The results obtained from the Grid calculations and experimental distributions are summarized in Table 4.9. The lowest Epoi for each interacting system is underlined.
Table 4.9
Interacting Predicted Distribution Experimental Match System DWAT=4.0 DFRO=4.0 DWAT=80.0 DPRO=4.0 Distribution Arginine/ Carboxyl Oxygen
5 predicted regions, 3 o f which coincide w ith that observed
experim entally. (-14.3 K cal/m ol)
3 predicted regions - all o f w hich are in agreem ent w ith
experim ent. (-4 .7 K cal/m ol)
3 reg io n s in the p lan e o f the targ et Arg.
G ood
Arginine / Carboxyl Group Probe
4 predicted
regions, 2 o f w hich are populated. (-28.5 K cal/m ol)
3 predicted regions, only 1 o f
w hich is in agreem ent w ith
experim ent. (-7 .8 K cal/m ol)
G ood
Phenylalanine/ Carboxyl Oxygen
Predictions essentially the sam e for both sets o f assum ptions
C arb o x y l O x y g en s in the
C ould be b etter M ost favourable position o f a carboxyl oxygen is above
and below the plane o f the arom atic ring.
p lan e and aro u n d th e face o f the aro m atic
fo r both p red ictio
-ns (-1.66 K cal/m ol) (-2.04 K cal/m ol) ring.
Phenylalanine/ Carboxyl Group
Probe
3 predicted regions. T w o are in and around th e plane o f the arom atic
ring, and the th ird is below its plane.
(-1.62 K cal/m ol)
A bove and below the plane o f the
arom atic ring.
(-2.04 K cal/m ol)
Arginine/ Aromatic Carbon
Predictions sam e fo r both sets o f assum ptions C arb o n s above and b elow
Fairly O K Predicts arom atic carbons above and below plane o f
guanidinium group. (-1.2 K cal/m ol)
the face o f th e ta rg e t Arg.
Phenyiaianine / Predictions sam e for both sets o f assum ptions C arb o n s above C o uld
Aromatic Carbon
Predicts A rom atic C arbons to be positioned above and below the plane o f the ring
(-1.2 K cal/m ol)
and b elo w the aro m a tic plane
Prediction o f Experimental Atom-Sidechain Distributions Using Energetic Considerations
In general the structures which involved hydrogen bonds such as the arginine / carboxyl oxygen and arginine/ carboxyl group interacting systems have much lower energies than the other systems in which hydrogen bonds cannot occur. Also the energies are much smaller when neutral species are involved compared to charged species.
Prediction o f atom-sidechain distributions using this ‘monopole approach’ does appear to have some measure of success. However, an area was identified in which this model did not accurately reproduce the expected results. This area appears to relate to the description of the n electron system of the target molecules arginine and
phenylalanine. From qualitative considerations one would not expect a negatively charged oxygen (like the carboxyl oxygen) to be situated either above or below the plane of the target molecules as is suggested by the Grid results, as it would experience repulsion from their n electron clouds. This view that a fuller description o f the 7C electron system is required has been subsequently supported by similar
calculations (Mitchell et al, 1993) using an "energetics package" which employs a different methodology to Grid. For these calculations the Distributed Multipole Analysis (DMA) method was used in combination with the program ORIENT (Price & Stone, 1987; Stone 1990). The differences in their approach were that:-
(i) The DMA method describes the K electron system by quadrupoles instead of dipoles.
(ii) In this method it is assumed that the interacting atom-sidechain pairs are in a vacuum.
(iii) W hole molecules or molecular groups have to be used as models in this system. These molecules have to retain the essential chemistry of the interacting probe and target molecules.
Calculations performed by Mitchell et a l (1993) showed the regions above the aromatic ring of phenylalanine and the guanidinium moiety o f arginine to be purely repulsive.
energy values which are being dealt with but relative values.
A brief summary o f the results obtained from the DMA calculations (Mitchell et at.,
1993) will now be given.
Before discussing the results it is necessary to define some terms to describe the different interaction geometries observed.
• ‘Parallel plate stacked’ structures -in these structures the centres of the delocalised regions o f the molecules are directly above each other.
• ‘Staggered stacked’ structures - the two structures are essentially parallel, but are somewhat displaced laterally.
• ‘Offset stacked’ structures - the planes are almost parallel with no overlap between the structures.
• ‘Edge-to-face’ - this occurs when the edge of one moiety interacts with the face of another.
• ‘Tilted edge-to-face’ - similar to ‘edge-to-face’ structures where the interplaner angles are close to 45°.
These are shown in Figs.4.19(a)-(d). ‘Tilted edge-to-face’ is not shown here as it is very similar to ‘edge-to-face’.
The discussion also makes reference to the experimental atom-sidechain distributions - these can be found in the Atlas o f Sidechain Interactions by Singh & Thornton (1992).
Prediction o f Experimental AtomSidechain Distributions Using Energetic Considerations
(a)
Parallel Plate Stacked Structure Toluene / Toluene
(b)
Staggered Stacked Structure Toluene / Toluene
(c)
Offset Stacked Structure Toluene/Toluene
(d)
Edge-to-Face Structure Toluene/Toluene
4.4.1 Phenylalanine / Carboxyl Oxygens
For these calculations a toluene / acetate system was used to model the phenylalanine / carboxyl Oxygen system. The calculations resulted in the production of three minima in which the two carboxylate oxygens of the acetate moiety were either close to or in the plane of the aromatic ring. The model also found ‘stacked structures’ to be energetically unfavourable. An examination of the ATLAS o f Sidechain Interactions
(Singh & Thornton, 1992) o f phenylalanine with aspartate or glutamate show an absence o f ‘stacked structures’. Thus the DMA calculations produced results which were in close agreement with experiment.
4.4.2 Phenylalanine / Aromatic Carbons
A toluene / toluene system was used to model the phenylalanine / aromatic system. These calculations found that the ‘staggered stacked’ and ‘parallel-plate’ structures were energetically unfavourable. This agrees with the experimental sidechain distribution of phenylalanine with phenylalanine in which these types of packings are absent. The minima found by these calculations exhibited mostly ‘offset stacking’ and a few examples of ‘edge-to-face’ packings. The experimental distribution comprised mainly of ‘edge-to-face’ and ‘tilted edge-to-face’ interactions. The DMA model was judged to be successful.
4.4.3 Arginine / Carboxyl Oxygens
For this system the compounds methylguanidinium and acetate were used in the calculations. The calculations involving these moieties resulted in minima produced in two the regions which correspond to regions 1 and 2 in Fig.4.11. The lowest energy configurations in the two regions correspond to coplanar structures. The energies in regions 1 and 2 are very similar at -439 and -438 kJ/mol respectively (or - 91.19 & -90.98 Kcal/mol). Thus they are very similar. The best energy for a structure corresponding to region 3 in Fig.4.11 was -385 kJ/mol (or -79.97 Kcal/mol). As all three of these regions are populated the DMA calculations can be regarded as successful.
Prediction o f Experimental AtomSidechain Distributions Using Energetic Considerations
4.4.4 Arginine / Aromatic Carbons
Modelling the arginine / aromatic carbon interactions with DMA calculations on the methylguanidinium /toluene system resulted in ‘local m inim a’ with aromatic rings perpendicular to the arginine plane. These were described as ‘edge-to-face’ interactions. The aromatic ring can lie in one of three regions with the aromatic carbons close to or in the plane o f the methylguanidinium. The energy o f interaction at these sites being —25 kJ/mol.
The experimental distribution of arginine and phenylalanine however shows a distinct preference for stacked structures where the aromatic carbons are found above the guanidinium plane. Despite this observation the prediction made by the DMA model is not actually incorrect. This can be said as the aromatic carbons probably do not form ‘edge face’ interactions as suggested by the DMA model as the carboxyl oxygens will form stronger interactions with the arginine at these positions, hence they have been displaced by other moieties which will form stronger interactions. This is in accord with the Legon-Millen rules (Legon & Millen, 1987) which were formulated from observing structures of small molecules. The rules state that a hydrogen bond donor (e.g. arginine) will preferentially form a hydrogen bond with a conventional acceptor (e.g. carboxyl oxygen) and only interact with a non-conventional acceptor
(e.g. aromatic ring) if a conventional acceptor is not available.
However, the geometries of the interactions formed by the aromatic carbons with the arginine are not energetically unfavourable as judged by the DMA calculations.
Thus overall the DMA methodology was judged to be very successful in these predictions.