Chapter 4. Modelling solvation by QM/MM molecular dynamics: the difficult case of the flexible zwitterion 3F-‐GABA
4.4 Summary and Future Work
In our computational study of 3F-‐GABA we:
1. Provided additional computational spectroscopic data that strongly suggest extended conformer F to be the dominant 3F-‐GABA conformer in aqueous solution. 2. Used an elaborate QM/MM MD approach to calculate free energy differences
between conformers of 3F-‐GABA that supports the interpretation of the experimental data, according to which the extended conformer F should be dominant in solution.
The microsolvated cluster calculations with up to 5 water molecules, with and without a surrounding continuum293 were not successful in predicting a
conformational energy surface with extended conformer F being lower in energy than
A. It may thus be that even larger clusters are required to fully capture the solvent effects that influence the energy surface of a zwitterion such as 3F-‐GABA. As mentioned before, larger clusters make traditional geometry optimisations
troublesome and a dynamic treatment may actually be needed for reliable results. Kamerlin et al. compared continuum models, mixed cluster-‐continuum models and QM/MM free energy simulations for the reaction of phosphate hydrolysis.311 It was
found that both continuum solvation calculation and full QM/MM free energy simulations arrived at the same result for the reaction barrier while mixed cluster-‐ continuum calculations instead introduced artifacts. Accounting for the orientation and entropy of the water molecules was found to be important for proper behaviour of cluster models which becomes hard to do if one does not perform molecular dynamics.
Unfortunately, it is very difficult to separate free energies into enthalpy and entropy contributions (in principle possible by running many simulations at different
temperatures and using the van’t Hoff relation), and gauging the importance of electrostatic interactions with increasing number of water molecules would require many more simulations. It is thus not completely clear what physical effects are most responsible for stabilising the extended conformer F. Intramolecular hydrogen-‐ bonding would stabilise folded conformers like A. Conformers that do not form an intramolecular hydrogen bond (E-‐J) would have both amino and carboxyl groups available for hydrogen bonding with the surrounding solvent, and if this results in an increased number of hydrogen bonds then this would presumably stabilise such conformers in solution relative to folded ones. We explored this possibility by
calculating radial distribution functions for trajectories involving conformers A and F.
130
The calculated radial distribution functions are shown in Figure 36. Integrals over the N...OH2O RDF up to r = 3.5 Å (an upper limit for hydrogen bonds) give a higher average
of contacts for conformer F (5.1) than for A (3.9). For the OCO2...OH2O RDFs (one for
each oxygen on the carboxylate group) the integrals give values of 4.2 and 4.3 for conformer F, while for conformer A we get values of 4.4 and 3.4. There is thus an increase by 1 in average N...OH2O contacts and OCO2...OH2O contacts for the carboxylate
and amino groups of 3F-‐GABA in going from conformer A to conformer F. This could be interpreted as 2 more solute-‐solvent hydrogen bonds that conformer F forms compared to A and after counting the intramolecular hydrogen bond that A forms but
F does not, 1 hydrogen bond still remains for potential stabilisation of the F conformer. This could explain the stability of F over A although a more detailed analysis remains to be performed, ideally for each 3F-‐GABA conformer which could potentially be correlated with relative free energies.
Figure 36 Radial distribution functions, g(r) between N of 3F-‐GABA and O atoms of the solvent (a) and between the carboxylate O atoms and the O atoms of the solvent (in b and c for each conformer). Dashed lines indicate integrals over g(r). From PM3/MM MD trajectories involving conformers A (2700 snapshots) and F (1300 snapshots). S8 gNO(r) r / Å gOO(r) gOO(r) a) b) c) A F F A gNO(r) r / Å gOO(r) gOO(r) a) b) c) A F F A
Figure S9. Radial distribution functions (RDFs) g(r) between N and O atoms of the charged F-GABA groups and the O atoms of the water molecules. (a) N...OH2O in conform- ers A and F, (b) and (c), OCO2...OH2O in conformers A and F, respectively (in green and red for each of the two different carboxylate O atoms). Dashed lines: integrals over g(r) affording the mean number n(r) of atoms up to r. At r = 3.5 Å, the typical upper limit for H-bonds, the resulting n(r) values for the N...O/O1...O/O2...O pairs are 3.9/4.4/3.4 and 5.1/4.2/4.3 for isomer A, and F, respectively. Note the increase
In addition, extended conformers, like F, are less rigid and would be entropically more favourable than folded conformers, as discussed in a recent combined
experimental and theoretical gas-‐phase study of neutral GABA conformers.312 Also,
since zwitterionic conformers become more stable with increasing number of water molecules and since the cationic and anionic parts are further apart in extended conformers this would likely result in more stabilising electrostatic interactions with the bulk solvent than for folded conformers in solution. Most likely, the
conformational equilibrium of zwitterions such as 3F-‐GABA in solution, is a delicate balance of hydrogen bonding, solvent electrostatic effects and entropic effects.
We note that due to the complexity of the QM/MM MD simulations we have not fully explored the conformational energy surface of zwitterionic 3F-‐GABA. The standard deviations of the free energy differences obtained from the MD simulations are also quite high which one would like to reduce for greater confidence in the results. It is clear, however, that our QM/MM solvation model predicts the energy difference between conformers A and F to be completely different than that predicted by PCM solvation models as shown in Figure 37.
Figure 37 The computed PM3/MM free energy profile (line) with the PM3-‐>DFT correction (QM/MM-‐B3LYP, marked as x) between A, H and F. Additionally, PCM computed potential energies of F (relative to A) with PM3 and B3LYP.
4.4.1 Possible improvements to QM/MM MD protocol
The QM/MM MD protocol for 3F-‐GABA that we ended up using, looks generally promising to model conformational changes of small molecules with non-‐negligible solvent effects, although being orders of magnitude more complicated than
continuum solvation calculations. We now discuss some problems with the protocol and possible improvements that could prove useful for similar simulations in the future: !"# !$# %# $# "# &# '# (# )# *# +# !" ,-## ./012341# 560/748#/449:;80<6# ="!=&!='!>## # # 560/748#/449:;80<6# =$!="!=&!='## # # #" $" ?=@!A&BC?# ?=@!?@&# D@2@@!A&BC?# ,E#F-!GHI### ./012341#
1. Contrained simulations wandering away from the important region: