*[Chapter 5.1*]
007 .ta 56r
006 .tg NI
005 .ul 1
059 Chapter 5 : Refinement of Approximate Molecular Structures.
005 .tc :
030 :"You've never had it so good"
010 :Macmillan
003 .tc
006 .tg NA
050 Basic thermodynamics shows that the degree to
063 which a given reaction will progress depends on the free energy
059 change in that reaction; the more negative the free energy
060 change, the more that reaction will tend to completion. In
060 terms of the structure of a molecular complex, the lower the
060 free energy of a given configuration, the more probable that
061 configuration is. For reasons discussed in chapter 2, it is
072 assumed that the internal energy of the complex *Iin vacuo *Nis the most
059 important term in producing this free energy and that other
050 terms, whilst perhaps not paralleling the internal
047 energy, do not outweigh it. Likely structures
064 for a complex therefore correspond to low energy configurations.
011 The sharper
064 and deeper a minimum is, the more confident we can feel that the
058 structure will correspond closely to that found in nature,
019 provided that there
064 is some reaction pathway connecting the uncomplexed constituents
061 with the final complex structure. In this chapter, we study
065 ways of finding these minimum energy configurations automatically
065 using the semi-empirical formulations of interaction energy given
011 previously.
006 .tg NI
005 .ul 1
041 5.1 : Methods used for Optimisation*S1*N.
006 .tg NA
069 We used two basic methods for locating minimum energy structures
054 of complexes and these can be described most simply as
067 "gridsearch" and "gradient" techniques respectively. Suppose, for
066 described in terms of "n" variables (and we are unconcerned at the
054 moment what these variables actually are), then we may
060 consider the variables as forming an n-dimensional space and
064 the problem is to find the minimum value of some energy function
080 f(x*d1*l,...,x*dn*l) within that space. Gridsearch techniques construct a mesh
067 of points over the space and evaluate the function at those points,
064 and it is immediately obvious which points correspond to minima.
059 Gradient techniques, on the other hand, start off from some
059 arbitrary point in the space and use the function value and
063 its corresponding gradient vector to move to successively lower
060 positions, until a minimum is located to within the required
063 tolerance. Both techniques have advantages and disadvantages.
064 A gridsearch technique is inherently very simple. All one
065 needs to do is produce a set of configurations covering the range
063 of values possible for the different variables and evaluate the
064 energy of each. Unfortunately, it is obvious that this becomes
061 impossibly time-consuming even with very few variables, since
062 the number of points which must be sampled grows exponentially
029 with the number of variables.
054 This limits the utility of the method to systems which
057 can be described in terms of a small number of variables.
062 On the other hand, one can see immediately from the results of
061 a gridsearch calculation what minima exist, whether there are
069 low-energy pathways between them and the starting point, and what the
052 rest of the conformational space looks like. There
064 are no problems associated with convergence such as we shall see
056 with gradient techniques. In other words, one can feel
050 and about the validity of the results it produces.
066 Gradient routines of the type we shall discuss here perform a
065 series of "linear-searches". Given an arbitrary starting point,
063 the algorithms determine a direction in the n-dimensional space
068 and the minimum function value is located in that direction. A new
063 search direction is then chosen and the entire process repeated
060 until some termination condition is satisfied. The various
058 gradient algorithms use different methods for choosing the
073 succession of search directions and we shall discuss three of these here.
059 Conceptually, the simplest method is that known as the
064 "Steepest Descent" algorithm. Each new line search takes place
062 along the direction in which the gradient is steepest, so that
052 the succession of points *Dx_*I*dk *N*lgenerated is:
006 .sp 1c
005 .ce 1
061 *Dx_*I*dk+1 *N*l= *Dx_*I*dk *N*l- *S*(*I*t***dk*)*D*lg_*I*dk
010 *N*l.sp 1c
099 where *Dg_*I*dk *N*lis the gradient vector and the scalar *S*(*I*t***dk*) *N*lindicates the use of
070 a linear-search within the routine. This would appear to ensure that
071 the function value always decreases during a search, which is true, but
026 the rate of convergence of
052 the algorithm can become very slow as the minimum is
064 approached. This is because the method takes no account of the
054 variation of curvature of the function with direction,
032 information which is provided by
042 the second derivative, or Hessian, matrix.
064 The other algorithms which we shall discuss generate search
005 .ne 4
064 directions which are conjugate*t** *lto one another with respect
005 .fn 1
032 *GG *Nif *Dp_*tT*G*lG*Dq_ *N= 0.
005 .en 1
067 to this Hessian matrix. It can be shown, for a quadratic function
059 (that is, one involving only terms of order two or less) of
064 n variables, that the minimum can be located in n searches along
062 conjugate directions if each search is performed exactly. In
052 other words, for quadratic functions, convergence is
066 guaranteed for these algorithms, which is obviously an improvement
042 on the steepest descent method. In fact,
069 convergence for non-quadratic functions is also improved considerably
035 by the use of conjugate directions.
073 Analytically, the succession of points *Dx_*I*dk *N*lwhich should be
085 generated for a quadratic function f(*Dx_*N) = *A*Dx_*tT*G*lG*Dx_ *N+ *Dg_x_ *N+ *Ic
049 *Nin terms of the Hessian matrix *GG*I*dk *N*lis:
006 .sp 1c
005 .ce 1
067 *Dx_*I*dk+1 *N*l= *Dx_*I*dk *N*l- *GG*(*N*t-*I*dk*)*N*t1*D*lg_*I*dk
010 *N*l.sp 1c
041 For a more general function, we would use
006 .sp 1c
005 .ce 1
085 *Dx_*I*dk+1 *N*l= *Dx_*I*dk *N*l- *S*(*I*t***dk*)*G*lG*(*N*t-*I*dk*)*N*t1*D*lg_*I*dk
010 *N*l.sp 1c
083 where the *S*(*I*t***dk*) *N*lindicates the need to locate the minimum along lines
010 of search.
071 However, the evaluation of the matrix *GG*I*dk *N*land its inverse
086 *GG*(*N*t-*I*dk*)*N*t1 *lcan be very time-consuming, and can also require considerable
061 storage space if there are many variables. When the storage
056 space is not a problem, the class of algorithms known as
065 "quasi-Newton" can give good results. These algorithms build up
093 an approximation *GH*I*dk *N*lto *GG*(*N*t-*I*dk*)*N*t1*l, which is initially the unit matrix
057 (making the first search a "steepest descent" search) but
042 the minimum is approached. The method of
070 updating *GH*I*dk *N*lvaries with the precise algorithm used; when we
064 used this type of algorithm, we updated *GH*I*dk *N*lby means of
054 the complementary Davidon-Fletcher-Powell*S2 *Nmethod.
062 If storage space is a problem, then a useful algorithm is
068 the conjugate gradient method suggested by Fletcher and Reeves*S3*N,
061 which generates the successive search directions using vector
032 arithmetic only. We have here:
003 .nj
003 .nf
006 .sp 1c
074 *Dx_*I*dk+1 *N*l= *Dx_*I*dk *N*l+ *S*(*I*t***dk*)*D*lp_*I*dk
073 *N*lwhere *Dp_*I*dk *N*l= -*Dg_*I*dk *N*l+ *Sb*I*dk*D*lp_*I*dk-1
059 *N*land *Sb*I*dk *N*l= 0, *Ik *N= 1
077 = *S?*Dg_*I*dk*S*l? *N/ *S?*Dg_*I*dk-1*S*l?*N, *Ik *S> *N1
003 .ju
003 .fi
006 .sp 1c
055 The first step is once again a steepest-descent search.
072 Results by Huang and Levy*S4*N, and later by Dixon*S5*N, have shown
053 that, when the minima along lines of search are found
064 exactly, then from a given starting point, the search directions
062 generated by various conjugate direction algorithms, including
060 complementary DFP and Fletcher-Reeves, are identical. This
058 would suggest that there was little point in incurring the
056 overhead of matrix arithmetic required with quasi-Newton
065 algorithms. However, this result holds only if the exact minima
066 are found along lines of search, and in practice this condition is
062 not satisfied. Usually, quasi-Newton algorithms are found to
064 approach minima more quickly than conjugate gradient algorithms.
064 This brings us to the next point, which concerns the method
065 to be of less importance than how these directions are generated.
066 In fact, there is considerable scope for wasting much machine-time
053 with the functions of interest here, if inappropriate
039 methods are used for the line-searches.
061 Conventional line-search routines follow the type of strategy
012 given below:
006 .sp 1c
006 .ll -3
006 .in 10
006 .ti -5
076 1.ZZZDetermine g1 = *Dg_*N.*Dp_*N, the gradient along the line of search; if
021 g1 *S> *N0 then exit.
006 .ti -5
068 2.ZZZ(Initial step) Take some step, a, and evaluate g2 = *Dg_*N.*Dp_
022 *Nat the new position.
006 .ti -5
075 3.ZZZ(Extrapolation) If g2 *S< *N0, set a = ka (where k is commonly 2), set
031 g1 = g2, and go back to step 2.
006 .ti -5
070 4.ZZZ(Interpolation) Otherwise, minimum along line has been bracketed.
070 Fit some curve (commonly a cubic or a parabola) between the two points
065 bracketing the minimum and move to the (algebraically-determined)
022 minimum of this curve.
006 .ti -5
064 5.ZZZReplace one of the two points used in (4) by this new point
066 and repeat operations (4) and (5) until some termination criterion
007 is met.
006 .ll +3
005 .in 0
067 The termination condition mentioned in (5) is usually that the
065 size of the gradient along the line of search has been reduced to
054 some proportion of its value at the start of the line.
059 The smaller this factor, the more accurately the minimum is
067 located along the line of search, but the more function evaluations
053 will be needed to locate it. It has been shown that
069 algorithms using conjugate directions converge satisfactorily if this
076 search should be reduced to half its initial value (Wolfe's condition*S6*N).
002 *?
*[Chapter 5.2*]
072 Haigh*S7 *Nhas investigated the behaviour of linesearch algorithms,
062 particularly when applied to functions of the type we consider
058 here, and has noted five main places in which conventional
026 algorithms are inadequate:
006 .sp 1c
006 .in 10
006 .ll -3
006 .ti -5
062 1.ZZZIn the choice of the initial step length. Some existing
058 optimisation routines are supplied with an estimate of the
062 minimum to be located. They then assume that the function is
066 parabolic, with given minimum and a known gradient at the start of
060 the line, and estimate an initial step-length on this basis.
043 Apart from rather begging the question, two
019 problems can arise:
006 .in +3
006 .ti -3
059 a.ZIf the estimate of the minimum is too high, the function
064 value at the start of the line will eventually become lower than
059 this estimate, which means that the equation specifying the
044 initial step will have no sensible solution.
006 .ti -3
064 b.ZIf the estimate is too low, then the initial step will become
047 excessively large as the minimum is approached.
006 .in -3
003 .br
063 Haigh solved this problem by basing the initial step-length for
058 linesearches after the first on estimates of the curvature
022 from earlier searches.
006 .ti -5
072 2.ZZZIn the method of extrapolation. Traditionally, each extrapolation
068 along the line of search doubled the previous step. If the initial
069 step was wrong by several orders of magnitude (as it quite frequently
060 was), then this would mean performing an excessive number of
069 function was parabolic and to increase the step length on this basis,
043 taking special measures if the curvature of
038 the function was found to be negative.
006 .ti -5
067 3.ZZZIn the method of interpolation. If the initial step made was
066 too large, then one of the two points bracketing the minimum would
051 be much further away from the minimum in value than
056 the other, and a phenomenon which he called "tortoising"
067 would occur. When a parabola was fitted between these two points,
064 the minimum calculated would be very close to the lower of them.
047 The process of fitting a parabola would then be
067 repeated a very large number of times before the true minimum along
062 the line of search was located. This was overcome by testing
045 for the situation on the first extrapolation,
042 and, if it occurred, backtracking from the
052 point with high function value before interpolating.
006 .ti -5
058 4.ZZZIn the method used to decide termination of a search.
057 We have mentioned Wolfe's criterion that convergence of a
062 conjugate direction algorithm is ensured if the gradient along
067 each line of search is reduced by at least half. Haigh found that
055 it was inefficient to demand higher accuracy than this.
006 .ti -5
060 5.ZZZBecause of the possibility of jumping out of the valley
063 containing a low minimum into another containing a higher local
059 minimum. The conventional logic would interpolate towards
063 a minimum whenever it found two successive points with opposite
068 gradients along the line of search, without checking whether in fact
064 these points bracketed a minimum with a value higher than points
068 elsewhere on the line. This problem was overcome by taking greater
053 care in the logic used to test for bracketing minima.
005 .in 0
064 Haigh had developed these conclusions mainly from examining
060 the behaviour of optimisation algorithms on certain standard
058 mathematical problems and also by studying small molecular
062 systems in which individual atoms interacted electrostatically
056 and through van der Waals potentials. Typical of these
063 was a system containing two O-H dipoles positioned close to one
059 another. After making the improvements mentioned above to
067 the standard linesearch algorithm, he found that the minimum energy
064 configuration of this system could be located in about one third
062 of the number of function evaluations required by the standard
011 algorithms.
061 The use of semi-empirical formulae of the type described
068 in this thesis to calculate energies of molecular systems results in
050 an overall function with the following properties:
006 .sp 1c
006 .ll -3
006 .in 10
006 .ti -5
066 1.ZZZIt does not behave quadratically except close to the minimum.
006 .ti -5
071 2.ZZZSome changes in variables (for example those which move non-bonded
065 atoms further apart) result in relatively small changes in energy
053 whereas others (those which stretch chemical bonds or
066 which move non-bonded atoms too close to one another) produce very
030 much larger changes in energy.
006 .ll +3
005 .in 0
059 When these functions are applied to systems containing
062 several hundred atoms (as they were here), two other important
018 properties appear:
006 .sp 1c
006 .in 10
006 .ll -3
006 .ti -5
005 .ne 5
058 3.ZZZEvaluation of the energy function is expensive*t***l.
005 .fn 1
061 of this function with carefully optimised code took about ten
008 seconds.
005 .en 1
006 .ti -5
060 4.ZZZRounding errors incurred during the function evaluation
022 become non-negligible.
006 .ll +3
005 .in 0
060 Points 1 to 3 provided good indication that attempts to
062 optimise molecular structures using semi-empirical interaction
064 potentials would be fraught with difficulty, and consequently we
068 used Haigh's linesearch algorithm throughout our studies (making one
057 or two minor improvements which will be mentioned later).
062 We did, however, perform one or two checks on the behaviour of
067 standard library algorithms such as those provided by NAG*S8*N; we
062 found that these algorithms behaved erratically, using grossly
055 excessive amounts of computer-time, when used to refine
044 structures containing several hundred atoms.
061 Point 4 warrants further discussion. When evalation of
067 a function involves calculating terms, each of which is obtained to
059 a certain precision, the relative error tends to accumulate
025 as the square root of the
065 number of terms. For example, if individual atom-atom terms are
071 obtained to ten significant figures (as would be the case on a computer
067 like the ICL 1906A) and there are ten thousand terms to accumulate,
068 the final answer will probably hold about eight significant figures.
066 Whenever an optimisation algorithm is taking steps small enough so
067 that the difference in energy between two successive points is less
056 than one part in 10*S8*N, the calculated difference will
066 be entirely without meaning. It is necessary to make appropriate
060 checks in optimisation algorithms to ensure that termination
040 occurs before this situation is reached.
067 Whilst points which differ in energy by only one part in 10*S8
067 *Nwill be so close together that it is physically not worthwhile to
070 procede further with the refinement, it is quite possible to calculate
072 the interaction terms in a way which gives far fewer significant figures
063 in the answer. We found that many of the approximations which
073 have commonly been used to speed up calculation of individual interatomic
069 terms produced effects which were akin to large-scale rounding error.
015 These included:
006 .ll -3
006 .in 10
006 .ti -5
006 .sp 1c
064 1.ZZZUse of "table look-up" techniques, in which the interaction
069 potentials for given atomic separations are obtained by interpolating
030 between two values in a table.
006 .ti -5
077 2.ZZZUse of polynomial approximations to functions such as *De*I*tx*N*l, when
044 only a few terms are included in the series.
006 .ti -5
071 3.ZZZNot evaluating interactions between atoms separated by more than a
017 certain distance.
006 .ti -5
077 4.ZZZUse of a function with a discontinuous derivative (such as the piecewise
070 linear approximation to a dielectric constant described in chapter 2).
006 .ll +3
005 .in 0
073 As an example of what can happen if these approximations are used to
069 speed up function evaluation, in figure 5.1 we show two contour plots
064 of the interaction energy between a dinucleotide molecule and an
056 intercalated acridine molecule, as the acridine is moved
074 *Ien masse *Nin its site in the dinucleotide. In one case the individual
068 interatomic terms were calculated to the full precision available on
075 the machine, whereas in the other case, approximations 1,3 and 4 were made.
071 being moved by about 1A in directions perpendicular to the helix axis.)
073 Whilst the two minimum energies found are almost identical, it is obvious
068 that an optimisation algorithm would locate one minimum considerably
061 faster than the other. What had been gained in the speed of
049 evaluation of the energy of any configation would
063 be lost several times over in the greater number of evaluations
031 required to locate the minimum.
052 Having learned the importance of avoiding those
065 "short-cuts" described above when evaluating the energy function,
067 we found that both the Fletcher-Reeves conjugate gradient algorithm
064 and the complementary DFP quasi-Newton algorithm were capable of
063 refining rapidly molecular structures possessing few degrees of
065 freedom, when coupled with Haigh's linesearch routine. We found
064 one main shortcoming in these circumstances, which was concerned
054 with the phenomenon of "tortoising". Haigh's routine
063 had tested whether the initial step made along a line of search
063 produced a new point on the opposite side of the minimum to the
058 starting point which had a much higher function value than
067 the starting point; if this occurred, then the routine backtracked
067 from the offending point. We found that the situation could arise
034 at any stage in the extrapolation,
070 owing to the rapid rise in non-bonded potentials at separations closer
066 than van der Waals minima. This fault was cured by ensuring that
063 points which bracketeed a minimum were of comparable magnitude,
020 and the behaviour of
056 the optimisation algorithms was improved in consequence.
063 Table 5.1 shows how the modified algorithms performed when
065 in fact was the system (9-aminoacridine.H+:dApA)). The variables
069 of the refinement were three coordinates describing the bulk position
070 of the acridine, which was therefore constrained to move *Ien masse*N.
063 With these degrees of freedom, the energy function behaves well
068 (see figure 5.1(a) for a two-dimensional slice through this function
058 for a similar system) and rapid convergence to the minimum
068 should be possible. As can be seen from the table, both algorithms
063 did locate the minimum rapidly; the conjugate direction method
058 required sixteen function evaluations to locate it to four
066 significant figures, whereas the quasi-Newton method required ten.
069 The quasi-Newton method is seen to be slightly better in terms of the
062 number of linear searches required to attain a given accuracy,
061 but is about twice as good in terms of the number of function
065 evaluations required. This is due to later linesearches made by
065 the quasi-Newton algorithm requiring only one function evaluation
058 to locate a minimum, because the algorithm has built up an
045 accurate approximation to the Hessian matrix.
062 The remainder of this chapter is devoted to a description
060 of the studies we made of intercalation complexes which were
062 based on numerical refinement of an energy function. Many of
044 the results can only be described by quoting
045 values obtained for interaction energies, and
065 we must point out here that these values depend critically on the
063 molecular fragments used in the calculations. This is largely
063 because of the ionic nature of the individual molecules and the
056 long range of electrostatic interactions. (The problem
065 constants for crystal structures*S9*N.) Consequently, it is not
067 possible to draw conclusions on the basis of the *Iabsolute *Nvalue
063 of the interaction energies quoted, other than that they appear
060 to be of the right order of magnitude. Comparisons between
068 *Irelative *Nvalues are more valid; we have tried wherever possible
039 to ascertain that the conclusions drawn
061 are unaffected by the precise molecular fragments used in the
013 calculations.
064 We start by studying the stacking of acridines in solution,
065 then examine the interactions of acridines with nucleic acid, and
057 finally see how daunomycin intercalation relates to this.
002 *?
*[Chapter 5.3*]
006 .tg NI
005 .ul 1
049 5.2 : Stacking of Acridine Molecules in Solution.
006 .tg NA
048 Some acridines aggregate in ionic solutions
034 by stacking on one another and the
059 degree of association varies depending on the nature of the
070 solvent, its ionic strength and on which member of the acridine family
076 is being studied. For example, Robinson and co-workers*S10*N, studying the
073 behaviour of acridine orange (3,6-di-(dimethylamino)-acridinium chloride)
065 in solution found that the equilibrium constant for the reaction:
006 .sp 1c
005 .ce 1
025 2A -*S> *NA*S...*NA dimer
006 .sp 1c
069 increased if the ionic strength of the solution increased and also if
069 small quantities of methanol, dioxan or urea were added. They found
084 that, in 0.1M NaCl, the free energy change *SD*DG*(?*T1*)2 *Nwas about -24kJZmol*t-1
066 *land that the enthalpy of the reaction was about -38kJZmol*t-1*l.
069 An approximate analysis of the various contributions to this enthalpy
065 acridine molecules and that other terms were small by comparison.
070 An intuitive model for the acridine stacks would place successive
051 molecules in van der Waals contact with one another
037 (and separations of between 3A and 4A
075 are suggested spectroscopically*S11*N), with the molecules aligned parallel
055 to one another so as maximise overlap. The similarity
075 between this model and the conventional model for intercalation is obvious;
071 instead of having a continuous stack of acridines, intercalation merely
036 replaces most of them by base-pairs.
075 However, there are two points to be noted before we accept this rather
071 nice model of acridine stacking. Firstly, Wright*S11 *Nhas found that
070 3,6-di-(t-butylamino)-acridine molecules stack with similar degrees of
064 association to other acridines. It is manifestly impossible to
065 align these t-butyl compounds parallel to one another at the same
067 spacing that would be found with a more completely planar acridine,
068 since the bulky t-butyl groups would interact very unfavourably with
070 one another. Therefore, it must be possible to introduce some degree
063 of randomness into the orientation of the stacked molecules (by
069 rotating each one relative to the one above, whilst still maintaining
064 the stacking) without losing much interaction energy. At first
069 sight, this would appear to be at variance with Robinson's conclusion
074 that the majority of the interaction energy results from dispersion terms,
039 since introducing such randomness would
043 lose much of the overlap between molecules.
071 More importantly, the individual acridine molecules are protonated
066 under the conditions of the experiments carried out to demonstrate
072 positive charges 3.5A apart, and although this would be reduced somewhat
077 when the charge was delocalised over the acridine molecules, our calculations
068 show that there is still a residual electrostatic interaction energy
054 of some 160kJZmol*t-1 *lbetween acridinium ions placed
072 3.5A apart in vacuo. This has great bearing on the neighbour-exclusion
060 principle of intercalation; if the protonated acridines can
064 be stable stacked 3.5A apart in ionic solution when an empirical
063 calculation would show them to be very much destabilised, it is
055 unreasonable to suppose that repulsion between residual
059 charges on these acridines prevents them from intercalating
020 at sites 6.8A apart.
068 Quite clearly, salt counterions in solution must be aggregating
068 around the acridine stacks so as to reduce the overall electrostatic
069 contribution to the interaction energy. This is confirmed partly by
073 the dependence of the degree of association on ionic strength, and partly
061 by the fact that the entropy of reaction becomes increasingly
072 unfavourable as the acridine concentration increases, demonstrating that
073 an increasing amount of ordering is taking place to stabilise the stacks.
070 Robinson regards this aggregation as a dielectric effect; we consider
068 this to be a rather loose use of the term and also not very helpful,
063 for we have no way of relating the ionic strength of a solution
060 around the system to the dielectric constant which should be
066 included when evaluating the interactions betwen residual charges.
070 We considered that a reasonable model for acridine stacking would
067 place successive protonated acridines in van der Waals contact with
070 with negative salt ions aggregating in the groove between each pair of
069 acridines so as to reduce the electrostatic interaction between them.
062 It was not possible to perform rigorous calculations on such a
063 model treating it as a set of discrete components, owing to the
059 large number of salt ions and solvent molecules which would
063 have had to be included. We therefore considered various less
062 rigorous techniques which might provide some information about
028 the properties of the model.
060 Firstly, we considered treating the aggregation of salt
060 ions around the acridine stack by means of a continuous band
063 possessing net negative charge close to the stack but gradually
054 merging into a continuous polarisable and electrically
063 neutral dielectric. This could be treated as a boundary value
063 problem; inside the cylinder defined by the stacked acridines,
061 the electrostatic potential would satisfy Laplace's equation:
006 .sp 1c
005 .ce 1
014 *SV2y*T1 *N= 0
006 .sp 1c
067 whereas, outside this region, the potential would satisfy Poisson's
005 .ne 3
009 equation:
006 .sp 1c
005 .ce 1
025 *SV2y*T2 *N= *Ik*T2*Sy*T2
008 *N.sp 1c
068 (where *Ik*T2 *Nis a screening constant, obtained, for example, from
067 Debye-Huckel theory) and the usual boundary conditions would apply,
061 that the potential and the normal component of its derivative
040 must be continuous across the interface.
067 In fact, this model is very similar to one used by Gilbert and
074 Claverie*S12 *Nto determine the effects of ionic strength on the degree of
063 intercalation of acridines into DNA, the only major differences
069 being that they included a fixed band of negatively-charged phosphate
042 acridine molecules were spaced 6.8A apart.
061 Their model of intercalation was stabilised by the attractive
066 electrostatic interactions between positive acridines and negative
059 phosphate groups and the solution to the equations defining
062 the system (similar to those given above, with another Laplace
065 equation describing the phosphate band) showed quite convincingly
048 that the size of this *Ifavourable *Ninteraction
047 was reduced as the ionic strength increased, in
070 accordance with experimental results. We felt that the model we have
061 described for acridine stacking was so similar to their model
063 that the same general conclusions would apply; the size of the
069 *Iunfavourable *Ninteraction between acridinium ions would be reduced
062 as the ionic strength increased. Correspondingly, we did not
032 pursue this calculation further.
064 It is of interest to enquire what excess negative charge is
059 required around a pair of stacked acridine ions in order to
067 counteract their electrostatic repulsion. A simple model was used
066 to answer this question; a pair of acridine ions were arranged in
069 a dimer separated by 3.4A (the normal van der Waals contact distance)
065 and we generated a series of configurations in which two chloride
069 ions of given charge were placed in the groove between the acridines,
054 determining the internal energy of the system for each
051 configuration, calculated as a sum of electrostatic
028 and dispersion energy terms.
065 Figure 5.2 shows the variation in the minimum energy of this
075 system as a function of ionic charge, for three separations of the acridine
063 ions. It can be seen quite clearly that only relatively small
067 whilst it would be foolish to read too much into the precise values
058 obtained, a residual charge of about -0.3 electronic units
067 yields an interaction energy for the system which is similar to the
071 enthalpy measured experimentally*S10*N. The reason why a low negative
071 charge can stabilise the repulsion between two unit positive charges is
052 that these positive charges are delocalised over the
071 entire acridine molecule; a charge of -0.3 units on an ion is as great
059 as the residual charge on any of the atoms in the acridine.
073 We calculated the interaction between two stacked acridine molecules
067 arising from dispersion energy terms, as a function of the relative
048 orientation of the two acridines. Robinson*S10
078 *Nestimated that this dispersion energy amounted to some -40kJZmol*t-1*l, but,
041 along with other workers, considered that
043 the stacked acridines were aligned parallel
073 to one another. We set up this model initially, with various members of
073 the acridine family, and calculated the dispersion energy as one molecule
067 was rotated about an axis passing through the centre of both. The
059 variation found for two 10-methylacridinium cations stacked
075 3.36A apart is shown in figure 5.3; 0*D? *Non this plot corresponds to the
073 two molecules being superimposed, atom for atom, on one another. It can
077 be seen that, apart from the region around 0*D?*N, where the methyl hydrogens
075 are placed unfavourably close to one another, the dispersion energy remains
070 remarkably constant at around -20kJZmol*t-1 *lfor all rotation angles.
070 With separations of around 3.25A between molecules, the minimum energy
061 was found to become somewhat lower, and with other members of
062 comparable to the value suggested by Robinson from analysis of
021 experimental results.
063 The following conclusions can be drawn from these results:
006 .in 10
006 .ll -3
006 .ti -5
006 .sp 1c
069 1.ZZZThat large interaction energies arising from electrostatic terms
049 must be treated with great caution if the systems
040 are in an ionic solution, because little
049 aggregation of positive and negative charges need
071 occur before the electrostatic interactions are completely neutralised.
044 (However, electrostatic interactions between
074 residual charges far removed from solvent are not necessarily negligible.)
006 .ti -5
006 .sp 1c
075 2.ZZZThat dispersion forces between large planar molecules are non-specific
073 and the subtle interplay between the interactions of closely spaced atoms
074 and those of others further apart means that the total interaction between
069 two planar molecules stacked on one another can be fairly independent
040 of the orientation of the two molecules.
070 (A similar conclusion has been obtained by Polozov*S13 *Nin connection
070 with the stacking energies of nucleic acid base-pairs on one another.)
006 .ti -5
006 .sp 1c
068 3.ZZZThat Scheraga's*S14 *Nparameterisation of dispersion potentials
037 predicts optimum interaction energies
066 between aromatic heterocycles which are similar to those suggested
059 experimentally. However, the predicted optimum separation
055 of stacked molecules is some 3-5*A> *Nlower than values
030 obtained crystallographically.
005 .in 0
002 *?
*[Chapter 5.4.1*]
005 .ul 1
006 .tg NI
029 5.3 : Acridine Intercalation.
006 .tg NA
061 between dinucleotides and intercalated acridines, in order to
052 explain the discrepancies arising in the correlation
068 between the acridines' degree of protonation and their antibacterial
071 properties (see figure 1.5). The calculations were made using methods
061 which we have since found to exaggerate interaction energies.
020 However, checks made
061 using CNDO/2 residual charges and Scheraga's parameterisation
056 of van der Waals terms showed that the following general
028 conclusions were reasonable:
006 .sp 1c
006 .ll -3
006 .in 10
006 .ti -5
061 1.ZZZThat the interaction between a protonated acridine and a
065 dinucleotide was appreciably greater than the corresponding value
030 for the unprotonated compound.
006 .ti -5
064 2.ZZZThat the interaction energy for the protonated acridine was
065 sufficiently high to result in the formation of a stable complex,
055 taking into account the likely loss in solvation energy
017 on intercalation.
006 .ti -5
066 3.ZZZThat the interaction energy between unprotonated acridine and
068 nucleic acid was generally insufficient to produce a stable complex.
061 However, in the case of acridines possessing a nitro-group, a
070 relatively large electrostatic interaction was found with both neutral
054 and protonated forms, and such compounds were expected
051 to interact well with nucleic acid in either state.
006 .ti -5
072 4.ZZZThat high interactions between protonated acridine and nucleic acid
066 could be obtained both with the long axis of the acridine parallel
058 to the base-pairs (Lerman's model*S15*N) and also with the
070 long axis at right angles to this (Pritchard's model*S16*N), but that,
063 slightly higher values were found with Pritchard-type complexes
022 than with Lerman-type.
006 .ti -5
067 5.ZZZThat compounds containing substituent groups which led to high
050 charge separations interacted more favourably with
066 dinucleotides containing G-C base-pairs than with those containing
010 A-T pairs.
006 .ll +3
005 .in 0
062 We now propose to give some explanation for these results
058 and also to study other aspects of acridine intercalation.
065 Many of the attempts which have been made to rationalise the
066 different properties of intercalation complexes have been based on
065 two assumptions: firstly, that protonation of an acridine places
063 a unit positive charge on the ring nitrogen, and secondly, that
064 suitably placed amino-groups can hydrogen-bond to DNA phosphate.
056 In figure 5.4, we indicate residual charges found on the
072 atoms in protonated acridine, 9-aminoacridine and proflavine, calculated
005 .ne 5
071 using the CNDO/2 approximation*t***l. (Charges on hydrogen atoms have
005 .fn 1
070 *t** *lCalculations of the residual atomic charges in acridine cations
065 have been made before, for example by Sharpless and Greenblat*S17
082 *Nand by Lang and L*(*S?*No*)ber*S18*N. It seems unfortunate that the sum of the
065 residual charges published by these workers was in no case unity.
005 .en 1
060 been condensed onto the heavy atom to which they are bound.)
059 Note that, whilst formally protonated on the ring nitrogen,
063 in all cases, very little residual charge is left on this atom,
061 which means that one of the reasons put forward by Pritchard,
069 Blake and Peacocke*S16 *Nfor their model of intercalation, namely the
061 ability of the charge on ring nitrogen to interact favourably
066 Substituting the acridines at positions 3 and 6 with amino-groups,
045 giving proflavine, makes little difference to
062 the amount of charge on the central ring (slightly over half),
048 but does result in almost one third of a unit of
044 charge moving onto each of the amino-groups,
053 leaving the remainder of the atoms in the outer rings
060 more negatively charged than in acridine. The calculations
060 described in chapter 3, showed that an *Ioutwards *Nrotation
053 of the phosphate groups was likely on helix extension
063 and this would disfavour hydrogen-bonding with the amino-groups
054 in compounds like proflavine. However, electrostatic
068 interactions are of longer range than hydrogen-bonding interactions,
067 and a movement of positive charge outwards onto the amino-groups in
059 proflavine would tend to stabilise the complex, even though
074 hydrogen-bonding could not occur. Previous results*S19 *Nhave shown that
061 hydrogen-bonding was not necessarily important in stabilising
058 complexes between ethidium analogues and nucleic acid, and
063 we would suggest that the changes in static charge distribution
050 caused by substituents on the aromatic nucleus are
015 more important.
068 To determine how the interaction energy between an intercalated
059 acridine and nucleic acid varied as a function of unwinding
074 angle at the intercalation site, we set up a model of (proflavine.H*t+ *l:
041 d(A-A).d(T-T)) in a Lerman-type structure
025 using dinucleotide models
080 with *SD*DB *Nvalues between 3*D? *Nand 39*D?*N, and refined the position of the
066 intercalated acridine by means of the quasi-Newton algorithm*S2*N.
066 The energy, calculated as a sum of van der Waals and electrostatic
073 norm of its gradient was typically less than 0.0001 kJ mol*t-1 *lA*t-1*l.
073 The variation in energy as a function of *SD*DB *Nis shown in figure 5.5,
066 and is seen to be relatively small over the range 15*D?*N-25*D?*N,
070 with a minimum when the dinucleotide was unwound by about 13*D? *Nfrom
063 the normal B-DNA value. Interestingly, this is the same value
063 which resulted from the process of helix extension described in
066 chapter 3. Measurements of supercoil reversal by proflavine have
080 suggested*S20 21 *Nthat 18*D? *Nunwinding occurs on binding to DNA, which is not
057 dissimilar to this figure. The minimum energy structure
057 is illustrated in figure 5.6; as well as a space-filling
064 representation looking towards the wide groove, we also show the
062 overlap between acridine and base-pairs looking down the helix
055 axis, and compare it with structures suggested by Patel
073 and Canuel*S22*N, from nmr data, and by Alden and Arnott23, from computer
064 modelling calculations. Although we used a different base-pair
061 sequence from these workers (ApA instead of CpG), it is clear
061 that the overlap between acridine and base-pairs found in our
070 calculations corresponds more closely to the experimentally-determined
044 structure than to the theoretical structure.
002 *?
*[Chapter 5.4.2*]
032 The position of the minimum
060 was determined by an interplay between various van der Waals
066 terms; starting from a structure unwound by 36*D?*N, in which the
055 base-pairs were superimposed on one another, increasing
076 *SD*DB *Nproduced a slight increase in the van der Waals interaction between
056 base-pairs and the acridine. Further winding swung the
062 between positive acridine and negative phosphate could only be
065 achieved by bringing the acridine into unfavourably close contact
065 with these sugar groups. It is interesting to see how the total
065 interaction energy was made up; for the minimum energy structure
065 (*SD*DB *N= 23*D?*N), a breakdown of terms is given in table 5.2.
071 Note the dominance of the electrostatic terms; favourable interactions
066 with the phosphate groups and the bases are offset by unfavourable
060 interactions with the sugar groups. (Interactions with the
055 phosphate groups are favourable, largely because of the
067 formal negative charge on these groups, but also because the oxygen
072 atoms linking phosphorus to sugar have abstracted some additional charge
064 from the sugar ring. A similar abstraction of about -0.2 units
065 of charge by each of the base groups makes these bases negatively
068 charged, but leaves a residual positive charge of about 0.5 units on
067 each of the sugar rings.) The total van der Waals energy of about
048 -37kJ mol*t-1 *lbound acridine, is mainly due to
058 interactions between acridine and base-pairs, as expected.
057 When these calculations were repeated for protonated
069 9-aminoacridine, a higher interaction energy between drug and nucleic
036 acid was found than with proflavine,
059 and this may explain the greater anti-bacterial activity of
022 9-aminoacridine*S27*N.
062 However, we found that the interaction between 9-aminoacridine
064 and nucleic acid was greater with a Pritchard-type model for the
070 complex than with a Lerman-type model. To see why this was the case,
063 look once again at figure 5.4. Because the positive charge on
066 a greater electrostatic interaction, both with base-pairs and with
055 phosphate, is obtained in the Pritchard-type structure.
072 It is interesting to note that kinetic studies have suggested*S24 *Nthat
064 the binding of 9-aminoacridine to DNA takes place by a different
039 mechanism to the binding of proflavine.
057 The relatively high electrostatic interaction energy
056 found between proflavine and the nucleic acid base-pairs
056 warrants further discussion, because this is a source of
055 stabilisation whose importance appears not to have been
065 generally appreciated. Seeman's*S25 *Ncrystal structure for the
060 complex formed between 9-aminoacridine and ApU, in which the
059 nucleic acid had not associated into a double-helical form,
058 showed that an electrostatic interaction between phosphate
060 and acridine was not necessary for the formation of a stable
071 complex. The figures we gave in table 5.2 indicate that electrostatic
063 interactions with base-pairs are of the same order of magnitude
061 as the interactions with phosphate in a normal double-helical
056 nucleic acid, and correspondingly, this may provide some
053 explanation of how Seeman's structure was stabilised.
065 We investigated next the interaction between 9-aminoacridine
034 and single-stranded nucleic acids.
061 Pritchard, Blake and Peacocke*S16 *Nsuggested their model for
065 acridine intercalation partly because of the observed interaction
037 with single-stranded polynucleotides,
038 and we were interested to know whether
061 their model did give an appreciably more stable structure for
034 the complex than the alternatives.
070 Approximate structures for (9-aminoacridine.H*t+*l:dApA) were set
072 varying between 3*D? *Nand 35*D? *Nand with the acridine positioned in a
071 Lerman-type or Pritchard-type manner. We then refined the position of
065 the acridine cation, once again using the quasi-Newton algorithm.
021 The resulting optimum
067 interaction energies found are plotted in figure 5.7. We see that
061 complexing in the manner of Pritchard's model gives an energy
050 of interaction between dinucleotide and drug which
030 becomes more favourable as the
062 helix is wound up, and, bearing in mind the change in internal
077 energy of the dinucleotide with winding shown in *S?*N3.2.2, is probably most
066 favourable when the twist-angle between bases at the intercalation
066 site is approximately the same as in the uncomplexed nucleic acid.
057 The optimum structure found is illustrated in figure 5.8.
066 With the acridine complexed in a Lerman-type orientation, the
052 interaction energy is seen always to be less than in
072 the alternative Pritchard-type orientation. It is interesting to note,
065 though, that only about one third of the interaction energy found
060 for 9-aminoacridine with a double-stranded dinucleotide in a
065 Pritchard-type structure was lost on removal of one strand of the
067 helix; this is due to the asymmetry of the complex. In fact, the
062 optimum interaction energy found between 9-aminoacridine and a
071 single-stranded dinucleotide is somewhat greater than the corresponding
070 optimum for proflavine intercalated in a double-stranded dinucleotide.
067 Although we have calculated only one term in the total energy cycle
059 for intercalation, this result is certainly in keeping with
070 the similar binding constants found between single- or double-stranded
034 nucleic acids and acridines*S26*N.
074 The greater interaction energies calculated between certain acridines
067 and dinucleotides containing G-C base-pairs than with dinucleotides
066 containing A-T base-pairs was due entirely to the greater polarity
067 of G-C pairs than A-T. If an acridine was substituted in a manner
063 which produced a large local charge separation, then this could
064 interact favourably with a complementary distribution on the G-C
062 pairs. This is one possible reason for base-pair specificity
079 by intercalating agents; other reasons are discussed in *S?*N5.4 and *S?*N6.2.
002 *?
*[Chapter 5.5*]
006 .tg NI
005 .ul 1
034 5.4 : Activity of Nitro-acridines.
006 .tg NA
034 The antibacterial activity of
061 the n-nitro-9-aminoacridines (n=1,2,3,4) is found*S27 *Nto be
038 unusually high, considering that these
043 compounds are only about 50*A> *Nprotonated
070 under the experimental conditions used to measure activity. Previous
054 calculations*S41 *Nshowed that the compounds possessed
074 relatively large charge separations on atoms around the nitro-group, which
076 could overlap favourably with complementary distributions on the base-pairs.
071 This would produce a high interaction energy with nucleic acid for both
064 protonated and unprotonated forms (see table 5.3 for some of the
063 interaction energies calculated) and we ascribed the biological
044 activity to these high interaction energies.
070 Further investigation of these compounds, however, has shown that this
052 may form only a part of the complete explanation for
069 the compounds' behaviour. In particular, note the following points:
006 .sp 1c
006 .ll -3
006 .in 10
006 .ti -5
005 .hy 3
077 1.ZZZThat, although each of the n-nitro-9-aminoacridines has an antibacterial
044 activity greater than that expected from the
084 compounds' pK*dA*l, this activity varied*S28 *Nas follows with 'n': 2=4*S<*N1*S<*N3.
006 .ti -5
077 2.ZZZThat recent studies*S29 *Non the anti-tumour properties of the compounds
073 n-nitro-9-(3'-dimethyl?amino?propyl?amino-)-acridine showed that activity
035 varied as follows: 2=4*S<*N3*Mj*N1.
006 .ti -5
053 3.ZZZThat a crystallographic study*S30 *Nperformed on
052 1-nitro-9-(3'-dimethyl?amino?propyl?amino-)-acridine
052 ("Ledakrin") showed that the compound was non-planar
072 (presumably due to the non-bonded contacts which would occur in a planar
064 compound between the nitro-group and the 9-amino group) with the
072 nitro-group twisted some 65*D? *Nout of plane and with the aromatic ring
049 system bent through 20*D? *Nabout C*T9*N-N*T10*N.
006 .ti -5
059 4.ZZZThat Ledakrin binds covalently to DNA *Iin vivo*S29*N.
006 .ti -5
081 5.ZZZThat the ease of polarographic reduction*S30 *Nof Ledakrin and its analogues
038 lies in the order 1*S>*N3*S>*N4*S>*N2.
006 .ti -5
059 6.ZZZThat reduction of aromatic nitro-compounds takes place
064 under anaerobic conditions in microsomes, by nitro-reductase and
059 utilising NADH as an electron donor, through hydroxylamino-
014 intermediates.
006 .ti -5
076 7.ZZZThat hydroxylamines are known to bind covalently to nucleic acid*S32*N.
006 .ll +3
003 .hc
005 .hy 1
005 .in 0
075 If the hydroxylamino derivatives of nitroacridines are responsible for
056 the anti-tumour properties of drugs related to Ledakrin,
050 then the approximate correlation found between the
082 Na*(*S?*Ni*)vely, the reason why, for example, the 3-nitro compound should be more
069 prone to reduction than the 2-nitro compound is illustrated in figure
066 5.10; an additional canonical form can be written for the 2-nitro
046 compound and this would be expected to lead to
058 greater stability of this compound, which would be lost on
039 addition of an electron (on reduction).
071 The non-planarity of Ledakrin in its crystalline state causes some
070 worry about the part intercalation can play in determining the effects
076 of this compound. If much of the bent aromatic system were to intercalate,
069 then it might be expected that a greater than normal extension of the
074 DNA helix would be required to accommodate it, and we have seen in chapter
073 3 that the helix does not possess sufficient flexibility for this. That
069 the nitro-group is also out-of-plane worries us less; because of the
005 .hc ?
071 adjacent dimethyl?amino?propyl?amino substituent, this group will have,
003 .hc
062 in any case, to be located in one of the grooves of the helix.
070 We performed molecular orbital calculations on the nitro-9-amino-
066 acridines using the CNDO/2 approximation, the results of which are
073 given in table 5.4. The calculated difference in energy between highest
074 occupied and lowest unoccupied molecular orbitals varied with the position
090 of the nitro-group as follows: 3 *S< *N1(ring bent) *S< *N4 *S< *N1(ring planar) *S< *N2.
076 This difference in energy has been used by other workers as a measure of the
073 ease of reduction of a compound (reduction being, to some extent, the end
052 result of adding an electron) and, for the compounds
066 substituted at positions 2,3 and 4, we see that there is a correct
071 prediction for the 1-nitro compound is incorrect, although it is better
046 with the ring system bent than with it planar.
073 The total energies calculated for the various molecules are similar,
070 with the exception of an entirely coplanar conformation of the 1-nitro
075 compound, which is shown to be some 1500 kJ mol*t-1 *ldestabilised relative
037 to the crystallographic conformation.
021 This 1-nitro compound
056 is found to be slightly more stable with the nitro-group
066 twisted out of plane, but with the ring system planar, than in the
071 crystallographic conformation, which might not perhaps be expected, but
077 the energy difference is small (being some 0.01*A> *Nof the total) and cannot
074 be expected to be accurate. The result does suggest, though, that little
051 energy penalty is paid for bending the ring system.
059 An intercalative binding of Ledakrin and its analogues
072 is therefore plausible, and the ease of reduction of the compounds could
034 explain their relative activities.
056 It only remains to discover why the anti-tumour activity
068 of Ledakrin is considerably greater than its 3-nitro analogue, since
070 experimental results show a relatively small difference in the ease of
072 reduction of the two compounds (and theoretical calculations predict the
075 opposite order*A?*N). To obtain an understanding of this, it is necessary
061 to consider what happens on covalent binding of hydroxylamino
017 compounds to DNA.
075 Relatively little is known about this reaction in the case of Ledakrin
047 and its analogues. However, related reactions
063 have been investigated (see Weisburger*S32 *Nfor a review); in
054 particular, Kriek*S33 *Nhas studied the interaction of
005 .hc ?
063 with DNA, and has found that attack occurs on the 8-carbon atom
037 of guanine, resulting in formation of
048 N-(deoxy?guanosine-8-yl)-2-acetyl?amino?fluorene
003 .hc
042 residues within the DNA (see figure 5.11).
077 We investigated the likely structures of intercalation complexes between
071 Ledakrin and its analogues and DNA, using the interactive graphics tool
071 described in chapter 4. It became clear that to obtain an appreciable
067 interaction between the molecules, it was necessary for the drug to
074 be placed in a Lerman-type complex; the long aliphatic sidechain attached
072 to the central ring of the acridine would prevent insertion of more than
069 one ring in a Pritchard-type complex. However, if the acridine were
066 inserted from the wide groove of the helix at an appropriate site,
055 a hydroxylamine group attached to C*T1 *Ncould approach
065 close to the guanine 8-carbon. On the other hand, a substituent
068 at C*T3 *Nof the acridine would be situated relatively far away from
069 this guanine atom, and it would be necessary to move the intercalated
073 acridine quite appreciably to improve the atoms' proximity. Figure 5.12
070 illustrates this point. (Intercalation from the narrow groove of the
071 helix would result in neither the 1- nor 3-carbon atoms in the acridine
066 being placed close to the 8-carbon in guanine, owing to the steric
034 effects of the deoxyribose groups.
047 The exceptional biological activity of the
071 n-nitro-9-aminoacridines and related compounds could be due to the high
073 interaction energy obtained when these compounds intercalate into nucleic
067 acid, both with protonated and unprotonated forms of the molecules.
043 It seems more satisfying, though, to assume
021 takes place, allowing
068 covalent binding to DNA to occur, and the relative activities of the
067 compounds would be determined partly by the ease of this reduction.
008 When the
071 structure of the intercalation complex is determined by the presence of
066 a bulky substituent on the aromatic nucleus, a hydroxylamino group
024 at some positions can be
046 considerably better disposed for reacting with
032 guanine residues than at others,
060 and, in the case of Ledakrin-like compounds, this results in
046 greatest activity with the 1-nitro derivative.
065 The ability to form a covalent linkage with one of the bases
063 in DNA gives us a second reason for base-pair specificity in an
020 intercalating agent.
002 *?
*[Chapter 5.6.1*]
006 .tg NI
005 .ul 1
042 5.5 : Bisintercalation of Acridine Dimers.
006 .tg NA
080 In *S?*N1.1.1, we described the work performed by Le Pecq's group*S34 *Nand
076 Waring's group*S35 *Non the interaction of various acridine dimers with DNA.
072 These dimers contained two acridine residues linked through an aliphatic
069 chain connected to amino-groups on position 9 of the nuclei, although
069 different nuclei and different backbones were used by the two groups.
069 Le Pecq's group found that intercalation of both nuclei occurred only
068 with those compounds whose backbones were sufficiently long to allow
070 intercalation to take place at non-adjacent sites along the helix, but
068 Waring's group found that certain dimers bisintercalated even though
038 their backbone of six -CH*T2*N- groups
056 was only long enough to place the 9-amino nitrogen atoms
078 at most 8.8A apart. More recent results by Waring's group*S36 *Nsuggest that
060 compounds contained substituents on the acridine nuclei, for
045 the ability to bisintercalate was found to be
042 critically dependent on this substitution.
063 Acridine dimers with backbones containing five -CH*T2*N- groups
070 (which allows about a 7.5A separation of the aromatic nuclei) produced
065 strange results, showing properties consistent neither with their
069 being purely monofunctional nor with their being purely bifunctional.
063 Compounds with shorter backbones intercalated only one nucleus.
056 (See figure 1.7 for an illustration of these compounds.)
075 The neighbour-exclusion principle is violated by these acridine dimers
075 if the nuclei are stacked perpendicular to the helix axis in the complexes.
078 Our results in chapter 3 show strong theoretical evidence for the existence of
072 such an exclusion principle, at least in a continuing helix possessing a
074 fixed axis, and Bond's studies*S37 *Non a (terpyridine)-platinum(II) : DNA
068 complex showed experimentally that neighbour-exclusion was satisfied
013 in this case.
036 Also, if the acridine dimers violate
044 neighbour-exclusion, bisintercalation should
058 occur whenever their backbone allowed more than about 6.8A
059 separation of the aromatic nuclei and this is not observed.
059 Consequently, we should prefer some alternative explanation
042 for the behaviour of these compounds which
033 is consistent with other results.
044 We investigated a model for interaction
050 of these compounds with DNA which involved kinking
065 of the helix between two non-adjacent sites. This model allowed
051 intercalation of both nuclei of the acridine dimers
050 with two base-pairs sandwiched between the nuclei.
062 suggested that bending and kinking of the helix can take place
055 relatively easily and we felt that these conformational
049 changes would be limited more by the unfavourable
067 contacts produced between atoms in the base-pairs on either side of
071 the kink than by geometric limitations in the backbone. We have shown
068 in *S?*N3.2.2 that, with intercalation occurring at alternate sites,
064 the remaining links could extend so as to place their glycosidic
071 link atoms 5.4A apart. We assumed that this amount of extension could
030 still occur in a kinked helix.
052 Our model was relatively simple, but allowed us
059 to ask certain relevant questions concerning the energetics
052 of interaction of acridine dimers with nucleic acid.
059 A schematic representation of this model is given in figure
064 5.13. The precise position at which the kinking occurs is left
064 undefined; we merely assume that it takes place somewhere along
069 the deoxyribose-phosphate backbone linking the sandwiched base-pairs.
071 Clearly, the amount of kinking required to accommodate the intercalated
035 nuclei is limited by the non-bonded
049 contacts incurred between atoms in the base-pairs
074 *DA *Nand *DB*N. Also, it is limited by the degree to which the aromatic
076 nuclei can intercalate, since this insertion causes the aliphatic side-chain
065 of the acridine dimer to come into contact with the nucleic acid.
078 Smaller degrees of insertion require smaller angles of kink when other factors
067 remain constant, but are likely to be associated with a loss in the
056 stacking interactions between acridine and nucleic acid.
023 We wished to know:
006 .sp 1c
006 .ll -3
006 .in 10
006 .ti -5
020 degree of insertion.
006 .ti -5
073 2.ZZZWhat upper bound could be placed on an angle of kink by the approach
054 of atoms in the base-pairs on either side of the kink.
006 .ti -5
063 3.ZZZHow the kink required for bisintercalation varied with the
065 length of the acridine backbone and with the degree of insertion.
006 .ll +3
005 .in 0
047 The first point was studied by considering
050 the interaction of a dinucleotide fragment of DNA,
063 extended so as to allow intercalation in the normal way, with a
072 molecule of 9-ethylaminoacridine, protonated on the ring nitrogen. The
060 latter compound was placed in a conformation similar to that
058 which would be adopted by the acridine dimers of interest.
071 We then calculated the energy of interaction between these molecules as
039 the acridine was inserted from the wide
050 groove of the helix, using a gridsearch technique;
035 a contour diagram of this energy is
072 given in figure 5.14. The minimum energy is obtained when the distance
029 *Dd *Nof figure 5.13 is 6.9A.
068 (With 9-aminoacridine, inserting the ring system by another angstrom
064 resulted in a slight increase in stability, but the gain was not
075 significant.) Insertion from the narrow groove of the helix resulted in a
005 .ne 8
046 considerable loss in interaction energy*t***l.
005 .fn 1
066 *t** *lThe question of the direction of intercalation of acridines
070 into DNA is a vexatious one. For example*S39*N, the binding constant
060 between proflavine and DNA which is glucosylated in the wide
060 groove is similar to that with normal DNA, and this has been
062 interpreted as implying that attack is from the narrow groove.
067 the rate of intercalation (as opposed to binding) into glucosylated
039 DNA is much lower than into normal DNA.
005 .en 1
049 The relatively small difference found between the
059 interaction energies of protonated 9-aminoacridine and this
071 f_r_a_g_m_e_n_t_ of an acridine dimer with a dinucleotide is consistent
063 with Waring's results*S35 *Nwhich indicate considerably greater
063 binding constants between acridine dimers and nucleic acid than
068 for monomers, since the total interaction energy for the dimers will
027 be correspondingly greater.
002 *?
*[Chapter 5.6.2*]
041 The maximum kink possible in the DNA
040 molecule was calculated using a model of
059 two adenine-thymine base-pairs stacked on one another. By
060 pivoting each base-pair about an axis joining the glycosidic
062 nitrogen link atoms (atom N*T9 *Nin the adenine group and atom
065 N*T1 *Nin the thymidine group), we calculated how the interaction
063 energy between the base-pairs varied with angle of pivot (which
063 is the same as the angle *Sq *Nin figure 5.13) as a function of
054 the separation of the glycosidic nitrogen atoms in the
069 base-pairs. The results are shown in figure 5.15 for the case where
061 the rotation axes in each base-pair were arranged parallel to
072 one another (that is, with 36*D? *Nunwinding in this part of the helix).
065 The important point to notice is the rapid rise in energy above a
069 given rotation angle for each separation of the base-pairs, caused by
035 atoms in the base-pairs approaching
064 one another more closely than the minimum in their van der Waals
056 potential curve. At 5.4A separation of the base-pairs,
043 15-17*D? *Nkink can occur on either side of
022 the base-pair sandwich
059 With smaller (and perhaps more reasonable) unwinding angles
048 at this point on the helix, the permissible kink
041 becomes smaller, until with no unwinding,
032 about 12-14*D? *Nkink can occur.
063 Finally, we considered what kink was required in the helix
062 to allow bisintercalation of an acridine dimer with a backbone
019 shorter than 10.2A.
035 The calculation was straightforward
060 (at least for the simple model considered here); elementary
027 trigonometry gives us that:
006 .sp 1c
005 .ce 1
043 *Dk *N= *Dq *N+ 2*Dd*Ntan*Sq *N- 6.72sec*Sq
008 *N.sp 1c
065 (where *Dk*N, *Dq*N, *Dd *Nand *Sq *Nare defined in figure 5.13).
052 Figure 5.16 shows how *Sq *Nchanges as a function of
068 *Dq *Nan*Dd *Nd with 5.4A extension of the non-intercalated residue;
053 maximum insertion of an acridine dimer whose backbone
040 is 8.8A long (with six -CH*T2*N- groups)
049 requires a kink of about 14*D? *Nwith this model.
059 These three calculations indicate that a model for the
060 bisintercalation of acridine dimers at non-adjacent sites is
068 reasonable. Whilst our representation of this model is simple, and
057 unlikely to be perfectly correct, it gives a satisfactory
064 explanation of the observed properties of these acridine dimers.
062 In particular, it explains why a dimer whose backbone contains
064 six -CH*T2*N- groups can bisintercalate without trouble, for the
055 kink required to obtain maximum insertion of the nuclei
058 can be obtained without causing undue strain in the helix.
036 The strange behaviour of the shorter
070 chain-length compounds*S35*N, containing five -CH*T2*N- groups, can be
061 explained by the fact that only very incomplete intercalation
060 of the two nuclei can occur without causing severe strain in
017 the nucleic acid.
063 We note that it is not necessary for the effects of such a
058 kink in the nucleic acid to be more than local. Sobell's
040 work*S40 *Non dinucleotide intercalation
065 complexes has indicated the possibility of another kink occurring
053 in the nucleic acid at the s_i_t_e_ of intercalation.
063 Although he too suggests that such kinking would be towards the
063 wide groove of the helix, we feel that small degrees of kink in
066 either direction are not ruled out, and it would be quite possible
069 for the various kinks to cancel one another out over several residues
013 of the helix.
062 An explanation can be given in terms of our model for the
060 lack of bifunctionality in the medium chain-length compounds
059 studied by Le Pecq's group*S34*N, which were substituted at
059 positions 2 and 6 on each nucleus with fairly bulky groups.
021 Since substituents at
068 these positions will approach the nucleic acid backbone more closely
066 than other atoms in the acridine nuclei, it is clear that a larger
059 total unwinding of the helix will be necessary at all three
055 residues involved in the interaction to accommodate the
054 acridine dimers than with the unsubstituted analogues.
048 Since the helix extension calculations described
059 in *S?*N3.2.2 showed that unwinding at an extending residue
063 was generally associated with a somewhat smaller winding at the
055 adjacent residue, we would expect that large amounts of
069 unwinding at consecutive residues would be unfavourable. This would
072 place steric constraints on the type of substituted acridine dimer which
021 could bisintercalate.
002 *?
*[Chapter 5.7.1*]
003 .br
006 .tg NI
005 .ul 1
031 5.6 : Daunomycin Intercalation.
061 Crystal structure determinations on daunomycin analogues
070 have been performed on N-bromoacetyldaunomycin*S42 *N(using relatively
067 poor quality crystals), on carminomycin*S43 *N(4-hydroxydaunomycin)
065 and on a pyridine adduct of daunomycin*S44 *Nitself. These show
064 similar properties and differ only in fine detail, with the main
039 structural attributes being as follows:
006 .ll -3
006 .in 10
006 .sp 1c
006 .ti -5
058 1.ZZZThe cyclohexene ring is in a half-chair conformation.
006 .ti -5
106 2.ZZZThe torsional angles *Sc*N(C*T9*N-C*T10*N-O*T29*N-C*T30*N) and *Sy*N(C*T10*N-O*T29*N-C*T30*N-O*T31*N)
069 are about 246*D? *Nand 292*D? *Nrespectively in the crystal structure
067 of daunomycin, and are very similar in carminomycin. However, the
066 value *Sy *Nis about 20*D? *Ndifferent in N-bromoacetyldaunomycin,
068 indicating a slightly altered disposition of the daunosamine residue
028 to the rest of the molecule.
006 .ti -5
065 3.ZZZThe daunosamine residue is located in an approximately axial
069 conformation on the cyclohexene ring in daunomycin, whilst the acetyl
022 residue is equatorial.
003 .br
006 .ll +3
005 .in 0
062 The preferred conformation of the cyclohexene ring in solution
061 has been found, using nmr spectroscopy, to be the same as the
036 crystallographic conformation*S57*N.
066 One model for the intercalative binding of daunomycin to DNA,
053 proposed by Pigram and co-workers*S45*N, is based on
038 the crystallographic conformation, and
058 involves intercalation of the quinone ring system and also
061 electrostatic binding of the daunosamine amino-group to a DNA
068 phosphate residue separated by two base-pairs from the intercalation
067 patterns obtained from fibres of daunomycin:DNA complexes, the most
072 reasonable structure for the complex was obtained with 12*D? *Nunwinding
068 of the helix per intercalated residue, and the ability of this model
074 to explain the dominant nature of electrostatic forces on the interaction,
065 to predict the maximum observed binding of one molecule per three
069 base-pairs and to rationalise the effects of structural modifications
064 such as N-acylation of daunomycin on its binding, has lead to it
030 gaining widespread acceptance.
067 Another model, proposed by Henry*S46*N, for the interaction of
067 daunomycin with DNA involved the alternative "flipped" conformation
066 of the cyclohexene ring. By means of this conformational change,
067 the daunosamine residue is suitably placed to allow the amino-group
062 to interact electrostatically with the phosphate one base-pair
058 away from the intercalated ring system. Furthermore, the
049 hydroxyl-group on the cyclohexene ring is allowed
023 to form a hydrogen-bond
064 to the phosphate group adjacent to the intercalated chromophore,
060 whilst the hydroxyl-group on the daunosamine ring could form
061 a hydrogen-bond to phosphate two base-pairs away. A maximum
066 number of functionalities were therefore involved in this model of
063 the interaction. Although the conformation of the cyclohexene
060 ring required was not that found crystallographically, Henry
067 suggested that there would be little energy penalty associated with
057 the transformation, because of the comparable bulk of the
063 equatorial acetyl-group and axial sugar group, and that, in any
067 case, this would be recouped by the greater interaction possible in
037 his model between DNA and daunomycin.
066 than that found crystallographically is not necessarily important.
055 However, analogues of daunomycin possessing an inverted
020 configuration of the
063 daunosamine hydroxyl-group show binding and activity comparable
069 to daunomycin itself*S47*N, which suggests that the hydroxyl-group is
056 not involved the interaction, contrary to Henry's model.
063 We investigated firstly the effects of conformation on the
061 stability of the daunomycin molecule, and secondly the nature
061 of the interaction between daunomycin-like compounds and DNA.
006 .tg NI
005 .ul 1
062 5.6.1 : Variations possible in the Conformation of Daunomycin.
006 .tg NA
071 The effect of varying the two torsional angles *Sc *Nand *Sy *Nwas
065 studied by performing a grid-search type of calculation, in which
059 we calculated the energy of the daunomycin molecule at 8*D?
080 *Nincrements about each of the bonds C*T10*N-O*T29 *Nand O*T29*N-C*T30*N. This
053 energy was considered to arise from van der Waals and
063 electrostatic interactions between atoms in the sugar group and
057 those in the rest of the molecule, ignoring terms between
066 bonded and next-neighbour atoms. The way the energy changed with
059 conformation is shown in figure 5.17; contours are plotted
065 at 20kJ intervals and show the behaviour around the minimum only.
080 The torsional angles found in crystal structure determinations*S42*NZ*S43*NZ*S44
066 *Nare marked, and are seen to lie in the region of minimum energy.
065 Whilst the contours plotted in figure 5.16 show a relatively
065 flat area around the minimum, outside this area, the energy rises
058 extremely quickly, due to unfavourable non-bonded contacts
063 We feel confident, therefore, that the area of stability of the
063 daunomycin molecule, when the sugar group is placed in an axial
072 conformation, is limited to about a 60*D? *Nrange in the torsional angle
080 *Sc*N(C*T9*N-C*T10*N-O*T29*N-C*T30*N) and to about a 120*D? *Nrange in the angle
039 *Sy*N(C*T10*N-O*T29*N-C*T30*N-C*T31*N).
056 For interest, we performed a similar calculation on
064 the hypothetical compound 'Q' (illustrated in figure A1.1) which
066 is a 1,2,3,4-tetrahydrobenzacridine bearing a daunosamine residue.
065 We assumed that the compound would be protonated both on the ring
060 nitrogen and on the sugar amino-group. (If this is not the
069 case for the unsubstituted compound under biological conditions, then
069 there will undoubtedly be some substituted analogue for which it is.)
033 The resulting contour plot, shown
045 in figure 5.18, is compressed in terms of the
070 angle *Sy *Ncompared to daunomycin, owing to repulsion between the two
046 positive charges, one of which at least is not
063 particularly delocalised. It is also rather expanded in terms
067 of the angle *Sc*N, due to the lack of substituents on the acridine
059 nucleus. However, the interesting point is that the range
046 of conformations possible is not dissimilar to
041 the range possible for daunomycin itself.
002 *?
*[Chapter 5.7.2*]
064 We then converted the standard daunomycin conformation into
037 a new form possessing an axial acetyl
057 residue (see figure 5.19), using the following algorithm:
006 .sp 1c
006 .ll -3
006 .in 10
006 .ti -5
094 1.ZZZConsider the atoms C*T9*N,C*T10*N,C*T11*N,C*T12*N,C*T13*N,C*T14 *Nin the cyclohexene ring
102 atom C8 at position *Dp_*T8*N, and also the points *Dq_*(*S1*T1*)0*N,*Dq_*(*S2*T1*)0*N, etc, which are
070 a unit distance along the side-chain bonds from atoms C*T10*N-C*T13*N.
006 .ti -5
052 2.ZZZDetermine the plane of the aromatic ring system
058 *Da_ *N= (*Dp_*T14*N-*Dp_*T9*N)*V^*N(*Dp_*T8*N-*Dp_*T9*N).
006 .ti -5
068 3.ZZZReflect *Dp_*T10 *Nto *Dp_*T13 *Nin the plane *Da_ *Nto produce
104 positions *Dp_*(*N'*T1*)0 *Nto *Dp_*(*N'*T1*)3 *Nand perform the same operation on *Dq_*(*S1*T1*)0 *Netc
052 to produce positions *Dq_*(*S1*T1*)*(*N'*T0*) *Netc.
006 .ti -5
131 4.ZZZThe new positions of atoms C*T10 *Nto C*T13 *Nare *Dp_*(*N'*T1*)0*N,*Dp_*(*N'*T1*)1*N,*Dp_*(*N'*T1*)2 *Nand *Dp_*(*N'*T1*)3*N.
006 .ti -5
079 5.ZZZThe group attached to atom C*I*dk *N*lat *Dp_*I*dk *N*lalong the direction
115 *Dq_*(*S1*I*dk*) *N*lhas rotated about an axis *Dq_*(*S1*I*dk*)*V*l^*Dq_*(*S2*I*dk*)*N*l', passing through a centre
160 *Dc_ *N= *Dp_*I*dk *N*l- *S*Dq_*(*S1*I*dk*)*N*l, where *Dp_*I*dk *N*l- *S*Dq_*(*S1*I*dk*) *N*l= *Dp_*(*N'*I*dk*) *N*l- *S*Dq_*(*S2*I*dk*)*N*l', to lie in the
096 direction *Dq_*(*S2*I*dk*)*N*l' from *Dp_*(*N'*I*dk*)*N*l. Perform these rotations to generate
065 the new positions of atoms in groups joined to the inverted ring.
005 .in 0
006 .ll +3
061 Evaluation of the energy difference between the standard
066 conformation of daunomycin and this "flipped" form of the molecule
065 was not easy, and it was necessary to make several approximations
063 before the calculation was possible. We adopted the following
010 procedure.
067 Firstly, since there was no guarantee that the most favourable
053 values for the torsional angles found in the inverted
064 structure would be those which had been produced by means of the
060 angles as variables and calculating the internal energy as a
060 sum of dispersion and electrostatic terms between non-bonded
066 and non-neighbour atoms. After twenty cycles of refinement using
064 the quasi-Newton algorithm, the internal energy had been reduced
064 by half and had become fairly stable, but was still considerably
060 higher than the corresponding value for the crystallographic
013 conformation.
059 We felt that the difference in internal energy between
062 the two conformations calculated using semi-empirical formulae
065 designed more for intermolecular interactions would be inaccurate
072 and consequently, we attempted to calculate this energy difference using
056 the CNDO/2 quantum approximation. Since the daunomycin
064 molecule contains more atoms than the available computer program
060 could handle, we studied a related molecule which lacked the
059 three aromatic rings of daunomycin, along with those groups
065 attached to them, and which contained merely the cyclohexene ring
065 and those groups attached to that ring. This molecule contained
068 forty four atoms, which was just within the capacity of the computer
008 program.
055 The total energies calculated for the molecule are
019 shown in table 5.5.
055 For both the protonated and unprotonated compounds, the
070 flipped conformation was found to be some 600 kJ mol*t-1 *lless stable
056 than its unflipped counterpart. However, the following
069 points must be borne in mind before this ridiculously large figure is
070 accepted as a true measure of the energy difference between the forms:
006 .sp 1c
006 .in 10
006 .ll -3
006 .ti -5
070 1.ZZZThe difference was only 0.1*A> *Nof the total energies calculated
058 that rounding error was limiting the precision attainable.
006 .ti -5
061 2.ZZZThere is no guarantee that the conformation generated by
056 the algorithm given above and subsequently refined using
060 semi-empirical potentials corresponded exactly with the true
069 minimum energy structure for the flipped form of the molecule; small
066 changes which might take place in the bond-angles and bond-lengths
058 could have relatively large effects on the internal energy
016 of the molecule.
006 .ti -5
064 3.ZZZThe CNDO/2 approximation*S53 *Nis known to exaggerate quite
064 grossly properties of molecules related to internal energy, such
028 as bond-stretching energies.
005 .in 0
006 .ll +3
063 Nonetheless, the result appears strange, even allowing for
070 possible gross errors in the calculation. After all, the sugar group
069 is at least as bulky as the acetyl group, and we might therefore have
059 expected that the opposite result would have been obtained.
054 The most rational explanation we can offer is that, in
077 the crystallographic structure, atoms O*T29 *Nand H*T23 *Nare well-positioned
062 for forming an intramolecular hydrogen-bond, which would close
086 the six-membered ring O*T29*N-C*T10*N-C*T11*N-C*T12*N-O*T23*N-H*T23*N, whereas, in the
042 "flipped" conformation, this cannot occur.
071 The existence of this hydrogen-bond has been suggested by Neidle*S44*N,
045 and, in carminomycin, the relevant proton has
046 been located in the required position for this
046 bond*S43*N. However, the energy of formation
073 of such a hydrogen-bond is unlikely to be more than about 25kJ mol*t-1*l,
063 over an order of magnitude less than the figure obtained above.
067 Other points, such as the fact that the amino-sugar group, adjacent
036 may have some bearing on the result.
060 It seems likely, on the basis of experimental evidence,
023 that daunomycin is more
058 stable with the cyclohexene ring in its crystallographical
070 conformation,. In this conformation, our results show that the sugar
061 group can adopt only a limited range of dispositions relative
066 to the aromatic ring system. Within the region of stability, the
070 internal energy appears well-behaved and relatively constant, which is
062 consistent with the different values of torsional angles found
052 in the crystal structure determinations performed on
050 daunomycin and its analogues. In particular, no
067 barriers are found separating one stable conformation from another,
066 which would hinder optimisation of the structure of daunomycin-DNA
022 complexes numerically.
064 The region of stability for a hypothetical daunoso-acridine
050 compound was similar to that found for daunomycin,
061 so that the existence of intercalation complexes between this
057 compound and DNA are not ruled out because of a different
023 preferred conformation.
002 *?
*[Chapter 5.7.3*]
003 .br
006 .tg NI
005 .ul 1
047 5.6.2 : Interactions between Daunomycin and DNA
006 .tg NA
053 The results of *S?*N5.6.1 led us to believe that
048 Pigram's model*S45 *Nfor the interaction between
061 daunomycin and DNA was more likely to be correct than Henry's
078 model*S46*N, and we based further studies on the crystallographic conformation
014 of daunomycin.
060 The interaction between daunomycin and nucleic acid was
065 studied in two stages. Firstly, we examined the molecules using
059 obtained approximate structures for the complex, these were
049 refined numerically on the basis of their energy.
069 Neidle's*S44 *Ncoordinates were used for the daunomycin molecule
043 and we studied the interaction of this with
060 nucleic acid fragments comprising a dinucleotide extended on
063 one chain by the sequence pdAp-, as illustrated in figure 5.20.
060 This was the smallest fragment which could illustrate models
058 similar to Pigram's without omitting potentially important
061 interactions, and was chosen so as to economise on the amount
066 of computation necessary. The nucleic acid structures were built
064 up from extended trinucleotide conformations obtained in chapter
036 3, with the terminal phosphate group
039 possessing a normal B-DNA conformation,
073 and were unwound at the intercalation site by between 5*D? *Nand 33*D?*N.
059 It will be recalled that the process of helix extension was
067 accompanied by a change in the twist of the helix at more than just
070 the intercalation site, so that these models corresponded to fragments
046 of DNA unwound by between -3*D? *Nand 25*D?*N.
057 The problems encountered when setting-up approximate
069 daunomycin:DNA complex structures using interactive computer graphics
067 have been discussed in *S?*N4.5. We had had particular difficulty
069 in finding the best interlock between the sugar residue of daunomycin
065 and the deoxyribose-phosphate backbone of DNA, owing to the large
036 number of atoms in the complex, and,
038 we chose to base further refinement on
064 structures which contained no obviously bad interactions, but in
063 which the amino-group of daunomycin and the appropriate nucleic
047 acid phosphate group were relatively far apart.
069 5.21, were based on a Pritchard-type*S16 *Norientation of the quinone
040 ring system between the base-pairs, with
044 insertion from the wide groove of the helix.
064 Adopting a Pritchard-type orientation for the initial model
068 meant that the methoxy-group at position 4 on the daunomycin nucleus
066 was inserted through the nucleic acid and lay in the narrow groove
052 of the helix. Pigram's model, however, placed this
055 group in the wide groove of the helix, by orienting the
065 quinone ring system more towards a Lerman-type*S15 *Norientation.
058 The two structures are not interconvertible by a numerical
064 optimisation, because there will be an energy barrier to passing
061 the methoxy-group through the helix. We do not believe that
057 this barrier will be large, since the methyl-group is not
061 very bulky, and the helix extension calculations described in
063 *S?*N3.2 showed that slightly more than a 6.72A spacing between
058 base-pairs could be achieved without causing undue strain.
067 The greater potency observed*S54 *Nfor the 4-methoxy derivatives of
066 both daunomycin and adriamycin (being as effective as their parent
064 compounds, but at up to ten times lower dose) could be explained
060 in terms of a larger activation energy to binding the parent
065 compounds than to binding of these derivatives, and this would be
060 expected if binding requires penetration of the helix by the
026 intercalating chromophore.
062 Ideally, we should have liked to compare the properties of our
065 model with those of Pigram's, but unfortunately the computational
023 expense ruled this out.
070 Also, because of this computational expense, it was necessary to treat
070 the nucleic acid molecule as a rigid unit, whose conformation had been
063 not realistic, but we hope that the errors incurred in this way
066 were not large. The assumption reduced the amount of calculation
068 required by at least half, since it eliminated the need to calculate
056 interaction terms between atoms within the nucleic acid.
070 We refined the approximate structures in three stages. Firstly,
067 we treated the daunomycin as a rigid unit, which could only move or
071 rotate *Ien masse*N, and we performed sufficient cycles of optimisation
062 using the quasi-Newton algorithm*S2 *Nto place the molecule in
067 an energetically-favourable position. This occurred very quickly,
067 and some ten line-searches were sufficient to reduce the derivative
022 of the energy function
006 .tg NI
060 in terms of the degrees of freedom available to the molecule
006 .tg NA
068 to negligible proportions. Due to the combination of a potentially
067 very strong electrostatic interaction between sugar amino-group and
070 nucleic acid phosphate two base-pairs away from the intercalation site
062 and the fact that the formulation used to calculate dispersion
061 and overlap energies did not indicate any great difficulty in
071 bringing planar aromatic systems somewhat closer than the 3.36A spacing
062 found crystallographically, the entire daunomycin molecule was
061 pulled towards this phosphate, moving the quinone ring-system
050 until it was less than 3A away from one base-pair.
065 The next stage of refinement treated the daunomycin molecule
070 as a set of rigid groups connected through bonds about which rotations
069 could occur, and attempted to minimise the interaction energy between
067 drug and nucleic acid, in terms of the torsional angles about these
063 quasi-Newton algorithm. This time, the optimisation proceeded
065 erratically, sometimes locating the minimum along lines of search
067 very quickly and sometimes wasting a great many energy evaluations.
066 Investigation showed that this was due to an inconsistency between
062 the values calculated for the energy and its derivatives; the
064 minimum energy value along a line of search did not occur at the
072 point at which the gradient along that line was zero. This meant that,
064 if the optimisation algorithm selected a point which lay between
071 that with minimum energy and that with zero gradient, the interpolation
042 routine would fail, and movement along the
029 line of search would be slow.
002 *?
*[Chapter 5.7.4*]
065 That the behaviour of the routine was sometimes good was due
061 to the fact that the routine did not attempt to locate minima
070 along lines of search precisely; if a point was found which satisfied
070 Wolfe's criterion*S6 *N(gradient along line of search reduced by half)
066 before the region of inconsistency was reached, then behaviour was
070 perfectly satisfactory. Since the discrepancy between energy minimum
056 and gradient zero was generally very small (of the order
072 of 0.01*D? *Nrotation about each bond), this termination condition could
024 frequently be satisfied.
066 Thorough testing showed that the discrepancy between function
063 and gradient occurred only when the degrees of freedom included
061 rotations. Whenever the variables involved merely cartesian
060 coordinates, the minima found from the two quantities agreed
058 to within machine accuracy. We were completely unable to
067 find out why this happened; the algebra derived seemed correct and
005 .ne 6
045 no errors could be found in the coding*t***l.
028 *t** *lIt seems particularly
058 galling that the difficulties arose because of attempts to
059 simplify the optimisation. Treating the molecule as a set
061 of units connected through rotatable bonds allows most of the
058 degrees of freedom available to the molecule, whilst still
059 retaining a managable number of variables. Because of the
066 potential utility of this method of structural refinement, we give
062 the algebra used in figure 5.22, in the hope that someone will
014 see the error.
005 .en 1
069 Because the discrepancy between energy minimum and gradient zero
063 was small, the refinements did in fact result in an appreciable
061 inprovement in the interaction between daunomycin and nucleic
054 acid, although they used some three to five times more
057 times more computer-time than should have been necessary.
064 Some form of order appeared in the relative interaction energies
061 with nucleic acids possessing different unwinding angles, and
067 the close approach of the quinone ring system to a base-pair, which
060 occurred in the first stage of refinement, was alleviated to
055 some extent by the adjustment in the relative positions
038 of the sugar group and aromatic system
065 of daunomycin which could occur through rotations about the bonds
036 C*T10*N-O*T29 *Nand O*T29*N-C*T30*N.
066 Finally, we allowed each atomic coordinate to vary within the
066 daunomycin molecule. This meant that there were some two hundred
059 variables, and the refinement was therefore performed using
032 a conjugate direction algorithm.
031 Some fifty linear searches were
048 performed on each complex structure, after which
069 the rounding error incurred in energy and gradient evaluation was too
063 At this stage, the energies obtained appeared to have converged
064 rather well, with each of the last few linear searches producing
052 less than a 1kJ mol*t-1 *limprovement in energy, and
054 individual terms in the gradient vector were typically
063 about 2 kJ mol*t-1 *lA*t-1*l, indicating that the complexes had
065 reached relatively flat areas in their potential energy surfaces.
060 In figure 5.23, we show the variation in the calculated
065 optimum interaction energies between daunomycin and nucleic acid,
067 as a function of the total helix unwinding. (The variation in the
057 internal energy of daunomycin in the different structures
061 has little effect on this graph.) The most stable structure
063 found was unwound by 13*D?*N, although the energy of the system
048 remained fairly constant in the range 8-16*D?*N,
024 with a 21*D? *Nunwinding
073 at this site being accompanied by an 8*D? *Nwinding at the adjacent site.
070 This figure of 13*D? *Nis almost identical with the 12*D? *Nwhich
066 is obtained from analysis of x-ray diffraction data*S44 *Nand from
045 measurements of supercoil unwinding*S20 21*N,
053 a point which we find particularly satisfying in view
055 of the computational expense involved in performing the
044 numerical refinements described above*t***l.
005 .fn 1
064 *t** *lEach point marked on figure 5.23 required about two hours
027 computer-time to determine.
005 .en 1
057 The optimum refined structure was characterised by having
068 the anthraquinone ring system some 4.3*D? *Nout of the plane defined
059 by the nucleic acid helix axis along the length of the ring
064 system, and about 12*D? *Nout of plane across its breadth. Had
068 optimisation, this would probably have been accommodated by twisting
063 the base-pairs in the vicinity of the interaction, a structural
061 change which has been found to involve little energy penalty.
058 Slight adjustment had taken place in some torsional angles
060 within daunomycin, mainly as a result of the second stage of
045 refinement, and we list these angles in table
004 5.6.
056 Table 5.7 shows how the total interaction energy of
066 some -460kJ mol*t-1 *lbetween daunomycin and nucleic acid was made
061 up. Whilst the true enthalpy of interaction between the two
071 systems will only be a small fraction of this internal energy*V*t*N*l,
005 .fn 2
077 *V*t *N*lQuadrifoglio*S48 *Nhas measured the enthalpy of interaction between
059 daunomycin and calf thymus DNA to be about -27kJ mol*t-1*l.
005 .en 2
060 owing to the other terms involved in a complete energy cycle
065 which we did not consider, the breakdown reveals some interesting
007 points.
002 *?
*[Chapter 5.7.5*]
060 Firstly, the dominance of the electrostatic interaction
058 between phosphate and amino-sugar is evident, in agreement
064 with previous suggesions*S45*N. This is almost entirely due to
052 the close approach of positively-charged nitrogen to
064 negatively-charged phosphate oxygen. The distance N*S..*NO was
057 3.4A, which is somewhat longer than would be expected for
059 a hydrogen-bond distance, but rotation of the the phosphate
057 group, a conformational change which we did not consider,
039 would undoubtedly reduce this distance.
061 The interaction between the anthraquinone ring system of
053 daunomycin and nucleic acid was made up of a moderate
053 term. In view of the lack of a formal charge on the
053 anthraquinone, the electrostatic contribution must be
063 due to a subtle interplay of the residual atomic charges in the
060 two systems. This contribution was, however, less than the
066 corresponding term found with an intercalating protonated acridine
059 (see table 5.2). We had ascribed much of the stability of
060 acridine intercalation complexes to this electrostatic term,
065 in particular to the interaction between acridine and base-pairs,
060 and it is clear that daunomycin intercalation (as opposed to
066 external binding to DNA) cannot be stabilised by the same factors.
061 However, the dispersion energy term between anthraquinone and
061 nucleic acid was much greater than the corresponding term for
074 acridine intercalation (-79kJ mol*t-1 *las against about -35kJ mol*t-1*l),
057 which means that the total interaction between the planar
060 intercalating section of the daunomycin molecule and nucleic
058 acid is very comparable to the total interaction found for
068 the acridines (-127kJ mol*t-1 *las against -90 to -150kJ mol*t-1*l).
057 The extra dispersion energy was caused by the larger size
059 of the anthraquinone ring system (four rings as against the
064 acridines' three) and by the presence of heavy atom substituents
020 on this ring system.
055 We see here a possible explanation for the lack of
064 anti-tumour activity in daunomycin analogues lacking a four-ring
060 system*S46*N. Unable to stabilise an intercalation complex
048 by electrostatic interactions in the same way as
063 the acridines or ethidium, daunomycin relies instead on a large
056 dispersion energy contribution, and this will be reduced
059 if the size of the intercalating moiety is reduced. It is
062 diffraction patterns for daunomycin:DNA complexes changed with
052 humidity, which was taken to indicate a considerable
066 hydrophobic contribution to the interaction, and this is certainly
058 in keeping with the large dispersion energy which we find.
061 Various views of the optimum refined structure are given
062 in figure 5.24. It can be seen that only a group attached to
064 C*T34 *Nin the manner of the daunomycin amino-group can approach
056 the appropriate phosphate group on DNA at all closely in
058 an intercalation complex. No other group of atoms in the
058 system appears to be quite so important in determining the
058 interaction, with the possible exception of the daunomycin
060 O*T23 *Natom, which appears to stabilise the conformation of
021 the cyclohexene ring,
041 allowing the amino-phosphate interaction.
056 We investigated the interaction of three daunomycin
063 analogues with the nucleic acid fragment previously considered.
044 Firstly, replacing the methoxy-group at C*T4
032 *Nby hydrogen resulted in a loss
052 of interaction energy of some 10kJ mol*t-1*l, mainly
068 due to the disappearance of the dispersion energy terms between this
065 methoxy-group and nucleic acid. The demethoxy-daunomycin showed
072 no tendency on refinement to withdraw itself from the intercalation site
060 and rotate round from its almost-Pritchard*S16 *Norientation
034 towards a Lerman*S15 *Norientation
060 and we must therefore conclude that the model set up for the
059 interaction with daunomycin was not prevented from changing
067 to a more favourable Lerman-type model because of an energy barrier
028 caused by the methoxy-group.
058 The next analogue studied was an epimer of daunomycin
060 This placed the amino-group further away from phosphate, and
063 there was a consequent loss of about 25kJ mol*t-1 *linteraction
058 energy, as expected. Refinement of the structure did not
036 lead to any significant improvement.
070 Thirdly, we investigated the interaction between nucleic acid and
067 the hypothetical daunoso-acridine compound discussed in *S?*N5.6.1.
037 Since this compound was assumed to be
054 protonated both on the amino-sugar and on the aromatic
059 ring system, and since its preferred conformation was found
060 to be similar to that of daunomycin, it was expected that it
041 would complex strongly with nucleic acid.
047 The energy of interaction between the molecules
074 was found to be about 25*A> *Nthan the corresponding value for daunomycin,
035 mainly due to the new electrostatic
062 contributions between the aromatic ring system of the acridine
060 and the phosphate groups and base-pairs of the nucleic acid.
069 Finally, we calculated the interaction energy between daunomycin
064 and nucleic acid fragments with different base sequences to that
059 used previously. It was not possible to perform more than
061 a cursory survey because of the computational expense, and we
058 were limited to investigating three analogues. Using the
054 optimum structure found for previously for the nucleic
067 acid : daunomycin complex (with 12*D? *Nunwinding of the helix), we
025 changed some of the bases
050 and then refined the daunomycin coordinates again.
054 Little movement occurred, and the interactions between
061 daunomycin and those parts of the nucleic acid fragment which
062 were unchanged were almost identical to their previous values.
065 present in the nucleic acid, because of the greater electrostatic
060 interaction with the more polar base, but decreased if there
021 was a pyrimidine base
053 between the amino-phosphate bond and the intercalated
066 chromophore, on the same side of the helix as the amino-phosphate.
061 In particular, a thymine group caused a large destabilisation
025 in this position, whereas
049 cytosine in this region caused a somewhat smaller
050 destabilisation. This was due to steric effects.
061 The interaction calculated between daunomycin and each of the
060 bases in the nucleic acid fragments is given in figure 5.25.
073 Care must be taken in interpreting these results, for it is possible
064 that refinement merely moved the daunomycin into a local minimum
070 of high energy, rather than finding a new configuration of low energy.
073 The results suggest, for example, that binding would occur preferentially
073 into G-C rich DNA, which has been observed in some studies*S49*N, but not
060 in others*S50*N. It also suggests, though, that binding to
068 poly(dA).poly(dT) would be stronger than to poly(dA-dT).poly(dA-dT),
051 because steric hindrance caused by pyrimidine bases
034 would always occur with the latter
060 polynucleotide, regardless of the position of intercalation,
061 and in fact the opposite result is observed*S51*N. However,
071 poly(dA).poly(dT) is known to adopt a non-B-DNA conformation*S52*N, and
063 it is obvious that results obtained from nucleic acid fragments
065 derived from the B-DNA structure are inapplicable to this system.
002 *?
*[Chapter 5.8*]
006 .tg NI
005 .ul 1
014 5.7 : Summary.
006 .tg NA
066 It is clear that the use of automatic optimisation algorithms
063 their internal energy using semi-empirical potential functions,
065 can allow reasonable predictions to be made of some properties of
060 the complexes. For example, the predicted unwinding angles
058 which occur in nucleic acid on intercalation of proflavine
060 or daunomycin agree well with the experimentally-determined
049 values. The method also allows an understanding
051 of why some properties are observed experimentally.
060 9-aminoacridine and proflavine appear to bind to DNA through
061 different mechanisms, and this could be explained in terms of
068 the preference shown by the former for Pritchard-type configurations
061 and by the latter for Lerman-type configurations. The total
049 stacking energy between intercalating chromophore
064 and base-pairs is apparently as important in determining whether
066 or not the interaction will occur as the electrostatic interaction
060 with phosphate, and it seems that either an electrostatic or
063 a dispersion contribution to this stacking may dominate. This
064 is demonstrated by the breakdown of total interaction energy for
073 proflavine and daunomycin, and partly confirmed by the non-double-helical
064 structure found by Seeman for the complex (9-aminoacridine:ApU),
062 and by the lack of biological activity in daunomycin analogues
034 lacking the four-ring chromophore.
058 The delocalisation of charge caused by substituents on the
068 intercalating ring systems is probably more important in determining
062 strength of interaction than is the potential ability of these
060 substituents to hydrogen-bond to DNA; thus the amino-groups
064 in proflavine (and presumably also in ethidium, although we have
058 not studied this) induce delocalisation of positive charge
049 present on both nucleic acid bases and phosphate.
062 However, it is also clear that the method is fraught with
055 difficulties. The computation required to perform the
043 optimisations was so large that only a very
059 small proportion of the calculations required to survey the
059 properties of intercalation complexes could be carried out.
026 We based most calculations
066 on one nucleic acid fragment, whilst there are ten distinguishable
062 dinucleotide fragments of DNA alone. Equally, we showed that
056 a modification to Pigram's model for daunomycin binding,
058 with a Pritchard-type insertion of the chromophore instead
063 of a Lerman-type insertion, provided a satisfactory explanation
057 of some of the observed properties of the drug. We were
055 not, however, able to show that Pigram's original model
059 did not provide an equally good explanation. Nor could we
073 demonstrate the stronger binding of daunomycin to poly(dA-dT).poly(dA-dT)
065 than to poly(dA).poly(dT), because our calculations did not allow
068 for variations in nucleic acid conformation caused by these sequence
012 differences.
063 It seems that most of the limitations apparent in the work
059 arose because of the computational expense of the numerical
059 refinements. Shortcomings in the methods used to estimate
060 conformational stability were not normally critical, because
069 most of the systems possessed well-defined minimum energy structures.
067 Energy calculations become less reliable when there are alternative
067 structures or conformations of similar energy, because the accuracy
065 of the potential functions, or quantum mechanical approximations,
056 may well be insufficient to predict the correct minimum.
002 *?
*[Chapter 5 Refs and Tables*]
007 .sp 10c
003 .nj
006 .tg NA
006 .ls 2c
005 .ul 1
033 1. Conjugate Direction Algorithm.
068 Linesearch Function Calls Energy after *MU*NGradient*MU
065 *NMade Search after Search
061 0 1 -117.3 30.92
062 1 3 -126.8 7.946
061 2 5 -130.4 19.89
062 3 7 -132.8 4.025
061 4 9 -137.4 14.31
062 5 12 -138.5 3.691
062 6 14 -138.8 3.176
062 7 16 -139.1 2.308
062 8 18 -139.1 0.857
062 9 21 -139.1 0.393
062 10 24 -139.1 0.130
062 11 27 -139.1 0.084
062 12 30 -139.1 0.018
062 13 33 -139.1 0.006
062 14 36 -139.1 0.002
005 .ul 1
026 2. Quasi-Newton Algorithm.
068 Linesearch Function Calls Energy after *MU*NGradient*MU
065 *NMade Search after Search
061 0 1 -117.3 30.92
062 1 3 -126.8 7.946
061 2 5 -130.4 16.20
061 3 7 -131.7 24.44
062 5 10 -139.1 1.371
062 6 11 -139.1 0.770
062 7 12 -139.1 0.404
062 8 13 -139.1 0.206
062 9 14 -139.1 0.073
062 10 15 -139.1 0.013
062 11 16 -139.1 0.001
006 .tg NI
005 .ul 1
049 Table 5.1 : Behaviour of Optimisation Algorithms.
006 .ls 3c
003 .bp
006 .tg NA
062 Dinucleotide section E(vdw) E(elect) kJ mol*t-1
008 *l.sp 1c
047 Deoxyribose group 1X -2.4 55.3
047 2X 4.9 84.0
047 1Y -2.4 74.7
047 2Y -1.4 44.0
006 .sp 1c
047 Phosphate group X -0.9 -106.4
047 Y -0.2 -76.7
006 .sp 1c
047 Bases : Adenine 1X -9.8 -53.2
047 2X -4.7 -28.9
047 Thymine 1Y -12.4 -27.7
047 2Y -8.1 -16.0
006 .tg NI
005 .ul 2
009 Table 5.2
067 Contributions to Energy of (Proflavine.H*A*t+ *N*l: d(A-A).d(T-T)).
003 .bp
006 .tg NA
031 1. Molecular orbital energies.
060 HOMO LUMO *SD
067 *N1-nitro 9-aminoacridine (1) -0.3547 0.0135 0.3682 au
065 (2) -0.3567 0.0161 0.3728 au
065 2-nitro 9-aminoacridine -0.3637 0.0126 0.3763 au
065 4-nitro 9-aminoacridine -0.3615 0.0084 0.3699 au
018 2. Total energies
046 1-nitro 9-aminoacridine (1) -449272 kJ
046 (2) -449312 kJ
046 (3) -447832 kJ
046 2-nitro 9-aminoacridine -449302 kJ
046 3-nitro 9-aminoacridine -449293 kJ
046 4-nitro 9-aminoacridine -449301 kJ
067 1) Crystallographic conformation for Ledakrin, viz -NO2 group 65*D?
048 *Nout of plane and 20*D? *Nbend about C9-N10.
060 2) -NO2 group 65*D? *Nout of plane; aromatic system planar.
009 3) Planar
006 .tg NI
005 .ul 2
009 Table 5.4
045 Various Energies of n-nitro 9-aminoacridines.
003 .bp
006 .tg NA
067 Compound Optimum energy (kJ mol*t-1*l)
064 Unprotonated Protonated
061 Acridine -142 -344
061 9-aminoacridine -145 -331
061 1-nitro 9-aminoacridine -193 -383
061 2-nitro 9-aminoacridine -201 -377
061 3-nitro 9-aminoacridine -178 -357
061 4-nitro 9-aminoacridine -206 -346
006 .tg NI
005 .ul 3
009 Table 5.3
060 Comparison of Optimum Interaction Energies found in Previous
047 Work*S41 *Nbetween Acridines and Dinucleotides.
062 (Calculations based on sum of electrostatic interactions,
066 calculated using PPP-determined*S55 *Natomic charges for the
059 acridines, and van der Waals interactions, calculated
045 using Giglio's*S56 *Nparameterisation.)
003 .bp
006 .tg NA
058 1.ZZZUnflipped, not protonated on amino-group -582203 kJ
058 2.ZZZFlipped, not protonated -581557 kJ
059 ZZZZZ(Difference between 1 and 2 646 kJ)
058 3.ZZZUnflipped, protonated on amino-group -580826 kJ
058 4.ZZZFlipped, protonated -580160 kJ
059 ZZZZZ(Difference between 3 and 4 666 kJ)
006 .tg NI
005 .ul 2
009 Table 5.5
037 Energies of Daunomycin Conformations.
003 .bp
006 .tg NA
051 Before After
065 Angle 1 2 3 4 5 6 7
109 C*T9*N-C*T10*N-O*T29*N-C*T30 *N246.2*D? *N240.0*D? *N240.5*D? *N237.5*D? *N241.6*D? *N227.8*D? *N232.0*D?
111 *NC*T10*N-O*T29*N-C*T30*N-O*T31 *N292.5*D? *N271.8*D? *N290.1*D? *N294.9*D? *N291.4*D? *N308.5*D? *N302.4*D?
008 *N.tg NI
005 .ul 3
009 Table 5.6
059 Torsional Angles in Daunomycin, before and after Refinement
033 of Drug : Nucleic Acid Complexes.
047 (1) Crystal Structure of Daunomycin*S44*N.
054 (2) Crystal Structure of N-bromodaunomycin*S42*N.
049 (3) Crystal Structure of Carminomycin*S43*N.
046 (4) With nucleic acid unwound by 17*D?*N.
046 (5) With nucleic acid unwound by 13*D?*N.
045 (6) With nucleic acid unwound by 9*D?*N.
045 (7) With nucleic acid unwound by 5*D?*N.
003 .bp
006 .tg NA
006 .ls 2c
057 Anthraquinone Daunosamine
029 Dispersion + Overlap Energies
054 Sugar groups residue 1 -7.99 -0.08
054 2 -9.97 -0.23
054 3 -1.38 -1.78
054 2 -29.24 -3.22
054 3 -1.12 -0.24
054 Phosphate residue 1 -1.19 -0.24
054 2 -0.52 -0.09
054 3 -0.20 -1.15
064 Total -79.06 -7.40 -86.46
022 Electrostatic Energies
054 Sugar groups residue 1 14.80 46.33
054 2 -12.69 58.65
054 3 6.57 78.50
054 Bases residue 1 -22.60 -12.38
054 2 -3.85 -19.60
054 3 -2.41 -44.13
054 Phosphate residue 1 -9.82 -82.85
054 2 -9.60 -68.10
054 3 -8.41 -276.59
064 Total -48.01 -320.17 -368.18
006 .ls 3c
006 .tg NI
005 .ul 3
009 Table 5.7
058 Contributions to Interaction Energy between Daunomycin and
042 Nucleic Acid (13*D? *NUnwinding of Helix).
034 (All figures in kJ mol*t-1*l)
003 .bp
006 .ls 3c
006 .tg NI
005 .ul 1
025 References for Chapter 5.
006 .tg NA
060 1. Walsh G.R. *I"Methods for Optimisation" *N(1975) Wiley
059 2. Broyden C.G. *IJ.Inst.Maths.Applic. *D6_ *N(1970) 222
061 3. Fletcher R. and Reeves C.M. *IComp.J. *D7_ *N(1964) 149
056 4. Huang H.Y. and Levy A.V. *IJ.Opt.Theory and Applic.
027 *D6_ *N(1970) 269
064 5. Dixon L.C.W. *IJ.Opt.Theory and Applic. *D1_0_ *N(1972) 34
039 7. Haigh N.P. *IPrivate Communication
062 *N8. The Numerical Algorithms Group, 7, Banbury Road, Oxford,
061 provide a library of mathematical routines to solve
055 common problems, most of which are excellent.
063 9. See, for example, Addison W.E. *I"Structural Principles in
049 Inorganic Compounds" *N(1961) Longmans
067 10. Robinson B.H. *IJ.Chem.Soc.Faraday Trans.1 *D6_9_ *N(1973) 56
050 11. Wright R.G. *ID.Phil. Thesis *N(1978) Oxford
068 12. Gilbert M. and Claverie P. *IJ.Theor.Biol. *D1_8_ *N(1968) 330
060 13. Polozov R.V. et al *IJ.Theor.Biol. *D5_5_ *N(1975) 491
061 14. Scheraga H.A. et al *IJ.Phys.Chem. *D7_8_ *N(1974) 1595
048 15. Lerman L.S. *IJ.Mol.Biol. *D3_ *N(1961) 18
058 16. Pritchard N.J. et al *INature *D2_1_2_ *N(1966) 1360
056 17. Sharpless N.E. and Greenblatt C.L. *IExp.Parisitol.
029 *D2_4_ *N(1969) 216
074 18. Lang H and L*(*S?*No*)ber G. *ITetrahed.Letters *D4_6_ *N(1969) 4043
060 19. Wakelin L.P.G. and Waring M.J. *IMol.Pharmacol. *D1_0_
022 *N(1974) 544
051 20. Waring M.J. *IJ.Mol.Biol. *D5_4_ *N(1970) 247
049 21. Wang J.C. *IJ.Mol.Biol. *D8_9_ *N(1974) 783
062 22. Patel D.J. and Canuel L.L. *IProc.Nat.Acad.Sci.USA *D7_4_
023 *N(1977) 2624
065 23. Alden C.J. and Arnott S. *INuc.Acid Res. *D2_ *N(1975) 1701
043 24. Wakelin L.P.G. *IPrivate Communication
056 *N25. Seeman N.C. et al *INature *D2_5_3_ *N(1975) 324
065 26. Various papers in *I"The Acridines" *Ned Acheson R.M., Volume
065 9 in series *I"The Chemistry of Heterocyclic Compounds"
024 *N(1973) Wiley
049 27. Albert A. *I"The Acridines" *N(1966) Arnold
021 28. Dean A.C. in (26)
064 30. Ledachowski A. *IMateria Medica Polona *D2_8_ *N(1976) 237
064 31. Testa B. and Jenner P. *I"Drug Metabolism" *N(1976) Dekker
061 32. Weisburger J.H. and Weisburger E.K. *IPharm.Rev. *D2_5_
020 *N(1973) 2
047 33. Kriek E. *IChem-Biol.Int. *D1_ *N(1969) 3
067 34. Le Pecq B. et al *IProc.Nat.Acad.Sci.USA *D7_2_ *N(1975) 2915
066 35. Wakelin L.P.G. et al *IStudia Biophysica *D6_0_ *N(1976) 111
043 36. Wakelin L.P.G. *IPrivate Communication
068 *N37. Bond P.J. et al *IProc.Nat.Acad.Sci.USA *D7_2_ *N(1975) 4825
059 38. Levitt M. *IProc.Nat.Acad.Sci.USA *D7_5_ *N(1978) 640
065 39. Li H.J. and Crothers D.M. *IJ.Mol.Biol. *D3_9_ *N(1969) 461
049 40. Sobell H. *IJ.Mol.Biol. *D4_4_ *N(1977) 301
059 41. Dearing A. *IThesis for Chemistry Part II Examinations
042 *N(1976) Oxford (see microfiche)
062 42. Kennard O. et al *INature New Biol. *D2_3_4_ *N(1971) 78
059 43. Von Dreele R.B. and Einck J.J. *IActa Cryst. *DB_3_3_
023 *N(1977) 3283
061 44. Neidle S. and Taylor G. *IBiochim.Biophys.Acta *D4_7_9_
022 *N(1977) 450
063 45. Pigram W.J. et al *INature New Biol. *D2_3_5_ *N(1972) 17
063 46. Henry D.W. in *I"Cancer Chemotherapy"*N, ed Sartorelli A.C.
042 (1976) Americal Chemical Society
057 47. Arcamone F. et al *IJ.Med.Chem. *D1_8_ *N(1975) 703
059 48. Quadrifoglio F. and Crescenzi V. *IBiophys.Chem. *D2_
021 *N(1974) 64
055 49. Kersten W. et al *IBiochemistry *D5_ *N(1966) 236
063 50. Schwartz I.S. *IPh.D. Thesis *N(1974) City Univ. New York
062 51. Phillips D.R. et al *IEur.J.Biochem. *D8_5_ *N(1978) 487
056 52. Selsing R. et al *IJ.Mol.Biol. *D9_8_ *N(1975) 243
060 53. Hoyland J.R. in *I"Molecular Orbital Studies in Chemical
068 54. Zuino F. et al *IBiochem.Biophys.Res.Comm. *D6_9_ *N(1976) 744
060 55. a) Pariser and Parr *IJ.Chem.Phys. *D2_1_ *N(1953) 446
059 b) Pople J.A. *ITrans.Farad.Soc. *D4_9_ *N(1953) 1375
046 56. Giglio E. *INature *D2_2_2_ *N(1969) 339
002 *?