Dihedral angle analysis suggests three separate

To investigate the changes in the GVK0153 structure suggested by the QHA and RMSD data analysis, it was decided to analyse the data further by using

17-DMAG simulation GVK0153 simulation Time (ps) Time (ps) R M S D (n m ) R M S D (n m )

the dihedral angle fluctuations. This approach is similar to that used in entropy estimations by the histogram based method.

As can be seen from Figure 4.16, the GVK0153 molecule is made up of a purine scaffold that is connected to an aryl moiety by a CH2linker [167]. Both ring structures of the GVK0153 are rigid due to the double bonds, but the CH2 linker as well as amide and methyl groups, highlighted in Figure 4.16, contain rotatable bonds. These rotatable bonds were selected for the dihedral angle fluctuation analysis.

The dihedral angle fluctuations over the simulation time were calculated using the Amber ptraj tool [80]. The bin sizes, that define what contributes a different conformation, was set to 10 degrees.

Based on the molecule structure, the methyl and the amide group dihedral angle fluctuations were expected to exhibit small fluctuations around an average position, rather than larger conformational re-arrangements. For the methyl group attached to the purine scaffold of GVK0153, the dihedral angle analysis showed three separate states around 60, 180 and 300 degrees, as seen in Figure 4.16. The size of the each peak was roughly the same, suggesting that the methyl group adopted three equal rotational states. A methyl group is made up of three equal hydrogens connected to a carbon. Given the bond geometry, these are expected to produce three interchangeable states. The three different states that were observed matched the expected distribution. The amide group dihedral angle analysis also produced the expected distribution of a single state, based on the chemical connectivity (data not shown).

In contrast to methyl and amide groups attached to the two different rings, any changes in the dihedral angle of the CH2linking the two rings, would result in large conformational changes in the GVK0153 molecule. From the dihedral angle analysis we observed three maxima centred around 65, 160 and 300 degrees. The probability distribution for the maxima was roughly 50%, 5% and 45% respectively. The least likely conformation is that of the two rings being stacked, as seen in the Figure 4.16. These different conformations of the molecule cause the underlying energy landscape to have multiple energy minima, rather than the single harmonic one, as is assumed by the QHA. This

explains why the configurational entropy calculations by the quasi harmonic approach did not converge.

Figure 4.16: To look further into the structural fluctuations of the GVK0153 molecule, three different dihedral angles were selected for analysis as indicated on the left by the G1, G2 and G3 arrows. The right panel shows the probability distribution of the G1 and the G3 dihedrals. The resulting changes in the molecule conformations for the G3 dihedral is shown in the bottom figure. (The histogram distribution were calculated and plotted by Max Holmes)

4.6 Conclusions

In this chapter we explored the use of the quasi-harmonic approach method to compute configurational entropies of Hsp90-NTD in complex with inhibitors. We also explored the amount of simulation data required to get an accurate description of the underlying conformational space.

The results presented here show that the quasi-harmonic approach can be adopted with relative ease for both smaller and more complex systems, as long as the system does not undergo large conformational re-arrangements. The quasi-harmonic approximation provided the expected ranking of the configurational entropy values (Sconf) for the different Hsp90 systems. However, the calculated values may not reflect the exact entropy; when more simulation data were used for calculations, the entropy value increased. Despite this, the calculations can be used to produce ‘entropy ranking’. This reflects the dynamics of the system, and this information can still be of use for drug design, if effects of molecule flexibility are of interest. Moreover, obtaining a value (here Sconf) to compare flexibilities of different systems will provide a more objective measure, rather than comparison of flexibilities of certain regions of the protein of interest, as in Chapter 3 using RMSF analysis and looking at PCA fluctuations in Chapter 3.

We also wanted to attempt to answer the question - how many simulations are needed to provide a “good coverage” of the conformational space (75% or greater)?. Here the results of the two largest eigenvector movements that were used to describe the conformational space suggested that at least 6 replica simulations that collectively provide several microseconds of data are needed. When the coverage of the underlying energy landscape is of interest, these results highlight the potential issue with the common practice of running three replica simulations. We have shown that data from three replica simulations cover under two-thirds the total conformational space. However, in Chapter 3, we found that the differences in the flexibility of the different Hsp90 complexes could be seen from analysis of only three replica simulations. The configurational entropies also provided the expected ranking when only 3 simulations were used for calculations, but the value was considerably larger when more replica data were used for the computations. The larger dataset is likely to provide a more accurate configurational entropy value and the question of how many replicas should be run will depend on what the data is used for; ranking of complexes or trying to obtain an accurate value for configurational entropy.

Finally, the method of choice for configurational entropy calculations does depend on the flexibility of the system under study. QHA cannot be used for

very flexible molecules, which occupy multiple energy minima. There are issues with the dihedral method relating to selection of the bin sizes and the complexity of the system it can describe, due to collective motions. This means that it may not be easy to compare the entropies of different systems, especially if they have been calculated by different methods. Thus it is clear that the currently used methods for entropy estimations still do not tell the whole story. It remains to be seen whether simply correction terms could be added to the existing methods to solve these issues, or whether a completely new way of looking into quantifying the flexibility of soft biomolecules is needed.