Computational Strategy.

The structural calculations presented in this chapter have all been carried out using the semi-empirical parameter sets contained within MOPAC. Of these three, MNDO is known to give poor core-core repulsions [63] and be unreliable for high valence phosphorus compounds [144], so would be likely to give the poorest quality results for molecules with severe steric crowding such as the higher inositol phosphates. While AMI generally gives a more accurate representation of the long- range repulsions, it is reported to be less accurate for hypervalent compounds [144]. Phosphorus was not considered in the original AMI parametrisation and although parameters were subsequently published [145], the results may not be as accurate for compounds outside those used for the parametrisation than would be the case for methods with all the atoms parametrised together. Early AMI calculations of phosphorus compounds (including Stewart's comparison with PM3 [64]) used the

MNDO parameters for phosphorus while retaining the AMI parameters for the other atoms. Version 3 of MOPAC gives results similar to those for MNDO parameters alone, but a bug in version 5 leads to highly spurious results, for example heat of formation of -13000 kcal mok^ and a value for GNORM of over 1000 for IP3.

Two approaches have been used in the calculations of the monophosphates. In the first approach, termed "anionic" approach, the energies were first minimised with the phosphate groups fully ionised, using the AMI paiameter set. Final energies were then obtained for all three parameter sets using these initial geometries as starting points, and adding the hydrogens to the structures. By ignoring the hydrogens in the initial stages, the number of necessary starting points can be reduced as there is no need to consider phosphate rotation as all the oxygens are equivalent. As the main phosphate-phosphate interaction was thought to be a steric and ionic repulsion, this simplification should not lead to a substantial change in the final geometry. The second approach, termed "hydrogen" approach, includes the hydrogens from the beginning. In this case, extra starting points were included to allow for rotation of the phosphate groups and of the phosphate hydroxyls, though in the case of the monophosphates, rotation of the hydroxyls could be ignored as the rotation barriers are very small and other considerations, such as electrostatics, tend tp dictate the nature of the energy minimum for these rotations. This method was used to confirm (or deny) the validity of the first approach.

Both approaches have potential drawbacks for the higher phosphates. The MNDO-like semi-empirical methods proved not to be reliable for highly charged species, in particular large positive energies were be obtained and energies for many occupied orbitals became positive. However, the geometries obtained from these

*

calculations are reasonable and appear less prone to error than the energies and as the hydrogens were replaced for the final calculations used in the structure / energy comparisons, there is good reason to have faith in the results. If on the other hand, the hydrogens are included from the beginning of the calculations, the problem of steric crowding is added to and there is a real danger of incorrect placement of the hydrogens, which can only be overcome by considering rotation of the phosphate group and

1

possibly also requiring consideration of rotation of the phosphate hydroxyls, so adding to the already large number of starting points. The problem this could pose can be seen from the fact that adding only the possibility of phosphate rotation to IP4 increases the

number of necessary starting points by a factor of 3"^, For this reason alone, this first method is preferable for higher phosphates.

5.2.1 Choice of Starting Points.

Initial model building shows eight basic ring conformations for a non- symmetrical six-membered ring such as is the case for most myo -inositol phosphates, namely two "chair" and six "boat" conformations. In addition, a phosphate group has potentially three minima for rotation about the "P-ester O" bond corresponding to the three non-equivalent staggered conformations, and a similar three potential minima produced by rotation of the phosphate group itself.. It is reasonable to neglect the effect of phosphate hydroxyl rotation as the barrier is so small that the relative energies of different orientations depend almost entirely on the position of neighbouring charged groups. There is a multiplicative relationship between these rotations so that the number of potential minima that would need to be examined rapidly rises to unmanageable proportions. (There are potentially over 52000 minima for IP4 even

when hydroxyl rotation is ignored.) Against this, the higher phosphates in particular suffer from considerable steric crowding so that many of these potential minima disappear from steric considerations alone. There remains, however, the problem of ensuring that the energies of all of the important minima are calculated for each compound, so starting points corresponding to most, if not all, of the minima must be used. It was found that the barriers for rotation of the phosphate groups were generally rather small ( < 2 kcal moF^) except for those conformations that showed strong

hydrogen bonding between phosphate or hydroxyl groups. In this situation however, the different starting points corresponding to phosphate rotations would usually all give the same final minima or be close to it, so it was reasonable to ignore the possibility of

phosphate rotation when setting the stalling points for the calculations. This reduced the number of starting points by a factor of 3N (where N is the number of phosphate groups).

Reduction of the number of starting points in this way left a total of 24 starting points required to ensure the calculation of all of the important minima for each of the mono-phosphates, though there still remained a considerable (and impracticably large) number of starting points for the higher phosphates. The required starting points for calculation on the higher phosphates are built up from the final structures obtained for the compound with one fewer phosphate group. Thus for each molecule, only three new starting points are required (corresponding to rotation about the phosphate C-0 bond) for each distinct conformation obtained for the previous molecule. This method is able to reduce the number of necessary calculations only if several starting points yield the same final geometry at the earlier stages, a situation which can easily arise in sterically crowded molecules where many potential minima are discounted by close contacts between groups. This method has been particularly useful in this study, reducing the potential 52000 starting points of IP4 to a mere 9. It is felt that this

method is valid for the inositol phosphates as the interaction between the phosphate groups is primarily repulsive in nature owing to the considerable negative charge on the oxygen atoms. In this situation, it is unlikely that minimum energy conformations for the higher phosphates will have no corresponding minimum energy structure in the lower phosphorylated analogs, thus important minima should not be missed using this method.

5.3 M vo -Inositol.

Initial calculations were performed using all three parameter sets on the eight basic ring conformations to examine their relative stability and to look for potential distortions from the simple geometries brought about by the particular positions of the

myo -inositol hydroxyl groups, especially that at position 2 as it is on the same side of

the ring as its neighbours.

Table 5.1 Mvo -inositol energies and geometries. Starting Geometry AMI MNDO PM3 Final Geometry Energy kcal mol"^ Final Geometry Energy kcal mol"^ Final Geometry Energy kcal mol'i I I -307.852 I -282.231 I -273.672 E E -303.607 E -273.233 E -272,098 lA lA -301.252 2E -276.159 lA -267.682 , 2E 2E -305.134 2E -276.173 2E -270.856 3A 3A -301.252 2E -276.050 3A -267.684 IE IE -303.465 1E/3A -273.192 IE -269.049 2A 2A/3E -303.613 2A -272.876 2A -271.800 3E 3E -303.470 1A/3E -273.189 3E -269.049

Thus for all three parameter sets, the "5 eq / 1 ax" chair conformation (termed "I", see table 5.2) is the most stable, though there is some difference in the positions and relative energies of the other local minima. The excessive long-range core-core repulsion present in the MNDO parametrisation is shown by the disappearance of minima involving eclipsed hydroxyl groups ("lA", "IE", "3A" and "3E" boat conformations) and the relative stability of the "2E" boat, which apart from the "I" chair has the greatest separation of the hydroxyl groups. Reduction of this core-core repulsion for the AMI parameter set does not alter the relative stability of the eight ring conformations, but reduces the importance of the hydroxyl-hydroxyl distances on the positions of the local minima, thus minima are found coiTesponding to the eclipsed conformations though at relatively high energy. The further changes to the evaluation

of the core-core potential within the PM3 parametrisation resulted in a further reduction in the importance of hydroxyl-hydroxyl repulsion in fixing the position of the local minima, such that minima are found conesponding to all of the conformations and the "2E" conformation is no longer the most stable of the boat conformations. The enhanced stability of the "2A" conformation comes from the greater contribution of hydrogen bonds to the final energy using PM3. Myo -inositol is a symmetrical m'olecule with the "lA" and "3A" boat confoimations being mirror-images (the same is true of the "IE" and "3E" boat conformations), though the energies obtained differ slightly. This comes from the fact that hydroxyl rotation is not considered when setting the starting points, so the small difference in energy between the mirror-images comes from different rotations of the hydroxyl groups and as the largest difference is

0 .1 kcal mol‘1 these rotations are not significant in terms of the effect on conformation.

The following abbreviations for the ring conformations have been used in all the tables in this chapter including the one above:

Table 5.2 Abbreviations of Ring Conformations.

Abbreviation Meaning

"I” 1 axial / 5 equatorial chair conformation (also called "2'ax chair")

”E' 5 axial / 1 equatorial chair (also called "2'eq chair") ”1A" Boat conformation with T OH (or H2PO4) axial

"IE" Boat conformation with T OH (or H2PO4) equatorial

"2A" Boat conformation with 2' OH (or H2PO4) axial

"2E" Boat conformation with 2' OH (or H2PO4) equatorial

"3A" Boat conformation with 3' OH (or H2PO4) axial

"3E" Boat conformation with 3' OH (or H2PO4) equatorial

OH OH HO H O ^

i

- I # '

V

_OH OH •C5 OH OH

V

lOH r ... ^ T jr m OH a/ "I" conformation b/ "E" conformation OH

%

OH OH 'Çe OH c/ "1 A'* conformation OH OH

/

•Ç4 OH OH - d/ "IE" conformation

OH OH OH lOH

I

I

_I OH OH e/ "2A" conformation OH OH HO HO. " f " " ... OH OH Ç 5— Ç4 OH

7

■Ç2- P3, lOH f/ "2E" conformation g/ "3A" conformation OH OH OH

i

OH OH OH h/ "3E" conformation Fig 5.3 Mvo -Inositol Ring Conformations.

Where the ring conformation is given by two of the above symbols (always two of the "boat" conformations), the actual conformation is someway between the two (produced by twisting the parallel ring bonds of either named conformation in the direction of the other). Such a twisting away from the classical boat conformations usually occurs to relieve close contacts between ring substituents. This twisting of the boat conformations is reflected in the order in which they are listed in the tables as a 60“ rotation of the parallel ring bonds of any conformation will transform it to either of the adjacent conformations in the table.

In addition, for the inositol phosphates, the phosphate position is always given as a dihedral angle measured conventionally in the sequence Pn-On-Cn-Cn+i around

tlie ring.

In document A theoretical study of TPA like tumour promotors and inositol polyphosphates (Page 156-164)