The initial aim of this project was to demonstrate that the relative binding affinities of
oligobenzamides can be predicted computationally. The prediction of accurate binding affinities requires that binding poses be generated for possible ligands, that molecular dynamics
simulations be run from the docked poses and the trajectories then analysed to estimate the free energy of binding for each compound.
One of the challenges of simulating oligobenzamides is correctly calculating the energy associated with the torsion angles of the backbone. Modification (using TI) of the barrier heights for the bonds about which rotation is restricted in the O and S-linked scaffolds had little effect on their binding energy so any effects side chains have on the scaffold torsion energies in these scaffolds is unlikely to prevent the accurate ranking of oligobenzamides. Because in the N1 scaffold the nitrogen atoms holding each side chain are within the backbone, the torsion parameters could vary depending on the choice of side chains, making this scaffold more challenging.
In an attempt to predict the affinities of 31 compounds based on the N1 scaffold, two
approaches were tried, namely, using TI and using implicit solvent methods. In the former, the effect of small changes to the side chain at each of the three side chain positions was evaluated and it was assumed that side chains made independent contributions to the binding energy. The correlation between the predicted free energies of binding and the experimentally determined affinity ranking of the compounds was found to be poor. Specifically, Spearman’s rank, the absolute value of which ranges from 0 for no correlation to 1 for a perfect correlation, was found to be just 0.4. In contrast, when the implicit solvent MM-PBSA and MM-GBSA methods were used to make predictions, a much greater correlation with experimental results was observed. While the exact correlation depended on the settings used, Spearman’s rank values of roughly 0.55 were typical, provided that the trajectory of the free protein was extracted from the trajectory of the complex and, when using the MM-PBSA method, the relative internal
dielectric was not increased from its default value of 1. The greater correlation obtained with the implicit solvent methods could reflect the fact that it was unnecessary to assume compounds all bound in the same pose; all of the compounds could be docked and simulated.
To investigate further the assumption that all oligobenzamides bind to Mdm2 in the paradigmatic pose of the O1 scaffold starting molecule (where the side chains occupy the binding sites of p53 residues Phe19, Trp23 and Leu26) regardless of their side chain structure, 25,000 compounds were docked using Autodock Vina. Oligobenzamides were predicted to bind in many different poses, indicating that this prerequisite for TI may be violated.
To investigate the extent to which the side chains of an oligobenzamide influence the binding of each other, both through their effect on binding pose and within a particular binding pose, the MM-PBSA method was used to predict the affinities of a large combinatorial library of oligobenzamides in different poses and the affinities were studied using ANOVA.
When the choice of side chain at each position was treated as a factor, a statistical interaction between the side chains was evident; however, inclusion of interaction terms in the models did not significantly increase their adjusted Nagelkerke R2 values, indicating that the interactions are small in magnitude.
Because the ANOVA results show a statistical interaction between binding pose and the choice of side chains, grouping compounds based on their likely binding position (from docking) would be appropriate when predicting the effect different side chains have at each side chain position. However, due to the small magnitude of the interactions between side chains, after accounting for the effect of side chain choice on the binding position, it might not be appropriate to test large combinatorial libraries in each binding site.
The models used do not explain a significant amount of variation in the results. This suggests that making predictions using longer simulations might be useful, something which would only be practical if independent contributions from each side chain were assumed, reducing the number of compounds that require testing. Within each possible oligobenzamide binding position, each side chain position could be investigated separately to determine the contribution different functional groups at that position are likely to make to the binding affinity. To predict the relative binding affinity for a new molecule, the compound could be docked to identify where it was likely to bind and this would indicate which set of side chain contribution predictions to sum to get the total predicted binding energy of the compound.
To predict the side chain properties likely to increase affinity at a particular binding site, it is useful to generate oligobenzamide poses within that site. Local optimisation of a docked oligobenzamide following subsequent in situ modification of its side chains using Autodock led to MM-PBSA values which were positive. This suggests that the optimised poses were not realistic.
FlexX is a docking program designed to place ligands in a pose close to a conformation
previously generated by high throughput screening. A fragment library was docked using FlexX and the docking scores were analysed to identify the desirable properties of side chains when an oligobenzamide binds in the expected, idealised conformation occupying the Phe19, Trp23 and Leu26 binding sites. A smaller side chain is favourable at the first side chain attachment site, a larger side chain is favoured at the second position and aliphatic side chains as opposed to aromatic ones are favourable at the last side chain position. These findings are consistent with the properties of the p53 side chains mimicked in this binding pose. However, the results also
suggested that more hydrophilic side chains would bind more strongly, a finding which is not consistent with earlier work31,253 and could be explained by the lack of terms to account for ligand and protein desolvation in the FlexX scoring function229,254. These findings highlight the need to run simulations and use more accurate methods of affinity prediction than scoring. Sampling of all the possible torsion angles of oligobenzamides may require tens of nanoseconds worth of simulation time172. Fuller et al. demonstrates how Hamiltonian replica exchange can be used to increase the efficiency of sampling203. Simulations (replicas) are started at various lambda values and the lambda values are then swapped between the simulations at intervals (equivalent to the exchange of coordinates and momenta between simulations running at different lambda values). This reduces the chance of each simulation becoming stuck in an energy minimum and ceasing to explore the phase space271. Replica exchange could be used in future work to reduce sampling error.
While the TI results presented in this chapter did not correlate strongly with experimental results this could reflect the way in which TI was applied; TI might be a useful method for comparing ligands which docking suggests have very similar binding poses. One of the problems with TI is the requirement to perform many simulations in order to determine the effect of the reaction coordinate (λ) on the potential energy of the system. In this respect, a method known as lambda dynamics272 could be a useful alternative. In this method, lambda is a variable which can change freely during the simulation so its effect on the potential can be ascertained in a single simulation. While a lambda dynamics simulation might have to be long, it would not necessary to simulate multiple systems to equilibration as when using the TI method. Multiple lambda variables can be used. This could allow multiple functional groups to be tested at a particular side chain position in a single simulation or even simultaneous
modification at multiple side chain attachment positions.
In order for methods such as TI and lambda dynamics to be effective, the poses of ligands must be determined accurately. When docking was performed in this project, the flexibility of the protein was neglected. In future work, flexible docking could be performed in which the entire protein or just the protein side chains can move152 or, alternatively, compounds could be docked into an ensemble of structures generated by a molecular dynamics simulation. Flexibility can lead to poorer docking because information in the in initial crystal structure is lost145. However, the Mdm2 binding site is flexible so conformational change might be essential to facilitate accurate determination of binding poses. (See Figure 1.3 on p32.) After fully flexible docking, it might be difficult to define where the p53 binding pockets are for the purpose of pose
interpretation. If an ensemble of structures were produced by molecular dynamics simulations, the p53 peptide could be simulated in the binding site. This would not only allow the pocket positions to be tracked but also force them to stay open.
Synthetic work on oligobenzamides has focussed on compounds with N-linked and O- linked49 side chains as opposed to ones where attachment is through sulphur. Modification of side chain attachment atoms using TI suggested that the sulphur atoms in oligobenzamides based on the S1 scaffold contribute more to binding energy than the corresponding oxygen atoms in the O1 structure. Consequently, some sulphur-linked oligobenzamides might bind more strongly than their equivalent oxygen-linked molecules and the sulphur linked scaffolds should be investigated further.
It is necessary to demonstrate a high correlation between predicted and experimental results to show the practical use of implicit solvent methods in the prediction of the oligobenzamide affinities. While the computational methods used in this chapter could be developed further the experimental results used for their evaluation must be accurate too for a high correlation to be obtained. The experimental results used in this chapter were generated using a fluorescence polarisation competition assay. In this assay, an inhibitor binding to Mdm2 displaces a fluorescently-labelled p53 peptide. The release decreases the anisotropy of the label
fluorescence and this is detected. Unfortunately, the collaborating chemistry group had found evidence of compounds binding directly to the fluorescently labelled peptide42. Furthermore, some variation in the ranking used in this chapter was observed when the assay was repeated. An orthogonal assay was thus needed to assist with validation of the computational findings. The next chapter details the development of a FRET-based assay which could be used instead of or in addition to the fluorescence polarisation assay in future.
The importance of correct binding pose prediction on the accuracy of predicted affinities warrants validation of the oligobenzamide docking poses generated by Autodock Vina. This is challenging because there is no crystal structure of an oligobenzamide bound to Mdm2. Chapter 4 describes the production of 15N-labelled Mdm2 L33E and its use in NMR studies to