Mechanistic Insights into Enzyme Catalysis from Explaining Machine-Learned Quantum Mechanical and Molecular Mechanical Minimum Energy Pathways

Abstract

With the increasing popularity of machine learning (ML) applications, the demand for explainable artificial intelligence techniques to explain ML models developed for computational chemistry has also emerged. In this study, we present the development of the Boltzmann-weighted cumulative integrated gradients (BCIG) approach for effective explanation of mechanistic insights into ML models trained on high-level quantum mechanical and molecular mechanical (QM/MM) minimum energy pathways. Using the acylation reactions of the Toho-1 β-lactamase and two antibiotics (ampicillin and cefalexin) as the model systems, we show that the BCIG approach could quantitatively attribute the energetic contribution in one system and the relative reactivity of individual steps across different systems to specific chemical processes such as the bond making/breaking and proton transfers. The proposed BCIG contribution attribution method quantifies chemistry-interpretable insights in terms of contributions from each elementary chemical process, which is in agreement with the validating QM/MM calculations and our intuitive mechanistic understandings of the model reactions.

Figure 1

Toho-1 β-lactamase, the β-lactam antibiotics, and the acylation pathways of Toho-1. (a) Toho-1/β-lactam complex and the selection of QM atoms. The carbon atoms of the amino acid residues are colored in dark gray. The Cα–Cβ bonds (used as the QM/MM boundary for the amino acid side chains) are colored in cyan. The carbon atoms of the β-lactam ligand are colored in magenta, except the carbonyl carbon in β-lactams, which is colored in dark purple. The catalytic water molecule is uniformly colored in green. All nitrogen, oxygen, sulfur, and hydrogen atoms are colored in blue, red, yellow, and white, respectively. All hydrogen atoms in the ligand are omitted for clarity. (b) Chemical structures of AMP and CEX. The penam and cephem scaffolds are colored in red; (c) Acylation pathways using Glu166 as the general base (R1-AE) and using Glu166/Lys73 concertedly as the general base (R2-AE).

Figure 2

Selected features, the 2D representation of the pathway conformations, and the architecture of the ML-MEP models. The selected features and chemical processes of (a) Toho/AMP: R1-AE and Toho/CEX: R1-AE datasets and (b) Toho/AMP: R2-AE and Toho/CEX: R2-AE datasets. The atomic distances that are included in feature vectors are noted in orange lines and the chemical processes are noted in blue; see also Table S1. (c) 2D principal component dimensionality reduction of the pairwise inter-heavy-atom distances in the QM region, and a schematic demonstration for the loss of pathway context of the replicas; (d) architecture of the QM/MM MEP learning deep-and-wide neural network.

Figure 3

The distribution of the acylation barriers (ΔE) at B3LYP-D3/6-31+G**/C36 level of theory. (a) Toho/AMP: R1-AE acylation pathways; (b) Toho/CEX: R1-AE acylation pathways; (c) Toho/AMP: R2-AE acylation pathways; and (d) Toho/CEX: R2-AE acylation pathways. The scatters show the locations of the energy barriers. The width of the histograms is 4 kcal mol^–1. The red curves note the density estimation from the GMMs. The labels “min. ΔE”, “expo. ”, “mean ”, “med. ΔE”, and “std” refer to the minimum, exponential average, arithmetic average, median, and standard deviation of the energy barriers from the QM/MM MEP profiles, respectively.

Figure 4

Predictive performance and the BCIG contributions of the ML-MEP models. The predictive performance of (a) replica energies and (b) pathway barriers of (left to right) the Toho/AMP: R1-AE, Toho/CEX: R1-AE, Toho/AMP: R2-AE, and Toho/CEX: R2-AE models. The BCIG contributions of the models: (c) Toho/AMP: R1-AE; (d) Toho/CEX: R1-AE; (e) Toho/AMP: R2-AE; and (f) Toho/CEX: R2-AE. The rankings (highest to lowest) of the BCIG contributions are noted below.

Figure 5

Predictive performance and the BCIG contributions of the unified ML-MEP models. The predictive performance of (left to right) the replica energies and the pathway barriers of (a) Toho/AMP&CEX: R1-AE and (b) Toho/AMP&CEX: R2-AE models. The BCIG contributions of (c) Toho/AMP&CEX: R1-AE and (d) Toho/AMP&CEX: R2-AE models.

Figure 6

Atomic distances between the ChElPG charges on critical heavy atoms in all reactant states at the B3LYP-D3/6-31+G**/C36 level. The (a) atomic distances and (b) ChElPG charge profiles of the Toho/AMP: R1-AE and Toho/CEX: R1-AE pathways. The (c) atomic distances and (d) ChElPG charge profiles of the Toho/AMP: R2-AE and Toho/CEX: R2-AE pathways. The meanings of the labels on x-axes are defined in the symbolic legend (right panel).