Christian Kramer

The Experimental Uncertainty of Heterogeneous Public Ki Data

The maximum achievable accuracy of in silico models depends on the quality of the experimental data. Consequently, experimental uncertainty defines a natural upper limit to the predictive performance possible. Models that yield errors smaller than the experimental uncertainty are necessarily overtrained. A reliable estimate of the experimental uncertainty is therefore of high importance to all originators and users of in silico models. The data deposited in ChEMBL was analyzed for reproducibility, i.e., the experimental uncertainty of independent measurements. Careful filtering of the data was required because ChEMBL contains unit-transcription errors, undifferentiated stereoisomers, and repeated citations of single measurements (90% of all pairs). The experimental uncertainty is estimated to yield a mean error of 0.44 pK(i) units, a standard deviation of 0.54 pK(i) units, and a median error of 0.34 pK(i) units. The maximum possible squared Pearson correlation coefficient (R(2)) on large data sets is estimated to be 0.81.

Comparability of Mixed IC50 Data – A Statistical Analysis

The biochemical half maximal inhibitory concentration (IC50) is the most commonly used metric for on-target activity in lead optimization. It is used to guide lead optimization, build large-scale chemogenomics analysis, off-target activity and toxicity models based on public data. However, the use of public biochemical IC50 data is problematic, because they are assay specific and comparable only under certain conditions. For large scale analysis it is not feasible to check each data entry manually and it is very tempting to mix all available IC50 values from public database even if assay information is not reported. As previously reported for Ki database analysis, we first analyzed the types of errors, the redundancy and the variability that can be found in ChEMBL IC50 database. For assessing the variability of IC50 data independently measured in two different labs at least ten IC50 data for identical protein-ligand systems against the same target were searched in ChEMBL. As a not sufficient number of cases of this type are available, the variability of IC50 data was assessed by comparing all pairs of independent IC50 measurements on identical protein-ligand systems. The standard deviation of IC50 data is only 25% larger than the standard deviation of Ki data, suggesting that mixing IC50 data from different assays, even not knowing assay conditions details, only adds a moderate amount of noise to the overall data. The standard deviation of public ChEMBL IC50 data, as expected, resulted greater than the standard deviation of in-house intra-laboratory/inter-day IC50 data. Augmenting mixed public IC50 data by public Ki data does not deteriorate the quality of the mixed IC50 data, if the Ki is corrected by an offset. For a broad dataset such as ChEMBL database a Ki- IC50 conversion factor of 2 was found to be the most reasonable.

Leave-cluster-out cross-validation is appropriate for scoring functions derived from diverse protein data sets.

With the emergence of large collections of protein-ligand complexes complemented by binding data, as found in PDBbind or BindingMOAD, new opportunities for parametrizing and evaluating scoring functions have arisen. With huge data collections available, it becomes feasible to fit scoring functions in a QSAR style, i.e., by defining protein-ligand interaction descriptors and analyzing them with modern machine-learning methods. As in each data modeling ansatz, care has to be taken to validate the model carefully. Here, we show that there are large differences measured in R (0.77 vs 0.46) or R² (0.59 vs 0.21) for a relatively simple scoring function depending on whether it is validated against the PDBbind core set or validated in a leave-cluster-out cross-validation. If proteins from the same family are present in both the training and validation set, the estimated prediction quality from standard validation techniques looks too optimistic.

A composite model for HERG blockade

hERG blockade is one of the major toxicological problems in lead structure optimization. Reliable ligand‐based in silico models for predicting hERG blockade therefore have considerable potential for saving time and money, as patch‐clamp measurements are very expensive and no crystal structures of the hERG‐encoded channel are available. Herein we present a predictive QSAR model for hERG blockade that differentiates between specific and nonspecific binding. Specific binders are identified by preliminary pharmacophore scanning. In addition to descriptor‐based models for the compounds selected as hitting one of two different pharmacophores, we also use a model for nonspecific binding that reproduces blocking properties of molecules that do not fit either of the two pharmacophores. PLS and SVR models based on interpretable quantum mechanically derived descriptors on a literature dataset of 113 molecules reach overall R2 values between 0.60 and 0.70 for independent validation sets and R2 values between 0.39 and 0.76 after partitioning according to the pharmacophore search for the test sets. Our findings suggest that hERG blockade may occur through different types of binding, so that several different models may be necessary to assess hERG toxicity.

Atomic multipoles: Electrostatic potential fit, local reference axis systems, and conformational dependence

Currently, all standard force fields for biomolecular simulations use point charges to model intermolecular electrostatic interactions. This is a fast and simple approach but has deficiencies when the electrostatic potential (ESP) is compared to that from ab initio methods. Here, we show how atomic multipoles can be rigorously implemented into common biomolecular force fields. For this, a comprehensive set of local reference axis systems is introduced, which represents a universal solution for treating atom‐centered multipoles for all small organic molecules and proteins. Furthermore, we introduce a new method for fitting atomic multipole moments to the quantum mechanically derived ESP. This methods yields a 50–90% error reduction compared to both point charges fit to the ESP and multipoles directly calculated from the ab initio electron density. It is shown that it is necessary to directly fit the multipole moments of conformational ensembles to the ESP. Ignoring the conformational dependence or averaging over parameters from different conformations dramatically deteriorates the results obtained with atomic multipole moments, rendering multipoles worse than partial charges.

Matched molecular pair analysis: significance and the impact of experimental uncertainty.

Matched molecular pair analysis (MMPA) has become a major tool for analyzing large chemistry data sets for promising chemical transformations. However, the dependence of MMPA predictions on data constraints such as the number of pairs involved, experimental uncertainty, source of the experiments, and variability of the true physical effect has not yet been described. In this contribution the statistical basics for judging MMPA are analyzed. We illustrate the connection between overall MMPA statistics and individual pairs with a detailed comparison of average CHEMBL hERG MMPA results versus pairs with extreme transformation effects. Comparing the CHEMBL results to Novartis data, we find that significant transformation effects agree very well if the experimental uncertainty is considered. This indicates that caution must be exercised for predictions from insignificant MMPAs, yet highlights the robustness of statistically validated MMPA and shows that MMPA on public databases can yield results that are very useful for medicinal chemistry.

Improving Docking Results via Reranking of Ensembles of Ligand Poses in Multiple X-ray Protein Conformations with MM-GBSA

There is a tendency in the literature to be critical of scoring functions when docking programs perform poorly. The assumption is that existing scoring functions need to be enhanced or new ones developed in order to improve the performance of docking programs for tasks such as pose prediction and virtual screening. However, failures can result from either sampling or scoring (or a combination of the two), although less emphasis tends to be given to the former. In this work, we use the programs GOLD and Glide on a high-quality data set to explore whether failures in pose prediction and binding affinity estimation can be attributable more to sampling or scoring. We show that identification of the correct pose (docking power) can be improved by incorporating ligand strain into the scoring function or rescoring an ensemble of diverse docking poses with MM-GBSA in a postprocessing step. We explore the use of nondefault docking settings and find that enhancing ligand sampling also improves docking power, again suggesting that sampling is more limiting than scoring for the docking programs investigated in this work. In cross-docking calculations (docking a ligand to a noncognate receptor structure) we observe a significant reduction in the accuracy of pose ranking, as expected and has been reported by others; however, we demonstrate that these alternate poses may in fact be more complementary between the ligand and the rigid receptor conformation, emphasizing that treating the receptor rigidly is an artificial constraint on the docking problem. We simulate protein flexibility by the use of multiple crystallographic conformations of a protein and demonstrate that docking results can be improved with this level of protein sampling. This work indicates the need for better sampling in docking programs, especially for the receptor. This study also highlights the variable descriptive value of RMSD as the sole arbiter of pose replication quality. It is shown that ligand poses within 2 Å of the crystallographic one can show dramatic differences in calculated relative protein-ligand energies. MM-GBSA rescoring of distinct poses overcomes some of the sensitivities of pose ranking experienced by the docking scoring functions due to protein preparation and binding site definition.

QSARs, data and error in the modern age of drug discovery.

The legacy of the advances made in high-throughput screening (HTS) in the 1990s is a large source of public data from which models can be derived using QSAR methods. This paper will examine the integrity of these public data sources and the implications for model building.

Leveraging Symmetries of Static Atomic Multipole Electrostatics in Molecular Dynamics Simulations

Multipole (MTP) electrostatics provides the means to describe anisotropic interactions in a rigorous and systematic manner. A number of earlier molecular dynamics (MD) implementations have increasingly relied on the use of molecular symmetry to reduce the (possibly large) number of MTP interactions. Here, we present a CHARMM implementation of MTP electrostatics in terms of spherical harmonics. By relying on a systematic set of reference-axis systems tailored to various chemical environments, we obtain an implementation that is both efficient and scalable for (bio)molecular systems. We apply the method to a series of halogenated compounds to show (i) energy conservation; (ii) improvements in reproducing thermodynamic properties compared to standard point-charge (PC) models; (iii) performance of the code; and (iv) better stabilization of a brominated ligand in a target protein, compared to a PC force field. The implementation provides interesting perspectives toward a dual PC/MTP resolution, à la QM/MM.

Multipole-Based Force Fields from ab Initio Interaction Energies and the Need for Jointly Refitting All Intermolecular Parameters

Distributed atomic multipole (MTP) moments promise significant improvements over point charges (PCs) in molecular force fields, as they (a) more realistically reproduce the ab initio electrostatic potential (ESP) and (b) allow to capture anisotropic atomic properties such as lone pairs, conjugated systems, and σ holes. The present work focuses on the question of whether multipolar electrostatics instead of PCs in standard force fields leads to quantitative improvements over point charges in reproducing intermolecular interactions. To this end, the interaction energies of two model systems, benzonitrile (BZN) and formamide (FAM) homodimers, are characterized over a wide range of dimer conformations. It is found that although with MTPs the monomer ab initio ESP can be captured better by about an order of magnitude compared to point charges (PCs), this does not directly translate into better describing ab initio interaction energies compared to PCs. Neither ESP-fitted MTPs nor refitted Lennard-Jones (LJ) parameters alone demonstrate a clear superiority of atomic MTPs. We show that only if both electrostatic and LJ parameters are jointly optimized in standard, nonpolarizable force fields, atomic are MTPs clearly beneficial for reproducing ab initio dimerization energies. After an exhaustive exponent scan, we find that for both BZN and FAM, atomic MTPs and a 9-6 LJ potential can reproduce ab initio interaction energies with ∼30% (RMSD 0.13 vs 0.18 kcal/mol) less error than point charges (PCs) and a 12-6 LJ potential. We also find that the improvement due to using MTPs with a 9-6 LJ potential is considerably more pronounced than with a 12-6 LJ potential (≈ 10%; RMSD 0.19 versus 0.21 kcal/mol).