*[Chapter 3.1.1*] 006 .ls 2c 006 .tg NI 007 .ta 56r 005 .ul 1 045 Chapter 3 : Studies of DNA Helix Flexibility. 005 .tc : 040 :"So it does?" said Pooh. "It goes in?" 027 :"So it does?" said Piglet. 020 :"And it comes out?" 027 :"Doesn't it?" said Eeyore. 036 :"It goes in and out like anything." 032 :"Winnie-the-Pooh", A.A. Milne. 003 .tc 006 .tg NA 006 .ls 3c 003 .fi 003 .ju 057 We have seen that models suggested for intercalation 048 and for processes leading to frameshift mutation 063 involve changes in the structure of the nucleic acid molecules. 074 In this chapter, we study how physical and chemical constraints limit what 052 structural changes can occur in the DNA double helix 036 in order to determine how reasonable 038 these models for the interactions are. 072 Let us look first of all at structural changes occurring in nucleic 074 acids during intercalation. We have seen in chapter 1 that intercalation 070 involves an extension of the helix so as to double the spacing between 073 successive base-pairs from 3.36A to 6.72A. This extension is associated 069 with a change in the twist of the helix around the intercalation site 075 and experimental values for this change cover a wide range (see table 3.1). 079 In their crystallographic studies on dinucleotide intercalation complexes, 081 Sobell and co-workers*S1 *Nhave found that an unwinding of about 26*D? *Noccurred 017 on intercalation. 005 .ne 5 030 The ribose sugar puckering*t** 007 *l.fn 1 065 *t***lZOur conventions for describing polynucleotide conformation 063 are taken from the appendix of the fifth Jerusalem Symposium on 041 Quantum Chemistry and Biochemistry*S25*N. 005 .en 1 086 C3'-*Iendo*N-(3'-5')-C2'-*Iendo *Npattern on complexing and an 8*D? *Nrelative tilt of 076 the base-pairs towards the wide groove of the helix occurred, coupled with a 074 dislocation of the helical screw axis of about 1A. On the basis of these 070 results, they suggested that kinking and axis dislocation were general 075 properties of nucleic acid intercalation complexes. They pointed out that 078 a requirement for C3'-*Iendo*N-(3'-5')-C2'-*Iendo *Npuckering on intercalation 070 would provide a satisfactory explanation for the "neighbour-exclusion" 074 principle (mentioned in chapter 1), since such puckering can occur at most 036 at every other site along the helix. 076 However, Neidle and co-workers*S2 *Nobtained different results in their 072 crystallographic studies on CpG : proflavine complexes. In particular, 075 these workers found that their miniature complexed helices were not unwound 070 at all relative to uncomplexed RNA-11 and the twist between base-pairs 076 was 33*D?*N. Furthermore, their structure possessed C3'-*Iendo *Npuckering 021 on all ribose sugars. 073 What are we to make of these apparently contradictory results? The 070 first point to make is that results obtained from dinucleotide studies 067 cannot necessarily be applied to the DNA system, since dinucleotide 070 molecules possess degrees of freedom not available to a polynucleotide 070 system. This is because, in a polynucleotide, each dinucleotide unit 064 must join on to the next; there are boundary constraints on the 075 units. We may also note that Neidle's crystal structure is better refined 076 than Sobell's, with an R-factor of 15.5*A> *Ncompared with Sobell's 20*A>*N. 072 Equally, they have studied different intercalation complexes and we must 060 (Furthermore, the dinucleotide systems used by these workers 053 were ribonucleotides, and we are really interested in 065 DNA intercalation. It is not obvious that RNA and DNA complexes 023 will behave similarly.) 072 Various groups have performed computer modelling studies to examine 074 structural changes occurring during intercalation. By describing various 072 equations constraining the atoms of oligonucleotides after intercalation 069 had occurred, these groups have refined the structure of hypothetical 024 intercalation complexes. 070 We shall describe the strategies adopted by some of these groups, 051 since it is relevant to compare their work with the 031 calculations that we performed. 039 Alden and Arnott*S3 *Nconsidered a 046 model containing three molecules: an aromatic 065 intercalating drug, which we shall consider to be proflavine, and 067 two nucleotide segments with complementary base sequences, composed 066 of 2N bases each. The base on the 3' terminus of each strand had 065 defined coordinates, to allow continuation of the nucleic acid in 064 either direction - in one study, these coordinates were fixed at 063 the values found in A-DNA and in another at the values found in 067 B-DNA. The distance between terminal base-pairs was fixed at 2Nh, 071 where "h" is the rise per residue in the uncomplexed systems; in other 063 words, they assumed that intercalation resulted in an extension 032 "h" of the intercalation region. 047 Bond-lengths and bond-angles were fixed at 064 standard values, and the variables were (12N-7) torsional angles 067 in the backbone of each strand plus three positional parameters for 063 the drug chromophore. None of these variable torsional angles 071 minimal changes occur in the sugar ring conformations on intercalation. 036 Constraints were applied to maintain 065 Watson-Crick base-pairing and to maintain certain characteristics 034 of A- or B-DNA, as the case may be 056 and the ends of their nucleotide chains were constrained 067 to join onto unmodified nucleic acid. Conformational identity was 064 imposed on the two nucleic acid strands, relating them through a 064 diadic axis passing through the centre of the intercalating drug 058 molecule. Finally, constraints were applied to alleviate 060 unfavourable non-bonded contacts and to simulate attractive, 066 van der Waals, stacking forces. They omitted hydrogen atoms from 060 their studies, since they found that including these did not 066 affect the results obtained, but did greatly slow their refinement 064 calculations. The effect of these atoms was simulated by tying 061 backbone torsional angles elastically to their normal values. 064 Their calculations were therefore based essentially on geometric 062 considerations, but included rudimentary formulations of terms 035 affecting the energy of the system. 062 The results they obtained for A- and B-DNA differed in an 066 interesting way. With B-DNA, they found that the optimum refined 051 structure possessed C3'-*Iendo*N-(3'-5')-C2'-*Iendo 067 *Npuckering of the ribose groups, with a helical unwinding of 18*D? 029 *Nspread over three residues. 022 With A-DNA, all sugars 072 possessed the C3'-*Iendo *Npucker characteristic of A-class nucleotides, 046 and virtually no helical unwinding took place. 068 We note the similarity of these results to the crystallographic 071 results of Sobell and Neidle respectively. Alden and Arnott suggested 067 complexes; our results will be seen to agree with this. However, 052 they also proposed, partly because of the consistent 068 C3'-*Iendo *Npuckering found in their A-DNA model and partly because 063 of the preference found for certain intercalative drugs to bind 042 preferentially to dinucleotides containing 076 pyrimidine-(3'-5')-purine base sequences*S26*N, that the neighbour-exclusion 062 principle does not arise from restrictions in the conformation 016 of the backbone; 054 we feel that they have not shown this - indeed our own 045 results will be seen to suggest the opposite. 048 In their paper on the binding of 2-hydroxy- 055 ethanethiolato(2,2',2"-terpyridine) platinum(II) to DNA 058 which results in the formation of an intercalation complex 050 satisfying the neighbour-exclusion principle, Bond 072 and co-workers*S19 *Ngave some results obtained from studies designed to 066 produce, by computer modelling, a structure for this complex which 056 would fit the x-ray diffraction data. They said little 058 about the techniques used, but concluded that an unwinding 055 of the helix by about 22*D? *Nper intercalated molecule 066 gave a model in which the conformational angles were changed least 021 from standard values. 056 They did not study what happened at lower concentrations 062 of the intercalating agent, nor did they consider what factors 060 were responsible for producing neighbour-exclusion with this 009 compound. 069 Berman, Neidle and Stodola*S20 *Nperformed calculations in which 060 they attempted to obtain dinucleotide RNA structures forming 059 part of an intercalation complex. Their calculations were 066 apparently based on geometric considerations only; they attempted 057 model in order to minimise its discrepancies from various 042 properties characteristic of nucleic acids 063 after intercalation. They found it relatively easy to satisfy 065 the constraints imposed, and suggested that properties like sugar 062 pucker and unwinding angle were relatively unimportant insofar 062 as the dinuclotide was concerned and that such properties were 062 likely to be determined by intermolecular interactions between 030 intercalator and nucleic acid. 002 *? *[Chapter 3.1.2*] 068 Our own studies of helix extension bear considerable similarity 062 to Alden and Arnott's work. We would point out, though, that 059 this work was performed independently to theirs and with an 070 appreciably different strategy. Since neither study has considered a 063 completely general model - each has its own assumptions - it is 066 particularly interesting to compare the results obtained, which do 068 not always agree. Our work continues that started by Hathway*S4*N; 068 many of the problems associated with the model did not come to light 046 until after Hathway had completed his studies. 035 We were interested in knowing: 006 .ll -3 006 .in 10 006 .sp 1c 006 .ti -5 005 .ne 2 058 1.ZZZWhether we could modify the structure of DNA so as to 032 provide sites for intercalation. 006 .ti -5 005 .ne 2 061 2.ZZZHow much limitation there is on the structure adopted by 034 DNA around the intercalation site. 006 .ti -5 005 .ne 4 051 3.ZZZHow the process of intercalation into a simple 065 dinucleotide differs from that in DNA, in which a regular helical 056 structure must be continued in either direction from the 019 intercalation site. 006 .ti -5 061 4.ZZZTo what extent "neighbour-exclusion" is a consequence of 060 limitations in the flexibility of a nucleic acid and how the 064 structure of the nucleic acid changes as density of intercalated 018 species increases. 006 .ll +3 005 .in 0 032 One model*S5 *Nproposed for 070 frameshift mutation induced by acridine systems involves stabilisation 064 of a "looped-out" base by the stacking of dye molecules onto it. 060 For such a model to be plausible, the helix must be shown to 064 possess sufficient flexibility to allow such looping-out without 061 causing damage to itself, and the latter part of this chapter 056 investigates whether this is the case. Our studies are 059 necessarily brief; we feel that the processes occurring in 060 frameshift mutation are poorly understood, and that we would 063 therefore be ill-advised to concentrate too much attention onto 016 this hypothesis. 049 We studied these matters by imposing various 052 constraints onto computer models of a nucleic acid. 077 The details of these constraints are given in later sections of this chapter, 067 and, at this stage, we shall merely describe the overall philosophy 070 adopted. Our models were constrained to retain those characteristics 072 which we thought most fundamental to a nucleic acid helix: bond-lengths 065 and angles, for example, are fairly basic to any molecule, whilst 064 Watson-Crick base-pairing underlies the structure of DNA to such 063 an extent that we felt we should not remove it. Somewhat more 063 arguable was our choice to retain a central helical axis in our 066 model; this immediately removed any possibility for "kinking", as 065 suggested by Sobell*S1*N, but made computation much simpler. In 045 natural processes can only be extrapolations. 061 Apart from constraining fundamental properties, we tried 063 equally to ensure that properties which were not basic were not 066 constrained: for example, particular sugar-pucker patterns may be 068 characteristic of A- or B-DNA, but they are not a requirement of the 064 nucleic acid. If a tendency for such-and-such a pucker pattern 064 emerged unaided from our calculations, all well and good, but we 069 tried not to assume such a result. Equally, we had no pre-conceived 065 notions about the part that hydrogen-bonding between intercalator 064 and nucleic acid might play in determining the final orientation 060 of phosphate groups. Our models were of nucleic acid only, 063 and we studied how such an acid could behave, without reference 038 to an intercalating or stacking agent. 065 The molecular fragments used in our investigations consisted 072 of two, three or four deoxyribose groups and associated atoms, excluding 061 hydrogen atoms; the residue containing three sugar groups is 020 shown in figure 3.1. 059 They were based on B-DNA structures with atomic coordinates 006 .ne 14 041 obtained from Langridge et al*S6*N*t***l. 005 .fn 1 064 *t** *lThese coordinates are rather old and have been refined in 062 recent years. Unfortunately, we did not discover the perhaps 059 more reasonable coordinates published by Arnott*S21 *Nuntil 061 some time into our studies, an oversight for which we have no 063 excuse. This raised a serious dilemma, since we could neither 055 repeat all the (very expensive) calculations performed, 058 nor could we change our basic coordinates half-way without 073 compromise. Whilst basing all calculations on those structures obtained 063 from Langridge's coordinates, we repeated critical calculations 061 using Arnott's coordinates in order to satisfy ourselves that 067 the conclusions drawn were not discounted by this later refinement. 032 We found no major discrepancies. 005 .en 1 005 .ne 6 005 .ul 1 006 .tg NI 028 3.1 : Method of Calculation. 006 .tg NA 054 We attempted to modify the nucleic acid fragments 051 whilst allowing some flexibility in the structures. 056 Any quantity which was required to possess a given value 051 throughout any modification was constrained to that 030 value using a weighting factor 069 which reflected the (experimentally determined) ease of distorting it 069 from that value. Similarly, any quantity which we wished to change, 069 such as the spacing between base-pairs at the intercalation site, was 073 altered using a weighting factor to constrain it to its new target value. 078 The weighting factor used is equal to the reciprocal of the standard deviation 077 desired in the quantity being constrained; thus a weighting factor of 100 on 064 a bondlength indicates that we wish there to be a 0.01A standard 066 deviation in that length. (We use the term "weighting factor" to 066 mean what would conventionally, in the theory of normal equations, 036 be the square root of the "weight".) 057 Thus, whilst the model used was really based on geometric 047 considerations, the use of appropriately chosen 047 weighting factors allowed it to behave in a way 060 which, we hope, was not too dissimilar to the real molecule. 052 Our variables were the cartesian coordinates of 060 atoms in the models; since there were more constraints than 064 This allowed us to use a least-squares optimisation technique to 069 determine how closely the various constraints could be obeyed. (The 060 theory of the least-squares method may be found elsewhere*S7 033 *Nand will not be repeated here.) 065 The method of least-squares optimisation is most easily used 047 when the constraint equations are linear. The 062 constraints imposed on a molecular system do not satisfy this. 025 However, we approximated 064 the problem in terms of linear equations by splitting structural 045 modifications into a series of small changes. 068 All the equations used to define the problem were of two types. 073 Firstly, there were equations relating to individual atoms, such as those 074 required to maintain symmetry in the DNA helix. If the coordinate *Iq*di 075 *N*l(we use cylindrical polar and cartesian coordinates interchangeably, as 083 convenient) was required to possess a value *Iq*(*di*tt*) *N*land in fact possessed 039 a value *Iq*(*di*ta*)*N*l, then we had: 006 .sp 2c 005 .ce 2 005 .ne 2 167 *S;*Nw*I*dq*bi*N*l(*Md*Iq*di*N*l/*Md*Ix*N)*Sd*Ix*di *N*l+ *S;*Nw*I*dq*bi*N*l(*Md*Iq*di*N*l/*Md*Iy*N)*Sd*Iy*di *N*l+ *S;*Nw*I*dq*bi*N*l(*Md*Iq*di*N*l/*Md*Iz*N)*Sd*Iz*di 069 *N*l= *S;*Nw*I*dq*bi *N*l. (*Iq*(*di*tt*) *N*l- *Iq*(*di*ta*)*N*l) 006 .sp 2c 093 where w*I*dq*bi *N*lwas the weighting factor constraining *Iq*di*N*l. Similarly, there were 071 equations relating to pairs of atoms, where we wanted to constrain some 072 quantity determined by the position of each atom, such as a bond-length. 012 Here we had: 005 .ce 4 006 .ls 5c 005 .ne 4 129 *N*l+ *S;*Nw*I*dq*bij*N*l(*Md*Iq*dij*N*l/*Md*Iz*di*N*l)*Sd*Iz*di *N*l+ *S;*Nw*I*dq*bij*N*l(*Md*Iq*dij*N*l/*Md*Ix*dj*N*l)*Sd*Ix*dj 131 *N*lZZ+ *S;*Nw*I*dq*bij*N*l(*Md*Iq*dij*N*l/*Md*Iy*dj*N*l)*Sd*Iy*dj *N*l+ *S;*Nw*I*dq*bij*N*l(*Md*Iq*dij*N*l/*Md*Iz*dj*N*l)*Sd*Iz*dj 075 *N*l= *S;*Nw*I*dq*bij *N*l. (*Iq*(*di*tt*)*dj *N*l- *Iq*(*di*ta*)*dj*N*l) 006 .ls 3c 051 We can write the set of equations obtained as: 006 .sp 1c 005 .ce 1 025 *GA *N. *Sd_f_ *N= *Db_ 008 *N.sp 1c 077 where *GA *Nis the (fairly sparse) matrix of coefficients from the equations, 080 *Sd_f_ *Nis the vector of coordinate changes for all the atoms and *Db_ *Nis the 070 discrepancy vector. We solved the corresponding least-squares normal 010 equations: 006 .sp 1c 005 .ce 1 045 *GA*N*tT*G*lA *N. *Sd_f_ *N= *GA*N*tT*D*lb_ 008 *N.sp 1c 071 by means of the Cholesky decomposition followed by forward and backward 013 substitution. 002 *? *[Chapter 3.2.1*] 006 .tg NI 005 .ul 1 030 3.2 : Helix Extension Studies. 005 .ul 1 017 3.2.1 : Strategy. 006 .tg NA 068 We divided up extensions into a number of steps (typically ten) 028 and at each step incremented 005 .ne 5 072 the target value for the z-coordinates*t** *lof the atoms comprising the 005 .fn 1 068 *t** *lIn the coordinate system used here, the z-axis lies along the 064 helix axis. r- and *Sq*N-coordinates refer to projections onto 013 the xy-plane. 005 .en 1 069 glycosidic link in the upper residue(s) by an appropriate amount. A 071 fairly high weighting factor was applied to the constraints (100). We 058 wished to maintain a fixed helical axis throughout the DNA 031 molecule and so constrained the 074 again with weighting factor 100. (This constraint excluded our obtaining 055 results which involved dislocation of the screw axis or 066 kinking of the helix, but to have allowed for these conformational 057 changes would greatly have complicated our calculations.) 052 To prevent the helix rotating *Ien masse *Nabout its 069 axis, we constrained the *Sq*N-coordinate of the nitrogen atom in the 061 lowest residue to remain constant, with weighting factor 500. 062 In order to maintain Watson-Crick hydrogen bonding of the 011 base-pairs, 072 we constrained the difference between the *Sq*N-coordinates of the atoms 043 in each glycosidic link to remain constant, 039 again with weighting factor 500. (The 074 figure of 500 was arrived at by dividing the mean radial coordinate of the 074 quantity being constrained by the required precision normal to this radial 012 coordinate.) 075 The important distinction between intercalation into dinucleotides and 075 into DNA, as has been noted, rests in the fact that the latter continues in 066 either direction from sites of intercalation. By using different 069 formulations of this distinction, we investigated the validity of the 075 neighbour-exclusion principle. For example, if it were possible to obtain 077 a model for intercalation in which the atoms around site 'n' adopted the same 070 conformation as those at site 'n+1', then we would have shown that the 070 neighbour-exclusion principle was not caused by structural limitations 047 in DNA. However, were this not possible, then 061 we would need to show the existence of a model in which atoms 065 at sites 'n' and 'n+1' were related by some symmetry operation to 035 those at sites 'n+2' and 'n+3' with 061 since we have seen, in chapter 1, experimental evidence which 063 which suggests that intercalation can occur at alternate sites. 075 (Note however that there are infinitely many possibilities. Intercalation 075 at every site, for example, may also be possible if the atoms at sites 'n', 070 'n+2','n+4', etc, are related by some symmetry operation, whilst those 076 at sites 'n+1','n+3','n+5' etc are differently related, with helix extension 025 occurring at every site.) 039 We tried the following strategies: 060 Firstly, using a residue containing three sugar groups, 028 we constrained the two outer 050 deoxyribose groups to adopt the same conformations 030 and orientations, by requiring 081 that the differences between z- and *Sq*N-coordinates for atoms C2, C3, C4 and C5 047 in these two deoxyribose groups were always the 036 same as the corresponding difference 076 for the atoms C1. We then attempted to extend one link, whilst leaving the 077 other unchanged. If this strategy were successful, then we would have found 072 a pathway for part of the experimentally-observed intercalation process. 078 Secondly, we applied these equal orientation and conformation constraints 068 to the deoxyribose groups in a fragment containing two sugar groups. 078 The third strategy was identical with the first, except that we attempted 046 to extend both links in a three-residue model. 052 Success in either the second or third strategy would 076 have shown that the neighbour-exclusion principle was probably not caused by 029 geometric limitations in DNA. 072 Fourthly, we studied a fragment containing four sugar residues and, 066 constraining the outer two groups to adopt identical conformations 070 of the three sites for intercalation. As was mentioned in chapter 1, 075 experimental results*S18 *Nsuggest that the anthraquinone drugs intercalate 041 only at every third site along the helix, 034 and this run strategy was designed 072 partly to study the nature of the DNA helix at this level of complexing. 073 Ability to extend two out of three sites would, again, have been contrary 040 to the principle of neighbour-exclusion. 073 Investigations of the differences between dinucleotides and DNA were 065 performed by omitting the boundary condition constraints from the 013 calculations. 061 Normal chemical constraints on bond-lengths, bond-angles 045 and non-bonded contacts were applied in terms 069 of constraints on inter-atomic distances. Any two bonded atoms were 074 required to be separated by their initial spacing throughout. Bond-angle 065 constraints were applied by requiring that the two next-neighbour 069 atoms maintain their initial spacing. Finally, unfavourable van der 077 Waals, non-bonded, contacts were prevented by producing a constraint equation 069 if any two atoms approached each other more closely than a prescribed 059 distance. The following contact distances were used*S8*N: 006 .sp 1c 005 .ce 3 048 P - C 3.35A O - O 2.75A N - C 3.00A 048 P - O 3.35A C - O 2.80A N - O 2.85A 012 C - C 3.10A 006 .sp 1c 063 (P-N and P-P contacts could not occur in any acceptable model.) 063 These constraints were purely repulsive; we took no account of 066 the fact that van der Waals potential curves possess an attractive 008 minimum. 056 Bond-lengths were constrained with precision 0.02A, 026 so that a weighting factor 076 *Nsuggests that the force necessary to move an atom defining a bond-angle at 075 right-angles to the bond direction is about one tenth of the force required 072 for the same movement parallel to the bond, for small (0.02A) movements. 064 Since most bond-angles are about c*(*M*t?*N*lo*)s(0.5), we have: 006 .sp 1c 005 .ce 1 060 w*I*dangles *N*l= *S? *N50/0.5 . *S;*N0.1 *S? *MW *N30 058 A significantly smaller weighting factor was selected 053 for contraints preventing unfavourable contacts (10). 080 Finally, to prevent an atom moving unless necessary, a very small constraint (2) 038 was applied to each atomic coordinate. 068 In some calculations, we found it necessary to apply additional 051 constraints with small weights (typically about 5). 076 These had generally little chemical basis, but were used in order to prevent 071 the system from entering "blind-alleys", which were difficult to leave. 071 The small weights used, however, ensured that these constraints did not 051 over-ride the more reasonable chemical constraints. 002 *? *[Chapter 3.2.2*] 005 .ne 6 006 .tg NI 005 .ul 1 016 3.2.2 : Results. 006 .tg NA 071 Hathway*S4 *Nhad attempted to modify the three-ribose system using 069 constraints marked (a) in table 3.2 below. Each increment of 0.336A 069 was applied in turn and no attempt was made to refine the coordinates 071 between increments, it being assumed that sufficiently accurate results 069 were obtained without such refinement, providing that no atomic shift 067 greater than a certain figure (he used 0.3A) had occurred. Such a 068 procedure gave rise to no unsatisfactory departures from the defined 066 resulted in certain bond-lengths and angles changing unacceptably. 069 When we repeated his calculations, applying up to four stages of 071 refinement after each increment, the structure became unacceptable much 075 earlier in the run. In particular, the twist angle between the base-pairs 073 in the extending link was found to increase dramatically. This was due 075 to the phosphate linkage between the two separating base-pairs not rotating 064 sufficiently during the initial stages of the extension process. 065 The system entered a "cul-de-sac" from which it could not emerge. 066 By applying a very small constraint to prevent this occurring 063 and to unwind the helix slightly (constraints (b) in table 3.2) 051 it was possible to extend the three-ribose fragment 069 of DNA to a model in which two base-pairs would be separated by 6.72A 075 whilst leaving the next two base-pairs separated by 3.36A. This extension 078 occurred without any bond-length change of more than 0.013A, no next-neighbour 075 distance change of more than 0.03A and no unfavourable non-bonded contacts. 074 The final twist angle between the extended base-pairs, which we shall term 080 *SD*DB*N, was +23*D?*N, corresponding to an unwinding of 13*D? *Nfrom the normal 071 helix conformation. The twist angle for the unextended link increased 080 to 44*D?*N, so there was an overall unwinding of 5*D? *Nfor the two links. The 073 pathway for this extension process may be regarded as a low-energy route; 041 figure 3.2 shows the helix backbone after 006 .ne 10 016 extension*t***l. 005 .fn 1 077 *t** *lWe repeated this calculation starting from Arnott's coordinates*S21*N. 051 Extension followed a similar pathway, and the final 065 the distribution of this unwinding was slightly different to that 067 found using Langridge's coordinates: the extended link had unwound 063 by 8*D? *Nand the link adjacent to this had wound up by 1*D?*N. 053 We do not consider this difference to be significant. 005 .en 1 066 Calculations on the four-sugar model showed that extension of 070 one residue could take place straightforwardly. It was not necessary 065 to apply any constraints to the backbone to prevent it entering a 071 "cul-de-sac". The final structure, which possessed no close contacts, 070 bond-length or angle changes greater than 1.4 standard deviations, had 080 unwound by only 1*D? *Noverall, with a 9*D? *Nunwinding at the extended residue. 059 The extended conformation from the three-sugar residue 042 was used as starting-point for determining 079 the range of *SD*DB *Nvalues possible for the extended link. This was done by 062 adopting a new set of constraints, in which we incremented the 058 *Sq*N-coordinate of the central glycosidic nitrogen. The 051 constraints used are those marked (c) in table 3.2. 084 It was found possible to vary the twist-angle, *SD*DB*N, through a considerable 078 range without incurring any great discrepancies in the constrained quantities. 072 Indeed, the range was so wide that it did not seem worth determining the 083 precise limits. Within the range -18*D? *S< D*DB *S< *N50*D? *Nit was possible to 071 find models with no unfavourable non-bonded contacts, in which no bonds 063 were more than 0.025A off target and in which no next-neighbour 071 distances were more than 0.04A off target. The modification of *SD*DB 073 *Noccurred with least discrepancy if the twist-angle for the non-extended 069 discrepancies occurred if the unextended link was left free, or if it 044 were heavily constrained to remain constant. 069 Clearly, the system required some flexibility in order to unwind, but 033 too much freedom caused problems. 065 We calculated the internal energies of related trinucleotide 049 structures to those generated here (with one link 057 extended and the other not), using the more sophisticated 066 van der Waals and electrostatic potentials described in chapter 2. 062 On to the deoxyribose-phosphate backbones were built base-pair 052 sequences to resemble complete nucleic acid systems. 063 The resulting plot of van der Waals internal energy is shown in 071 figure 3.3. We see a minimum when *SD*DB *Nfor the extended link lies 064 between 30*D? *Nand 40*D?*N, with a gentle increase occurring on 063 unwinding, but a severe rise in energy occurring on winding the 058 helix up by more than 8*D?*N. This sharp increase occurs 056 because certain sugar atoms become unduly close to atoms 063 in the associated base; such contacts had, of course, not been 059 considered in the strategy described above. The curve for 058 electrostatic internal energy possesses a similar shape to 061 that for van der Waals energy, but is shifted towards smaller 055 *SD*DB *Nvalues, with the overall result that the total 066 internal energy curve shows a minimum at about *SD*DB *N= 22*D?*N. 061 The position of this minimum is in good agreement with values 062 found experimentally (see table 3.1). Furthermore, the rapid 063 rise in energy found on winding the helix may well form part of 065 the reason why none of the currently accepted experimental values 022 indicate such winding. 063 or unwinding additional to that caused during extension) showed 063 similar sugar ring shapes on two of the three residues to those 064 present in the starting coordinates. The sugar ring in residue 071 1 (defined in figure 3.1) possessed C2'-*Iendo *Npucker, whilst that on 070 residue 3 had changed somewhat to C3'-*Iexo *Npucker. The difference 067 in coordinates between these two groups was minimal (they had been 062 constrained to adopt identical conformations). Residue 2 had 067 changed to a C1'-*Iendo *Npucker, which is an unusual shape, having 054 been found, apparently, in only one crystal structure. 052 As this structure unwound at the intercalation site, 068 the pucker of the central sugar group remained "strange", whilst the 064 shapes of the other two groups also became unusual. When 33*D? 068 *Nunwinding had occurred at the intercalation site, they had adopted 068 an O6'-*Iendo *Npucker. It is interesting to compare these results 059 with those found by Levitt, whose work on modelling the DNA 060 molecule has been described previously. Levitt*S22 *Nfound 064 "strange" pucker patterns emerged after refining his model using 066 empirical potential energy functions. In another paper*S23*N, he 058 found that the strain energy of a five-membered sugar ring 068 was fairly independant of pucker over a wide range of conformations, 064 including those found here. This was ascribed to the fact that 051 the ring must always have certain atoms arranged in 031 a *Icis-*Nconformation which is 049 unfavourable over the entire range of structures. 062 The torsional angles (defined, once again, in figure 3.1) 064 found in the extended models indicated that atoms had attempted, 047 main reasons for this. Firstly, the increased 064 separation between the base-pairs at the intercalation site must 045 result from "pulling-out" the helix backbone. 067 Secondly, the constraint equations used to prevent non-bonded atoms 028 from approaching one another 045 too closely tended to force apart atoms which 075 which were in a *Icis-*Nconformation. Particularly large changes occurred 074 in the values for angles *Sw *Nand *Sy *Nin residues 1 and 2 on extension. 064 Unwinding the helix also was accommodated mainly through changes 026 in these torsional angles. 061 In table 3.4, we give the values found for the torsional 064 angles after helix extension, and also quote values published by 059 some other workers. (A much more complete analysis of the 060 structures produced, along with their atomic coordinates, is 067 given on the microfiche insert.) Our coordinates for the extended 067 helix correspond most closely to Alden and Arnott's structure*S3*N; 062 there is little correspondence between the values found in our 070 structure and those given by Berman's group*S20*N. This latter point 055 is perhaps hardly suprising, since their model was of a 049 dinucleotide system and their constraint strategy 039 was based on geometrical considerations 063 only. Note also that Alden and Arnott's model was constrained 058 to form part of an otherwise unchanged helix, whereas ours 066 attempted to model part of a maximally intercalated helix. There 061 is no reason, therefore, to expect good agreement between the 007 values. 073 All attempts to show the possibility for intercalation at every site 066 along a DNA helix were unsuccessful. It was possible to increase 065 5.4A whilst maintaining equal conformation and orientation of the 036 sugar groups but, beyond this point, 047 very great distortion occurring in bond-lengths 064 and angles. Approximately this amount of extension could occur 057 at sites adjacent to an already-extended link in both our 060 trinucleotide and tetranucleotide models constrained to form 054 part of a continuing helix in which the maximum degree 054 of intercalation observed experimentally had occurred. 065 Finally, we attempted to extend the helix at alternate sites 066 beyond the 6.72A separation between base-pairs previously achieved 069 whilst maintaining the boundary conditions on the ribose groups. It 070 was found possible to increase the separation of two base-pairs in the 077 trinucleotide fragment to about 6.85A without incurring any great distortion, 065 but, beyond this point, many bonds became unacceptably stretched. 070 We found it much simpler, however, to modify the structure of the 069 dinucleotide fragment when we made no requirement for it to join onto 073 a continuing helix in either direction. By using the constraints (d) in 070 table 3.2, we found that the change from the normal, unextended, state 067 to a form in which intercalation could occur proceeded easily, with 071 no appreciable distortions at any stage. The final structure is shown 071 in figure 3.4. Note that there is considerable difference between the 066 orientations of the two ribose groups; it is clearly not possible 069 to build an undistorted helix from this structure. The final *SD*DB 073 *Nangle found here was +33*D?*N, corresponding to an unwinding of 3*D?*N. 002 *? *[Chapter 3.2.3*] 006 .tg NI 005 .ul 1 051 3.2.3 : Discussion of Helix Extension Calculations. 067 The calculations that we have carried out demonstrate at least 071 one geometrically-favourable pathway for the extension of the DNA helix 075 to accommodate an intercalated planar species at every other site along the 066 helix. We have also shown that the helix can exist in relatively 083 unstrained conformations with the twist-angle, *SD*DB*N, varying from *A-18*D? *Nto 073 +42*D? *Nfor the extended link. The ease of modification of twist-angle 065 shown by our calculations indicates that the precise structure of 065 intercalation complexes is determined primarily by intermolecular 072 interactions between nucleic acid, intercalator and solvent, rather than 038 by any inflexibility in the DNA helix. 070 The range of feasible *SD*DB *Nvalues found for the extended link 062 includes all those values previously suggested on the basis of 072 experimental results (see Table 3.1). However, it is worth noting that 078 the process of helix extension was associated with a change in the twist-angle 075 for the unextended link, in agreement with Alden and Arnott's work*S3 *Nbut 048 a point not always realised by experimentalists. 054 Energy calculations indicated that the most favourable 065 structure for DNA complexed at alternate sites will be unwound by 070 some 10 to 15*D?*N, but these were based on considerations of internal 062 energy only. The variation of energy with *SD*DB *Nwas small 025 over a fairly wide range. 063 The tendency found for the DNA helix to lock itself during 013 the extension 051 of alternate residues is interesting, although this 053 is no indication that similar processes will occur in 074 nature, since there will always be an element of thermal agitation present 039 to aid the exit from such blind-alleys. 069 the helix is straightforward (on geometric grounds) until every third 066 site is occupied. Further extension is more difficult, but still 063 relatively straightforward, until every other site is occupied. 053 Some extension of the remaining sites can still occur 058 allowing the base-pairs at these sites to become separated 025 by 5.4A - in other words, 068 there is still some flexibility remaining, even with alternate sites 046 extended - but this is not sufficient to allow 029 further intercalation. This 070 structural limitation appeared to be due primarily to the orientations 068 adopted by the deoxyribose sugars relative to the rest of the helix, 074 rather than by a requirement for particular conformations of these sugars. 050 The weak constraints applied to the extending 059 phosphate linkage to prevent the system locking resulted in 020 this phosphate group 056 moving outwards away from the intercalator into solvent. 069 This result agrees with that found in Sobell's*S1 *Ncrystal structure 056 for ethidium : CpG and with Alden and Arnott's model for 063 proflavine : B-DNA, but differs from the latter's model for the 063 A-DNA complex and from Neidle's*S2 *Ncrystal structure in which 036 the phosphate groups rotate so as to 048 point one oxy-anion in towards the intercalator, 072 allowing hydrogen-bonding. Fuller and Waring*S10 *Nhave suggested that 061 such hydrogen-bonding would explain the greater antibacterial 061 activity of proflavine over acridine itself, which presumably 063 corresponds to the greater stability of complexes involving the 072 former. Other work*S24*N, however, has suggested that hydrogen-bonding 063 is not particularly important and, in chapter 5, we shall offer 019 another explanation 050 overall interaction between drug and nucleic acid. 062 Correspondingly, we do not consider that the outwards rotation 061 of phosphate groups is in any way disastrous. Indeed, since 065 the phosphate groups carry a relatively large negative charge, it 063 could be thought that such rotation into the solvent would ease 060 the extension process through the change in solvation energy 009 possible. 062 Although no consistent sugar pucker pattern appeared from 062 our models - there was certainly no indication of the dominant 071 C3'-*Iendo *Nor C3'-*Iendo*N-(3'-5')-C2'-*Iendo *Npatterns suggested by 058 Alden and Arnott's models and corroborated by Neidle's and 060 Sobell's crystal structures - we are relatively unconcerned. 064 Theoretical results*S23 *Nsuggest that different pucker patterns 055 possess similar energies; only small changes in atomic 057 coordinates need occur to change one pattern into another 043 and such small changes may be brought about 061 by interactions more subtle than those included in our model. 064 The existence of particular pucker patterns in compounds studied 065 crystallographically indicates that those patterns can exist, but 053 says nothing about the possibility of other patterns. 063 Own own models included no constraints designed specifically to 005 limit 070 sugar conformation; equally, we would suggest that Alden and Arnott's 073 calculations did pre-suppose the type of result they obtained, since they 062 allowed very little freedom in the sugar rings in their model. 046 The tendency for atoms separated by two others 038 to adopt *Itrans-*Nconformations after 069 extension is satisfying, since such conformations will undoubtedly be 048 of lower energy than their *Icis-*Ncounterparts. 062 by cyclic boundary conditions (ie on the DNA helix) with those 064 performed on models not so constrained (ie oligonucleotides), we 066 note both that the structural modifications progressed rather more 064 easily in the latter case and that the resulting structures were 030 considerably different. This 057 indicates the care which must be taken before conclusions 063 obtained either from crystallographic work on, or from computer 064 simulations of dinucleotide systems, can be extended to the full 060 DNA system and we are therefore loath to compare our results 062 for the full DNA molecule with the crystallographic structures 052 determined for dinucleotide intercalation complexes. 037 However, our model for a dinucleotide 035 complex is similar to that obtained 059 experimentally by Neidle, with an identical *SD*DB *Nvalue. 025 The agreement is probably 073 partly a lucky coincidence, but clearly there is no confict between these 022 two items of evidence. 076 Finally, the inability to extend the helix far beyond the 6.72A spacing 070 necessary for intercalation of a planar aromatic species is consistent 066 with the experimentally-determined low association constants found 073 for non-planar acridines such as 1,2,3,4-tetrahydroacridine*S11 *Nbecause 060 complete insertion of such compounds would require extension 046 beyond 6.72A to accommodate the non-planarity. 002 *? *[Chapter 3.3*] 006 .tg NI 005 .ul 1 028 3.3 : Base Rotation Studies. 006 .tg NA 075 We were attempting here to show the possibility for a single base in a 071 nucleic acid helix to rotate from its normal position out into solvent. 073 to stack onto the base, or equally to intercalate into the space provided 072 in the helix; either of these interactions would stabilise the modified 070 nucleic acid structure and could induce a deletion frameshift mutation 073 at the position where structural change had occurred. As in our studies 070 on helix extension, we were concerned only with determining structural 066 limitations on a nucleic acid molecule and not with the energetics 015 of the process. 054 We studied first a model of a trinucleotide. We 071 attempted to rotate the central portions of this molecule about an axis 070 parallel to the helix axis which passed mid-way between the phosphorus 061 atoms above and below the central sugar group, whilst keeping 070 all bases perpendicular to the helix axis. Since only the glycosidic 067 nitrogen atoms of the bases were included in our model, maintaining 055 this perpendicularity was performed by constraining the 044 difference between the coordinates of carbon 066 and nitrogen atoms in all glycosidic links at their normal values. 022 No attempt was made to 065 require the outer residues to maintain standard conformations and 067 orientations relative to the helix axis so as to allow them to link 070 onto a continuing and undistorted helix, and correspondingly the model 066 was typical of an isolated trinucleotide molecule rather than of a 016 fragment of DNA. 072 Rotation, which was such as to move the (notional) base out through 068 the narrow groove of the miniature helix, proceeded easily until the 073 base had turned through 90*D?*N. Beyond this point, large discrepancies 065 from target values occurred for the constrained quantities. The 070 and the final structure could not form part of a continuing DNA helix. 070 It appeared that some freedom at least was required in the position of 042 the sugar groups adjacent to the rotation, 064 since, when we repeated this calculation with strong constraints 071 placed on the conformation and orientation of these groups, we found it 053 difficult to induce more than a few degrees rotation. 070 Our next set of calculations were performed on a model containing 073 five sugar residues. By imposing strong conformational constraints only 072 on the outer two residues, we attempted to show that base rotation could 072 occur within the DNA helix without causing more than local disruption to 074 the molecule. We considered that residues adjacent to the rotating group 074 could possess abnormal conformations, provided that the orientation of the 070 bases joined to them was not markedly changed but we required that the 076 structure beyond these groups be normal. The complete strategy is given in 074 table 3.3. Note that the sense of rotation this time was such as to move 075 the base out through the wide groove of the helix - we felt that this would 066 result in a structure which could be stabilised sooner by stacking 057 interactions, since a small rotation into the wide groove 055 will make the base considerably more accessible than an 043 equivalent rotation into the narrow groove. 074 The results obtained were particularly interesting, since they showed 076 that, whilst it was relatively hard to rotate the base through the first few 064 degrees away from its normal position (four cycles of refinement 073 were necessary to achieve convergence on the initial increments), further 072 (we did not try to go beyond this), all constrained quantities were well 051 within the tolerances imposed on them; the maximum 039 bond-length discrepancy was 0.0029A and 045 discrepancies on other constrained quantities 060 were similarly small. (The final structure, after building 072 up a complete nucleic acid framework around it, is shown in figure 3.5.) 058 This tends to suggest that, if a base should move outwards 066 from its normal position, it will be relatively straightforward to 041 continue the process, especially with the 055 increasing stabilisation caused by stacking of aromatic 034 molecules externally to the helix. 059 The torsional angles in those sections of the backbone 062 close to the rotated base are given in table 3.4. There have 066 been relatively large changes in almost all these angles, which is 065 perhaps to be expected with the large amount of structural change 064 which has taken place in the helix. The sugar groups on either 066 side of the rotated base were found to possess C3'-*Iexo *Npucker, 065 whilst that group attached to the base itself possessed C2'-*Iexo 009 *Npucker. 002 *? *[Chapter 3.4*] 006 .tg NI 005 .ul 1 017 3.4 : Discussion. 006 .tg NA 060 We have described a model of a nucleic acid helix which 069 appears to behave in a manner which is consistent with the properties 071 expected of DNA. It has sufficient flexibility to allow intercalation 064 to take place at every other site along its length (but not more 027 frequently) without causing 055 great distortion in any of the quantities most basic to 021 a molecular structure 006 .tg NI 029 at any stage during extension 006 .tg NA 063 untwisted indicated that the precise structure of intercalation 066 complexes would be determined as much, if not more, by more subtle 065 interactions between the component molecules as by limitations in 030 the nucleic acid helix itself. 065 The model did, however, possess structural constraints whose 064 existence in real molecules is debatable. Axis dislocation and 060 kinking are both processes which may occur to some degree on 066 complexing with other molecules, and we cannot at this stage state 068 firmly that such distortions would not result in intercalation being 061 possible at adjacent sites. It seems unlikely, though, that 064 these processes would greatly affect the results obtained, since 059 our results showed so unequivocally that the required helix 053 extension could not take place within the model used; 022 there would have to be 061 a fairly large deviation from it for the necessary structural 061 freedom to appear. Such deviation would be expected to show 071 up experimentally in its effect on the gross structure of DNA; no such 065 effects seem to occur - for example, the retention of layer-lines 057 on the x-ray diffraction patterns obtained from fibres of 064 DNA intercalation complexes suggests that kinking is not severe. 046 Nonetheless, we do not have a model which will 074 explain the known properties of medium-length bisacridine compounds*S12*N. 071 We shall return to this point in chapter 5, when we shall consider what 069 scale of distortion from our model would be necessary to complex such 048 compounds without violating neighbour-exclusion. 070 An important aspect of the model studied was that it demonstrated 068 *Ipathways *Nfrom known structures to hypothesised ones. It is not 068 built, given the available atoms, bond-lengths etc; it must also be 066 possible to change from the starting conformation to it through an 028 acceptably low-energy route. 068 We are particularly interested in the calculations which showed 063 that a nucleic acid base could rotate from its normal position, 069 embedded in the helix, out into the wide groove of the helix, without 059 changing more than the local structure of the helix. This 057 would place the rotated base in a position where it could 061 interact with other systems without affecting the rest of the 056 nucleic acid. The mechanism has been proposed*S5 *Nfor 062 one form of frameshift mutation; stabilisation of an abnormal 061 conformation of DNA by means of stacked aromatic heterocycles 055 could easily affect replication. However, it is worth 060 considering whether normal biological processes which access 062 information on DNA use a similar mechanism, for this mechanism 053 could well reduce the topological problems associated 058 with accessing and transcribing the sequence of purine and 065 pyrimidine bases which normally lie deep within the double-helix. 002 *? *[Chapter 3 Refs and Tables*] 003 .bp 003 .nj 003 .nf 005 .ul 1 006 .tg NI 009 Table 3.1 005 .ul 1 056 Values proposed for DNA twist angle after intercalation. 006 .tg NA 042 (Value in unextended B-DNA = 36*D?*N) 061 A_u_t_h_o_r_ V_a_l_u_e_ M_e_t_h_o_d_ 068 Lerman*S13 *N-9*D? *NModel-building studies 058 on acridine complex. 068 Lerman*S14 *N0*D? *NModel-building studies 077 Paoletti *A^ *NLe Pecq*S15 *N49*D?*N*t** *lTheoretical studies on 059 ethidium fluorescence 070 Wang*S16 *N10*D? *NEthidium buoyant density 046 studies. 071 Sobell*S1 *N10*D? *NX-ray data for ethidium : 059 dinucleotide complex. 073 Neidle*S2 *N33*D? *NX-ray data for proflavine : 059 dinucleotide complex. 073 Alden *A^ *NArnott*S3 *N18*D? *NComputer model-building 066 studies on acridine complex. 069 Waring*S28 *N18*D? *NProflavine unwinding of 054 supercoiled DNA. 069 Waring*S28 *N24*D? *NDaunomycin unwinding of 054 supercoiled DNA. 073 Pigram et al*S27 *N24*D? *NX-ray data for daunomycin : 050 DNA complex. 053 *t** *lThis result is not now considered valid*S17*N. 003 .bp 006 .tg NI 006 .ls 2c 005 .ul 1 009 Table 3.2 005 .ul 1 006 .sp 1c 049 Constraints used in Helix Extension Calculations. 006 .tg NA 095 C_o_n_s_t_r_a_i_n_t_ D_e_s_c_r_i_p_t_i_o_n_ W_e_i_g_h_t_i_n_g_ _f_a_c_t_o_r_ 063 a. Hathway's*S4 *Ncalculations : Extension of single residue in 057 trinucleotide constrained to form part of a DNA helix. 006 .sp 1c 055 1 Fix atoms C1 and N9 in (r,z) 100 059 residue 1 (*Sq*N) 500 006 .sp 1c 040 N9 in residues 2 and 3 006 .sp 1c 059 3 Maintain difference in *Sq*N-coords. 500 046 between residues 1 and 3 for 043 all atoms at value for C1 006 .sp 1c 055 4 Ditto, difference in z-coords. 100 006 .sp 1c 055 5 Increment z-coordinate of atoms 100 047 C1 and N9 in residues 2 and 3 039 by 3.36A in ten steps 006 .sp 1c 055 6 Maintain bond-lengths 50 006 .sp 1c 055 7 Maintain next-neighbour distances 30 006 .sp 1c 055 8 Prevent unfavourable non-bonded 10 026 contacts 006 .sp 1c 055 9 Fix all atomic coordinates 2 006 .sp 1c 056 10 Maximum coordinate change allowed 0.3A 033 in a refinement 006 .sp 1c 055 11 Refinements allowed per increment 1 052 b. Our calculations : Extension of single residue in 057 trinucleotide constrained to form part of a DNA helix. 050 Constraints 1-9 with the following additions: 006 .sp 1c 059 12 Decrement *Sq*N-coordinate of 5 047 atom N9 in residue 2 by 10*D? 008 *N.sp 1c 055 13 Increase r-coordinate of atom 5 048 O4 in linkage between residues 033 1 and 2 by 0.5A 006 .sp 1c 063 14 Ditto, *Sq*N-coordinate by -7*D? *N5 006 .sp 1c 055 15 Ditto, z-coordinate by 1.6A 5 006 .sp 1c 055 16 Ditto, r-coordinate of atom C5 in 5 035 residue 1 by 0.4A 055 17 Ditto, z-coordinate by -0.5A 5 006 .sp 1c 056 18 Maximum coordinate change 0.4A 006 .sp 1c 055 19 Refinements per increment 4 003 .bp 006 .tg NI 005 .ul 1 020 Table 3.2 continued. 006 .tg NA 095 C_o_n_s_t_r_a_i_n_t_ D_e_s_c_r_i_p_t_i_o_n_ W_e_i_g_h_t_i_n_g_ _f_a_c_t_o_r_ 059 c. Winding/unwinding of intercalation site in trinucleotide 043 constrained to form part of a DNA helix. 060 Constraints 1-4,6-9,18,19 with the following additions: 006 .sp 1c 059 20 Increment or decrement *Sq*N-coord. 500 041 of atom N9 in residue 2 006 .sp 1c 062 21 Increment or decrement *Sq*N-coord. 0,5,500 041 of atom N9 in residue 3 057 d. Extension of dinucleotide not constrained to form part 025 of a continuing helix. 030 Constraints 1,2,5-9,18,19 006 .tg NI 005 .ul 1 009 Table 3.3 005 .ul 1 006 .sp 1c 048 Constraints used for base-rotation calculations. 006 .tg NA 095 C_o_n_s_t_r_a_i_n_t_ D_e_s_c_r_i_p_t_i_o_n_ W_e_i_g_h_t_i_n_g_ _f_a_c_t_o_r_ 006 .sp 1c 055 1 Fix atoms C1 and N9 in (r,z) 100 059 residues 1 and 5 (*Sq*N) 500 006 .sp 1c 055 2 Ditto, residues 2 and 4 (r,z) 50 059 (*Sq*N) 250 006 .sp 1c 055 3 Fix r- and z- coords. of atoms 10 040 C1 and N9 in residue 3 006 .sp 1c 059 4 Decrement *Sq*N-coord. of atoms C1 500 036 *Nin fifteen steps 008 *D.sp 1c 061 *N5 Maintain difference in *Sq*N-coords. 500 046 between residues 1 and 5 for 043 all atoms at value for C1 006 .sp 1c 055 6 Ditto, difference in z-coords. 100 006 .sp 1c 055 7 Maintain bond-lengths 50 006 .sp 1c 055 8 Maintain next-neighbour distances 30 006 .sp 1c 055 9 Prevent unfavourable non-bonded 10 026 contacts 006 .sp 1c 055 10 Fix all coordinates 2 006 .sp 1c 056 11 Maximum coordinate change allowed 0.6A 033 in a refinement 006 .sp 1c 055 12 Refinements allowed per increment 4 003 .bp 006 .tg NI 006 .ls 3c 005 .ul 2 009 Table 3.4 058 Some torsional angles found in helix modification studies. 072 angle *Sw f y y*N' *Sf*N' *Sw*N' 006 .tg NA 006 .sp 1c 086 1. Unextended values*S6 *N281*D? *N212*D? *N58*D? *N130*D? *N147*D? *N282*D? 008 *N.sp 1c 093 2. Alden and Arnott's 299*D? *N220*D? *N25*D? *N156*D? *N174*D? *N274*D? *N(res. 1) 097 model with B-DNA*S3 *N192*D? *N180*D? *N187*D? *N84*D? *N177*D? *N274*D? *N(res. 2) 093 318*D? *N189*D? *N32*D? *N156*D? *N178*D? *N256*D? *N(res. 3) 006 .sp 1c 082 3. Berman et al*S20 *N300*D? *N225*D? *N50*D? *N213*D? *N281*D? 008 *N.sp 1c 093 4. Our trinucleotide 1_6_3_*D?_ *N166*D? *N1_9_4_*D?_ *N140*D? *N(res. 1) 113 (*SD*DB*S*d12 *N*l= 23*D?*N, *SD*DB*S*d23 *N*l= 44*D?*N) 146*D? *N185*D? *N252*D? *N(res. 3) 006 .sp 1c 097 5. Our pentanucleotide 1_2_3_*D?_ *N1_3_6_*D?_ *N1_7_3_*D?_ *N158*D? *N(res. 2) 112 model after rotation 3_5_4_*D?_ *N8_5_*D?_ *N1_1_3_*D?_ *N103*D? *N2_3_3_*D?_ *N1_9_6_*D?_ *N(res. 3) 089 of residue 3 164*D? *N2_4_1_*D?_ *N2_0_7_*D?_ *N(res. 4) 056 (Underlined values in (4) and (5) are those which have 039 undergone large changes.) 003 .bp 006 .tg NI 006 .ls 3c 005 .ul 1 025 References for Chapter 3. 006 .tg NA 056 1. Sobell H. et al *IJ.Mol.Biol. *D4_4_ *N(1977) 301 053 2. Neidle S. et al *INature *D2_6_9_ *N(1977) 304 066 3. Alden C.J. and Arnott S. *INuc.Acid Res. *D2_ *N(1975) 1701 060 4. Hathway R. *IChemistry Part II Thesis *NOxford (1975) 055 5. Drake J.W. and Boltz R.H. *Iin "Ann.Rev.Biochem." 026 *N(1976) 11 056 6. Langridge R. et al *IJ.Mol.Biol. *D2_ *N(1960) 38 052 7. Rollett J.S. *Iin "Crystallographic Computing" 046 *Ned. Ahmed, Munkesgaard (1970) 060 8. Scheraga H. et al *IJ.Phys.Chem. *D7_8_ *N(1974) 1595 054 9. Linnett J.W. *IQ.Rev.Chem.Soc. *D1_ *N(1947) 73 055 10. Fuller W. and Waring M.J. *IBer.Bunsen.Phys.Chem. 034 *D6_8_ *N(1964) 805 055 11. Dean A. *Iin "The Acridines" *Ned Acheson, Wiley 025 (1973) 789 067 12. Wakelin L.P.G. et al *IStudia Biophysica *D6_0_ *N(1976) 111 050 13. Lerman L.S. *IJ.Mol.Biol. *D3_ *N(1961) 18 059 14. Lerman L.S. *IJ.Cell.Comp.Physiol. *D6_4_ *N(1964) 1 056 15. Paoletti J. and Le Pecq J-B. *IJ.Mol.Biol. *D5_9_ 026 *N(1971) 43 058 17. Pigram W.J. et al *IJ.Mol.Biol. *D8_0_ *N(1973) 361 067 18. Zunino F. et al *IBiochim.Biophys.Acta *D2_7_7_ *N(1972) 489 068 19. Bond. P.J. et al *IProc.Nat.Acad.Sci.USA *D7_2_ *N(1975) 4825 066 20. Berman H. et al *IProc.Nat.Acad.Sci.USA *D7_5_ *N(1978) 828 056 21. Arnott S. and Hukins D.W.L. *IBiochem.Biophys.Res. 042 Comm. *D4_7_ *N(1972) 1504 060 22. Levitt M. *IProc.Nat.Acad.Sci.USA *D7_5_ *N(1978) 640 051 23. Levitt M. *IJ.Am.Chem.Soc. *Nin press (1978) 053 24. Wakelin L.P.G. and Waring M.J. *IMol.Pharmacol. 034 *D1_0_ *N(1974) 544 057 25. *IFifth Jerusalem Symposium on Quantum Chemistry and 054 Biochemistry*N, ed Bergmann and Pullman 036 (1973) Academic Press 055 26. Patel D.J. and Canuel L.L *IProc.Nat.Acad.Sci.USA 035 *D7_4_ *N(1977) 2624 064 27. Pigram W.J. et al *INature New Biol. *D2_3_5_ *N(1972) 17 052 28. Waring M.J. *IJ.Mol.Biol. *D5_4_ *N(1970) 247 002 *?