MathDL: mathematical deep learning for D3R Grand Challenge 4

Abstract

We present the performances of our mathematical deep learning (MathDL) models for D3R Grand Challenge 4 (GC4). This challenge involves pose prediction, affinity ranking, and free energy estimation for beta secretase 1 (BACE) as well as affinity ranking and free energy estimation for Cathepsin S (CatS). We have developed advanced mathematics, namely differential geometry, algebraic graph, and/or algebraic topology, to accurately and efficiently encode high dimensional physical/chemical interactions into scalable low-dimensional rotational and translational invariant representations. These representations are integrated with deep learning models, such as generative adversarial networks (GAN) and convolutional neural networks (CNN) for pose prediction and energy evaluation, respectively. Overall, our MathDL models achieved the top place in pose prediction for BACE ligands in Stage 1a. Moreover, our submissions obtained the highest Spearman correlation coefficient on the affinity ranking of 460 CatS compounds, and the smallest centered root mean square error on the free energy set of 39 CatS molecules. It is worthy to mention that our method for docking pose predictions has significantly improved from our previous ones. * Corresponding to Guo-Wei Wei. The Drug Design Data Resource (D3R) offers blind communitywide challenges of ligand pose and binding affinity ranking predictions. 1-3 Benchmarks in D3R contests contain high quality structures and reliable binding energies supplied by experimental groups before the publication. These challenges provide computer-aided drug design (CADD) community a great opportunity to validate, calibrate, and develop drug virtual screening (VS) models. The latest D3R Grand Challenge 4 (GC4), took place from September 4th 2018 to December 4th, 2018. GC4 presented two different protein targets, Cathepsin S (CatS) and beta secretase 1 (BACE), which were generously supplied by Janssen Pharmaceuticals and Novartis, respectively. There were two stages in GC4. The first one has two subchallenges, namely Stage 1a and Stage 1b. In Stage 1a, participants were asked to predict the pose, rank the affinity, and estimate the free energy of BACE ligands. Following Stage 1a, Stage 1b revealed the receptor structures and participants were asked again to predict the crystallographic poses of 20 BACE ligands. There was no affinity calculation in this stage 1b. The second part of GC4 was called Stage 2 which contained the affinity rankings and free energy challenges for both BACE and CatS compounds. In this last stage, participants were able to take advantage of experimental structures of BACE complexes released right after stage 1b.A successful VS model requires a reliable ligand conformation generation and highly accurate scoring function to predict binding affinities. There are several state-of-the-art software packages to take care of the first component of VS, for example, Autodock Vina, 4 GOLD, 5 GLIDE, 6 ICM, 7 etc. Unfortunately, one may fail dramatically to achieve decent poses if blindly using t...

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“…The bioactivities of those compounds are further estimated by the structure-based deep learning model named MathDL. 18 The druggable properties predicted by this last component of our GNC are used as an indicator to select the promising drug candidates. Figure 1: A schematic illustration of the generative network complex.…”

“…Promising drug candidates are fed into a MathPose unit to generate 3D structures, which are further validated by a mathematical deep learning (MathDL) center to select new drug candidates. 18…”

“…Our MathDL is a mathematical representation-based deep learning platform designed for predicting various druggable properties of 3D molecules. 18 Mathematical representations used in MathDL are algebraic topology (such as persistent homology), differential geometry, and graph theory-based algorithms developed over the past many years. These approaches were repeatedly validated by their top performance in free energy prediction and ranking at D3R Grand Challenges, a worldwide competition series in computer-aided drug design (https://drugdesigndata.org/about/grand-challenge).…”

“…These approaches were repeatedly validated by their top performance in free energy prediction and ranking at D3R Grand Challenges, a worldwide competition series in computer-aided drug design (https://drugdesigndata.org/about/grand-challenge). 18,23 More details about the mathematical representation of complex molecules can be found in a recent review. 24 A variety of datasets, particularly, PDBbind datasets, 25 were used in our training of deep learning networks.…”

“…Our MathPose was the top performer in D3R Grand Challenge 4 in predicting the poses of 24 beta-secretase 1 (BACE) binders. 18 3 Results…”