Catalytic Effects of Active Site Conformational Change in the Allosteric Activation of Imidazole Glycerol Phosphate Synthase.

Imidazole glycerol phosphate synthase (IGPS) is a class-I glutamine amidotransferase (GAT) that hydrolyzes glutamine. Ammonia is produced and transferred to a second active site, where it reacts with N1-(5'-phosphoribosyl)-formimino-5-aminoimidazole-4-carboxamide ribonucleotide (PrFAR) to form precursors to purine and histidine biosynthesis. Binding of PrFAR over 25 Šaway from the active site increases glutaminase efficiency by ∼4500-fold, primarily altering the glutamine turnover number. IGPS has been the focus of many studies on allosteric communication; however, atomic details for how the glutamine hydrolysis rate increases in the presence of PrFAR are lacking. We present a density functional theory study on 237-atom active site cluster models of IGPS based on crystallized structures representing the inactive and allosterically active conformations and investigate the multistep reaction leading to thioester formation and ammonia production. The proposed mechanism is supported by similar, well-studied enzyme mechanisms, and the corresponding energy profile is consistent with steady-state kinetic studies of PrFAR + IGPS. Additional active site models are constructed to examine the relationship between active site structural change and transition-state stabilization via energy decomposition schemes. The results reveal that the inactive IGPS conformation does not provide an adequately formed oxyanion hole structure and that repositioning of the oxyanion strand relative to the substrate is vital for a catalysis-competent oxyanion hole, with or without the hVal51 dihedral flip. These findings are valuable for future endeavors in modeling the IGPS allosteric mechanism by providing insight into the atomistic changes required for rate enhancement that can inform suitable reaction coordinates for subsequent investigations.

Modeling Catalysis in Allosteric Enzymes: Capturing Conformational Consequences.

Greater understanding of enzymatic mechanisms aids the discovery of new targets for biologics, the development of biocatalytic transformations, and de novo enzyme design. Methods using quantum mechanical (QM) potentials, such as Density Functional Theory (DFT), have enabled complex multistep enzymatic mechanisms to be studied, often in quantitative detail. Nevertheless, the dynamic interconversion of enzyme conformations between active and inactive catalytic forms, involving length- and timescales inaccessible to QM treatments, presents a formidable challenge for the development of computational models for allosterically modulated enzymes. We present an overview of the key concepts underlying multistate models of enzyme catalysis, enzyme allostery, and the challenge that large-scale conformational changes pose for methods using QM, QM/MM, and MM potentials. Structural clustering is highlighted as a valuable approach to bridge molecular dynamics conformational sampling of MM potentials and quantum chemical cluster models of catalysis. Particularly relevant to this discussion is structural allostery, which serves as the exemplar of conformational consequences. Here, a well-characterized allosteric enzyme, Imidazole Glycerol Phosphate Synthase (IGPS), is used to showcase the importance of multiple conformations and guide a new direction for qualitative understanding and quantitative modeling in enzyme catalysis.

Size-and-Shape Space Gaussian Mixture Models for Structural Clustering of Molecular Dynamics Trajectories.

Determining the optimal number and identity of structural clusters from an ensemble of molecular configurations continues to be a challenge. Recent structural clustering methods have focused on the use of internal coordinates due to the innate rotational and translational invariance of these features. The vast number of possible internal coordinates necessitates a feature space supervision step to make clustering tractable but yields a protocol that can be system type-specific. Particle positions offer an appealing alternative to internal coordinates but suffer from a lack of rotational and translational invariance, as well as a perceived insensitivity to regions of structural dissimilarity. Here, we present a method, denoted shape-GMM, that overcomes the shortcomings of particle positions using a weighted maximum likelihood alignment procedure. This alignment strategy is then built into an expectation maximization Gaussian mixture model (GMM) procedure to capture metastable states in the free-energy landscape. The resulting algorithm distinguishes between a variety of different structures, including those indistinguishable by root-mean-square displacement and pairwise distances, as demonstrated on several model systems. Shape-GMM results on an extensive simulation of the fast-folding HP35 Nle/Nle mutant protein support a four-state folding/unfolding mechanism, which is consistent with previous experimental results and provides kinetic details comparable to previous state-of-the art clustering approaches, as measured by the VAMP-2 score. Currently, training of shape-GMMs is recommended for systems (or subsystems) that can be represented by ≲200 particles and ≲100k configurations to estimate high-dimensional covariance matrices and balance computational expense. Once a shape-GMM is trained, it can be used to predict the cluster identities of millions of configurations.

Residue-Level Allostery Propagates through the Effective Coarse-Grained Hessian.

The long-ranged coupling between residues that gives rise to allostery in a protein is built up from short-ranged physical interactions. Computational tools used to predict this coupling and its functional relevance have relied on the application of graph theoretical metrics to residue-level correlations measured from all-atom molecular dynamics simulations. The short-ranged interactions that yield these long-ranged residue-level correlations are quantified by the effective coarse-grained Hessian. Here we compute an effective harmonic coarse-grained Hessian from simulations of a benchmark allosteric protein, IGPS, and demonstrate the improved locality of this graph Laplacian over two other connectivity matrices. Additionally, two centrality metrics are developed that indicate the direct and indirect importance of each residue at producing the covariance between the effector binding pocket and the active site. The residue importance indicated by these two metrics is corroborated by previous mutagenesis experiments and leads to unique functional insights; in contrast to previous computational analyses, our results suggest that fP76-hK181 is the most important contact for conveying direct allosteric paths across the HisF-HisH interface. The connectivity around fD98 is found to be important at affecting allostery through indirect means.