*[Chapter 6.1*] 006 .tg NI 005 .ul 1 059 Chapter 6 : Other Factors Affecting Molecular Interactions. 005 .tc : 007 .ta 56r 027 :"Non omnia possumus omnes" 018 :Virgil, Eclogues. 003 .tc 006 .tg NA 065 In this chapter, we shall discuss certain limitations of the 060 methods used to study intercalation. The chapter is brief, 060 even though the points not considered far outnumber the ones 060 we did consider, because it is merely intended to illustrate 019 these shortcomings. 006 .tg NI 005 .ul 1 016 6.1 : Solvation. 006 .tg NA 066 The major criticism of the methods of conformational analysis 059 used must be that they ignore completely the effects of the 070 environment. This environment includes not only the solvent (water), 070 but also salt ions, and the influence that these have on intercalation 069 is demonstrated clearly by the variation in the degree of interaction 067 with ionic strength*S1*N. Also, the values calculated in the last 055 chapter for the interaction energy between acridines or 063 anthraquinones and nucleic acid were generally over an order of 069 magnitude greater than the overall enthalpies measured experimentally 037 by Quadrifoglio*S2 *N(see table 6.1). 062 Thirdly, compounds generally intercalate only when protonated, 067 and it is therefore important to know whether an arbitrary compound 066 will be protonated under physiological conditions before it can be 068 postulated as a DNA-binding drug. Peradejordi*S27 *Nfound that the 065 change in interaction with the solvent environment on protonation 063 was as important in determining a compound's pK*dA *las was the 069 *Iin vacuo *Ndifference in energy between protonated and unprotonated 044 Examination of a simple Born-Haber cycle for 055 the intercalation process (figure 6.1) demonstrates the 030 importance of solvation terms. 064 Methods available for modelling solvent behaviour fall into 065 three types: continuum, discrete and empirical techniques. The 071 first two are discussed briefly by Richards*S3 *Nand by Claverie*S14*N, 068 whilst the third is discussed by Hopfinger*S4*N. Continuum methods 059 treat the solvent as a continuous medium, and, although the 065 interaction energy between solvent and solute should be expressed 060 as a series of terms in much the same way as we split up the 061 interaction between two molecules, it has been most common to 061 consider only an electrostatic interaction between the charge 064 distribution on the solute and a polarisable dielectric solvent. 051 This is described in terms of the Laplace equation: 006 .sp 1c 005 .ce 1 019 *SV*N*t2*S*ly *N= 0 006 .sp 1c 056 if the solvent is pure and homogeneous, or in terms of a 066 combination of Laplace and Poisson equations, where the latter is: 006 .sp 1c 005 .ce 1 024 *SV*N*t2*S*ly *N= *Ik*Sy 008 *N.sp 1c 053 if some attempt is made to consider saline solutions. 068 The differential equations are solved subject to the condition that, 066 at the interface between solvent and solute, the potential and the 066 component of its derivative normal to the interface be continuous. 064 This approach can work well if the interface possesses high 066 symmetry. For example, Gilbert and Claverie*S5 *Nused the method 063 to study the variation in interaction between acridines and DNA 026 with ionic strength, using 062 a cylindrical model of the complex, and describing the solvent 060 observed change in degree of association with ionic strength 049 was predicted from the solution to the equations. 068 However, the utility of the method is limited by the complexity 065 of the equations when the boundary conditions do not possess high 066 symmetry. For a spherical cavity*S6*N, the calculation is quick; 059 for example, with a molecule containing about thirty atoms, 067 some twenty seconds computer-time is required. For an ellipsoidal 067 cavity*S7*N, this increases about a thousand-fold, depending on the 067 size of the molecular system. In the general case*S8*N, where the 061 cavity shape is defined in terms of a set of basis functions, 065 the calculation becomes prohibitive for more than very few atoms. 055 It is also not possible to obtain reliable results if a 061 molecule is treated as having higher symmetry than it in fact 071 does have*S7*N. Some checks we made, where we evaluated the solvation 067 energies of acridines by assuming that they were spherical, yielded 061 results which were typically an order of magnitude too small. 066 Discrete models treat the solvent environment in the same way 061 as the solute, as a set of molecules which interact according 061 to defined potential functions. This type of calculation is 065 not only made more complex by the large number of molecules which 066 must be considered (for example, it would probably be necessary to 081 include between 10*t4 *land 10*t5 *lmolecules around a dinucleotide intercalation 005 .ne 4 033 complex to obtain a statistically 052 reasonable sample of the solvent environment*t***l), 005 .fn 1 068 *t** *lThe electrolyte content of cellular fluid is equivalent to an 058 approximately 0.6 molar solution of sodium chloride*S15*N. 005 .en 1 057 cannot be treated as having only one important structure. 065 Also the limitations in semi-empirical potential functions of the 054 type used in chapter 5 become much more important when 060 applied to systems of many molecules. This has limited the 048 application of discrete models to small systems. 064 Barker*S9 *Nhas calculated the properties of water, sampling the 064 configurations available to sixty four water molecules using the 063 Monte-Carlo technique and evaluating energies semi-empirically, 059 and has found good agreement between theory and experiment. 070 Mruzik*S10 *Nused much more complex potential functions, parameterised 067 to agree with *Iab initio *Ncalculations, in his study of ion-water 064 clusters and produced results which described well the behaviour 062 of heavy ions, such as potassium, but which were less accurate 061 in their descriptions of light ions. It is not obvious that 062 this type of approach will lead to successful treatment of the 065 solvation proerties of pharmacologically important species in the 044 foreseeable future; the computational power 030 required is unlikely to become 055 available, even if accurate descriptions of energies of 027 interaction can be devised. 058 One method of simplifying a discrete model of solvent 060 environment around a complex is to consider only those sites 064 on the complex to which solvent is likely to be bound. This is 070 the so-called supermolecule approach*S11 *Nand Richards*S3 *Ndescribes 063 its application to the study of *Sg*N-aminobutyric acid (GABA). 063 PCILO calculations performed on a hydrated GABA molecule reveal 065 several regions of stability for the molecule, whilst nmr studies 066 However, Richards warns against reading too much into this result. 060 A combination of supermolecule and continuum models has been 043 developed by Beveridge and Schnuelle*S17*N. 062 Empirical methods for estimating solvation energies carry 059 the supermolecule approach one step further. For example, 067 Hopfinger's*S4 *Nmodel considers the existence of a hydration shell 064 around atoms in complexes of interest. The solvation energy of 067 a given configuration of a complex is determined by calculating how 069 much of the volume of each atom's hydration shell is still accessible 064 to solvent and multiplying this by a figure corresponding to the 067 total solvation energy of that atom. The total solvation energies 066 of individual atom types have been determined using semi-empirical 063 methods similar to those described in chapter 2 of this thesis. 068 Hopfinger claims that the method gives good results; in particular, 005 .ne 5 052 partition coefficients between octanol and water*t** 007 *l.fn 1 073 *t** *lThe partition coefficient between octanol and water has frequently 056 been used as a measure of how well a drug will penetrate 015 cell membranes. 005 .en 1 064 were well predicted*S13 *Nusing this method. We performed some 061 calculations on acridine:dinucleotide intercalation complexes 064 using Hopfinger's method and found that the values obtained were 066 unreliable; in particular, unprotonated acridines were frequently 065 found to show a greater loss in solvation energy on intercalation 035 than their protonated counterparts. 063 In essence, what we are saying is that currently available 055 techniques cannot be used to study solvation properties 058 simple cases. It seems unlikely that the improvements in 067 computational power which are likely in the next few years will, by 034 themselves, change this situation. 002 *? *[Chapter 6.2*] 006 .tg NI 005 .ul 1 058 6.2 : Inadequacies in the In Vacuo Interaction Potentials. 006 .tg NA 061 These are many-fold, and it would be foolish to dwell on 063 them. A review of theoretical work on the DNA molecule, which 060 is probably the most relevant review available as far as the 061 work described in this thesis is concerned, has been given by 057 Rein*S16 *Nand describes limitations in detail. In this 058 section, we shall discuss two aspects of the intercalation 061 phenomenon which require more sophisticated treatment than we 031 have been capable of providing. 069 Some intercalating agents, in particular actinomycin*S17*N, bind 071 very specifically to regions of nucleic acid containing G-C base-pairs, 070 whereas others, such as daunomycin, have shown differnt specificities, 061 or even a lack of specificity. The behaviour of actinomycin 064 has been explained*S17 *Nin terms of an ability to hydrogen-bond 026 specifically to G-C pairs. 057 In chapter 5, we saw three reasons why a specificity 058 for a particular base-pair sequence could arise: firstly, 061 because of electrostatic effects, secondly, because of steric 062 effects, and thirdly, because of an ability to bind covalently 059 to certain bases. For example, the charge distribution on 061 nitro-acridines could overlap favourably with a complementary 068 distribution on G-C base-pairs. Althernatively, if the nitro-group 059 were reduced to the hydroxylamine, then covalent binding to 052 intercalation required a purine base adjacent to the 067 phosphate group to which the amino-group bound, for steric reasons. 060 A fifth reason has been suggested, on the basis of good 067 experimental evidence, as to why base-pair specificity might arise. 065 Muller and Crothers*S21 *Nstudied the binding to DNA of acridines 048 and their analogues containing heteroatoms other 067 than nitrogen, and found a clear correlation between the preference 061 for G-C base-pairs and the position of the visible absorption 056 band of the chromophore, implying a relationship between 054 binding and polarisability. This was rationalised by 060 recognising the greater polarity of the G-C pair than of the 062 A-T pair. Muller's results were analysed further by Sharples 057 and Brown*S22*N, who agreed with the previous conclusion. 067 Muller's results suggested that the specificity of actinomycin 061 binding was due to the polarisability of actinomycin, and not 059 to its ability to form specific hydrogen-bonds. The truth 064 is probably that the five factors mentioned above, static charge 062 overlap, ability to hydrogen-bond, ability to bond covalently, 059 steric hindrance, and polarisability, all play some part in 060 determining the specificity of binding of different drugs to 066 particular base-pair sequences. However, the empirical potential 059 functions we have used in this thesis, and which many other 058 workers have used, could not demonstrate the dependence on 053 polarisability, because they do not take into account 037 charge : induced charge interactions. 067 The calculations we described in chapter 3, on the flexibility 055 of the DNA helix, showed no tendency to produce the two 069 commonly found in crystallographic studies, and unusual patterns have 068 also emerged from other theoretical work, for example that performed 064 by Levitt*S24*N. The dominance of these patterns had led other 067 workers*S23 *Nto constrain models of the DNA molecule to retain one 068 or other of these pucker patterns. Only recently has a theoretical 025 study*S25 *N(based on the 058 PCILO quantum mechanical approximation) suggested that the 059 experimentally-observed pucker patterns are indeed the most 062 stable shapes available, but even this study found very little 056 energy penalty to attaining any of the possible puckers. 063 It is important to realise that, even though certain structural 064 attributes appear experimentally to be very much associated with 066 particular molecules, there may be little difference in the energy 058 of the molecules, with or without those attributes, and to 041 impose strong constraints to retain those 056 structural attributes may well cause much more important 044 properties of the molecule to go undetected. 058 These two examples are typical of the shortcomings of 056 studies performed on macromolecules using semi-empirical 069 potential functions. Pullman*S26 *Nis fairly scathing of the use of 057 these functions and prefers PCILO calculations, which are 063 frequently found to predict correctly fine details of molecular 062 structure. However, the systems we have studied were too big 062 for a quantum mechanical approach to be adopted; indeed, some 067 of the larger calculations were nearly too big for a semi-empirical 058 approach, a point which should have been quite apparent in 060 the limited number of calculations described in the previous 023 chapter. Nonetheless, 006 .tg NI 036 provided care is taken in their use, 049 semi-empirical potential functions can be used to 057 obtain some measure of understanding of the properties of 014 large systems. 002 *? *[Chapter 6 Refs and Tables*] 003 .bp 006 .pl 63 006 .tg NI 005 .ul 1 024 References for Chapter 6 006 .tg NA 057 1. Drummond D.S. et al *IBiopolymers *D3_ *N(1965) 135 059 2. Quadrifoglio F. and Crescenzi V. *IBiophys.Chem. *D2_ 021 *N(1974) 64 053 3. Richards W.G. *I"Quantum Pharmacology" *N(1977) 022 Butterworths 067 4. Hopfinger A.J. *I"Conformational Properties of Macromolecules" 033 *N(1973) Academic Press 068 5. Gilbert M. and Claverie P. *IJ.Theor.Biol. *D1_8_ *N(1968) 330 058 6. Weintaub H.J.R. *IPh.D. Thesis *N(1975) Case-Western 028 Reserve University 061 7. Harrison S.W. et al *IJ.Phys.Chem. *D8_0_ *N(1976) 2580 061 8. Huron M. and Claverie P. *IJ.Phys.Chem. *D7_8_ *N(1974) 070 9. Barker J.A. and Watts R.O. *IChem.Phys.Letters *D3_ *N(1969) 144 058 10. Mruzik M.R. et al *IJ.Chem.Phys. *D6_4_ *N(1976) 481 065 11. Pullman A. and Pullman B. *IQ.Rev.Biophys *D7_ *N(1975) 505 061 12. Beveridge D.L. and Schnuelle G.W. *IJ.Phys.Chem. *D7_8_ 023 *N(1974) 2064 062 13. Hopfinger A.J. and Battershell R.D. *IJ.Med.Chem. *D1_9_ 022 *N(1976) 569 067 14. Claverie P. in *I"Intermolecular Interactions"*N, ed Pullman B. 019 (1978) 69 057 15. Fulton *I"Textbook of Physiology" *N(1950) Saunders 063 16. Rein R. in *I"Intermolecular Interactions"*N, ed Pullman B. 020 (1978) 307 064 17. Sobell H.M. and Jain S.C. *IJ.Mol.Biol. *D6_8_ *N(1972) 21 055 18. Kersten W. et al *IBiochemistry *D5_ *N(1966) 236 063 20. Schwartz I.S. *IPh.D. Thesis *N(1974) City Univ. New York 070 21. Muller W. and Crothers D.M. *IEur.J.Biochem. *D5_4_ *N(1975) 267 066 22. Sharples D. and Brown J.R. *IFEBS Letters *D6_9_ *N(1976) 37 065 23. Alden C.J. and Arnott S. *INuc.Acid Res. *D2_ *N(1975) 1701 059 24. Levitt M. *IProc.Nat.Acad.Sci.USA *D7_5_ *N(1978) 640 060 25. Saran A. et al *ITheoret.Chem.Acta. *D3_0_ *N(1973) 31 066 26. Pullman B. in *I"Quantum Mechanics of Molecular Conformations" 039 *Ned Pullman. B. (1976) Wiley 054 27. Peradejordi F. *ICahier Rev. *D1_7_ *N(1963) 435 002 *? *[Chapter 7.1*] 006 .ls 2c 006 .tg NI 005 .ul 1 024 Chapter 7 : Conclusions. 005 .tc : 007 .ta 56r 031 :"I am not bound to please thee 018 :with my answers." 039 :"The Merchant of Venice", Shakespeare 003 .tc 006 .ls 3c 006 .tg NA 062 In this chapter, we shall draw conclusions, firstly about 028 the intercalation phenomenon 034 and secondly about the application 058 of computer modelling in general to the study of molecular 013 interactions. 006 .tg NI 005 .ul 1 020 7.1 : Intercalation. 006 .tg NA 056 Perhaps the most obvious result to appear about the 024 intercalation phenomenon 053 is that, far from being rigid and well-defined, it is 064 a very flexible interaction which can vary appreciably depending 057 on conditions. The precise amount of helical unwinding, 021 the exact orientation 065 and position of the intercalated chromophore, and the specificity 064 of binding to particular regions of nucleic acid are all seen to 071 depend on fairly subtle interactions between the constituent molecules. 047 values for helical unwinding given in table 3.1 070 cover a wide range of values, kinetic studies*S1 2 *Non the binding of 058 proflavine, ethidium and 9-aminoacridine suggest different 064 mechanisms in each case, and the specificity of binding shown by 067 daunomycin seems to change with every experiment that is performed. 047 Some points are clear, however. Firstly, 066 "neighbour-exclusion" is seen to arise from the inability of sites 058 adjacent to already-extended sites to extend. This seems 064 a much more reasonable explanation than that proposed by Gilbert 066 and Claverie*S3*N, who suggested that the mutual repulsion between 058 two protonated acridines 6.72A apart would destabilise the 060 complex. No doubt some destabilisation does occur, but the 066 fact that protonated acridines, by themselves, stack 3.5A apart in 071 solution*S12 *Nshows that this repulsion cannot be dominant. Equally, 062 the preference shown by some acridines for pyrimidine-(3'-5')- 003 .jo 064 purine sequences*S4 *Nof nucleic acid may provide another reason 069 why intercalation does not take place at adjacent sites, but it seems 052 unlikely, in view of the wide range of specificities 053 shown by different intercalating agents, that this is 046 always going to result in neighbour-exclusion. 068 Secondly, constraints imposed on the structure of the complexes 065 by secondary features in the structure of the intercalating agent 066 can result in specific interactions being possible. For example, 058 substituting the various n-nitro-9-aminoacridines on their 063 amino-groups with a side chain that constrains the intercalated 062 complex to adopt a Lerman-type configuration produces one very 051 compounds, because in one case, a metabolite of the 059 drug is ideally placed in the complex to bind covalently to 069 the nucleic acid. Analogues of daunomycin, in which the disposition 063 of the amino-group relative to the chromophore has changed, are 062 found*S5 *Nto have reduced anti-tumour properties and previous 062 explanations*S14 *Nof this have stressed the importance of the 069 electrostatic amino-phosphate interaction in stabilising the complex. 056 However, our results have suggested that the interaction 061 energy between the aromatic chromophore and nucleic acid was, 066 by itself, comparable to the total interaction between an acridine 068 and nucleic acid, and was made up more from (hydrophobic) dispersion 025 terms. We would suggest 062 that the requirement for the disposition of the amino-group is 051 caused more by the fact that the initial binding of 067 daunomycin to DNA places the chromophore in a position where it can 070 intercalate readily, rather than by a requirement for an electrostatic 057 binding to stabilise the complex. (The lack of activity 067 in aglycone derivatives of daunomycin*S5 *Nis presumably due to the 046 fact that this external binding never occurs.) 062 We should like to end our discussion of the intercalation 059 phenomenon with some suggestions on how the results we have 048 obtained could be applied to the process of drug 007 design. 064 An ideal drug for treating cancer would be a compound which 063 exhibited strong toxicity to tumour cells whilst leaving normal 068 cells unaffected. Daunomycin and adriamycin both possess the first 066 property (although adriamycin shows a broader spectrum of activity 044 than does daunomycin), but are very toxic to 069 loss, and application of these drugs is limited by the seriousness of 071 the side-effects. It has been suggested*S6 *Nthat daunomycin toxicity 067 is due to a structural similarity between its anthraquinone residue 069 and the quinone part of compounds like coenzyme Q*T10*N, which causes 058 the drug to inhibit mitochondrial enzymes. Consequently, 020 daunomycin analogues 065 with some functionality other than an anthraquinone residue could 035 possess more favourable properties. 066 The strong intercalative binding of daunomycin and adriamycin 059 appears to be responsible, at least in part, for the drugs' 055 anti-tumour properties. It is unfortunate that normal 075 cells are also affected by cytotoxic drugs, something which is demonstrated 069 all too clearly by the long list of side effects associated with each 076 drug*S17*N. This means that it is not necessarily advantageous to increase 071 the strength of binding of a drug to DNA, for this might merely produce 072 a more potent poison to all cells. What is needed is a selective drug, 076 one which would bind to, and inhibit, tumour cells, without affecting normal 071 cells. It seems unlikely that any one compound would act equally well 062 against all malignancies, owing to the diversity of properties 077 associated with the various types of tumour*S18*N; instead, it will probably 071 be necessary to select some particular trait associated with one tumour 048 and to design a selective therapy on that basis. 069 One way suggested for increasing the selectivity of the drug for 036 tumour cells relied on the different 044 pH of some tumour cells from ordinary cells; 053 for example, the cytoplasm in mouse P388 tumour cells 036 Wilson and co-workers*S7 *Nattempted 050 to produce daunomycin analogues with a lower pK*dA 054 *lthan the parent compound by reacting the amino-group 059 with peptides. Since binding to DNA requires a protonated 065 drug, this was expected to improve selectivity by producing drugs 046 which existed predominantly in an unprotonated 068 and inactive form in normal cells. However, the desired properties 064 were not shown, partly because the derivatives were less soluble 063 than daunomycin, and partly because the presence of substituent 065 groups around the amino-group caused steric hindrance, preventing 045 close approach of amino and phosphate groups. 068 The hypothetical daunosoacridine studied in chapter 5, compound 019 'Q' of figure A1.1, 062 would seem to possess certain desirable traits. Firstly, the 053 quinone group has been replaced by an acridine group, 033 which might be expected to reduce 067 toxicity, but retains the daunosamine residue, allowing the initial 051 binding to DNA which would result in intercalation. 032 Secondly, the compound possesses 071 a region of conformational stability similar to that of daunomycin, and 063 since the change in conformation of daunomycin on intercalation 022 was found to be small, 060 it would seem likely that the acridine compound would indeed 067 intercalate into DNA. Thirdly, unlike anthraquinone compounds, it 068 is possible to protonate the compound on its aromatic nucleus, which 058 would increase the interaction energy between the compound 061 and DNA, and this might result in a greater binding affinity. 062 Although stronger DNA binding is not necessarily advantageous, 046 because of the loss in selectivity which might 062 the compound on the acridine nucleus in such a way as to place 066 its pK*dA *lbetween the pH of normal cells and of the tumour cells 061 mentioned above. Another possibility would be to produce an 064 intercalating agent which bound covalently to specific base-pair 030 sequences. We have seen that 066 "Ledakrin", when reduced to the hydroxylamine, binds covalently to 058 DNA, apparently to guanine. An appropriately substituted 058 daunoso-nitro-acridine might therefore be expected both to 067 bind strongly to, and then to inhibit, cells which were rich in G-C 011 base-pairs. 002 *? *[Chapter 7.2*] 003 .br 006 .tg NI 005 .ul 1 038 7.2 : Appraisal of Computer Modelling. 006 .tg NA 061 We have used three different types of computer modelling 067 in this thesis, each of which has had advantages and disadvantages. 066 In the first method, we took a model of a fragment of nucleic 057 acid and attempted to modify its structure from a natural 057 conformation to new conformations which might exist after 061 intercalation or base-rotation. The properties of the model 051 were defined in terms of constraint equations which 057 did not attempt to describe accurately the true potential 044 functions imposed on a molecular system, but 043 indicated the optimum value and approximate 060 ease of varying a quantity relative to the other constrained 062 quantities. The penalty functions were quadratic, which made 060 the constraint equations linear and therefore easy to solve. 065 In spite of the approximate nature of the equations defining 055 the model's properties, the results obtained were good. 059 Those deformations which appeared possible within the model 055 and similarly, those deformations which did not proceed 055 satisfactorily within the model were those which do not 067 appear to take place in reality. The calculations were relatively 061 quick when the structural modification being attempted worked 063 (extending one site in a three-residue fragment of nucleic acid 057 to simulate intercalation used about two minutes computer 063 time), but were slower when they failed (attempting to extend a 063 site next to an already extended site took about five minutes). 058 It is clearly bad that an unsuccessful modification should 058 require much more machine-time than a successful one, when 034 the calculation has not determined 006 .tg NI 003 why 006 .tg NA 023 the modification should 057 fail. The reason why this happened lay in the manner of 062 calculation. Any requested structural modification was split 061 into a series of increments. After performing an increment, 066 checks were made that the resulting conformation was satisfactory, 063 that is, that there were no unacceptably large discrepancies in 063 the constrained quantities. If there were discrepancies, then 057 the program would "back-track" and attempt to perform the 061 remaining structural change in a larger number of increments, 060 using smaller steps. However, our experience was that only 061 very occasionally would this help; normally, if an increment 059 produced large discrepancies in the constrained quantities, 063 then it meant either that the structural modification could not 060 take place at all, or that an early increment had pushed the 062 system into a "blind alley". In neither of these cases would 062 taking smaller steps help. What was necessary was to examine 062 out whether this strain could be alleviated. We normally did 054 this by comparing tabulations of discrepanicies in the 053 constrained quantities with pictures of the molecular 064 system drawn by the **PLUTO***S16 *Npackage, a process which was 024 tedious and long-winded. 060 Another problem associated with the method of modelling 055 concerned the large number of variables involved in the 061 calculation. To modify the structure of a system containing 067 *Gn *Natoms requires storage for a matrix of (3*Gn*N)*t2 *lelements 061 if the equations are solved by a direct method, and this very 056 rapidly becomes excessive with moderately large systems; 033 indeed, we had to investigate the 055 structural properties of the DNA helix using a fragment 065 containing deoxyribose-phosphate atoms only for just this reason. 065 There are alternative methods available for solving large sets of 067 linear equations which do not require this amount of storage space, 052 but these are not necessarily useful. An iterative 063 approach can be adopted; then the conjugate gradient algorithm 048 (described in chapter 5) can be used; but, with 061 the constraints used in this type of calculation, with a wide 068 range of weights, the equations are ill-conditioned, and Chadwick*S9 066 *Nhas found that the behaviour of the conjugate gradient algorithm 059 is poor under these circumstances. Another approach is to 050 use the sparsity of the normal matrix; since each 065 row has a maximum of six non-zero elements, a considerable amount 059 of storage space can be saved with a numerical method which 064 considers only these non-zero elements. To take full advantage 061 of the sparsity, however, it seems necessary to have a matrix 056 an algorithm which will reduce the bandwidth of the type 040 of normal matrix produced in this model. 063 We see, therefore, two basic difficulties in the modelling 058 method. One is rather philosophical; the method is good 060 when it works but unhelpful when it does not. The other is 059 more technical, and will need to be investigated before the 063 method can be used on large systems. However, we feel that it 070 is an inherently useful method; before a mechanism for an interaction 061 between molecules can be accepted as correct, it is necessary 064 to show that the molecules can attain the conformations required 061 by the interaction. It is not sufficient to show that these 064 conformations can be built, as some workers have done; pathways 055 must be shown between the starting and finishing states 054 and this method of modelling allows the pathways to be 011 determined. 064 The model used in chapter 5 was of a set of atoms connected 067 in a defined way to form molecules and interacting with one another 058 in a manner defined by semi-empirical potential functions. 062 Two methods were used to find the optimum configuration of the 057 model; either the conformational hyperspace available to 058 it was sampled over an appropriate grid, or an approximate 062 starting configuration was allowed to relax to a minimum. In 060 either case, the energy of interaction between the atoms was 049 taken as a measure of the stability of the model. 002 *? *[Chapter 7.3*] 058 The gridsearch technique presented no difficulties in 061 implementation. It was applicable to systems possessing few 059 relevant degrees of freedom, and, with such systems, it was 061 amount of computer-time. An example of the results obtained 063 by this method was given in the plot of the region of stability 056 of the daunomycin molecule as a function of the relative 059 dispositions of sugar and aromatic groups. Because of the 067 method's simplicity and because of its ability to reveal more about 058 the conformational space available to a molecule than just 064 the minimum energy point in the space, it has been used for some 063 time by other workers. (Gridsearch routines form the basis, for 078 example, for Hopfinger and Weintraub's **CAMSEQ** package*S10*N, which carries 053 out automatic conformational analyses on molecules.) 022 Quite clearly, though, 064 the exponential increase in computation with number of variables 038 does severely limit its applicability. 057 The other method we used for locating minimum energy 061 structures of molecular systems used a numerical optimisation 058 algorithm. The application of this type of algorithm has 070 frequently been dismissed in the past; for example, Ford*S11 *Nused a 050 gridsearch rather than a gradient technique to fit 068 conformations of molecules like AMP to nmr data, on the grounds that 058 a gradient technique would not necessarily find the global 065 optimum. This is a valid criticism, and we feel that the method 057 is only useful when refining structures which are already 068 approximately correct. However, even under these conditions, there 058 are still great problems to be overcome before a numerical 067 refinement can be expected to work well. Some previous workers in 066 non-mathematical fields seem to have been unaware of the magnitude 060 of these difficulties; existing methods, based on first and 061 second derivatives, can easily be presented with pathological 070 problems, whereby the optimisation algorithm wastes much computer-time 024 making little headway**. 005 .fn 1 059 ** Those who feel that numerical optimisation should not be 062 very difficult might consider how they would locate the lowest 062 point in, for example, the Lake District, blindfold and in the 019 absence of gravity. 005 .en 1 063 Haigh's modifications to the linesearch algorithm have improved 067 the performance of the routines under these circumstances, but they 058 remain very expensive nonetheless. If the function being 059 optimised is "corrugated", either inherently or through the 059 use of approximations to speed up calculation, or if errors 061 exist in the code which evaluates the energy function and its 050 derivative, then this expense becomes prohibitive. 032 The use of a semi-empirical 045 interaction energy between molecules (instead 068 of the total free energy of the system) as a measure of conformation 064 stability appeared reasonable for ionic systems in much the same 062 way as has previously been found to be the case with non-ionic 008 systems, 065 provided that care was taken in interpreting the values obtained. 056 In ionic systems, very large electrostatic contributions 061 to these interaction energies appear, which can be completely 058 dissipated by the effects of solvent. In suitable cases, 063 though, results obtained by numerical refinement were credible; 060 for example, the daunomycin:nucleic acid complex revealed an 055 optimum unwinding angle in agreement with two different 057 pieces of experimental evidence, although at considerable 045 expense in terms of the computation required. 067 The third modelling method was based on the use of interactive 056 because, in spite of the difficulties encountered during 029 its development, we feel that 053 the method may help overcome many of the difficulties 043 associated with other modelling techniques. 063 Interaction with a computer model through a visual display 068 is useful for several reasons. From the point of view of the user, 062 he can follow the progress of a manipulation, or optimisation, 061 or whatever, as it is taking place. It is not necessary for 046 him to determine afterwards what has happened, 006 .tg NI 031 because he saw it taking place. 006 .tg NA 061 He is given the opportunity to notice a potential interaction 057 between two chemical groups, such as the phosphate of DNA 065 and the amino-sugar of daunomycin, or to notice that a structural 060 modification, such as extension of the DNA helix, has stuck, 062 or that a numerical refinement is carrying out an unacceptably 068 large number of function evaluations, whilst making little progress. 054 From the point of view of the programmer producing the 063 computer model (who may, of course, be the model's final user), 064 the ability of the model to interact with the user means that it 061 is not necessary to provide facilities within the model to do 058 those things which the user can do more efficiently. The 062 human brain possesses two features which are important in this 064 context; firstly, it can store a large amount of data which can 064 be accessed rapidly in a controlled manner, and secondly, it can 058 recognise patterns. (The two points are, to some extent, 063 synonymous.) With current programming techniques and computer 060 hardware, it might conceivably be possible for a computer to 062 DNA base-pairs, and therefore for it to set up a stacked model 060 for the intercalation complex. It is very doubtful whether 058 an equivalent interlock between non-planar groups could be 064 determined by a computer program more quickly than by a chemist. 056 It is difficult with many existing graphics display 069 devices to produce a representation of a molecular structure which is 062 as easy to understand as an equivalent mechanical model. The 063 reasons for this, largely associated with device resolution and 063 depth perception, have been discussed in chapter 4 and we shall 070 assume that it will be possible to overcome the problem. Once having 063 accomplished this, though, we feel that attempts should be made 064 not just to emulate the mechanical model but instead, to utilise 063 the power of the computational hardware to illustrate much more 046 than a mechanical model is capable of showing. 002 *? *[Chapter 7.4*] 006 .tg NI 005 .ul 1 014 7.3 : Summary. 006 .tg NA 066 The application of computer modelling techniques to the study 057 of drug-receptor interactions is seen to allow reasonable 066 understanding to be achieved of the basis behind the interactions. 065 As they stand, the models are intended for use when the structure 066 of the drug and receptor site are both known, and it is relatively 063 rare for biological receptor sites to be as well-defined as the 070 DNA molecule. Richards*S11 *Ngives an introduction to the subject of 062 "receptor mapping", and it is outside the scope of this thesis 030 to discuss the matter further. 068 It is clear that theoretical tools do not yet possess the power 061 of pharmacological importance. Nonetheless, we feel that we 055 have shown that questions , which might previously have 059 been answerable only by performing difficult experiments or 053 through intuition, can be examined theoretically with 069 relative ease. This type of approach may well help experimentalists 066 in their search for compounds possessing desirable pharmacological 011 properties. 002 *? *[Chapter 7 Refs and Tables*] 006 .tg NI 005 .ul 1 025 References for Chapter 7. 006 .tg NA 065 1. Li H.J. and Crothers D.M. *IJ.Mol.Biol. *D3_9_ *N(1969) 461 043 2. Wakelin L.P.G. *IPrivate Communication 070 *N3. Gilbert M. and Claverie P. *IJ.Theor.Biol. *D1_8_ *N(1968) 330 063 4. Patel D.J. and Canuel L.L. *IProc.Nat.Acad.Sci.USA *D7_4_ 023 *N(1977) 2624 064 5. Henry D.W. in *I"Cancer Chemotherapy"*N, ed Sartorelli A.C. 042 (1976) American Chemical Society 066 6. Falkers K. et al *IBiochem.Biophys.Res.Comm. *D7_7_ *N(1977) 014 1536 057 7. Wilson D.A. et al *IJ.Med.Chem. *D1_9_ *N(1976) 381 056 8. Ross W.C.J. *IBiochem.Pharmacol. *D8_ *N(1961) 235 049 9. Chadwick M. *ID.Phil.Thesis *N(1978) Oxford 061 10. Hopfinger A.J. and Weintraub H.J.R. *IInt.J.Quant.Chem., 045 Quant.Biol.Symp. *D2_ *N(1975) 203 045 11. Ford L. *ID.Phil.Thesis *N(1974) Oxford 067 12. Robinson B.H. *IJ.Chem.Soc.Faraday Trans.1 *D6_9_ *N(1973) 56 065 13. Konopa J. et al *IMateria Medica Polona *D2_8_ *N(1976) 258 063 14. Pigram W.J. et al *INature New Biol. *D2_3_5_ *N(1972) 17 053 15. Richards W.G. *I"Quantum Pharmacology" *N(1977) 022 Butterworths 034 16. See reference (3) of chapter 3 002 *? *[Appendices*] 006 .tg NI 005 .ul 1 005 .tc : 007 .ta 56r 035 :"The Greeks had a word for it ..." 008 .tr z*IZ 011 *N:z. Akins 003 .tc 006 .tg NA 067 As far as is possible, we attempt to use standard nomenclature 071 in this thesis for molecular systems. This falls into two categories: 067 trivial names for compounds of interest and descriptions of nucleic 066 acid structure and conformation. Figure A1.1 illustrates typical 058 molecules studied in these pages or otherwise of interest. 063 Proflavine is one of the acridines, a family of three-ring 068 linear aromatic nitrogen heterocycles. Ethidium is a phenanthrene. 060 Daunomycin is a relatively complex anthraquinone, rigorously 005 .hy 2 005 .hc ? 085 named 8-acetyl 10-*D[*N3'-amino 2',?3',?6'-tri?deoxy *Sa*N-*DL*N-lyxo?hexo?pyranosyl) 078 oxy*D] *N7,?8,?9,?10-tetra?hydro 6,8,11-tri?hydroxy 1-methoxy (8*DS*N-*Icis*N) 005 .hy 1 065 5,?12-naph?thacenedione. Its analogue, adriamycin, is identical 003 .hc 064 apart from having the 8-acetyl group replaced by a hydroxyacetyl 065 group; carminomycin lacks the 1-methoxy group and has a hydroxyl 066 group instead. We do not use this (Chemical Abstracts) numbering 060 for the family of molecules in the text, but, instead, adopt 071 the system used by Kennard et al*S1 *Nto describe the crystal structure 065 of N-bromoacetyldaunomycin. The essence of this system is given 015 on figure A1.1. 063 Nucleic acids are named conventionally and an introduction 070 to the nomenclature has been given by Davidson*S2*N. The nucleosides 057 adenosine, guanosine, cytidine, uridine and thymidine are 066 represented by the letters A,G,C,U and T respectively. Phosphate 064 sugars are assumed unless 'd' is specified, meaning deoxyribose. 066 Thus ApG refers to the ribonucleotide adenosine-(3':5')-guanosine, 063 whereas dApG refers to the equivalent deoxyribonucleotide. If 068 no ambiguity can arise, the complementary strand of a double-helical 059 nucleic acid is omitted from the description; in ambiguous 068 cases, the pairing is indicated by a full-stop. Thus d(A-A).d(T-T) 041 indicates a double-stranded dinucleotide. 060 Three aspects of nucleic acid conformation arise in the 065 discussion. Firstly, torsional angles in the backbone are named 066 using the conventions given in the Appendix of the fifth Jerusalem 053 Symposium on Quantum Chemistry and Biochemistry*S3*N. 063 A torsional angle refers to the conformation about one bond and 053 requires the position of two additional atoms, one at 063 either end of the bond. Looking straight down a bond B-C, the 066 torsional angle *Sq*N(A-B-C-D) is the angle between the projection 067 of A-B and the projection of C-D on the plane perpendicular to B-C, 029 measured in a clockwise sense 070 and given between 0*D? *Nand 360*D?*N. This is illustrated in figure 005 A1.2. 036 Secondly, sugar ring shapes are 037 described in terms of their "pucker". 062 In the case of ribose and deoxyribose sugars in nucleic acids, 060 use is made of the nitrogen atom in the pyrimidine or purine 054 base to which the sugar is bound to define the pucker. 084 Suppose that the five atoms in the sugar ring are C*T1*N,C*T2*N,C*T3*N,C*T4 *Nand Ox 069 respectively. The plane is found which gives the best least-squares 047 fit to four of these atoms, ignoring the fifth. 033 If the remaining atom, C*T3 *Nfor 074 pyrimidine nitrogen, then the sugar is said to have C*T3*N-*Iexo *Npucker. 052 Otherwise it is said to have C*T3*N-*Iendo *Npucker. 059 Thirdly, the twist-angle between successive base-pairs 061 in the nucleic acid is termed *SD*DB*N. In the normal B-DNA 068 structure, this angle is 36*D?*N. Careful note must be made of the 077 distinction between *SD*DB *Nand the unwinding angle caused by intercalation, 039 which may spread over several residues. 059 Computer terminology (or jargon) is omitted, or, where 032 absolutely essential, explained. 003 .bp 006 .tg NI 005 .ul 1 044 Appendix 2 : Contents of Microfiche Inserts. 006 .tg NA 075 There are nine microfiche appended to this thesis, containing items of 073 data, text and results of calculations which were superfluous to the main 070 discussion, but which would be needed to repeat the calculations or to 071 continue the work further. The types of information contained on each 065 fiche is indicated by the colour of the stripe on it, as follows: 006 .sp 1c 006 .ll -3 005 .in 5 072 Red : text of thesis presented for Part II of the Oxford Chemistry first 034 degree course in 1976 (one fiche). 006 .sp 1c 040 Yellow : computer programs (four fiche). 006 .sp 1c 069 Blue : coordinates resulting from structural modifications to nucleic 070 acid fragments, and analyses of the torsional angles and sugar puckers 043 in these modified structures (three fiche). 006 .sp 1c 074 Green : coordinates of daunomycin : nucleic acid complexes after numerical 023 refinement (one fiche). 006 .sp 1c 006 .ll +3 005 .in 0 077 The fiche are reduced twenty four times in size, but because of the different 072 the text of the Part II thesis is recorded horizontally, with successive 070 pages following across the fiche, whereas the other fiche are recorded 011 vertically. 072 The yellow fiche include the text of the computer programs used for 070 numerical refinement of molecular complexes, for performing structural 073 modifications, for running an interactive graphics system, for performing 064 CNDO/2 and INDO quantum calculations, and for plotting molecular 073 structures (**PLUTO**). Note that copyright for these last two programs 072 is not held by the author, and their texts are included for completeness 070 only. All the programs are available in machine-readable form, along 064 with instructions as to their use, on application to the author. 069 Careful scrutiny of the texts will reveal some discrepancies from the 073 descriptions given in chapter 1; these exist because of the shortcomings 070 of the computing equipment used, and are a means of imposing the ideal 066 philosophy described in chapter 1 onto real equipment. Beware of 063 assuming that the computer programs are error-free; there are 029 undoubtedly errors remaining. 002 *?