The conformational energy map resulting from the static calculations
is shown in Figure 
. 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.
Figure: Conformational
energy map for central dihedral angles of acetylcholine resulting from
unrelaxed calculations. The energy scale is kcal 
relative
to the lowest calculated energy. The point corresponding to the
conformation of the acetylcholine chloride crystal is marked as a
`+'.
Figure: Energy
surface of acetylcholine with respect to the two central dihedral
angles for relaxed molecular structures. The energy scale is kcal 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
.
| Point |  |  | Description | Reference |
| A | 180 | 70 | Implicated in nicotinic action | [68] |
| B | 180 | 60 | NMR studies in  | [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  -resorcylate
| [73] |
| G | 162.6 | 77.9 | Crystal structure of acetylcholine (+)-hydrogen tartrate | [74] |
| H | 102 | 79 | Crystal structure of acetylcholine (  )-hydrogen
tartrate | [74] |
| I | 193 | 85 | Crystal structure of acetylcholine chloride | [67] |
Figure: Plot of energy
difference between static and relaxed calculations. The energy scale
is kcal .
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 , changes dramatically. A
plot of the differences between the static and relaxed energies is
shown in Figure . 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 . More importantly, the standard
deviation of the differences in calculated energies is 6.3 kcal , with a maximum deviation from the mean difference of 19.5
kcal . Thus, we can see that the errors introduced by
forcing the structure to remain static are significant. In particular,
the point {180,180} 
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 the positions of experimentally observed
conformations of acetylcholine are marked by + symbols. A summary of
these points is given in Table . The conformations
corresponding to biologically active forms (A,C and D) of
acetylcholine and that found by NMR studies of acetylcholine in 
(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 ( )-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.
