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Conformation Energy Maps

The conformational energy map resulting from the static calculations is shown in Figure gif. The conformation corresponding to the crystal structure of acetylcholine chloride is marked as a +. This lies close to the global minimum shown on the plot and lies within the possible range for the true absolute minimum which is uncertain due to the coarse sampling grid used.

 

  sidewaysfigure1198


Figure: Conformational energy map for central dihedral angles of acetylcholine resulting from unrelaxed calculations. The energy scale is kcal tex2html_wrap_inline3057 relative to the lowest calculated energy. The point corresponding to the conformation of the acetylcholine chloride crystal is marked as a `+'.

 

  sidewaysfigure1205


Figure: Energy surface of acetylcholine with respect to the two central dihedral angles for relaxed molecular structures. The energy scale is kcal tex2html_wrap_inline3057 relative to the lowest calculated energy. Points corresponding to experimentally observed conformations are plotted as `+' symbols. The identities of these points are summarised in Table gif.

 

Point tex2html_wrap_inline3089 tex2html_wrap_inline3091 Description Reference
A 180 70 Implicated in nicotinic action [68]
B 180 60 NMR studies in tex2html_wrap_inline3093 [69]
C 180 150 Implicated in Hydrolysis by cholinesterase [70]
D 180 180 Implicated in nicotinic action [71]
E 79 77 Crystal structure of acetylcholine bromide [72]
F 158.8 84.3 Crystal structure of acetylcholine tex2html_wrap_inline2866 -resorcylate [73]
G 162.6 77.9 Crystal structure of acetylcholine (+)-hydrogen tartrate [74]
H 102 79 Crystal structure of acetylcholine ( tex2html_wrap_inline3097 )-hydrogen tartrate [74]
I 193 85 Crystal structure of acetylcholine chloride [67]
Table: Experimentally observed conformations of acetylcholine.

 

 

  sidewaysfigure1236


Figure: Plot of energy difference between static and relaxed calculations. The energy scale is kcal tex2html_wrap_inline3057 .

When the structure of the molecule is allowed to relax, while constraining the two dihedral angles of interest, the conformational energy map, shown in Figure gif, changes dramatically. A plot of the differences between the static and relaxed energies is shown in Figure gif. If we exclude the very high energy regions of this space which are conformationally unimportant, we find that the average energy difference between the static and relaxed energies is 296.5 kcal tex2html_wrap_inline3057 . More importantly, the standard deviation of the differences in calculated energies is 6.3 kcal tex2html_wrap_inline3057 , with a maximum deviation from the mean difference of 19.5 kcal tex2html_wrap_inline3057 . Thus, we can see that the errors introduced by forcing the structure to remain static are significant. In particular, the point {180,180} gif is a minimum on the relaxed energy surface but a maximum on the static energy map, and a new minimum is found at the point {180,0} on the relaxed energy surface.

In Figure gif the positions of experimentally observed conformations of acetylcholine are marked by + symbols. A summary of these points is given in Table gif. The conformations corresponding to biologically active forms (A,C and D) of acetylcholine and that found by NMR studies of acetylcholine in tex2html_wrap_inline3109 (B) all lie near to local minima on this energy map. In addition, the range of conformations {144 to 213, 60 to 120} has been suggested by Chothia for the muscarinic action of acetylcholine [75]. This region contains the minimum centred near the point corresponding to the crystal structure of acetylcholine chloride. It is not surprising that the experimentally found geometries differ significantly from one another, as the flexibility of the molecule with respect to torsional displacements means that the conformation favoured under given conditions can be expected to depend somewhat on environmental effects.

The conformations corresponding to the crystal structures of acetylcholine bromide and acetylcholine ( tex2html_wrap_inline3097 )-hydrogen tartrate (points E and H) do not lie close to any calculated minimum. Previous studies which have identified this minimum [64, 63] have shown it to be highly localised. Thus, it is possible that the entire minimum lies between the grid points for which energies have been calculated. Alternatively, as the structure of the acetylcholine molecule in these systems differs significantly from that in the acetylcholine chloride system used as an initial geometry, it is possible that greater relaxation would be necessary to identify the minimum in the energy map associated with these points.

It is noteworthy that the minimum located at {180,0} is not associated with any of the experimental points. However, in a detailed study, Froimowitz and Gans [64] found this minimum to be very narrow and surrounded by steep energy gradients and hence conformationally unimportant due to entropic considerations.


next up previous contents
Next: The Ground State Conformation Up: Results and Discussion Previous: Results and Discussion

Matthew Segall
Wed Sep 24 12:24:18 BST 1997