Probabilistic Modeling of Conformational Space for 3D Machine Learning Approaches

Abstract

We present a new probabilistic encoding of the conformational space of a molecule that allows for the integration into common similarity calculations. The method uses distance profiles of flexible atom-pairs and computes generative models that describe the distance distribution in the conformational space. The generative models permit the use of probabilistic kernel functions and, therefore, our approach can be used to extend existing 3D molecular kernel functions, as applied in support vector machines, to build QSAR models. The resulting kernels are valid 4D kernel functions and reduce the dependency of the model quality on suitable conformations of the molecules. We showed in several experiments the robust performance of the 4D kernel function, which was extended by our approach, in comparison to the original 3D-based kernel function. The new method compares the conformational space of two molecules within one kernel evaluation. Hence, the number of kernel evaluations is significantly reduced in comparison to common kernel-based conformational space averaging techniques. Additionally, the performance gain of the extended model correlates with the flexibility of the data set and enables an a priori estimation of the model improvement.

4D Flexible Atom-Pairs: An efficient probabilistic conformational space comparison for ligand-based virtual screening

“…In an earlier study we already presented the comparable performance of the heuristic in comparison to model selection criterions [23]. This heuristic avoids the model selection step and reduces the runtime of the preprocessing step.…”

“…The original 4D FAP, as applied in QSAR/QSPR studies [23,27], sums up the entries of the S matrix and normalizes the sum to obtain a value in the range [0.0, 1.0]. Another possibility to compute a final similarity value represents the optimal assignment.…”

Boltzmann‐Enhanced Flexible Atom‐Pair Kernel with Dynamic Dimension Reduction

“…The 4D FAP column shows the results of the previous implementation of the 4D FAP kernel function. Please note that the different results of the old 4D FAP version in comparison to our previous publication [3] are based on different GMM implementations. In the previous paper we applied the python package pymix [15] to calculate the GMMs.…”

“…For a detailed explanation of the approach we refer to our previous publication. [3] The aim of the 4D FAP is to incorporate the complete conformational space of molecules into pair-wise similarity calculations as used in instance-based machine learning methods such as support vector machines. For this purpose, we developed a conformational space encoding that enables the 4D FAP to compute similarity values that are based on an implicit comparison of the complete conformational space.…”

“…Based on the quality of the geometrical information, this additional information source can either provide valuable data or introduce undesirable noise to the final model. As a consequence, the conformational space of molecules was integrated as a fourth dimension and yielded several extensions of traditional 3D-QSAR approaches like CoMFA [1] or GRIND.[2]In a recently published paper, [3] we introduced a 4D kernel function that additionally applies the information of the conformational ensembles of molecules in order to cut the dependency on biologically active conformations. The results demonstrated that this approach is able to create more robust models in comparison to the solely 3D-based approach on minimized conformations.…”