a very deep trough and a very narrow one at the same time, as shown in fig.1. This is the characteristic of macro- molecules and their association, and what I have called a long time ago-a word which has not really stuck in chemistry-their heterodesmisity. But unlike most heterodesmic compounds, such for instance as inorganic oxy-salts and simple molecular crystals where there are two different kinds of bonds in the structure, in most macromolecules and their associations there are three, four, or even five different grades of forces building them up. The first grade is essential for the very existence of a macromolecule, these are the homopolar forces which link up, so to speak, the skeleton or more often merely (0) FIG. 1 .-Shape of energy curves for different types of interatomic forces (diagrammatic only) : (a) homopolar bond, (b) hydrogen bond, (c) van der Waals’ bond.the backbone of the whole structure. Until recently the chemist was satisfied both in analysis and synthesis if he had established this skeleton or found the structural formula. Many of these macromolecules, indeed nearly all of them, are polymers. Most are linear polymers. The chemist’s task used to be deemed to be complete when he had established for any polymer the nature of the monomers of which it consisted and their mode of attachment, their order in a chain or their mode of branching and cross-linking in more complicated cases. However, as long as our interests were largely physical more than chemical, or let us say, biochemical rather than simple chemical, the knowledge of the actual skeleton of the macromolecules was not enough to determine the most interesting properties-the chemical or the colloidal properties of the macromolecule.This is because, as we all now recognize, a linear polymer can, while retaining all its covalent forces, be found in a large number of different conformations or con- figurations-as I think we should call them in this discussion-and so avoid the more special meaning of the word conformation in chemistry. The freedom of rotation around single bonds and other variations in the skeleton leads to a very large number of these possible configurations. The actual determination of these configurations will not be the main object of our discussions here. For apart from the interesting contribution of Morgan, Deer and Beers on the structureJ .D. BERNAL 9 of adenine polynucleotide and of Franklin and Klug on ribonucleoprotein par- ticles, this is more a discussion on physico-chemical properties than on X-ray structure determination. Here for the most part we will take the configurations, as far as they have been determined for granted, and see how they relate on the one hand to intermolecular forces and on the other to the physical chemical properties of the resulting structures. What 1 want to do in this introductory lecture is merely to set out what might be called the grammar of the subject, to try and arrange the possible configurations in some kind of logical spatial order so that we can see the relations that exist between the subjects treated in the various detailed scientific papers that will come later.I will take the knowledge of the physical forces for granted and discuss mainly the geometrical limiting factors that determine how these physical forces lead to the different patterns-not only those that have already been observed, but those that are geometrically possible and may yet be made. It is hardly worth recalling here the kind of forces we shall have to deal with. They are set out for comparative purposes in table 1 at end. Main chain homopolar forces I have already spoken of but here I must add a group of homopolar forces which are particularly important in configuration, namely those of the relatively weak homopolar cross-links that can exist both in natural and artificial polymers chiefly the S-S link so important on the one hand in proteins and on the other in vulcanized rubbers, and also ester links between carboxy side-groups and hydroxyls.The phenomena of denaturation and of vulcanization depend on the breaking or making of such cross links. The breaking of the main links, however, falls rather outside our field into that of the decomposition or hydrolysis of the polymers essential for analysis or digestion. The next strongest force, that of the ionic or salt bond, has played a relatively small part in polymer systems which have been carefully studied though we get hints of it for instance in the paper by Waugh on the role of calcium in casein formation and by Bresler on the stabilizing function of doubly charged ions. While energetically such links may be as strong as some of the homopolar links, they cannot be so permanent a feature in that they can be readily affected by the ionic environment particularly in water solution.Overwhelmingly the most im- portant force determining configuration is the hydrogen bond whether that between oxygen and oxygen in carboxy links discussed by Dr. Morawetz or the common CO . . . NH hydrogen bond of the proteins which appears in a large number of the papers presented. Finally, we come to the London-van der Waals’ forces predominant in the hydrocarbon-covered polymers and playing a considerable role elsewhere. For all the kinds of macromolecules heretofore studied-which do not contain extended electron orbits of a metallic character-these van der Waals’ forces may be treated as acting only between immediately contiguous atoms in different molecules or in different parts of the same molecule.With them are usually taken the omnipresent repulsive forces, ill understood theoretically but relatively easy to deal with practi- cally on the old conception of the billiard ball, or as we would now rather say, the rubber-ball-type of atom limiting the closest approach of atoms in different molecules or in different parts of the same molecule. These steric considerations may be the determining factor in configuration, the simplest case being the spiral nature af polytetrafluoroethylene (PTF) which was shown by Bunn to be due to the impossibility of a simple straight paraffinoid arrangement of CF:! groups. At least a qualitative account of most of the structures actually determined for polymer or polymer associations can be explained in terms of these forces and a quantitative explanation is clearly possible although the amount of com- puting required for it would stid be rather forbidding.As already indicated the kind of macromolecules that we will be dealing with here are nearly all of them polymers but they include certain molecules that, because they are found in Nature and are not very large, we are not accustomed to10 STRUCTURE ARRANGEMENTS OF MACROMOLECULES call polymers, namely the long-chain hydrocarbons. Even if they do not come strictly into the definition given above for macromolecules with respect to molec- ular weight, their peculiar properties of aggregation which are discussed here in the section on liquid crystals may point the way to an understanding of the behaviour of far longer chained polymers.Most of the polymers we will be dealing with here are linear. Later no doubt the colloid chemist will have to deal with arrangements of small molecules linked not only by a pair of bonds into chains but also by three bonds into sheets or by four bonds or more into three-dimensional aggregates, the familiar ino, phyllo and tecto series of mineralogy. However, not only the synthetic chemist but the organic cell seems to find it easier to start by a linear polymerization process and to make the more complicated structures they need by methods of coiling or folding the original polymer into fibres, sheets or massive structures. We will find that there is enough complexity in the various configurations of linear polymers without introducing at this stage those due to branching or looping or higher degrees of complexity in the arrangement of the covalent forces.In order to approach the problem in some kind of order we will consider first of all the intrinsic limitations on the configurations of isolated linear polymer molecules, then the associations formed by small numbers of such molecules, double and treble coiling, and finally the far more complex structures formed from aggregations of similar or dissimilar polymer molecules either in the extended or in the folded form. Isolated linear polymer molecules have been known now for some 30 years in a great variety of possible configurations. Despite the knowledge gained in the intervening period there is still much that can be usefully said about the pure thermodynamics of these configurations and contributions to this theme will be found in the papers of Longuet-Higgins, Temperley, Bunn and Rice who have all worked with the essential assumption that the intrinsic determination of con- figuration-that is its determination apart from interaction between non-neigh- bouring monomers-is very weak.For on account of the relative freedom of rotation and the small amount of steric hindrance-except in such extremely simple polymers as the polymethylenes-the energies of the different configurations will not differ much among themselves. In my opinion, however, it would be a pity to neglect, except possibly because of its mathematical complexity, the relatively small restoring forces which tend to keep small portions of a linear polymer in some regular relationship to each other ; either straight, or in the more general case curved and at the same time twisted.Neglecting heat motion every linear polymer should, therefore, have in general the form of a helix taking as extreme cases those of a straight line and a circle. In the latter case, steric limitations will ensure either that the circle is completed producing a ring molecule or that the circle is slightly twisted into a close sprung helix (see fig. 2). Even without heat motion, however, such in- trinsically determined configurations are likely to be unstable in the sense as having higher potential energies than closely coiled or folded forms, for whatever the nature of the polymer there will be at least van der Waals’ forces which can be exerted between its covering atoms and those of another part of the same chain.In other words, quite apart from entropy considerations, the two configurations which are known as F (fibrous) or G (globular) would be likely to be found and in the absence of strong interactions with either neighbouring fibres or a medium favouring a large surface the globular will have the lower internal energy. Looked at mechanically the essential feature of a linear polymer is its lack of lateral rigidity even if it is not-as some rubber models would make it--com- pletely flexible at every point and therefore more like a chain than a string, it still can hardly be expected to stand up all by itself and therefore it requires some lateral support.The same considerations apply even to such polymers which are only weak in one direction, those of the lath-shaped variety such for instance asJ . D . BERNAL 11 the paraffins. Here we have a very powerful analogy, as Astbury was the first to point out, between the behaviour of the monomolecular chains of linear polymers and the gross physical fibres which are used in industry. All the processes in the classical textile industry, those of drawing out, spinning, coiling, crimping and folding, all indeed except weaving itself for which we have not yet found a molecular analogue, have their parallel in the molecular field. Spirally coiled wool fibre contains in itself many more grades of molecular spirals.Several examples of these phenomena are brought out in the subsequent dis- cussions. The essential static argument is that configuration is determined by the balance between the energy of deformation of the flexible chain and that gained by folding back on itself. Perhaps the clearest case is shown by the work FIG. 2.-Arrangements of simple polymer chain : (a) straight polymer-successive links collinear ; (b) high pitched spiral polymer-successive links nearly collinear but twisted ; (c) ring polymer-successive links nearly collinear but untwisted ; (d) low pitched spiral polymer-successive links as in (c) but twisted to allow coiling. of Keller, whose beautiful studies of regular folding of polymethylene molecules show that the favoured fold is l20A or some 100 methylene residues.In this way overall packing is almost as close as in a long-chain hydrocarbon except for the few residues taken up in the actual turnover of the folds. We badly need a quanti- tative theory of this static instability to balance that of the statistical arguments used for rubber. The fact that such arguments for configurations have served so well in the past is that they have mainly dealt with molecules which for steric reasons could not pack very conveniently, at least in the unstretched state. This irregularity would seem to have a decisive role to play in the appearance of rubber- like-that is entropy-elasticity in polymers. Where, however, hydrogen bonds exist the tendency to the coiled or folded forms is very much increased.Here the requirement is that all hydrogen containing OH or NH2 groups should be bonded to a corresponding receptor 0 or OH and the type of structure will depend on whether this bonding is predominantly inside the same polymer chain or between one polymer chain and the next, giving the classical Astbury ct and /3 configurations later so beautifully explained in the Pauling cc-helix and pleated sheet structures. Even without a complete analysis of the geometrical configuration of any protein, we have plenty of physico-chemical12 STRUCTURE ARRANGEMENTS OF MACROMOLECULES evidence, the presence of more or less protected hydrogen bonds of this sort particularly the work of Linderstrram-Lang and Bresler on the exchangeability of the hydrogens thus protected or left unprotected by denaturation.Even without a quantitative theory we are beginning to see, partly as a result of papers presented here, something of the factors that determine under what conditions a regular linear polymer will coil or alternatively will fold. CuiZing will be favoured by the presence of large inflexible monomers which ensure that any abrupt turn will lead to considerable energy increase through lack of effective packing. Folding will be favoured by the presence of small flexibly joined monomers in conditions where parallel packing of straight runs of polymer give low energy arrangements. Freedom of the molecule favours coiling, that is the dissolved or swollen state. Lateral compression or solvent-free conditions favour folding. Drawing or stretching favours both uncoiling and unfolding for here the lateral bonding between straight chains comes most into play.Irregular polymers such 2s proteins should favour a mixture of coiling and folding. Special flexible links which fit badly into a coil such as proline will favour a bend. Here, however, as Kendrew has shown in the myoglobin structure, the folding is not of a simple back and forth parallel character, but three-dimensional and very com- plicated. The mEjor geometrical feature which applies to the inner linking of polymers, when van der Waals’ hydrogen bonds or other stronger forces such as S-S groups are present, is that there are no such limitations of symmetry such as holds for the more extended regular three-dimensional piling of ordinary crystals.Pauline, in effect, liberated us from the restrictions of two-, three- and four-fold rotation and screw axes into the much wider world of irrational spiral symmetry. The corresponding X-ray patterns can now be analyzed by Bessel functions, in the use of which Cochran, Watson and Crick have made such rapid and significant advances in the field of protein and DNA structures. By moving out of the crystallographic limitations and entering a new geometrical world we have to consider the possible configurations of single spirals, their mutual relations and their further complication by folding. From what has already been said it is evident that it is very academic to treat a linear polymer in isolation. It cannot avoid having internal relations and if in bulk, apart from very dilute solutions, also having external relations with other polymer molecules of the same or different kind.The protean nature of macro- molecules arises from these interactions which are to be the main subject of our discussion. It is indeed, through their relations with their neighbours, that other physical factors such as solvents and temperature affect the arrangement of macromolecules. Temperature, for instance, affects the linkages between neigh- bouring lengthy macromolecules and permits them greater freedom which may itself be a co-operative phenomenon leading to a kind of two-dimensional melting such as discussed in Klug’s paper for polytetrafluoroethylene. Of particular interest here is Luzzati’s communication which shows the variety of structures in what used to be called micelles in soap melts and solutions.Here he has demonstrated the existence of a new kind of liquid crystal in which the carboxy groups form a solid array while the hydrocarbon chains attached to them are in other respects free and liquid. The complex possibilities of structures which are partly melted and partly solid is also brought out in the paper of Lawrence, and the mixtures of soap and sterol molecules with the production of myelinic figures whose complex he has simply explained. Conditions favouring the existence of straight forms of polymers or at most of simple coiled forms may be various. Two striking new methods of achieving this are being reported here by Willems who has succeeded in orienting polymers on crystals such as sodium chloride and by Joly who has done the same by dynamical methods of rapid shearing tending to form not only parallel chains but associatioiis based on them.J. D .BERNAL 13 The extremely beautiful cholesteric phenomena studied by Conmar Robinson, in the case of some synthetic polypeptides show the extent of coiling and folding even in a non-ionic solvent which he has analyzed by an elegant balancing of birefringence and optical rotating studies. Besides conditions leading to the loosening of the molecules such as occur in all the liquid crystalline stages of polyiners there are also those that are deter- mined by their greater attachments to each other. These attachments can be in the form of hydrogen bonding or they may be strengthened by secondary linking.This formation of cross linking by homopolar bonds or vulcanization is a very general phenomenon. It is related to the inner and outer cross-linking characteristic of the deizatirration not only of proteins but of other polymers as discussed by Rice. These latter phenomena? depending as they do on high degree of irregularity can still be treated best thermodynamically but we are beginning to knGw enough about the actual ordering of polymeric molecules to be much more detailed in our treatment of the variety of regular arrangements. The most radical change which can occur in polymers in all states, solid, liquid or gaseous, is that of depolymerization and repolymerizaticn. This is, in general, outside our field but one aspect still lies within its confines, that is the simultaneous depolymerization and repolymerization that occurs in the classical ring-chain transformation, first carefully studied in polyoxymethylene-a universal phenom- enon among the simpler polymers and occurring in the crystalline state. When found in the more complicated polymers it is the probable explanation of the G-F transformation, globular-fibrous transformation? studied in such detail in insulin by Waugh.The logical ordering of macromolecular structures is best done to bring out the hierarchical nature of the larger and more complicated forms (see table 2, fig. 3 at end). The primary structure is that of the chain itself as determined, for instance, by chemical analysis even in the most complicated cases of proteins and nucleic acids.Next follows secondary structure already referred to as that determined by links, van der Waals’ or hydrogen bonds or other between relatively close members of the chain. This is the feature that gives rise to the various spiral forms. Next and necessarily less regular is the tertiary structure characterized by coiled coiling or by folding. Folding is not necessarily tertiary in itself as Keller has shown for the polymethylenes that folding may supervene without preliminary coiling in which case it is strictly secondary. Where, however, folding is imposed on previous coiling there is necessarily a degree of uncoiling at the places where the folding occurs and it is this comparative rigidity of the coiled structure that un- doubtedly gives rise to the extreme complexities-until recently defying analysis -of the globular proteins.We now, however, know, thanks to the beautiful work of Kendrew that the typical a-helix protein of haemoglobins does consist of relatively short stretches of some 20A of helices joined together by uncoiled sectors. The relative amount of coiled and uncoiled chain in globular proieins was first determined by Doty using optical rotation methods and a further ayplica- tion of this method to both artificial and natural polypeptides is being given here by Elliott and Hanby. There is intrinsically no reason why the complexity of a macromolecule should be limited to the tertiary stage. Indeed the larger natural macromolecules must be constituted in just the same way. There could be further foldings on the already folded chains but no such example has yet been studied in sufficient detail to bring out its precise geometry. The further complexity that does occur is due to combinations between different chains in the uncoiled, coiled or folded states.The simplest of such arrangements is the parallel packing of polymer chains in straight or spiral con- figurations. This is usually of the two-dimensional hexagonal close-packed type (see fig. 4). Only where different chains are the same length such as occurs for instance in elongated virus crystals is it possible to get end-on coherence and hence three-dimensional crystals. More usually the result is a fibre regular in14 STRUCTURE ARRANGEMENTS OF MACROMOLECULES only two dimensions. Such regular fibres held together laterally by long-range forces besides occurring in viruses have been demonstrated by Huxley and others in muscle and is here discussed by Luzzati as occurring in one of the phases of soap melts. FIG.3.-Hierarchy of polymer complexes : (a) primary structure-no intrachain links, polypeptide in j? links (after Pauling) ; (6) secondary structure--coiling with intrachain hydrogen bonds, polypeptide in a helix (c) tertiary structure-folded coils, melhaemoglobin molecule (after Kendrew) ; (d) quaternary structure (homogeneous type), linked groups of tertiary molecules, (e) quaternary structure (heterogeneous typeblinking of different types of ternary form (after Pauling) ; haemoglobin structure (hypothetical structure) ; protein and primary ribonuclease, tobacco mosaic virus (after Franklin).In the close packing of spiral molecules, however, difficulties of accommodation must occur if all the spirals are of the same kind-right- or left-handed. They can engage effectively with each other only when the pitch is low (see fig. 5), and this spiral close packing has been shown by Franklin to occur in dry tobacco mosaic virus. For high-pitched spirals, as Klug and Fr a n k h show in their paper, accommodation is more difficult. This may be a reason why such spirals tend to be multiple, for multiple spirals can pack much more economically than single onesJ . D. BERNAL 15 To understand the mechanism of multiple coiling with cross-links between the elements, it is easiest to begin with a topological consideration of cross-linking between straight polymer chains.The simplest possible way of combining two polymer chains is by adhering side by side. Such a compound is formally ana- logous to a diatomic molecule, but because it extends in three dimensions it is essentially more complicated. In a diatomic molecule each component is effec- tively monovalent, that is without regarding double bonds as essentially different from single ones. But when one such bond between two spherical atoms is re- placed by a whole series of bonds between two parallel chains forming a kind of ladder (see fig. 5 ) monovalent linking is not necessarily limited to two chains. ... . . . . . . . . . . . . . . . . .......... ........... . . . . . . . . . . . . . . . . . . . .... .... . .. . . . . ...... . . . . . . . (4 (4 (b) FIG. 4.-Types of packing of long chain molecules : (a) molecules of equal lengths forming sheets, (b) molecules of unequal lengths forming fibrous aggregates (tactoids) ; (c) cross section of both types showing simple hexagonal packing. The same arrangement could give rise to three chains if the bonds at diEerent parts of the chains point in different directions, to a flat network of chains such as are produced in the /I form of the protein fibres such as silk, or finally to a com- pletely cross-linked fibrous block. In general, however, the chains will not be straight and parallel but will have their own tendency to spiral form and therefore the simplest combination is not a parallel-sided ladder but a double spiral. Now the most famous of these double spirals is that of the DNA structures and corresponding polynucleotides of the RNA type discussed by Morgan and his associates in their paper. When three chains are involved there is a treble spiral now typified by the collagen structure which will be discussed by Bradbury and his associates.Double and multiple spirals will be formed most easily from the same types of molecules that necessarily have a concordance in the period of their twist. Of greater biological interest, however, are those where two different kinds of polymer molecules are twisted together. This requires a very considerable con- cordance and so far it is only known in what appears to be the all-important case of the nucleoproteins particularly the DNA-protamine complexes found by Wilkins to be already crystalline in live sperm cells.Even more complex structures can be formed by associations together of already coiled and folded molecules, This seems to be the case for a very large number of proteins in which the globular molecule itself may be considered as an association of smaller globular molecules sufficiently stable to withstand the disruptive forces of the solution. These associations may be in different orders. For instance in insulin the normal form in solution has a molecular weight of some 44,000 but this is not found in most of the crystal forms which show a molecular weight of16 STRUCTURE (a’) - ARRANGEMENTS OF MACROMOLECULES a pair of chains forming limited ladder ; a‘ plan :J ::ition} sets of chains forming unlimited sheet ; c‘ plan triplet of chains forming spiral ladder ; d’ section simple spiral ; ‘, e section ;, ;yon} triplet of linked spirals.pair of linked spirals ; FIG. 5.-Types of bonding of crosslinked polymers each forming one link per monomer.J . D. BERNAL 17 33,000 indicating the presence in the former of four and of the latter of three sub- molecules of 11,080 closely held together. In turn these units of 11,000 seem to be composed of two identical units of 5,500 each of which consists of two unequal protein chains. The haemoglobin series shows a number of different degrees of multiplicity from the simple kind found in the myoglobin of molecular weight of about 17,000 to those of the foetal haemoglobins of 34,000 and the normal 4 haematin haemoglobin of 56,000.The components of these may not be of the same kind though it is too early now to tell what the difference is. A case where they are definitely different is being discussed at this conference by Waugh in the case of the cc, and K caseins which can be separated and can also be made to combine to form a variety of complexes either soluble or insoluble as in the coagulation of curds, the latter involving the presence of calcium. Discussions of other types of association will also be presented in Bresler’s paper. The greatest complexity so far met is, however, found in the structures of viruses which will be reported on by Franklin and Klug. Here, unlike the sperm nucleoprotein we have an association between what appears to be a single or few stranded nucleic acid polymer and a number of relatively small protein molecules arranged in what is effectively a regular quasi-crystalline pattern either in the form of an indefinite spiral as in tobacco mosaic virus or in that of a closed sphere-turnip yellow, tobacco bushy stunt, and other spherical viruses.This discussion by no means exhausts the complexities that can exist in macro- molecules even without recourse to the long-range forces which give rise to the larger scale structures such as micelles, tactoids, coacervates, and gels. However, the field covered by the present discussion should be full enough to point the way to the analysis of further complexities. We may hope that in the present dis- cussion the experiences of workers using very different methods, X-ray, physical- chemical, spectroscopic and optical rotation, will open further perspectives.I hope I may consider my task fulfilled if I have indicated the frame in which his picture can be set. TABLE 1 .-TYPES OF lNTERPARTICULATJ2 FORCES order of magnitude of interac- range of kinds of unit between mechanism tion energy action A which such forces act name kcaI/mg mole homo- electron sharing 60 polar hydrogen action of incom- 6 bond pletely screened hydrogen atom attached to one atom or other polarizable atoms ionic coulomb attrac- 10-20 tion between ions or charged atoms of different sign van der mutual induction 1-2 Waals of moments from electrically apolar molecules 1-2 electron deficient in organic atoms com- pounds 2.4-3.2 OH- and NH- usually groups in re- 2.7 lation to OH and CO 2-3 basic NHz or NH3 groups and acid coo groups, halogens, etc. ‘CHz+-CH3 / 3-5 groups and halogens examples all organic com- pounds long chain polymers water, acids, sugars, urea, purines (nucleic acids) proteins soaps basic hydrochlor- ides, zwitterions, glycine paraffins and hydrophobic molec- ules or parts of molecules18 STRUCTURE ARRANGEMENTS OF MACROMOLECULES TABLE 2.-oRDERS OF MACROMOLECULAR STRUCTURES order of order of nature of last magnitude of magnitude of stage binding molecular particle name of particle weight dimensions simple molecule homopolar 50-200 10 A3 (monomer) bonds chain polymer the same 1000- 5 X 1 0 X homo or hetero 100,Ooo 1 m A coiled polymers hydrogen bonds the same 10 x 10 x or S - S link 500 A folded or coiled coil the same 10,OOO- 50A3 polymer 100,000 globular particle homogeneous agglom- ionic or cryo- 50,000- 100 A3 ated particle hydric forces l,OOO,O00 20 x 20 x twined fibres 1000A3 heterogeneous agglom- the same 10,000,OOO 200 A3 erated particles, or loox 100 examples amino acids, purines, porphyrins, sugars, lipids silk fibroin ,%type denatured proteins cellulose, rubber coiled fibrous protein a-type desoxyri bose nucleic acid smaller globular pro- teins, ribonuclea5e larger globular proteins, haemoglobin, seed globulins haemocyanin, fibrous insulin, collagen nucleoproteins, lipo- nroteins, mucoproteins, fibre aggregates x 5000 8, etc., smaller viruses