A dynamic view of enzyme catalysis

Globally optimal catalytic fields for a Diels-Alder reaction

In a previous paper [M. Dittner and B. Hartke, J. Chem. Theory Comput. 14, 3547 (2018)], we introduced a preliminary version of our GOCAT (globally optimal catalyst) concept in which electrostatic catalysts are designed for arbitrary reactions by global optimization of distributed point charges that surround the reaction. In this first version, a pre-defined reaction path was kept fixed. This unrealistic assumption allowed for only small catalytic effects. In the present work, we extend our GOCAT framework by a sophisticated and robust on-the-fly reaction path optimization, plus further concomitant algorithm adaptions. This allows smaller and larger excursions from a pre-defined reaction path under the influence of the GOCAT point-charge surrounding, all the way to drastic mechanistic changes. In contrast to the restricted first GOCAT version, this new version is able to address real-life catalysis. We demonstrate this by applying it to the electrostatic catalysis of a prototypical Diels-Alder reaction. Without using any prior information, this procedure re-discovers theoretically and experimentally established features of electrostatic catalysis of this very reaction, including a field-dependent transition from the synchronous, concerted textbook mechanism to a zwitterionic two-step mechanism, and diastereomeric discrimination by suitable electric field components.

Globally Optimal Catalytic Fields - Inverse Design of Abstract Embeddings for Maximum Reaction Rate Acceleration

The search for, and understanding of, good catalysts for chemical reactions is a central issue for chemists. Here, we present first steps toward developing a general computational framework to better support this task. This framework combines efficient, unbiased global optimization techniques with an abstract representation of the catalytic environment, to shrink the search space. To analyze the resulting catalytic embeddings, we employ dimensionality reduction and clustering techniques. This not only provides an inverse design approach to new catalytic embeddings but also illuminates the actual interactions behind catalytic effects. All this is illustrated here with a strictly electrostatic model for the environment and with two versions of a selected example reaction. We close with detailed discussions of future improvements of our framework.

Using entropy maximization to understand the determinants of structural dynamics beyond native contact topology

Comparison of elastic network model predictions with experimental data has provided important insights on the dominant role of the network of inter-residue contacts in defining the global dynamics of proteins. Most of these studies have focused on interpreting the mean-square fluctuations of residues, or deriving the most collective, or softest, modes of motions that are known to be insensitive to structural and energetic details. However, with increasing structural data, we are in a position to perform a more critical assessment of the structure-dynamics relations in proteins, and gain a deeper understanding of the major determinants of not only the mean-square fluctuations and lowest frequency modes, but the covariance or the cross-correlations between residue fluctuations and the shapes of higher modes. A systematic study of a large set of NMR-determined proteins is analyzed using a novel method based on entropy maximization to demonstrate that the next level of refinement in the elastic network model description of proteins ought to take into consideration properties such as contact order (or sequential separation between contacting residues) and the secondary structure types of the interacting residues, whereas the types of amino acids do not play a critical role. Most importantly, an optimal description of observed cross-correlations requires the inclusion of destabilizing, as opposed to exclusively stabilizing, interactions, stipulating the functional significance of local frustration in imparting native-like dynamics. This study provides us with a deeper understanding of the structural basis of experimentally observed behavior, and opens the way to the development of more accurate models for exploring protein dynamics.

As more protein structures are solved, we are able to perform a more critical assessment of the relationship between protein structure and dynamics, and to gain a deeper understanding of the major determinants of structural dynamics. Here we perform a systematic study on a set of proteins structurally determined by NMR spectroscopy. The dynamics are analyzed using elastic network models and a novel method based on entropy maximization to demonstrate that properties such as contact order and secondary structure do play a role in defining the experimentally observed covariance data. Most importantly, an optimal description of observed cross-correlations requires the inclusion of destabilizing, as well as stabilizing, interactions, stipulating the functional significance of local frustration in imparting native-like dynamics.

Loop-tryptophan human purine nucleoside phosphorylase reveals submillisecond protein dynamics

Human PNP is a homotrimer containing three tryptophan residues at positions 16, 94, and 178, all remote from the catalytic site. The catalytic sites of PNP are located near the subunit-subunit interfaces where F159 is a catalytic site residue donated from an adjacent subunit. F159 covers the top (beta) surface of the ribosyl group at the catalytic site. QM/MM calculations of human PNP have shown that F159 is the center of the most mobile region of the protein providing access to the substrate in the active site. F159 is also the key residue in a cluster of hydrophobic residues that shield catalytic site ligands from bulk solvent. Trp-free human PNP (Leuko-PNP) was previously engineered by replacing the three Trp residues of native PNP with Tyr. From this active construct, a single Trp residue was placed in the catalytic site loop (F159W-Leuko-PNP) as a reporter group for the ribosyl region of the catalytic site. The F159W-Leuko-PNP fluorescence is red shifted compared to native PNP, suggesting a solvent-exposed Trp residue. Upon ligand binding (hypoxanthine), the 3-fold fluorescence quench confirms conformational packing of the catalytic site pocket hydrophobic cluster. F159W-Leuko-PNP has an on-enzyme thermodynamic equilibrium constant (Keq) near unity in the temperature range between 20 and 30 degrees C and nonzero enthalpic components, making it suitable for laser-induced T-jump analyses. T-jump relaxation kinetics of F159W-Leuko-PNP in equilibrium with substrates and/or products indicate the conformational equilibria of at least two ternary complex intermediates in the nano- to millisecond time scale (1000-10000 s-1) that equilibrate prior to the slower chemical step (approximately 200 s-1). F159W-Leuko-PNP provides a novel protein platform to investigate the protein conformational dynamics occurring prior to transition state formation.

Protein flexibility and metal coordination changes in DHAP-dependent aldolases

The mobility of rhamnulose-1-phosphate aldolase (RhuA) was analysed with a normal mode description and high level calculations on models of the active site. We report the connection between the mobility and the chemical properties of the active site, and compare them to a closely related enzyme, fuculose-1-phosphate aldolase (FucA). Calculations show that the different coordination number for the zinc ion, reported in the crystal structures of RhuA and FucA, was due to a different spatial arrangement of the residues, not to their different chemical nature. Moreover, the metal coordination change is correlated with activity. The domain mobility of the enzyme can reshape the active site of RhuA into the arrangement found in the FucA structure, and vice-versa. This has a direct influence on the energy barrier for the aldol reaction catalyzed by these enzymes, thus showing a coupling of the domain movements and the catalytic effects. Hence domain movements and the coordination chemistry of the active site metal suggest an explanation of why these enzymes have similar experimental turnover rates.