Protein allosteric pathways are investigated in the imidazole glycerol phosphate synthase heterodimer in an effort to elucidate how the effector (PRFAR,formimino]-5-aminoimidazole-4-carboxamide ribonucleotide) activates glutaminase catalysis at a distance of 25 Å from the glutamine-binding site. We apply solution NMR techniques and community analysis of dynamical networks, based on mutual information of correlated protein motions in the active and inactive enzymes. We find evidence that the allosteric pathways in the PRFAR bound enzyme involve conserved residues that correlate motion of the PRFAR binding loop to motion at the protein-protein interface, and ultimately at the glutaminase active site. The imidazole glycerol phosphate synthase bienzyme is an important branch point for the histidine and nucleotide biosynthetic pathways and represents a potential therapeutic target against microbes. The proposed allosteric mechanism and the underlying allosteric pathways provide fundamental insights for the design of new allosteric drugs and/or alternative herbicides.glutamine hydrolysis | protein networks | generalized correlation analysis | network theory A llostery is a fundamental property that allows for the regulation of function and dynamic adaptability of enzymes and proteins. Allosteric enzymes contain at least two distant binding sites, including the active site responsible for catalytic activity, which binds the substrate, and the allosteric site, which binds the effector and initiates the allosteric signal propagation to the active site. In V-type systems, substrate binding is not affected by the presence of the effector but if the effector is not bound, the allosteric protein is usually catalytically inactive (or poorly active), indicating that the effector binding is coupled to the kinetic and/or thermodynamic parameters of the biochemical reaction in the active site. Allosteric information transfer can range from large, enthalpically driven conformational changes to purely entropically driven motions or a combination of both enthalpic and entropic effects, but in each case the kinetic parameters of the catalyzed reaction at the substrate binding site are altered. At the heart of allosterism there is intramolecular thermodynamic coupling over long distances (>10 Å), between the active and allosteric sites. An important challenge for fundamental studies is the elucidation of the allosteric pathways that connect the two ligand-binding sites.In this work, we combine community network analysis based on molecular dynamics (MD) simulations and NMR studies of protein motion based on relaxation dispersion techniques and chemical shift titrations experiments to provide an atomistic description of allostery in the V-type allosteric enzyme imidazole glycerol phosphate synthase (IGPS) from the thermophile Thermotoga maritima (Fig. 1). IGPS is a tightly associated heterodimeric enzyme in which each monomer enzyme catalyzes a different reaction (1-3). The 23 kDa HisH enzyme is a member of the glutamine amidotransferas...

MSMBuilder is a software package for building statistical models of high-dimensional time-series data. It is designed with a particular focus on the analysis of atomistic simulations of biomolecular dynamics such as protein folding and conformational change. MSMBuilder is named for its ability to construct Markov state models (MSMs), a class of models that has gained favor among computational biophysicists. In addition to both well-established and newer MSM methods, the package includes complementary algorithms for understanding time-series data such as hidden Markov models and time-structure based independent component analysis. MSMBuilder boasts an easy to use command-line interface, as well as clear and consistent abstractions through its Python application programming interface. MSMBuilder was developed with careful consideration for compatibility with the broader machine learning community by following the design of scikit-learn. The package is used primarily by practitioners of molecular dynamics, but is just as applicable to other computational or experimental time-series measurements.

Often the analysis of time-dependent chemical and biophysical systems produces high-dimensional time-series data for which it can be difficult to interpret which individual features are most salient. While recent work from our group and others has demonstrated the utility of time-lagged covariate models to study such systems, linearity assumptions can limit the compression of inherently nonlinear dynamics into just a few characteristic components. Recent work in the field of deep learning has led to the development of the variational autoencoder (VAE), which is able to compress complex datasets into simpler manifolds. We present the use of a time-lagged VAE, or variational dynamics encoder (VDE), to reduce complex, nonlinear processes to a single embedding with high fidelity to the underlying dynamics. We demonstrate how the VDE is able to capture nontrivial dynamics in a variety of examples, including Brownian dynamics and atomistic protein folding. Additionally, we demonstrate a method for analyzing the VDE model, inspired by saliency mapping, to determine what features are selected by the VDE model to describe dynamics. The VDE presents an important step in applying techniques from deep learning to more accurately model and interpret complex biophysics.

Metadynamics is a powerful enhanced molecular dynamics sampling method that accelerates simulations by adding history-dependent multidimensional Gaussians along selective collective variables (CVs). In practice, choosing a small number of slow CVs remains challenging due to the inherent high dimensionality of biophysical systems. Here we show that time-structure based independent component analysis (tICA), a recent advance in Markov state model literature, can be used to identify a set of variationally optimal slow coordinates for use as CVs for Metadynamics. We show that linear and nonlinear tICA-Metadynamics can complement existing MD studies by explicitly sampling the system's slowest modes and can even drive transitions along the slowest modes even when no such transitions are observed in unbiased simulations.

As molecular dynamics simulations access increasingly longer time scales, complementary advances in the analysis of biomolecular time-series data are necessary. Markov state models offer a powerful framework for this analysis by describing a system's states and the transitions between them. A recently established variational theorem for Markov state models now enables modelers to systematically determine the best way to describe a system's dynamics. In the context of the variational theorem, we analyze ultra-long folding simulations for a canonical set of twelve proteins [K. Lindorff-Larsen et al., Science 334, 517 (2011)] by creating and evaluating many types of Markov state models. We present a set of guidelines for constructing Markov state models of protein folding; namely, we recommend the use of cross-validation and a kinetically motivated dimensionality reduction step for improved descriptions of folding dynamics. We also warn that precise kinetics predictions rely on the features chosen to describe the system and pose the description of kinetic uncertainty across ensembles of models as an open issue. Published by AIP Publishing. [http://dx

Selection of appropriate collective variables (CVs) for enhancing sampling of molecular simulations remains an unsolved problem in computational modeling. In particular, picking initial CVs is particularly challenging in higher dimensions. Which atomic coordinates or transforms there of from a list of thousands should one pick for enhanced sampling runs? How does a modeler even begin to pick starting coordinates for investigation? This remains true even in the case of simple two state systems and only increases in difficulty for multi-state systems. In this work, we solve the "initial" CV problem using a data-driven approach inspired by the field of supervised machine learning (SML). In particular, we show how the decision functions in SML algorithms can be used as initial CVs ( ) for accelerated sampling. Using solvated alanine dipeptide and Chignolin mini-protein as our test cases, we illustrate how the distance to the support vector machines' decision hyperplane, the output probability estimates from logistic regression, the outputs from shallow or deep neural network classifiers, and other classifiers may be used to reversibly sample slow structural transitions. We discuss the utility of other SML algorithms that might be useful for identifying CVs for accelerating molecular simulations.

Variational autoencoder frameworks have demonstrated success in reducing complex nonlinear dynamics in molecular simulation to a single nonlinear embedding. In this work, we illustrate how this nonlinear latent embedding can be used as a collective variable for enhanced sampling and present a simple modification that allows us to rapidly perform sampling in multiple related systems. We first demonstrate our method is able to describe the effects of force field changes in capped alanine dipeptide after learning about a model using AMBER99. We further provide a simple extension to variational dynamics encoders that allows the model to be trained in a more efficient manner on larger systems by encoding the outputs of a linear transformation using time-structure based independent component analysis (tICA). Using this technique, we show how such a model trained for one protein, the WW domain, can efficiently be transferred to perform enhanced sampling on a related mutant protein, the GTT mutation. This method shows promise for its ability to rapidly sample related systems using a single transferable collective variable, enabling us to probe the effects of variation in increasingly large systems of biophysical interest.

The influence of electrostatic interactions on the free energy of proton-coupled-electron-transfer (PCET) in biomimetic oxomanganese complexes inspired by the oxygen-evolving complex (OEC) of photosystem II (PSII), are investigated. The reported study introduces an enhanced Multi-Conformer Continuum Electrostatics (MCCE) model, parameterized at the density functional theory (DFT) level with a classical valence model for the oxomanganese core. The calculated pKas and oxidation midpoint potentials (Ems) match experimental values for eight complexes indicating that purely electrostatic contributions account for most of the observed couplings between deprotonation and oxidation state transitions. We focus on pKas of terminal water ligands in [Mn(II/III)(H2O)6]2+/3+ (1), [Mn(III)(P)(H2O)2]3- (2, P = 5,10,15,20- tetrakis (2,6-dichloro-3-sulfonatophenyl) porphyrinato), [Mn(IV,IV)2(μ-O)2(terpy)2(H2O)2]4+ (3, terpy = 2,2’:6’,2”-terpyridine) and [Mn3(IV,IV,IV)(μ-O)4(phen)4(H2O)2]4+ (4, phen = 1,10-phenanthroline) and the pKas of μ-oxo bridges and Mn Ems in [Mn2(μ-O)2(bpy)4]2+ (5, bpy = 2,2’-bipyridyl), [Mn2(μ-O)2(salpn)2] (6, salpn= N,N′-bis(salicylidene)-1,3-propanediamine), [Mn2(μ-O)2(3,5-di(Cl)-salpn)2] (7) and [Mn2(μ-O)2(3,5-di(NO2)-salpn)2] (8) which are most relevant to PCET mechanisms. The analysis of complexes 6-8 highlights the strong coupling between electron and proton transfers, with any Mn oxidation lowering the pKa of an oxo bridge by 10.5±0.9 pH units. The model also accounts for changes in the Ems due to ligand substituents, such as those in complexes 6-8, due to the electron withdrawing Cl (7) and NO2 (8). The reported study provides the foundation for analysis of electrostatic effects in other oxomanganese complexes and metalloenzymes, where PCET plays a fundamental role in redox-leveling mechanisms.