Prediction of Enzyme Catalysis by Computing Reaction Energy Barriers via Steered QM/MM Molecular Dynamics Simulations and Machine Learning.

The prediction of enzyme activity is one of the main challenges in catalysis. With computer-aided methods, it is possible to simulate the reaction mechanism at the atomic level. However, these methods are usually expensive if they are to be used on a large scale, as they are needed for protein engineering campaigns. To alleviate this situation, machine learning methods can help in the generation of predictive-decision models. Herein, we test different regression algorithms for the prediction of the reaction energy barrier of the rate-limiting step of the hydrolysis of mono-(2-hydroxyethyl)terephthalic acid by the MHETase ofIdeonella sakaiensis. As a training data set, we use steered quantum mechanics/molecular mechanics (QM/MM) molecular dynamics (MD) simulation snapshots and their corresponding pulling work values. We have explored three algorithms together with three chemical representations. As an outcome, our trained models are able to predict pulling works along the steered QM/MM MD simulations with a mean absolute error below 3 kcal mol-1 and a score value above 0.90. More challenging is the prediction of the energy maximum with a single geometry. Whereas the use of the initial snapshot of the QM/MM MD trajectory as input geometry yields a very poor prediction of the reaction energy barrier, the use of an intermediate snapshot of the former trajectory brings the score value above 0.40 with a low mean absolute error (ca. 3 kcal mol-1). Altogether, we have faced in this work some initial challenges of the final goal of getting an efficient workflow for the semiautomatic prediction of enzyme-catalyzed energy barriers and catalytic efficiencies.

Partial least squares for dependent data.

We consider the partial least squares algorithm for dependent data and study the consequences of ignoring the dependence both theoretically and numerically. Ignoring nonstationary dependence structures can lead to inconsistent estimation, but a simple modification yields consistent estimation. A protein dynamics example illustrates the superior predictive power of the proposed method.

Partial least-squares functional mode analysis: application to the membrane proteins AQP1, Aqy1, and CLC-ec1.

We introduce an approach based on the recently introduced functional mode analysis to identify collective modes of internal dynamics that maximally correlate to an external order parameter of functional interest. Input structural data can be either experimentally determined structure ensembles or simulated ensembles, such as molecular dynamics trajectories. Partial least-squares regression is shown to yield a robust solution to the multidimensional optimization problem, with a minimal and controllable risk of overfitting, as shown by extensive cross-validation. Several examples illustrate that the partial least-squares-based functional mode analysis successfully reveals the collective dynamics underlying the fluctuations in selected functional order parameters. Applications to T4 lysozyme, the Trp-cage, the aquaporin channels Aqy1 and hAQP1, and the CLC-ec1 chloride antiporter are presented in which the active site geometry, the hydrophobic solvent-accessible surface, channel gating dynamics, water permeability (p(f)), and a dihedral angle are defined as functional order parameters. The Aqy1 case reveals a gating mechanism that connects the inner channel gating residues with the protein surface, thereby providing an explanation of how the membrane may affect the channel. hAQP1 shows how the p(f) correlates with structural changes around the aromatic/arginine region of the pore. The CLC-ec1 application shows how local motions of the gating Glu(148) couple to a collective motion that affects ion affinity in the pore.