*[Thesis Title Pages*] 003 .nj 003 .nf 006 .tg NO 005 .ce 3 039 Computer Studies of Molecular Structure 013 and Function. 007 .ta 56r 005 .tc : 006 .tg NG 055 Thesis presented for the degree of Doctor of Philosophy 012 :A. Dearing, 017 :Linacre College, 008 :Oxford. 016 :September 1978. 003 .bp 006 .tg NA 006 .sp 20 005 .ce 2 051 This thesis is dedicated to George, without whom we 042 would have had very little to write about. 006 .tg NI 048 :"Tis pleasant sure, to see one's name in print; 049 :A book's a book, although there's nothing in't." 006 .sp 1c 007 :Byron. 037 :"English Bards and Scotch Reviewers." 003 .bp 003 .tc 006 .tg NA 006 .ls 2c 003 .fi 003 .ju 005 .ce 1 018 C_o_n_t_e_n_t_s_._ 006 .ll -7 008 Abstract 007 Preface 006 .in 14 007 .ti -14 060 ChapterZ1ZZ:ZZIntroduction to biological systems of interest 044 and to techniques adopted for studying them; 052 review of various phenomena related to intercalation 039 and of computer model-building studies; 042 description of basic computer models used. 007 .ti -14 060 ChapterZ2ZZ:ZZFormulation of intermolecular interactions for 053 isolated systems; semi-empirical potential functions 051 and their relationship to theory and to experiment; 023 parameterisations used. 007 .ti -14 061 ChapterZ3ZZ:ZZStudies on the flexibility of the DNA helix and 049 related nucleic acid structures; rationalisation 046 of experimental results relating to structural 015 changes in DNA. 007 .ti -14 067 ChapterZ4ZZ:ZZUse of graphical aids in modelling work; description 042 of existing systems and development of new 051 implementation; discussion of system's application 048 to study of nucleic acid complexes; limitations 051 of currently available machinery as graphical aids. 007 .ti -14 059 ChapterZ5ZZ:ZZMethods for automatic refinement of molecular 049 complexes by considering energies of interaction; 053 application of such methods to complexes of interest. 007 .ti -14 067 ChapterZ6ZZ:ZZOther facets of molecular interactions not considered 024 here, but of importance. 005 .in 0 025 Chapter 7 : Conclusions 027 Appendix 1 : Nomenclature. 045 Appendix 2 : Contents of Microfiche Inserts. 010 References 006 .ll +7 003 .bp 006 .tg NI 005 .ul 1 055 "Computer Studies of Molecular Structure and Function." 006 .tg NA 046 Abstract of thesis presented for the degree of 003 .br 021 Doctor of Philosophy. 011 A. Dearing, 003 .br 016 Linacre College, 003 .br 007 Oxford. 003 .br 019 Trinity Term, 1978. 071 The application of computer modelling to the study of interactions 063 between aromatic heterocycles and nucleic acid is investigated. 062 Three types of model are developed, based on representation of 066 molecular systems as a connected set of data-structures containing 020 atomic descriptions. 068 The first model is used to investigate nucleic acid flexibility 059 and to determine what limits are placed on the structure of 053 intercalation complexes by lack of flexibility. The 069 "neighbour-exclusion" principle and the possibility for variations in 062 helical unwinding on intercalation are seen to arise naturally 044 from structural properties of the DNA helix. 065 The second model allows manipulation of molecular structures 068 through an interactive graphical display system. The importance of 063 using such a tool prior to, and during, numerical refinement of 060 complex structures is stressed, and the ability of available 064 computing equipment to provide a suitable graphical interface is 055 investigated, resulting in a definition of requirements 028 in future graphical systems. 062 The third model is used to refine structures of molecular 065 complexes automatically, using semi-empirical potential functions 064 to measure interaction energies and to define stability. It is 059 found that recently-developed algorithms allow fairly rapid 064 refinement of molecular configurations, although this is limited 062 severely by the time taken to evaluate the energy function for 065 large systems. Approximations which speed up evaluation of this 060 function are found to have a deleterious effect on numerical 060 refinement. The model allows prediction of some properties 067 of acridine and daunomycin intercalation complexes which correspond 070 well with experiment, and also allows rationalisation the behaviour of 042 the nitro-aminoacridines and bisacridines. 065 The models are seen to offer a reasonable method of studying 035 general drug-receptor interactions. 002 *? *[Thesis Preface*] 006 .tg NI 005 .ul 1 015 Thesis Preface. 006 .tg NA 062 This thesis is concerned with the application of computer 064 modelling to the study of various aspects of molecular structure 060 and function. It is an attempt to determine how techniques 067 developed for computing can be applied to the study of interactions 059 which are of pharmacological importance, through the use of 067 methods obtained from theoretical chemistry and numerical analysis. 068 Partly, we were motivated by a desire to try to automate the process 060 of drug design; to a very large extent, a drug is merely an 064 appropriately-shaped key which fits into some biological keyhole 059 to produce its effect, a fact which has long been known but 062 which has only recently started to be applied to the design of 060 new or improved drugs. Given a suitable tool for modelling 069 molecules, we felt that it should be possible to examine interactions 062 between compounds of interest quickly, without actually having 069 to make them. Of course, this is part of the function of mechanical 053 models, such as those built from space-filling CPK or 060 framework Dreiding units, but such models are of limited use 058 since they can only demonstrate a small range of molecular 054 properties. The use of a computer model should allow 062 a greater range of properties to be studied, because, provided 060 the framework of the model is suitable, its behaviour can be 016 changed at will. 042 We have chosen to base our studies on 064 various interactions between organic macromolecules which relate 057 to the formation of nucleic acid intercalation complexes. 068 The phenomenon of intercalation is explained in detail in chapter 1, 044 and we shall content ourselves here with the 062 following summary of the interactions involved. When certain 063 polynuclear aromatic molecules, in particular the acridines and 056 some quinonoid compounds, are allowed to react with DNA, 046 it is found that these molecules stack between 059 the base-pairs in the DNA helix. This produces structural 062 changes in the nucleic acid, of which the most apparent is the 060 doubling of the spacing between base-pairs at intercalation 026 sites from 3.36A to 6.72A. 060 Only very occasionally are new chemical bonds formed by this 052 interaction; mainly the complexes are stabilised by 052 dispersion forces between the bases and intercalated 059 molecules. Electrostatic interactions also appear to play 047 an important part in stabilising the complexes, 054 for it is commonly found that intercalating agents are 041 positively charged, whilst DNA carries an 067 overall negative charge under biological conditions, and the degree 045 of interaction can be affected quite markedly 039 by the ionic strength. In appropriate 065 cases, hydrogen-bonding may also help to stabilise the complexes. 072 We were concerned, therefore, with modelling an interaction between 070 ionic systems, which takes place in saline solutions; furthermore, in 068 modelling molecules which are much too large to study directly using 070 non-empirical quantum mechanical techniques. All these points raised 032 difficulties. Previous workers 051 have applied various semi-empirical formulations of 067 interaction potential to the description of structure and behaviour 062 of moderately-sized biomolecules, but have generally concerned 070 themselves with systems possessing no overall charge. Equally, other 022 workers have performed 006 .tg NI 009 ab initio 006 .tg NA 043 quantum calculations, but on small systems. 051 Solvent effects will also be particularly important 064 in an ionic system and the absence of an effective technique for 056 describing solvent behaviour has been painfully obvious. 070 We have had to use semi-empirical methods to evaluate interaction 045 energies in this thesis. However, once the 059 energy of a molecular complex was specified mathematically, 057 our problem became one of determining the most favourable 030 interaction energy obtainable. 069 This can be considered to be equivalent to the numerical optimisation 068 of the energy function, but the complexity of the function made it a 046 severe test of numerical methods available and 046 we found that many of the approximations which 068 previous workers had used to simplify calculations were not helpful. 065 Since a numerical optimisation might not distinguish between 065 global and local minima, even though these were well separated in 068 energy, and since the potential energy surfaces corresponding to the 060 interaction of large molecules were expected to possess many 068 false minima, it was important to ensure that approximate structures 064 were set up for molecular complexes prior to optimisation, using 047 non-numerical techniques. To facilitate this, 027 we developed an interactive 031 graphics system. Such systems 044 have been written by other workers, but have 041 generally handled only one molecule. We 072 extended this to allow several molecules to be manipulated individually, 028 and also considered how well 064 the computing equipment available allowed the system to be used. 044 The format of the thesis is as follows: 069 In chapter 1, we describe the biological systems of interest and 070 review what is known about these. We then discuss techniques used in 070 computer modelling and indicate previous work in this field. Chapter 068 2 describes in detail the formulations of intermolecular interaction 071 potential used and the reasons for these choices. Chapter 3 considers 063 the DNA helix in isolation, and studies its flexibility, with a 064 view to determining the structural limitations placed on this by 065 interatomic interactions. Thus we arrive at an indication as to 066 whether certain proposed models of drug action on DNA are tenable. 055 In chapter 4, we describe the development and use of an 056 interactive computer graphics system to explore possible 057 structures for the complexes considered, and chapter 5 is 059 concerned with optimising the approximate structures set up 060 using the methods of chapters 3 and 4. Chapter 6 discusses 063 some of the points which are of relevance to our work, which we 026 have been unable to study. 065 Finally chapter 7 attempts to summarise the results obtained, and 053 indicates possible methods to be used in future work. 046 All material required for reference only, 026 such as computer programs, 071 extended tables of results and so on, has been relegated to microfiche. 065 The work described in this thesis continues that carried out 070 for Part II of the Chemistry first degree course at Oxford in 1975-76. 067 Certain results are taken directly from this earlier work, although 067 the interpretation of these results has frequently changed; in any 063 event, we acknowledge such duplication where it occurs, and, to 064 allow the reader access to this (unpublished) work, we provide a 028 microfiche copy of its text. 059 One problem of a thesis concerned with the interaction 059 of various disciplines is that it is quite impossible to do 076 justice to all the previous work done in these disciplines. The literature 059 in any one of the fields of theoretical chemistry, computer 059 science and molecular pharmacology is immense, and it would 065 not be possible to enumerate all the relevant references in these 062 pages if we tried. The literature on DNA intercalation alone 056 is overwhelming and we have had to omit much which is of 058 interest. Some of the omissions may seem suprising; for 055 example, in a thesis concerned in part with energies of 068 interaction of aromatic molecules with DNA, practically no reference 071 is made to previous theoretical studies on DNA. We have included only 056 those references which appeared germane to the argument, 053 and we must ask for the reader's forebearance on this 064 matter. Another consequence of the interdisciplinary nature of 062 this work is that many parts will be of only marginal interest 062 to specialists in one field. Again, we apologise if at times 040 we appear circumlocuitous or irrelevant. 055 Whenever the results described in these pages have 055 resulted from direct collaboration with others, this is 054 acknowledged. Most of the time, however, many people 063 were involved in providing an environment within which progress 063 could be made and we are grateful to them all. In particular, 049 exceptional thanks are due to the staff of Oxford 059 University Computing Service for placating an irascible and 061 demanding "user", to members of Oxford University Programming 056 Research Group, especially Steven Powell, Malcolm Harper 018 and Andrew Newman, 048 for helping to crystallise the author's thoughts 055 about the art of computer programming and for providing 069 facilities for formatting and typing this tome, to the staff of Roche 069 Products Limited, with whom a "CASE" studentship was held, especially 062 Drs. Kroehn and Thomas who acted as the industrial supervisors 056 and occasionally managed to persuade the author to leave 063 the ivory towers of Oxford for a few days, and to Gordon Wright 061 from the Biochemistry Department in Oxford, and Larry Wakelin 064 from the Pharmacology Department in Cambridge, who intrigued the 064 author with apparantly absurd, but repeatable, experimental data 023 which needed explaining 059 and who did something to improve his appalling knowledge of 030 biological science and method. 055 Finally, though, particular thanks must go to John 063 Rollett, an exceptionally conscientious and helpful supervisor. 001 002 *? *[Chapter 1.1.1*] 006 .tg NI 005 .ul 1 025 Chapter 1 : Introduction. 006 .ls 2c 005 .tc : 007 .ta 56r 036 :"If you are all sitting comfortably 021 :Then I shall begin." 041 :BBC radio programme "Listen with Mother" 003 .tc 006 .ls 3c 006 .tg NA 065 In this chapter, we shall describe the molecular systems and 065 interactions we have chosen to model, define problems of interest 039 and then examine methods available with 020 which to solve them. 068 The terminology used throughout is standard, but frequently obscure, 031 and is described in Appendix 1. 006 .tg NI 005 .ul 1 026 1.1 : Systems of Interest. 006 .tg NA 056 The main phenomenon studied is that of nucleic acid 061 intercalation, which is of pharmacological importance because 069 it is involved in the inhibition of nucleic acid synthesis by certain 058 drugs. The interaction can be split into two main parts: 058 the conformational changes which take place in the nucleic 052 acid helix and the stacking interactions which arise 049 between intercalating agent and the nucleic acid. 063 The two other phenomena of interest are the stacking of certain 057 polynuclear heterocycles on one another in solution and a 037 process which, it has been suggested, 040 may cause a particular type of mutation, 062 involving fairly specific conformational changes in DNA. The 066 relationship between these and the two aspects of intercalation is 006 clear. 067 Before these phenomena are reviewed, we shall describe briefly 058 the DNA and RNA molecules, because an understanding of the 050 phenomena requires a knowledge of their structure. 062 At least one of these compounds is found in all living systems 063 (although the use of the term 'compound' is misleading, because 067 RNA and DNA are really generic terms for a type of compound). DNA 063 is found on degradation to consist of two types of purine base, 064 adenine and guanine, two pyrimidine bases, thymine and cytosine, 054 a sugar, deoxyribose, and phosphate (see figure A1.1). 032 In 1953, Watson and Crick*S26*N, 062 in their now-famous piece of work, determined that these units 070 fitted together to form a double-helical polymer, with two intertwined 066 polynucleotide chains held together by a specific hydrogen-bonding 068 pattern: guanine was bound to cytosine, adenine to thymine, and all 059 four were bound covalently to the two deoxyribose-phosphate 067 backbones. The sequence of base-pairs along the helix defines the 064 genetic code of an organism, enabling the production of proteins 068 to take place. Detailed analysis of x-ray diffraction patterns*S57 064 *Nhas shown the existence of two distinct conformational classes 066 for the molecule, termed A- and B-DNA. The former has C3'-*Iendo 065 *Npuckering of the sugar rings, with eleven base-pair residues to 063 a complete turn of the helix and has the base-pairs tilted away 006 .ne 10 076 from orthogonality to the helix-axis. B-DNA has C2'-*Iendo *Npuckering*t** 007 *l.fn 1 067 *t** *lWhilst this uniformity of sugar geometry in A- and B-DNA has 066 always been accepted in the interpretation of x-ray data, a recent 069 paper by Kennard and co-workers*S56 *Nhas demonstrated that sugars in 064 d-pApTpApT are puckered C3'-*Iendo *Nwhen attached to purine and 072 C2'-*Iendo *Nwhen attached to pyrimidine. In this section, we describe 066 the accepted structures of nucleic acid, which are probably a good 066 approximation to the truth. Much of recent work, the contents of 069 this thesis included, shows that it would be quite wrong to treat the 050 molecules as rigid entities of fixed conformation. 005 .en 1 067 of the sugar rings, and has ten base-pair residues to a turn of the 063 helix, with only slight twisting of the bases. The transition 065 between A- and B-DNA depends on the ionic strength of the solvent 058 medium, with the B form being considered more likely under 062 physiological conditions. Models in this thesis are based on 017 B-DNA structures. 062 In B-DNA, we have, therefore, a succession of base-pairs, 067 each one rotated by 36*D? *Nfrom the one next to it, and stacked in 063 van der Waals contact on one another, separated by about 3.36A. 065 The two strands of deoxyribose-phosphate backbone are arranged in 061 such a way as to leave two grooves in the helix, one "narrow" 060 and one "wide". These points are illustrated schematically 017 in figure 1.1(a). 048 In some natural systems, the DNA molecule exists 058 in closed circular form. Because the molecules are wound 070 to a somewhat smaller extent than in B-DNA found *Iin vitro*N, but yet 056 are topologically constrained by the circular structure, 070 strain exists, which is relieved by the formation of supercoils*S61*N, 058 with the circular DNA molecule twisting round on itself to 054 form a particularly compact system. This is known as 017 superhelical DNA. 061 RNA is found in many different forms, but double-helical 062 RNA appears to exist only in a conformation which is a variant 063 on A-DNA. The chemical differences between DNA and RNA lie in 068 the substitution of thymine by uracil and deoxyribose by ribose, and 062 the inability of RNA to adopt a B-type structure is probably a 047 consequence of the 2'-hydroxyl group in ribose. 005 .ne 6 006 .tg NI 005 .ul 1 037 1.1.1 : The Intercalation Phenomenon. 006 .tg NA 054 The term "intercalation" conventionally refers to 064 the process by which certain aromatic molecules stack in between 066 the base-pairs of DNA and other nucleic acids (see figure 1.1(b)). 035 It is a very convenient interaction 045 to model since many aspects of it are thought 064 to be well-understood; if, in fact, the understanding is not as 059 great as is commonly thought, at least the phenomenon is of 068 sufficient interest for there to be much experimental data available 062 against which to check the predictions of a theoretical model. 069 Many different compounds interact with DNA in a way which is now 065 thought indicative of intercalation, but all understanding of the 069 phenomenon has grown up from what was discovered about the acridines. 072 Consequently, we shall start by reviewing the history of these compounds 064 insofar as it relates to intercalation. Later we shall see how 068 other types of molecule interact with DNA in ways which cast further 068 light on the processes occurring during intercalation or which raise 058 problems whose solutions will be attempted in these pages. 066 (A very good review of the acridines*S14 *Nis given elsewhere 017 and we shall only 060 describe salient points here.) Interest in these compounds 066 as antibacterial agents started in 1913 when Ehrlich and Benda*S15 047 *Nobserved that 3,6-diamino 10-methylacridinium 071 chloride ("tryptaflavine") possessed trypanocidal activity. At almost 040 the same time, Shiga*S16 *Nreported that 074 this same compound was active against cholera infections and other workers 070 discovered that proflavine and acridine yellow inhibited the growth of 050 other bacteria. These and related compounds were 034 used as wound disinfectants since, 045 unlike most other substances then known, they 066 retained their antibacterial properties in the presence of pus and 012 body fluids. 063 Investigation of the action of a number of other acridines 062 showed that not all were biologically active. In the 1940's, 021 Albert and co-workers 064 carried out a large-scale investigation of the factors affecting 064 antibacterial activity of these compounds and drew the following 074 conclusions, which are described in greater detail in Albert's book*S17*N: 006 .sp 1c 006 .ll -3 006 .in 10 006 .ti -5 072 1.ZZZThat effective bacteriostasis occurred only when the compounds were 062 more than 50 ionised as cations; anions and zwitterions were 012 ineffective. 006 .ti -5 061 2.ZZZThat the chemical nature of substituents on the acridine 060 nucleus was seldom important except insofar as it influenced 047 either ionisation or planarity of the compound. 006 .ti -5 071 3.ZZZThat because of the dependence of activity on the planarity of the 044 acridine, the receptor site was also planar. 006 .ll +3 005 .in 0 068 The ability of the acridines to stain those structures in cells 049 which contained nucleic acid led naturally to the 065 inference that their pharmacological activity was associated with 070 interaction with nucleic acid. In fact*S14*N, acridines bind readily 066 to DNA *Iin vitro*N. Complexing alters their absorption spectra, 063 typically shifting these to longer wavelengths and lowering the 069 extinction coefficient, and also affects their fluorescence emission. 061 These spectral changes provide a method for investigating the 061 binding process, although the lack of a good isosbestic point 063 sometimes means that other techniques, such as ultracentrifugal 065 methods, must be used. In figure 1.2, we show a typical binding 058 curve, for proflavine interacting with DNA, and this curve 070 suggests that two different types of binding are involved. These are 061 commonly known as type I and type II binding and further work 040 has characterised them as follows*S14*N: 006 .sp 1c 006 .ll -3 006 .in 10 006 .ti -5 015 Type I binding: 006 .sp 1c 006 .ti -5 057 1.ZZZIs strong, with a *SD*DH *Nof between -40 and -60 kJ 027 per mole of bound acridine. 006 .ti -5 051 2.ZZZNeeds a flat acridine for complexing to occur. 006 .ti -5 052 3.ZZZChanges the viscosity and apparent chain length 007 of DNA. 006 .ti -5 051 4.ZZZDepends on the ionic strength to determine the 059 degree of interaction (but not as much as type II binding). 006 .ti -5 065 5.ZZZResults from interaction not only with normal double-helical 061 DNA but also with denatured DNA and, to a lesser extent, with 032 single-stranded polynucleotides. 006 .ti -5 048 6.ZZZHas an upper limit of complexed acridine of 058 between 0.2 and 0.25 of the number of nucleotides present. 006 .sp 1c 006 .ti -5 016 Type II binding: 006 .sp 1c 006 .ti -5 013 1.ZZZIs weak. 006 .ti -5 056 2.ZZZInvolves interactions with already bound acridines. 006 .ti -5 057 3.ZZZIs affected very considerably by the ionic strength. 006 .ti -5 049 4.ZZZInvolves the bound molecules being much more 034 disordered than in type I binding. 005 .ti 5 044 5.ZZZCan take place up to electroneutrality. 002 *? *[Chapter 1.1.2*] 006 .ll +3 005 .in 0 070 The two types of binding are now thought to involve intercalation 056 into (type I), or external aggregation on (type II), the 066 nucleic acid helix. We shall have relatively little to say about 059 the external binding process, since it appears to be fairly 046 unimportant in determining the pharmacological 028 properties of the acridines, 058 although it will be mentioned again in connection with the 055 phenomena of acridine stacking and frameshift mutation. 060 Drug action is usually thought to result from intercalation, 063 although it is unlikely that all the pharmacological properties 059 of "intercalating agents" can be explained in terms of this 016 one interaction. 064 A tabulation of the antibacterial activities of the acridines as 069 a function of their degree of protonation under biological conditions 062 has been given by Dean*S14*N, and this is shown graphically in 065 figure 1.3. Some form of correlation is apparent, but it is not 060 good. Indeed, it is debatable what line or curve should be 067 drawn through the points marked. Two particular types of compound 063 lie well-away from the others: acridines which are non-planar, 060 either through hydrogenation of one of the aromatic rings or 063 through possessing a bulky substituent, show low anti-bacterial 059 activities even though almost entirely protonated under the 063 experimental conditions used to measure activity, and compounds 064 containing a nitro-group show relatively high activities, whilst 074 being only about 50*A> *Nprotonated. Albert*S17 *Nhas suggested that the 070 high activity of the nitroacridines is due to some special interaction 035 and recently it has been found that 005 .hc ? 068 1-nitro-9-(3'-dimethyl?amino?propyl?amino-)-acridine ("Ledakrin") is 003 .hc 063 reduced *Iin vivo *Nto the hydroxylamine which binds covalently 013 to DNA*S29*N. 065 Several features of the strong binding process point towards 068 the basic model of intercalation with which we started this section. 069 Firstly, the changes in viscosity*S18 *Nand sedimentation rate of DNA 061 after acridine binding can be attributed to a lengthening and 070 stiffening of the DNA molecule. This is in keeping with an extension 070 of the DNA helix, followed by insertion of the acridine into the space 074 provided. X-ray diffraction patterns*S19 *Nindicate that, after binding, 069 the regular 3.36A spacing characteristic of DNA is retained, although 047 the long-range regularity of the helix is lost. 066 The dependence of binding on degree of protonation of the acridine 066 and on ionic strength indicates the importance of an electrostatic 064 contribution to the interaction. This is understandable if the 069 interaction is with nucleic acid, since, under biological conditions, 056 the phosphate groups of the acid are negatively charged. 028 On the basis of these facts, 056 Lerman*S20 *Nproposed that the DNA helix extended at the 018 intercalation site 066 so as to place successive base-pairs 6.72A apart. This extension 062 involved quite large amounts of unwinding of the helix, almost 069 superimposing the base-pairs on either side of the intercalation site 072 on one another. The acridine was then inserted so that it was parallel 041 with the base-pairs and had its long axis 035 lying along the phosphate-phosphate 068 line. This model had the attraction of allowing maximum overlap of 072 the base-pairs and acridine, of not producing voids in the structure and 064 of allowing electrostatic interaction between negatively-charged 046 phosphate and positively charged acridine, and 062 hydrogen-bonding of nucleic acid phosphate to the amino-groups 051 in compounds like proflavine (3,6-diaminoacridine). 040 However, quantitative discrepancies were 070 noted between the observed x-ray diffraction patterns for DNA:acridine 077 complexes and the patterns expected from Lerman's model*S21*N. Furthermore, 068 the observed strong interaction between acridines and denatured DNA, 071 in which the regular pairing of purine to pyrimidine has been lost, and 064 also the interaction with single-stranded polynucleotides*S25*N, 021 seemed at odds with a 041 Lerman-type structure for the complex and 047 consequently, Pritchard, Blake and Peacocke*S22 074 *Nsuggested an alternative model in which the acridine was intercalated at 063 one side of the helix, parallel to the base-pairs, but with its 067 long axis directed perpendicularly to the phosphate-phosphate line. 066 Their proposal was based partly on the (misguided) belief that the 075 positive charge on a protonated acridine was situated on the ring nitrogen, 071 and that, therefore, such a model would allow close interaction between 073 this charge and the negative charge on adjacent phosphate. Nonetheless, 069 the model does have attractive features over and above its ability to 065 rationalise the interaction of acridines with single-stranded and 066 denatured nucleic acid. Firstly, 1,2,3,4-tetrahydroacridine does 073 interact with nucleic acid*S17*N, apparently intercalatively, although to 069 a much lesser extent than acridine itself. Complexing this compound 068 in the manner of Lerman's model would require extension of the helix 063 beyond the 6.72A normally required, in order to accommodate the 070 non-planar ring. On the other hand, it is possible to insert most of 069 the ring system between base-pairs in a Pritchard-type model. Other 056 intercalating agents such as daunomycin may also require 068 this mode of complexing. In figures 1.4 and 1.5, we illustrate the 062 two modes of complexing; henceforth we shall refer to them as 035 "Lerman-type" and "Pritchard-type". 061 Interactions resembling intercalation have been observed 058 crystallographically with both single- and double-stranded 065 nucleic acids. Damioni and co-workers*S23 *Nhave cocrystallised 062 tetramethyluric acid (a methylated purine) and benzpyrene, and 054 found that parallel stacks were formed consisting of a 058 benzpyrene molecule sandwiched between two tetramethyluric 059 acid molecules 3.45A away on either side, in an orientation 060 similar to Pritchard's model for intercalation. Seeman and 071 co-workers*S24 *Ndetermined the structure of the complex formed between 063 9-aminoacridine and ApU, which was found to be another sandwich 072 complex. In this complex, though, purine and pyrimidine bases were not 074 hydrogen-bonded in the conventional Watson-Crick*S26 *Nmanner, which meant 065 that association of the ApU units did not result in the formation 069 of miniature double helices. Instead, adenine atoms N*T6 *Nand N*T7 064 *Nbonded to uracil atoms N*T5 *Nand O*T4*N, an arrangement which 070 had been observed quite frequently in pyrimidine-purine complexes, but 064 which placed the phosphate groups of nucleic acid well away from 064 the acridine. Consequently, electrostatic interactions between 072 the opposite charges on acridine and phosphate could not be as important 026 in stabilising the complex 067 as had been suggested for double-helical nucleic acid intercalation 010 complexes. 058 Some other crystal structure determinations have been 063 carried out on intercalation complexes of di-(ribo)nucleotides. 066 Sobell*S27 *Nhas studied the interaction of ethidium with iodo-UpA 076 and with iodo-UpG, whilst Neidle*S28 *Nhas studied proflavine:CpG complexes. 061 Both workers found that the complexes were of the Lerman-type 069 and the fine details of the structures will be discussed in *S?*N3.1, 052 when we investigate conformational changes occurring 058 in nucleic acids on intercalation. There is, however, an 062 important consideration which limits the utility of studies on 064 dinucleotide complexes in understanding the DNA complexes. The 062 DNA helix can be considered to be a succession of dinucleotide 056 units linked together, and there is clearly some form of 062 conformational constraint on these units to allow them to join 061 onto one another. The structural changes which can occur in 059 any dinucleotide unit on intercalation are limited by these 063 boundary constraints, a point that is illustrated schematically 014 in figure 1.6. 062 Lerman's first model*S20 *Nfor intercalation had involved 066 a 45*D? *Nunwinding of the helix. Later work has suggested other 019 values, and some of 062 these are listed in table 3.1. It is generally accepted that 061 intercalation involves some degree of unwinding of the helix, 059 although it is not clear from experimental work how this is 061 distributed. Originally, the unwinding was considered to be 068 localised at the intercalation site, but some theoretical studies*S3 065 *Nhave cast doubt on this. Only once has it been suggested that 068 intercalation produced helical winding*S59*N, and the basis for this 060 lay in a novel interpretation of fluorescence depolarisation 049 data, which has subsequently been disputed*S60*N. 066 Since intercalation unwinds the DNA helix, it also alters the 065 supercoiling of superhelical DNA*S61*N, and one of the diagnostic 063 tests for intercalation is based on the amount of drug required 062 to cause reversal of this supercoiling, measured, for example, 057 using sedimentation rates. The technique can be used to 061 estimate the degree of helical unwinding on intercalation, by 058 comparing the amount of drug needed with the corresponding 061 value for ethidium. However, this requires an initial value 067 for ethidium, and, whilst early work*S40 *Ntook this to be 12*D?*N, 065 subsequent analysis of ethidium-DNA complexes in caesium chloride 071 density gradients has suggested*S62 *Nthat the value should be 26*D?*N. 063 Furthermore, it is worth noting that irediamine, which does not 058 possess the geometric requirements for intercalation, also 031 unwinds superhelical DNA*S63*N. 002 *? *[Chapter 1.1.3*] 068 The notion of a "neighbour-exclusion" principle*S30 *Ngoverning 058 intercalation of acridines into DNA, such that an acridine 063 molecule could not intercalate at a site adjacent to an already 058 occupied site, arose from the observation that the maximum 058 observed ratio of intercalated acridines to nucleotides in 061 the DNA helix lay between 0.2 and 0.25. Clearly, if such an 056 exclusion principle does apply, then only half the sites 040 along the helix can possibly be occupied 039 and the random arrival and departure of 049 molecules will tend to lower this ratio, owing to 057 the presence of sets of two adjacent and unoccupied sites 035 sandwiched between complexed sites. 065 Page*S31*N, considering the related problem of selecting pairs of 060 adjacent points at random from a line such that no point was 034 included in two pairs, showed that 034 the probability that a given point 058 remained unselected tended to *De*N*t-2 *las the number of 069 points became large, which, in terms of intercalation, means that the 060 expected ratio of intercalated acridines to nucleotides in a 059 saturated DNA helix obeying a neighbour-exclusion principle 078 is *A<*N(1-*De*N*t-2*l), or 0.216, in good agreement with experimental values. 064 However, direct experimental evidence for such an exclusion 065 principle has proved difficult to obtain. Although in principle 015 a 10.2A spacing 047 of acridines should occur in a saturated helix, 026 it has proved difficult to 058 see this spacing in x-ray data collected on polynucleotide 059 intercalation complexes. We can see two reasons for this. 057 Firstly, the random distribution of unoccupied and doubly 061 unoccupied sites along the helix will tend to confuse such an 064 indication. More importantly, though, the x-ray data available 059 is not easy to decipher; in particular, at the resolutions 070 obtainable, an aromatic acridine molecule looks much like a base-pair. 068 Recently, however, Bond and co-workers*S32 *Nhave studied x-ray data 005 .hc ? 063 obtained from a 2-hydroxy?ethane?thiolato?(2,2',2"-terpyridine) 003 .hc 062 platinum(II) : DNA complex. This complex had previously been 057 shown to involve intercalation, and it was found that the 068 presence of heavy metal ions produced layer-lines on the diffraction 062 patterns corresponding to a periodic 10.2A spacing. The only 073 explanation consistent with the available evidence was that intercalation 056 was indeed taking place subject to a neighbour-exclusion 010 principle. 061 Three reasons can be suggested as to why there should be 059 a neighbour-exclusion principle. Firstly, the correlation 062 found between degree of protonation of the acridines and their 069 ability to bind to DNA*S17 *Nsuggests that intercalation involves the 045 protonated species. A calculation performed 059 by Gilbert and Claverie*S33*N, based on the solution of the 064 Poisson equation for an appropriate set of electrostatic charges 060 placed in a cylinder immersed in solvent, has indicated that 068 complexing protonated acridine molecules at adjacent sites along the 068 helix would result in an overall positive free-energy change, due to 057 the mutual repulsion of the acridine molecules. Another 061 possibility is that the DNA helix does not possess sufficient 059 flexibility to allow extension at every site, but Alden and 064 Arnott*S3*N, modelling the behaviour of the DNA helix during its 063 extension to accommodate intercalating acridine molecules, have 047 suggested that this is not the case. Thirdly, 059 a preference for binding to certain sequences of base-pairs 060 could give rise to an apparent exclusion principle. It has 062 been shown*S35 *Nthat some acridines bind more strongly to the 052 dinucleoside-phosphate CpG than to GpC, preferring a 059 pyrimidine-(3'-5')-purine sequence, a result which was also 063 found for the intercalating drug ethidium. On the other hand, 067 preliminary work*S36 *Nsuggests that daunomycin binds more strongly 061 to purine-(3'-5')-pyrimidine sequences. In either case, the 061 preferred sequence can occur at most at alternate sites along 010 the helix. 060 Recently, interest has been shown in the interaction of 052 bisacridines with DNA, because of the possibility of 042 investigating neighbour-exclusion further. 067 Le Pecq and co-workers*S37 *Nhave prepared various compounds of the 038 type shown in figure 1.7(a), where 'R' 040 is an aliphatic chain containing varying 069 numbers of -CH2- and -NH- groups. They investigated the interaction 066 of these compounds with various DNA systems at pH 5.0, at which pH 068 ring nitogens and those nitrogens in the 'R' chain can be considered 067 fully protonated. Their results showed that intercalation of only 065 one aromatic ring occurred when the backbone was such as to place 063 the rings less than about 10A apart if stacked parallel to each 074 other, but that with systems possessing longer backbones, bisintercalation 064 occurred. Since the neighbour-exclusion principle requires two 065 base-pairs between successive intercalated acridines, it would be 066 expected that a spacing of 10.2A was required between the aromatic 065 rings in bisacridines in order for intercalation of both rings to 060 occur and Le Pecq's results tend to support this conjecture. 060 More recently though, Waring's group*S38 *Nhave studied 060 compounds of the type shown in figure 1.7(b), where, in this 067 case, 'R' contained solely -CH*T2*N- groups. Their investigations 070 took place at a somewhat higher pH, but still sufficiently low for the 032 ring nitrogens to be protonated. 037 With 'R' chains containing up to four 075 -CH*T2*N- groups, measurements of supercoil unwinding and viscosity changes 068 indicated that only one ring was intercalating. as expected from the 076 length of the backbone. With five -CH*T2*N- groups, results were confused, 070 but at longer chain-lengths, an unambiguous bisintercalation occurred. 077 The compound of particular interest was that containing six -CH*T2*N- groups, 071 whose backbone was only long enough to place parallel ring systems 8.8A 061 apart. They felt that the bisintercalation of this compound 066 cast doubt on the validity of the "neighbour-exclusion" principle. 065 It can be seen that three main differences exist between the 066 compounds studied by Le Pecq's group and those studied by Waring's 063 group - the presence of substituents on the aromatic rings, the 065 presence of secondary amine functions in the backbone linking the 067 nuclei and the use of a different pH, sufficiently low to protonate 074 these amino-groups. Waring's group have studied these points further*S39 067 *Nto ascertain which is primarily responsible for the difference in 065 results obtained. Preliminary work tends to indicate that it is 063 the presence of substituents on the ring systems which prevents 067 bisintercalation of moderate chain length, and that the differences 056 in backbone structure and pH are relatively unimportant. 060 Another set of compounds which intercalate into DNA are 060 the phenanthrenes and most work on this type of compound has 064 been performed on ethidium, which, as the bromide, has been used 061 as an anti-parasitic agent in veterinary medicine. Ethidium 059 is illustrated in figure A1.1; basically, it consists of a 058 phenanthrene nucleus, quaternised on the ring nitrogen and 048 bearing phenyl and two amino substituents. The 058 compound shows most of the previously-described properties 054 considered indicative of intercalation, and Fuller and 071 Waring*S40 *Nhave proposed a model for the DNA complex which is similar 066 to that suggested by Lerman*S20 *Nfor the acridines. Their model 067 involved unwinding of the helix by 12*D? *Nand had the phenyl-group 063 resting in the wide groove of the helix. It was stabilised by 058 stacking interactions and also by hydrogen-bonding between 031 amino-groups and DNA phosphate. 067 Sobell's*S27 *Ncrystal structure of the complex formed between 062 ethidium and Ap-*Iiodo*N-U showed it to involve intercalation. 060 However, 25*D? *Nunwinding of the miniature double helix was 061 observed, and, notably, the bulky phenyl-group projected from 063 the narrow groove of the helix, contrary to Fuller and Waring's 071 model. Wakelin and Waring*S41 *Ninvestigated the role of substituents 059 on the behaviour of ethidium and found, in particular, that 065 derivatives in which amino-groups had been replaced or complexed, 066 frequently bound to DNA to a comparable extent to ethidium itself, 064 which suggested that hydrogen-bonding between these amino-groups 058 and DNA phosphate might not be crucial to the interaction. 002 *? *[Chapter 1.1.4*] 053 An important group of drugs which are thought to 055 intercalate into DNA are the anthracycline antibiotics. 028 These are produced naturally 055 by various streptomyces organisms and are characterised 041 by having a tetrahydro-naphthacenequinone 052 moiety linked to an amino-sugar. They bear several 073 additional oxygen functions in the aromatic and saturated portions of the 073 aglycone, and variations in the number and position of these substituents 076 (usually hydroxyls) distinguishes individual compounds. Two members of the 061 family, daunomycin and adriamycin, are particularly important 052 cytotoxic drugs, and are illustrated in figure A1.1. 070 Daunomycin (R=H) was discovered independently in three laboratories in 071 the mid-1960's and has achieved a significant place in the treatment of 041 leukemia. Adriamycin (R=OH), discovered 039 some three years later, is also used as 070 an anti-leukemicia drug but is of much greater interest because of its 076 activity against a broad spectrum of solid tumours. A good review of these 072 drugs may be found elsewhere*S36*N; we shall only summarise some of the 021 relevant points here. 080 *IIn vitro *Nbiophysical studies*S42 *Nhave established that daunomycin and 070 adriamycin form stable complexes with native DNA and that the aglycone 077 portion of the drugs intercalates between base-pairs of DNA. Characteristic 042 alterations in the ultraviolet and visible 067 spectrum of the drug demonstrate significant association, as does a 070 pronounced decrease of daunomycin fluorescence in the presence of DNA. 074 Ionisation of the phenolic hydroxyls on the drugs at high pH is inhibited, 071 and the susceptibility of the quinone groups to polarographic reduction 057 is virtually eliminated. As expected, the intercalation 055 complexes sediment more slowly and have lower densities 060 than native DNA. Viscosity of drug:DNA solutions increases 060 with increasing drug concentrations, and the drugs stabilise 036 helical DNA to thermal denaturation. 032 Binding*S43 *Nsaturates at about 060 one drug molecule for every five nucleotides with adriamycin 021 and at about one drug 039 molecule for every six nucleotides with 058 daunomycin, to be replaced by weaker interaction processes 041 at higher drug:DNA ratios, which suggests 025 that these drugs can only 040 occupy every third site along the helix. 045 Pigram and co-workers*S44 *Nhave studied 034 fibres of DNA-daunomycin complexes 068 using x-ray diffraction methods and have concluded that the patterns 065 obtained are consistent only with an intercalative binding of the 061 aromatic chromophore. They proposed a model for the complex 037 which left the daunosamine side-chain 070 projecting into the major groove of the helix, with its ammonium group 038 interacting ionically with a phosphate 067 separated by two base-pairs from the intercalated aromatic nucleus. 019 They also noted the 076 possibility of a hydrogen-bond between the 12-hydroxyl group and an adjacent 057 phosphate. With C2'-*Iendo *Npucker on the sugar groups 070 (B-DNA structures), their model indicated that an unwinding of between 075 10*D? *Nand 25*D? *Nwould be likely, whilst with C3'-*Iendo *Npucker (A-DNA 012 structures), 057 this value would probably be between 24*D? *Nand 38*D?*N. 072 The best fit to the x-ray data was found with a 12*D? *Nunwinding angle. 066 Doskocil and Fric*S45 *Nstudied the interaction of daunomycin 065 with double stranded RNA. They found that, although the visible 049 spectrum of the daunomycin changed on adding RNA, 058 indicating some interaction between the two molecules, the 068 thermal melting curve of the RNA remained unaltered. The viscosity 066 of RNA solutions also remained unchanged on addition of daunomycin 033 and they concluded that, although 064 interaction could occur between drug and RNA (presumably similar 063 to the type II interaction of the acridines), intercalation was 065 not involved, and they therefore suggested that a B-DNA structure 031 was required for intercalation. 060 The anthraquinone drugs, daunomycin and adriamycin, are 066 particularly interesting examples of naturally-occurring compounds 062 whose properties it has been difficult to improve upon. Most 059 of the straightforward structural changes which can be made 064 chemically (or, at least, which have been made so far) result in 049 a marked decrease, or total loss, of drug action. 011 In a review 070 paper published in late 1976, Henry*S46 *Nindicated that, of the large 056 number of compounds which had been produced by modifying 057 the chemical structure of daunomycin and adriamycin, only 060 few possessed greater efficacy than the native compounds and 005 .ne 6 057 none had had superior potency*t***l, and since this time, 068 only the 4-demethoxy compound has emerged to change this view*D47*N. 005 .fn 1 063 *t** *lThe potency of a drug is the amount necessary to cause a 061 desirable effect, whilst efficacy is the degree to which that 064 dose produces the effect required. The distinction is much too 050 subtle for the modelling studies we shall perform. 005 .en 1 065 Two types of derivative can be considered, namely those with 064 a modified sugar residue and those with a modified anthraquinone 047 residue. We shall deal with the latter first. 038 As already stated, removal of the 056 methoxy-group at position 4 produces a compound which is 051 more potent than its parent*S47*N. Similarly, the 068 4-hydroxy compound, carminomycin, has also been reported*S46 *Nto be 046 an active drug. In terms of an intercalative 059 model, this can be understood, because a demethoxy-compound 062 would be more completely planar than the methoxy-analogue, and 064 would therefore be expected to penetrate between base-pairs more 062 easily. Compounds with two, or sometimes three, rings in the 065 chromophore do not appear to intercalate*S46 *Nto any appreciable 056 extent, which has been explained in terms of the smaller 057 degree of stacking which can occur between base-pairs and 058 chromophore with these compounds. The groups attached to 066 C*T12*N, on the cyclohexene ring, appear fairly important from the 061 point of view of drug action, although this may be due solely 063 to the molecular conformation which these substituents produce. 070 It has been suggested*S49 *Nthat an axial hydroxyl-group at this point 060 stabilises the crystallographically-observed conformation of 055 daunomycin by hydrogen-bonding to the glycosidic oxygen 061 linking sugar to quinone. The other group at this position, 065 which is -COCH*T3 *Nin daunomycin and -COCH*T2*NOH in adriamycin, 068 appears fairly unimportant as far as DNA binding is concerned (which 064 is interesting, since it shows that DNA intercalation may not be 053 the only factor responsible for the drugs' activity). 063 Mechanical models of the complex show that this group protrudes 056 out of the intercalation site, and analogues such as the 069 semi-carbazone and octanoate*S48 *Nshow similar interactions with DNA 081 to their parents. Daunomycin and adriamycin possess*S49 *N10(*DS_*N),12(*DS_*N) 050 conformations at the chiral centres, and synthetic 064 analogues possessing 10(*DR_*N),12(*DR_*N) conformation have low 023 affinity for DNA*S47*N. 060 The effect of changing the structure of the daunosamine 058 residue is generally either indifferent or bad, insofar as 061 binding to DNA is concerned. The normal daunomycin molecule 062 possesses an *Sa*N-anomer of the sugar ring, and *Sb*N-anomers 064 bind considerably more weakly*S50 *Nto DNA and have much reduced 060 anti-tumour activity. Compounds with the hydroxyl group at 073 C*T32 *Nepimerised show*S34 *Ncomparable binding properties to the parent 047 compound, which suggests that this group is not 058 involved in the interaction with DNA. The most important 063 structural point, however, seems to be the relative disposition 066 of the positively-charged amino-group to the rest of the molecule. 072 Mechanical models indicate*S44 *Nthat this group, attached to C*T34 *Nin 065 daunomycin, can bind to an adjacent phosphate on DNA. If it is 060 blocked or its basicity reduced, for example by acetylation, 062 the pharmacological properties are reduced, as they are if the 061 amino-group is attached to some other atom on the sugar ring. 069 If, however, the daunosamine group is replaced by another group which 053 keeps the disposition of the amino-group, activity is 015 retained*S46*N. 055 The specificity shown by daunomycin for binding to 026 areas of nucleic acid with 061 different base-pair sequences is poorly understood. Buoyant 071 density measurements*S51 *Nindicated that there was a slight dependence 063 on the G-C content of the nucleic acid, but this was not always 066 shown in other studies*S58*N. In particular, measurements of DNA 066 melting curves*S52 *Nhave shown the opposite dependence, and other 069 conflicting results have been published. Neidle*S36 *Nhas suggested 062 that the drug shows a preference for purine-(3'-5')-pyrimidine 063 sequences, which is the opposite to that found for ethidium and 011 proflavine. 059 Comparison of the reversal of supercoil winding of DNA 056 by daunomycin with that by ethidium indicated*S54 *Nthat 049 a 5.2*D? *Nunwinding of the nucleic acid occurred 051 on binding of daunomycin. However, reappraisal of 076 ethidium binding has suggested*S53 *Nthat this unwinds the helix by 26*D?*N, 027 instead of 12*D? *Non which 057 the daunomycin value was based. This changes the 5.2*D? 064 *Nfor daunomycin to 11.3*D?*N, which is close to the value which 065 Pigram*S44 *Nfound gave the best agreement between his mechanical 033 model and fibre diffraction data. 002 *? *[Chapter 1.1.5*] 006 .tg NI 005 .ul 1 027 1.1.2 : Mutation Processes. 006 .tg NA 058 The study of processes involved in mutation is a vast 063 field of research in itself, and it is impossible to do justice 064 to the subject here. However, there are some close connections 062 between intercalation and mutagenesis and, in this section, we 028 shall try to describe these. 065 That nucleic acids provide the means for storing the genetic 064 code of an organism has been accepted for some time. In higher 064 species, it is thought that DNA is the genetic material and that 061 RNA molecules are involved in the transcription of the stored 063 information into a useful form, whereas, in some lower species, 065 RNA is used throughout. The elucidation of the structure of DNA 068 by Watson and Crick*S26 *Nallowed the development of ideas as to how 060 the genetic code was stored on the molecule, and Crick's*S64 071 *Ndetermination of the triplet code provided further insight into this. 063 Each possible sequence of three nucleotides on the DNA molecule 064 was considered to represent one amino-acid in a protein molecule 062 (with the exception of two triplets which marked the end of a 071 "gene", or sequence coding for one peptide chain). Recent work*S65*N, 063 determining the complete genetic code of a simple viral system, 064 has indicated that the situation is more complex than this, but, 059 in essence, it is the basis for the entire process of life. 061 However, the mapping of nucleotide triplets onto peptide 066 sequences is clearly very sensitive to changes in the nucleic acid 060 molecule, and this provides the basis for mutagenesis. One 058 mechanism, proposed by Freese*S66*N, involved altering one 059 base-pair in DNA. This would result in a protein molecule 064 which was a mutant because it contained an incorrect amino-acid, 067 but which could still be functional. Another mechanism, suggested 070 by Brenner and Crick*S67*N, involved the loss or gain of base-pairs in 072 the DNA molecule. This would produce a sequence of nucleotide triplets 063 which was more than likely to be out-of-phase with the original 063 sequence, and would result in a mutant protein whose amino-acid 060 sequence was grossly altered. This second type is known as 068 "frameshift" mutation, and Brenner and Crick explained the mutagenic 067 effect of acridines on T4 bacteriophage in terms of this mechanism. 069 Details of the mechanism of frameshift mutation are complex, and 055 not well-understood, and we refer the interested reader 067 elsewhere for a review of these*S68*N. However, as implied in the 059 preceeding paragraph, the process is induced by many of the 064 compounds which bind intercalatively to DNA. Certain locations 066 on genes ("hot-spots") seem to be particularly prone to frameshift 063 mutation, and analysis suggests that these regions contain long 065 sequences of one base or of a simple repeating sequence of bases. 069 Streisinger*S69 *Naccounted for this in a model involving looping-out 067 of one strand of the DNA molecule, a process which could take place 064 particularly readily at the "hot-spots". The looped-out region 061 could then be stabilised by interaction with an intercalating 059 agent; depending on the size of the loop, either type I or 054 type II binding could take place. The information on 065 the two strands of the helix would then be out of synchronisation 065 with one another, and it is quite easy to see how this would lead 012 to mutation. 066 As it stands, Streisinger's model is attractive, but fails to 062 explain the lack of correlation between strength of binding to 066 DNA by the acridines and their mutagenic properties*S70*N. This 067 could be due to many factors; the subject is poorly understood and 062 we do not intend to pursue it here. However, the interesting 063 aspect of the model as far as this work is concerned is that it 061 requires a particular degree of conformational flexibility in 074 the DNA molecule, and in *S?*N3.3, we investigate whethisr the flexibility 061 does exist, for a simple case of moving out one base from its 033 normal position within the helix. 006 .tg NI 005 .ne 6 005 .ul 1 036 1.1.3 : Other Stacking Interactions. 006 .tg NA 063 The stacking of intercalating agents between base-pairs is 065 by no means a unique interaction, and indeed, stacking has become 062 a ubiquitous term in biology, and has been the subject of many 037 experimental and theoretical studies. 060 Just as intercalation involves the stacking of aromatic 062 molecules between base-pairs in nucleic acid, so too, stacking 070 interactions occur with both nucleic acids and with some intercalating 062 agents in isolation. In DNA, successive base-pairs are found 070 using x-ray diffraction to be spaced some 3.4A apart, in van der Waals 062 contact with one another. This stacking is demonstrated very 063 well by CPK-type mechanical models; perhaps too well, in fact, 064 because recent work has suggested that the stacking interactions 069 do not hold the molecule rigid. Levitt*S5 *Nhas found little energy 061 penalty for bending the DNA helix, and calculations performed 060 on the stacking of base-pairs have produced relatively small 067 values for the energy of interaction (see Rein*S71 *Nfor a review). 029 The acridines aggregate 057 in solution, in a way indicative of stacking*S72*N. The 049 degree of aggregation is found to depend on ionic 026 strength, with an increase 065 in ionic strength producing a corresponding increase in stacking. 019 There is a negative 067 entropy of aggregation, which becomes more negative as the acridine 072 concentration increases*S73*N, and this suggests that increasing amounts 068 of reordering need to be done to stabilise the stacks. Measurement 074 of the structural properties of the aggregates has proved difficult*S70*N; 053 there is no reason why the solution properties of the 069 acridines should be identical to their crystal properties. However, 069 most interpretation of results has revolved around a model maximising 043 overlap between molecules by aligning their 059 long axes. The stacking of 3,6-(t-butylamino)-acridine in 073 solution*S73 *Ncasts doubts on the universal applicability of this model. 006 .tg NI 005 .ne 6 005 .ul 1 016 1.1.4 : Summary. 006 .tg NA 050 In the chapters that follow, we study some of 061 aspects of intercalation which have seemed to be particularly 066 pertinent to an understanding of the interaction. In particular, 065 we examine the DNA helix, to determine its flexibility and to see 067 whether the phenomenon of neighbour-exclusion has any justification 069 or whether the binding of bisacridines discounts it. The energetics 066 of binding of acridines and anthraquinones to DNA are investigated 062 to see how well-defined the interactions are, and to determine 060 why different intercalating agents behave in different ways. 002 *? *[Chapter 1.2*] 006 .tg NI 005 .ul 1 034 1.2 : Previous Computer Modelling. 006 .tg NA 069 Several fundamentally different types of model have been used to 074 study molecular properties in order to relate these to biological function 065 or activity. Most are used at some stage in this thesis, and we 071 therefore give a brief introduction to them in this section, along with 026 a review of previous work. 069 The following questions are relevant to a study of drug:receptor 013 interactions: 006 .sp 1c 006 .ll -3 006 .in 10 006 .ti -5 073 1.ZZZWhat conformations of the molecules are involved in the interaction? 006 .ti -5 073 2.ZZZGiven that we know the nature of the interaction, how is it affected 053 by the chemical structure of the component molecules? 006 .ll +3 005 .in 0 051 These questions have been answered in the past 037 using techniques which range from the 077 theoretically sound but difficult to apply, to the empirical and conceptually 073 simple. We would class studies based on quantum mechanical calculations 073 as being, perhaps, as sound as have been achieved, and an example of this 074 approach has been given by Richards*S1 *Nin his work on the histamines and 075 *Sb*N-andrenoceptor agonists. Using a relatively simple molecular orbital 069 approximation (backed up sometimes by *Iab initio *Ncalculations), he 068 found good correlation between the pharmacological activities of the 072 compounds and their predicted ability to adopt particular conformations. 071 Interestingly, the conformations which did correlate with activity were 074 not necessarily those which were preferred in solution, and this serves as 074 a good warning against building models of interactions using conformations 042 determined for the molecules in isolation. 074 However, the computational expense of performing quantum calculations 070 on large molecules, even when using fairly drastic approximations, has 053 led workers to use semi-empirical potential functions 042 which represent terms like "van der Waals" 034 interactions, and so on. Coupled 073 with numeric optimisation algorithms, these potential functions have been 070 used to help refine molecular structures derived from crystallographic 082 data*S2*N, to model protein and nucleic acid flexibility*S5 *Nand, in the field of 077 pharmacology, to study preferred conformations of drugs. Weintraub*S4 *Nhas 070 used this approach to relate the conformational proprties of compounds 071 such as acetylcholine, certain anti-epilepic drugs, narcotic analgesics 076 and the phenylethylamines and tryptamines, to their activity. His studies, 077 in fact, resulted in a complete suite of computer programs*S55 *N(**CAMSEQ**) 074 being written to perform conformational analyses on compounds of interest. 068 In a related field, Levitt*S5 *Nhas studied how the structure of DNA 070 changes in solution and when supercoiled in chromatin. The energy of 075 arbitrary conformations of the helix was defined in terms of semi-empirical 071 interaction potentials, and the structure was then allowed to relax, by 069 optimising this internal energy using a conjugate gradient algorithm. 048 His results showed that the structure adopted by 046 DNA in the solid state was not necessarily the 044 form which would be most stable in solution. 073 Whilst Richards' and Weintraub's studies have used different methods 076 for determining conformational stability, we can see that their studies were 068 related, and different from Levitt's work on DNA. In Richards' and 070 Weintraub's work, the molecules of interest were relatively small, and 067 possible variations in conformation were limited to a few torsional 071 angles; it was therefore possible to survey most of the conformational 064 space available to the molecule. By comparison, Levitt's model 073 of DNA was large, possessing some four thousand variable coordinates, and 059 his studies were limited to allowing one known conformation 068 to relax slightly into a more stable conformation. It could not be 040 said that Levitt's calculations surveyed 048 more than a fraction of the conformational space 066 available to the DNA helix; furthermore, because of the method of 047 refinement used, those conformations which were 044 generated were successively lower in energy. 070 However, Richards' work has shown that the conformations of drugs 073 which are responsible for activity may not be those found in a crystal or 071 in solution. Furthermore, there is no reason to suppose that a drug's 063 receptor, generally a large molecule possessing many degrees of 030 freedom, will remain unchanged 072 on complexing, or even that the conformations adopted will be arrived at 071 along pathways of ever-increasing stability. There may well be energy 069 barriers separating complexed and uncomplexed forms of the molecules. 075 Recently, a method has become available for modelling possible changes 072 in conformation of systems too large to be studied exhaustively, without 075 the limitation imposed by numerical optimisation techniques that successive 067 conformations be of decreasing energy. For some years, one of the 080 methods*S2 *Nused to refine molecular structures determined crystallographically 070 has involved constraining the structure to fit both its x-ray data and 075 also standard chemical quantities such as bond-lengths, angles and distance 071 of approach of non-bonded atoms. The equations determining the energy 069 penalty for changing these quantities are quadratic and relate to the 071 true potential functions only in that they give the same optimum values 066 and relative ease of distortion, but the quadratic behaviour makes 072 their solution much simpler than is possible with more precise potential 070 functions. This method of structural refinement can be used to study 070 large-scale conformational changes by replacing equations constraining 067 the structure to fit its x-ray data by others which constrain it to 070 change towards a new target conformation. Relatively little work has 074 been done using this approach, although it was used by Alden and Arnott*S3 056 *Nto study the ability of the DNA helix to extend during 061 intercalation. Their work is described in detail in chapter 002 3. 073 Perhaps the simplest, but most immediately understandable, method of 068 modelling molecular interactions on a computer is through the use of 068 interactive graphical aids. The mathematical equations used in the 071 previous methods are almost all thrown away, and the computer becomes a 052 means of presenting displays of molecular structures 058 which can be altered by means of instructions input by the 067 operator. This means that decisions about which conformations are 058 plausible are made by the human operator, perhaps aided by 029 some elementary checking from 070 the computer. Potentially, this is a very good method, since it uses 067 the human brain for a function (pattern recognition) to which it is 072 particularly well-adapted and for which current computing techniques are 073 inadequate. The method has been used for some years in crystallographic 079 applications, fitting molecular structures to electron-density maps*S6*N; once 067 again, its use in pharmacology is more recent, although it has been 076 reported*S7 *Nthat Apple has devised a new anti-cancer drug by examining the 064 interactions between an existing drug (daunomycin) and DNA using 021 interactive graphics. 002 *? *[Chapter 1.3.1*] 006 .ls 2c 006 .tg NI 005 .ul 1 033 1.3 : Methods Used for Modelling. 005 .tc : 007 .ta 56r 037 :"Then you should say what you mean," 024 :the March Hare went on. 031 :"I do," Alice hastily replied; 030 :"at least I mean what I say - 033 :that's the same thing you know." 013 :Lewis Caroll 003 .tc 006 .ls 3c 006 .tg NA 072 Whilst this thesis is entirely concerned with computer modelling of 066 molecular properties, we have attempted, as far as is possible, to 069 refrain from discussing aspects of computation along with the results 073 obtained from modelling. This is because we feel that too much emphasis 068 has frequently been placed on computerisation, and indeed there is a 069 widespread feeling that a result is good because it has been obtained 073 from a computer. This, of course, is absurd; the validity or otherwise 072 of a study is determined by the assumptions made and the equations used, 058 and the method of solution of the equations is a matter of 071 convenience only. Furthermore, as anyone who has used a computer will 055 know, the scope for error in programming is very great. 069 Nonetheless, we feel that there is considerably more to computer 038 modelling than merely coding equations 043 and then letting the computer do its stuff. 068 A model is useful because it lets its user ask appropriate questions 065 about a system and a good model represents its system in some way 073 which its user can appreciate without having to worry about side-effects. 072 This is why, for example, mechanical models, either of the space-filling 067 type, or of the framework variety, are so widely used in chemistry. 053 Quite clearly, a program which merely expresses a set 070 of equations in a form capable of solution by a computer is not a good 068 model, because the questions that program can answer are limited and 072 because the relationship between the program and the system it describes 017 may not be clear. 061 As well as this rather aesthetic point, there was also a 061 very practical reason why we wished to develop a satisfactory 066 computer model for the systems being studied. These systems were 060 large and a wide range of their properties were of interest. 065 It was not always obvious what set of equations should be used to 059 calculate a given property and, indeed, we frequently found 061 a need to make considerable changes to the equations adopted. 051 It was also found that some quantities were used in 029 quite disparate calculations. 070 We were therefore faced with producing a large amount of computer 005 .ne 4 059 software**, much of which formed a common framework for the 005 .fn 1 063 ** Computer software is the set of coded instructions which the 024 computer hardware obeys. 005 .en 1 059 various calculations performed, and we had to allow for the 067 possibility of changing parts of the framework as better techniques 061 became available. Without due care, it would have been very 065 easy for the programs to have become inconsistent or inefficient. 065 Whilst computers have become very powerful in recent years, it is 053 still easy to attempt calculations which require more 072 computation than can reasonably be done. The calculations we performed 060 frequently lay on the borderline between what was reasonable 063 and what was not. Clearly, any inefficiencies in our programs 059 would have exacerbated this problem and any inconsistencies 067 would have increased the chance of errors occurring, with resulting 036 waste of computer-time finding them. 070 Just as important as considerations of efficiency in computation, 059 though, were considerations of the time taken to encode and 065 test new pieces of program. Since all the programs used were in 058 a continual state of development, it was important to make 067 their meaning as transparent as possible. The use of clear coding 056 tends to reduce the time taken to decipher and amend old 054 material, whereas it is very difficult to be sure that 065 an ambiguous piece of coding does express what the programmer had 054 intended. Scientists frequently tend to use "tricks" 068 in their programs to speed up calculation; our experience has shown 058 that such tricks are often not worthwhile, since more time 069 is wasted in trying to make them work than is saved when they finally 067 do. (We were not immune from this tendency ourselves, so we speak 027 with considerable feeling?) 058 In this section, therefore, we shall describe the way 061 in which we attempted to endow our computer programs with the 065 characteristics of a model and show how this helped in expressing 053 ideas and in posing different types of question about 024 the systems of interest. 061 The most fundamental point was that, as far as possible, 055 we tried to avoid using FORTRAN, a programming language 060 which has found very widespread use in scientific computing. 065 This is not because FORTRAN is inherently incapable of expressing 060 the program structures that we wished to use, but because it 057 does not, by itself, provide a framework which encourages 063 clear expression of ideas and it is certainly less concise than 055 is desirable. (The reasons for this are many-fold and 068 we shall not pursue them here; the interested reader will find that 062 almost any of the computer journals contain continual argument 057 on this point.) Instead, we used one of the more recent 065 languages*S8*N, Algol-68, which allows more precise expression of 058 ideas through the facilities it provides. In particular, 060 operators can be defined to act on arbitrary data-structures 064 instead of having to deal with individual numbers or arrays, and 064 we found that the concepts involved in molecular modelling could 066 be expressed clearly in terms of such data-structures. (Algol-68 066 is fairly typical of a wide range of modern programming languages; 064 it is by no means perfect, since its attempt to be all things to 060 all men whilst still retaining a rigorous framework makes it 066 a more difficult language to learn than many, but better languages 062 which have actually been implemented are rare.) The language 064 possesses the virtue of encouraging those programming techniques 061 which allow the final program to be efficient, without making 036 the user unduly aware of this point. 064 Systems of interest in this thesis consisted of one or more 056 molecules (where "molecule" is used in a general sense, 070 meaning a collection of atoms). The atoms possessed various relevant 064 properties and the molecules containing them, as well as being a 068 collection of atoms, also had properties which were of a more global 064 nature. We found it very helpful always to consider systems in 055 this way. Properties associated with atoms which were 064 relevant to our studies included their positions, their residual 067 charges, other atoms to which they were bound and the normal values 066 of bond-lengths to these other atoms, the molecule which contained 061 them and the type of atom they were. Molecules consisted of 070 a number of atoms linked together by a set of bonds, some of which lay 060 within rings and some of which did not. Also each atom and 047 molecule was given a name, which was irrelevant 042 to the computer but which was a great help 052 in relating our thoughts to the systems of interest. 002 *? *[Chapter 1.3.2*] 065 A summary of the data-structures used to describe atomic and 062 molecular properties is given in figure 1.8. Note that these 046 structures are pragmatic, since they allow the 058 programmer to relate information with which he is familiar 060 to the functional information which the programs will use in 050 calculations. They are also in a sense abstract, 057 because storing the bonding information in the way chosen 041 joined the individual atomic descriptions 046 together into a "graph", which led very simply 059 to using graph-theoretic algorithms for determining certain 011 properties. 059 All calculations relating to the positions of atoms in 005 .ne 9 077 the molecular systems were performed using an explicit vector notation*t***l. 005 .fn 1 072 *t** *lThe vector algebra required to perform the calculations described 064 in this thesis is relatively straightforward and can be found in 064 standard mathematical textbooks, or, for example, in the book by 071 Hopfinger*S9*N. The only place where difficulties may arise is in the 058 form of the matrix required to perform a rotation about an 070 arbitrary axis; this matrix was derived by Gibbs*S10*N, and is given, 041 in explicit form, in Ford's*S11 *Nthesis. 005 .en 1 065 We defined the notion of a vector in three dimensions (see figure 063 1.8) and then defined various standard operators which acted on 066 vectors, such as *D+ - VEC *Nand *DDOT *N(where the last two stand 044 for vector and scalar product respectively). 059 These definitions of data-types and vector operators, along 064 with a few basic procedures and operators relating to *DATOM*Ns, 067 *DMOLECULE*Ns and *DBOND*Ns provided the framework for the programs 008 written. 062 We discovered very early on in our studies that much time 076 could be wasted in setting up coordinate data for molecules. Consequently, 063 we defined a format for such data which was used throughout the 066 programs written and which specified a bare minimum of information 057 about the molecules concerned. This format consisted of 060 a molecule's name followed by the number of atoms in it, and 066 then, for each atom in the molecule, an arbitrary name, its atomic 055 number, a position vector and, optionally, its residual 064 charge and a name relating it to a sub-group of atoms within the 059 molecule. This last item was purely pragmatic; when, for 064 example, we wished to analyse the interactions occurring between 052 two molecules, we found it more useful to give these 064 component interactions in terms of the sub-groups we had defined 067 rather than allowing the programs to decide for themselves what was 063 useful. With one exception, all other information required by 049 the programs was generated by themselves from the 060 atoms' coordinates and their atomic numbers. The exception 061 was the bonding structure within a molecule, since there were 064 situations where we wished to refine the structure of a molecule 061 whose starting coordinates corresponded to a very high energy 040 conformation, owing to the juxtaposition 020 of non-bonded atoms. 052 In such cases, determining the bonding automatically 065 could result in error, and so we allowed such bonding information 051 to be provided with the coordinate data if desired. 070 The evaluation of the remaining data required by the programs was 063 straightforward, but frequently used recursive algorithms. We 033 shall describe one of these here. 037 A method examined for optimising 057 the structure of a molecular complex involved considering 064 each molecule as a set of groups connected through bonds capable 062 of allowing some degree of free rotation about themselves, and 059 treating the variables of the optimisation as being the set 067 of torsional angles about these bonds. Before this could be done, 068 it was necessary to find out which bonds would allow rotations about 054 themselves. The algorithm we used for locating these 058 "rotatable bonds" was typical of algorithms encountered in 064 graph theory, but rarely found in other fields. More important 059 than its origin, though, is the fact that it determined the 065 complete set of rotatable bonds in one scan through the molecular 059 graph, in a time which varied linearly with the size of the 059 molecule. The speed of more conventional algorithms would 064 probably vary with the square of the size of the molecule, which 061 could result in a considerable overhead with large molecules. 059 Because of the unusual nature of this algorithm and because 054 of its utility, we quote it in figure 1.9; we make no 056 claims about its originality, although we have not found 031 it elsewhere in the literature. 063 Six main computer programs were used to carry out the work 051 described in this thesis, along with others written 067 for "one-off" calculations, usually to perform structural analyses. 067 Two of these main programs were obtained from other sources, whilst 059 the remaining four were written by ourselves. We consider 053 it to be a very favourable reflection on the value of 060 recent programming languages, and on Algol-68 in particular, 059 that writing and correcting about fifteen thousand lines of 048 code took only some twelve man-months of effort. 063 The programs obtained from other sources included one used 060 to perform quantum calculations by means of the CNDO or INDO 076 approximation*S12 *Nand another*S13 *N(**PLUTO**) which produced pictures of 052 molecular structures such as those contained in this 060 thesis. Little change was made to these, except to correct 062 a few mistakes in the quantum program, to increase the maximum 060 size of molecule on which calculations could be done, and to 061 change the graphical routines in **PLUTO** to those available 027 on the University computer. 061 Of the other programs, three were based on the framework 069 described above, and were the most frequently used. One, relatively 066 short, was used to produce approximate structures for molecules of 048 interest geometrically. Initially, we obtained 061 structures for compounds from published crystallographic data 058 using the Cambridge crystallographic data-files*S13*N, and 063 it was necessary to add hydrogen coordinates to these. Later, 051 however, we found that we wished to study analogues 062 of these molecules for which no structural data was available. 069 This program was capable of generating coordinates for commonly-found 066 groups of atoms using standard bond-lengths and angles, which were 067 then added to the starting coordinates to form the new molecules of 059 interest. Although molecular structures generated in this 070 way were not expected to be totally accurate, the error was considered 012 unimportant. 062 Another program, used to produce the results described in 056 chapter 3, allowed us to impose various constraints onto 061 a molecular system and to determine how the structure of that 057 system would change to satisfy them. It was possible to 061 describe fairly arbitrary limitations on molecular structures 067 in terms of constraints on the position of one atom or the relative 071 positions of two atoms, forcing a value to remain constant or to change 064 to a new value, and each constraint was associated with a weight 052 which ensured that the structural changes took place 031 in a chemically reasonable way. 067 The next program was used to refine the structure of molecular 061 complexes by optimising the energy of interaction between the 060 component molecules. Methods used to evaluate energies are 067 described in chapter 2, and optimisation techniques and the results 067 obtained using them are described in chapter 5. Various different 045 types of refinement could be requested, using 062 control instructions given to the program, and the program was 064 also capable of analysing the interactions present in a complex. 062 The final program, which provided an interactive graphics 046 facility, is described in detail in chapter 4. 061 Most of the computation was done on an ICL 1906A machine 065 provided by the Oxford University Computing Service. This was a 056 moderately powerful, general-purpose machine with a good 060 operating system providing a wide range of facilities. For 067 those unaware of such matters, we would point out that time on this 061 machine costs about four hundred pounds an hour commercially. 044 The calculations we performed used about two 065 hundred hours of machine-time. Whilst it is somewhat misleading 062 to talk about the cost of this time, since the facilities were 062 provided to us free of charge, the cost was real in one sense. 064 For most of the time during our studies, the computing machinery 061 was overloaded with work, which meant that both the amount of 060 calculation we could do and the rate at which we could do it 067 were less than we would have wished. Many potentially interesting 061 calculations have had to be left undone, and we would ask the 064 reader to bear this in mind whenever it appears that an argument 061 could have been made more convincing had they been performed. 002 *? *[Chapter 1 Refs and Tables*] 006 .ls 2c 006 .tg NA 003 .nj 003 .nf 048 *DMODE VECTOR *N= *DSTRUCT *N( *DREAL *Nx,y,z ); 028 *DMODE ATOM *N= *DSTRUCT *N( 070 *D\ *Npragmatic information *D\ STRING *Nname, section (ie which bit 065 of the molecule the atom is in) 063 *D\ *Nfunctional information *D\ VECTOR *Ncoord, initial coord, 065 *DINT *Natomic number, no in molecule, 043 *DREAL *Ncharge, 067 *D[]REAL *Nbondlengths, next neigh dist, 062 . . . . (various terms to optimise 060 energy calculations) 052 *D\ *Nabstract information *D\ REF MOLECULE *Nmol, 066 *D[]REF ATOM *Nbonded, next neigh (thus 057 forming a graph), 062 *D[]REF BOND *Nrotation moving atom 060 (actually coded as a 064 bit-pattern, for economy) 062 . . . . (various terms storing the 059 atom's environment) 021 ); 057 *DMODE BOND *N= *DSTRUCT *N( *DREF ATOM *Nend 1, end 2 ); 070 *DMODE MOLECULE *N= *DSTRUCT *N( *DSTRING *Nname, *DREF[]ATOM *Natoms, 059 *DREF[]BOND *Nrotatable bonds); 081 *DMODE LIST *N= *DSTRUCT *N( *DREF BOND *Nbond, *DREF LIST *Nlast) *D\ *Nprovides 066 a structure for graph-theoretic algorithms *D\ 007 *N.ul 1 006 .tg NI 058 Figure 1.8 : Data Structures used for Molecular Modelling. 003 .bp 006 .tg NA 003 .nj 003 .nf 051 *DPROC *Nwalk = ( *DREF ATOM *Ncurrent, last ): 028 ( *DREF ATOM *Nnext; 037 met *DOF *Ncurrent := TRUE; 057 *DFOR *Nk *DTO *NUPB bonded *DOF *Ncurrent *DDO 057 *Nnext := (bonded *DOF *Ncurrent)*D[*Nk*D]*N; 076 *DIF *Nnext *DISNT *Nlast *DAND NOT *Ntraversed((current, next)) 018 *DTHEN 048 *Nmark traversed((current, next)); 045 store *DPLUS *N(current, next); 043 *DIF *Nmet *DOF *Nnext *DTHEN 038 REF LIST *Nb := store; 070 *DWHILE *Nend1 *DOF *Nbond *DOF *Nb *DISNT *Nnext *DDO 053 *Nbondlist *DMINUS *Nbond *DOF *Nb; 036 b := last *DOF *Nb 023 *DOD*N; 048 bondlist *DMINUS *Nbond *DOF *Nb 020 *DELSE 037 *Nwalk(next, current) 021 *DFI*N; 027 *DDEC *Nstore 016 *DFI 012 OD 012 *N); 056 *DLIST *Nbond list := list of all bonds in molecule, 037 store := (*DNIL*N, *DNIL*N); 049 *DREF ATOM *Na := arbitrary atom in molecule; 023 walk( a, *DNIL *N); 003 .ju 003 .fi 006 .tg NI 065 Figure 1.9 : Algorithm to locate "rotatable bonds" in a molecule. 067 This algorithm is given in a "pigeon" Algol-68, which reflects 067 the form of the finished code and the succinctness of the language, 063 without worrying too much about technicalities. We assume the 047 existence of the data-types proviously defined, 067 and also the following operators acting on *DLIST*N-type variables: 050 *DPLUS*N, to add a new bond to the end of the list 070 *DMINUS*N, to remove a bond from the list wherever it might occur, and 046 *DDEC*N, to remove the top bond from the list. 068 After executing the call of "walk" in the last line, "bondlist" 063 contains just those bonds in the molecule which are potentially 010 rotatable. 003 .bp 003 .nj 003 .nf 006 .tg NI 006 .ls 3c 005 .ul 1 025 References for Chapter 1. 006 .tg NA 061 1. Richards W.G. et al *IPhil.Trans.R.Soc.Lond. *DB_2_7_2_ 021 *N(1975) 75 059 2. Isaacs N.W. et al *IActa Cryst. *DA_3_2_ *N(1976) 311 066 3. Alden C.J. and Arnott S. *INucl.Acid Res. *D2_ *N(1975) 1701 067 4. Weintraub H.J.R. *I"Applications of Theoretical Conformational 058 Analysis in Drug Design" Ph.D. Thesis *N(1975) 047 Case-Western Reserve University, USA. 059 5. Levitt M. *IProc.Nat.Acad.Sci.USA *D7_5_ *N(1978) 640 063 6. Diamond R. is at the Medical Research Council Laboratories, 032 Hills Road, Cambridge. 053 7. Reported in the *INew York Times*N, 9th May 1978. 064 8. van Wijngaarden A. *I"Revised Report on Algol-68" *N(1976) 025 Springer-Verlag 067 9. Hopfinger A.J. *I"Conformational Properties of Macromolecules" 033 *N(1973) Academic Press 062 10. Gibbs J.W. *I"Vector Analysis" *N(1901) Yale Univ. Press 045 11. Ford L. *ID.Phil. Thesis *N(1974) Oxford 062 12. Pople J.A. and Beveridge *I"Approximate Molecular Orbital 039 Theory" *N(1970) McGraw-Hill 054 13. Kennard O. is at the Crystallographic Data Centre, 061 University of Cambridge, Lensfield Road, Cambridge. 059 14. Various papers in *I"The Acridines"*N, ed Acheson R.M., 065 volume 9 in the series *I"The Chemistry of Heterocyclic 035 Compounds" *N(1973) Wiley 062 15. Ehrlich P. and Benda L. *IChem.Ber. *D4_6_ *N(1913) 1931 061 16. Shiga K. *IZ.Immun.Forsch.Exp.Theory *D1_8_ *N(1913) 65 048 17. Albert A. *I"The Acridines" *N(1966) Arnold 058 18. Giglio E. et al *INuova Cimento *D5_6_B_ *N(1968) 57 040 19. Wright R.G. *IPrivate Communication 050 *N20. Lerman L.S. *IJ.Mol.Biol. *D3_ *N(1961) 18 067 21. Neville D.M. and Davies D.R. *IJ.Mol.Biol. *D1_7_ *N(1966) 57 058 22. Pritchard N.J. et al *INature *D2_1_2_ *N(1966) 1360 050 23. Damiani A. *IJ.Mol.Biol. *D2_0_ *N(1966) 211 054 24. Seeman N.C. et al *INature *D2_5_3_ *N(1975) 324 059 25. Leng M. *IPhysico-Chemical Properties of Nucleic Acids 026 *D3_ *N(1973) 20 065 26. Watson J.D. and Crick F.H.C. *INature *D1_7_1_ *N(1953) 737 059 27. Sobell H. *IProc.Nat.Acad.Sci.USA *D7_2_ *N(1975) 628 052 28. Neidle S. et al *INature *D2_6_9_ *N(1977) 304 065 29. Konopa J. et al *IMateria Medica Polona *D2_8_ *N(1976) 258 053 30. Cairns J. *ICold Spring Harbour Symp.Quant.Biol. 029 *D2_7_ *N(1962) 311 057 31. Page E.S. *IJ.Roy.Statis.Soc. *DB_2_1_ *N(1959) 364 052 32. Bond P.J. et al *IProc.Nat.Acad.Sci.USA *D7_2_ 023 *N(1975) 4825 064 33. Gilbert M. and Claverie P. *IJ.Theor.Biol. *D1_8_ *N(1968) 013 330 057 34. Arcamone F. et al *IJ.Med.Chem. *D1_8_ *N(1975) 703 063 35. Patel D.J. and Canuel L.L. *IProc.Nat.Acad.Sci.USA *D7_4_ 023 *N(1977) 2624 063 36. Neidle S. *I"Progress in Medicinal Chemistry" *N(in press) 067 37. Le Pecq B. et al *IProc.Nat.Acad.Sci.USA *D7_2_ *N(1975) 2915 066 38. Wakelin L.P.G. et al *IStudia Biophysica *D6_0_ *N(1976) 111 043 39. Wakelin L.P.G. *IPrivate Communication 064 *N40. Fuller W. and Waring M.J. *IBer.Bunsen.Phys.Chem. *D6_8_ 022 *N(1964) 805 059 41. Wakelin L.P.G. and Waring M.J. *IMol.Pharmacol. *D1_0_ 022 *N(1974) 544 059 42. Di Marco A. and Arcamone F. *IArzneim.-Forsch. *D2_5_ 022 *N(1975) 368 065 43. Zuino F. et al *IBiochem.Biophys.Acta *D2_7_7_ *N(1972) 489 063 44. Pigram W.J. et al *INature New Biol. *D2_3_5_ *N(1972) 17 060 45. Doskocil J. and Fric I. *IFEBS Letters *D3_7_ *N(1973) 012 55 063 46. Henry D.W. in *I"Cancer Chemotherapy"*N, ed Sartorelli A.C. 042 (1976) American Chemical Society 068 47. Zuino F. et al *IBiochem.Biophys.Res.Comm. *D6_9_ *N(1976) 744 057 48. Lenaz L. et al *ICancer Chemotherapy Reports *D5_8_ 022 *N(1974) 769 061 49. Neidle S. and Taylor G. *IBiochem.Biophys.Acta *D4_7_9_ 022 *N(1977) 450 064 50. Barthelemy-Clavey V. et al *IBiochimie *D5_5_ *N(1973) 859 055 51. Kersten W. et al *IBiochemistry *D5_ *N(1966) 236 062 52. Phillips D.R. et al *IEur.J.Biochem. *D8_5_ *N(1978) 487 049 53. Wang J.C. *IJ.Mol.Biol. *D8_9_ *N(1974) 783 051 54. Waring M.J. *IJ.Mol.Biol. *D5_4_ *N(1970) 247 061 55. Weintraub H.J.R. and Hopfinger A.J. *IInt.J.Quant.Chem., 045 Quant.Biol.Symp. *D2_ *N(1975) 203 050 56. Kennard O. et al *INature *N2_7_3_ (1978) 687 064 57. Arnott S. in *I"Proceedings of the first Cleveland Symposium 062 on Macromolecules"*N, ed Walton H.G. (1977) Elsevier 055 58. Schwartz I.S. *I"Interaction of Daunomycin and DNA" 051 Ph.D. Thesis *N(1974) City Univ. New York 062 59. Paoletti J. and Le Pecq B. *IJ.Mol.Biol. *D5_9_ *N(1971) 012 43 057 60. Pigram W.J. et al *IJ.Mol.Biol. *D8_0_ *N(1973) 361 063 61. Waring M.J. in *I"The Molecular Basis of Antibiotic Action" 051 *N62. Wang J.C. *IJ.Mol.Biol. *D8_9_ *N(1974) 783 068 63. Waring M.J. and Henley S.M. *INucl.Acid.Res. *D2_ *N(1975) 567 056 64. Crick F.H.C. et al *INature *D1_9_2_ *N(1961) 1227 052 65. Sanger F. et al *INature *D2_6_5_ *N(1977) 687 062 66. Freese E. *IBrookhaven Symp. in Biol. *D1_2_ *N(1959) 63 054 67. Brenner S. et al *IJ.Mol.Biol. *D3_ *N(1961) 121 052 68. Roth J.R. *IAnn.Rev.Genetics *D8_ *N(1974) 319 053 69. Streisinger G. cited by Drake J.W. and Baltz R.H. 041 *IAnn.Rev.Biochem. *N(1976) 11 047 70. Wright R.G. *ID.Phil. Thesis (1978) Oxford 050 71. Rein R. in "Intermolecular Interactions : From 059 Diatomics to Biopolymers", *Ned Pullman B. (1978) 015 Wiley 064 72. Robinson B.H. *IJ.Chem.Soc.Faraday Trans.1 *D6_9_ *N(1973) 012 56 002 *? ****