Transient access to the protein interior: simulation versus NMR

A Futile Cycle?: Tissue Homeostatic Trans-Membrane Water Co-Transport: Kinetics, Thermodynamics, Metabolic Consequences

The phenomenon of active trans-membrane water cycling (AWC) has emerged in little over a decade. Here, we consider H2O transport across cell membranes from the origins of its study. Historically, trans-membrane water transport processes were classified into: A) compensating bidirectional fluxes ("exchange"), and B) unidirectional flux ("net flow") categories. Recent literature molecular structure determinations and molecular dynamic (MD) simulations indicate probably all the many different hydrophilic substrate membrane co-transporters have membrane-spanning hydrophilic pathways and co-transport water along with their substrates, and that they individually catalyze category A and/or B water flux processes, although usually not simultaneously. The AWC name signifies that, integrated over the all the cell's co-transporters, the rate of homeostatic, bidirectional trans-cytolemmal water exchange (category A) is synchronized with the metabolic rate of the crucial Na+,K+-ATPase (NKA) enzyme. A literature survey indicates the stoichiometric (category B) water/substrate ratios of individual co-transporters are often very large. The MD simulations also suggest how different co-transporter reactions can be kinetically coupled molecularly. Is this (Na+,K+-ATPase rate-synchronized) cycling futile, or is it consequential? Conservatively representative literature metabolomic and proteinomic results enable comprehensive free energy analyses of the many transport reactions with known water stoichiometries. Free energy calculations, using literature intracellular pressure (Pi) values reveals there is an outward trans-membrane H2O barochemical gradient of magnitude comparable to that of the well-known inward Na+ electrochemical gradient. For most co-influxers, these gradients are finely balanced to maintain intracellular metabolite concentration values near their consuming enzyme Michaelis constants. The thermodynamic analyses include glucose, glutamate-, gamma-aminobutyric acid (GABA), and lactate- transporters. 2%-4% Pi alterations can lead to disastrous concentration levels. For the neurotransmitters glutamate- and GABA, very small astrocytic Pi changes can allow/disallow synaptic transmission. Unlike the Na+ and K+ electrochemical steady-states, the H2O barochemical steady-state is in (or near) chemical equilibrium. The analyses show why the presence of aquaporins (AQPs) does not dissipate the trans-membrane pressure gradient. A feedback loop inherent in the opposing Na+ electrochemical and H2O barochemical gradients regulates AQP-catalyzed water flux as an integral AWC aspect. These results also require a re-consideration of the underlying nature of Pi. Active trans-membrane water cycling is not futile, but is inherent to the cell's "NKA system" - a new, fundamental aspect of biology.

Conformational Dynamics in Proteins: Entangled Slow Fluctuations and Nonequilibrium Reaction Events

Proteins exhibit conformational fluctuations and changes over various time scales, ranging from rapid picosecond-scale local atomic motions to slower microsecond-scale global conformational transformations. In the presence of these intricate fluctuations, chemical reactions occur and functions emerge. These conformational fluctuations of proteins are not merely stochastic random motions but possess distinct spatiotemporal characteristics. Moreover, chemical reactions do not always proceed along a single reaction coordinate in a quasi-equilibrium manner. Therefore, it is essential to understand spatiotemporal conformational fluctuations of proteins and the conformational change processes associated with reactions. In this Perspective, we shed light on the complex dynamics of proteins and their role in enzyme catalysis by presenting recent results regarding dynamic couplings and disorder in the conformational dynamics of proteins and rare but rapid enzymatic reaction events obtained from molecular dynamics simulations.

Dichotomy in TCR V-domain dynamics binding the opposed inclined planes of pMHC-II and pMHC-I α-helices

Ligand recognition by the human α/β T-cell antigen receptor (TCR) heterodimer protein, unlike the surface immunoglobulin (sIg) B-cell receptor, is not governed by relative binding affinity. Its interaction with the peptide (p) plus major histocompatibility complex (MHC) protein (abbrev. pMHC) likely involves some different molecular mechanism linking pMHC binding to T-cell functions. Recent analytical geometry of TCR:pMHC-II solved crystallographic structures (n = 40) revealed that each variable (V)-domain is bound in similar, yet mathematically unique orientations to its target pMHC groove. The relative position of the central cysteine of each V-domain was examined by multivariable calculus in spherical coordinates, where a simple volume element (dV) was found to describe clonotypic geometry with pMHC-II. Here, the study was expanded to include TCR:pMHC-I structures, and to model a physical mechanism, specifically involving the two directionally opposed inclined planes (IP) manifest by the two major α-helices prominent in both MHC-I and MHC-II proteins. Calculations for rotational torque of each V-domain, together with acceleration up and down the slopes of both MHC α-helices were used to estimate the time a given V-domain spends sliding down its cognate MHC IP. This V-domain rotation/sliding mechanism appears to be quantitatively unique for each TCR:pMHC V-domain (n = 40). However, there is an apparent and common dichotomy between the mobility of each V-domain with respect to the two classes of MHC proteins. Evolutionary motifs in the MHC helices support that the V-domains negotiate the opposed inclined planes of pMHC ligands in clonotypic fashion. Thus, this model is useful in understanding how mechanical forces are linked to TCR function.

Heterogeneous and Allosteric Role of Surface Hydration for Protein-Ligand Binding

Atomistic-level understanding of surface hydration mediating protein-protein interactions and ligand binding has been a challenge due to the dynamic nature of water molecules near the surface. We develop a computational method to evaluate the solvation free energy based on the density map of the first hydration shell constructed from all-atom molecular dynamics simulation and use it to examine the binding of two intrinsically disordered ligands to their target protein domain. One ligand is from the human protein, and the other is from the 1918 Spanish flu virus. We find that the viral ligand incurs a 6.9 kcal/mol lower desolvation penalty upon binding to the target, which is consistent with its stronger binding affinity. The difference arises from the spatially fragmented and nonuniform water density profiles of the first hydration shell. In particular, residues that are distal from the ligand-binding site contribute to a varying extent to the desolvation penalty, among which the "entropy hotspot" residues contribute significantly. Thus, ligand binding alters hydration on remote sites in addition to affecting the binding interface. The nonlocal effect disappears when the conformational motion of the protein is suppressed. The present results elucidate the interplay between protein conformational dynamics and surface hydration. Our approach of measuring the solvation free energy based on the water density of the first hydration shell is tolerant of the conformational fluctuation of protein, and we expect it to be applicable to investigating a broad range of biomolecular interfaces.

Ion influence on surface water dynamics and proton exchange at protein surfaces - A unified model for transverse and longitudinal NMR relaxation dispersion

In all biologically relevant media, proteins interact in the presence of surrounding ions, and such interactions are water-mediated. Water molecules play a crucial role in the restructuring of proteins in solution and indeed in their biological activity. Surface water dynamics and proton exchange at protein surfaces is investigated here using NMR relaxometry, for two well-known globular proteins, lysozyme and bovine serum albumin, with particular attention to the role of surface ions. We present a unified model of surface water dynamics and proton exchange, accounting simultaneously for the observed longitudinal and transverse relaxation rates. The most notable effect of salt (0.1 M) concerns the slow surface water dynamics, related to rare water molecules embedded in energy wells on the protein surface. This response is protein-specific. On the other hand, the proton exchange time between labile protein-protons and water-protons at the protein surface seems to be very similar for the two proteins and is insensitive to the addition of salts at the concentration studied.

Protein 3D Hydration: A Case of Bovine Pancreatic Trypsin Inhibitor

Characterization of the hydrated state of a protein is crucial for understanding its structural stability and function. In the present study, we have investigated the 3D hydration structure of the protein BPTI (bovine pancreatic trypsin inhibitor) by molecular dynamics (MD) and the integral equation method in the three-dimensional reference interaction site model (3D-RISM) approach. Both methods have found a well-defined hydration layer around the protein and revealed the localization of BPTI buried water molecules corresponding to the X-ray crystallography data. Moreover, under 3D-RISM calculations, the obtained positions of waters bound firmly to the BPTI sites are in reasonable agreement with the experimental results mentioned above for the BPTI crystal form. The analysis of the 3D hydration structure (thickness of hydration shell and hydration numbers) was performed for the entire protein and its polar and non-polar parts using various cut-off distances taken from the literature as well as by a straightforward procedure proposed here for determining the thickness of the hydration layer. Using the thickness of the hydration shell from this procedure allows for calculating the total hydration number of biomolecules properly under both methods. Following this approach, we have obtained the thickness of the BPTI hydration layer of 3.6 Å with 369 water molecules in the case of MD simulation and 3.9 Å with 333 water molecules in the case of the 3D-RISM approach. The above procedure was also applied for a more detailed description of the BPTI hydration structure near the polar charged and uncharged radicals as well as non-polar radicals. The results presented for the BPTI as an example bring new knowledge to the understanding of protein hydration.

Collective variable discovery in the age of machine learning: reality, hype and everything in between

Understanding the kinetics and thermodynamics profile of biomolecules is necessary to understand their functional roles which has a major impact in mechanism driven drug discovery. Molecular dynamics simulation has been routinely used to understand conformational dynamics and molecular recognition in biomolecules. Statistical analysis of high-dimensional spatiotemporal data generated from molecular dynamics simulation requires identification of a few low-dimensional variables which can describe the essential dynamics of a system without significant loss of information. In physical chemistry, these low-dimensional variables are often called collective variables. Collective variables are used to generate reduced representations of free energy surfaces and calculate transition probabilities between different metastable basins. However the choice of collective variables is not trivial for complex systems. Collective variables range from geometric criteria such as distances and dihedral angles to abstract ones such as weighted linear combinations of multiple geometric variables. The advent of machine learning algorithms led to increasing use of abstract collective variables to represent biomolecular dynamics. In this review, I will highlight several nuances of commonly used collective variables ranging from geometric to abstract ones. Further, I will put forward some cases where machine learning based collective variables were used to describe simple systems which in principle could have been described by geometric ones. Finally, I will put forward my thoughts on artificial general intelligence and how it can be used to discover and predict collective variables from spatiotemporal data generated by molecular dynamics simulations.

Data driven collective variable discovery methods to capture conformational dynamics in biological macromolecules.

Non-Fickian single-file pore transport

Single-file diffusion exhibits anomalously slow collective transport when particles are able to immobilize by binding and unbinding to the one-dimensional channel within which the particles diffuse. We have explored this system for short porelike channels using a symmetric exclusion process with fully stochastic dynamics. We find that for shorter channels, a non-Fickian regime emerges for slow binding kinetics. In this regime the average flux 〈Φ〉∼1/L^{3}, where L is the channel length in units of the particle size. We find that a two-state model describes this behavior well for sufficiently slow binding rates, where the binding rates determine the switching time between high-flux bursts of directed transport and low-flux leaky states. Each high-flux burst is Fickian with 〈Φ〉∼1/L. Longer systems are more often in a low-flux state, leading to the non-Fickian behavior.

Multiscale Water Dynamics on Protein Surfaces: Protein-Specific Response to Surface Ions

Proteins function in crowded aqueous environments, interacting with a diverse range of compounds, and among them, dissolved ions. These interactions are water-mediated. In the present study, we combine field-dependent NMR relaxation (NMRD) and theory to probe water dynamics on the surface of proteins in concentrated aqueous solutions of hen egg-white lysozyme (LZM) and bovine serum albumin (BSA). The experiments reveal that the presence of salts (NaCl or NaI) leads to an opposite ion-specific response for the two proteins: an addition of salt to LZM solutions increases water relaxation rates with respect to the salt-free case, while for BSA solutions, a decrease is observed. The magnitude of the change depends on the ion identity. The developed model accounts for the non-Lorentzian shape of the NMRD profiles and reproduces the experimental data over four decades in Larmor frequency (10 kHz to 110 MHz). It is applicable up to high protein concentrations. The model incorporates the observed ion-specific effects via changes in the protein surface roughness, represented by the surface fractal dimension, and the accompanying changes in the surface water residence times. The response is protein-specific, linked to geometrical aspects of the individual protein surfaces, and goes beyond protein-independent Hofmeister-style ordering of ions.

Microscopic insights into dynamic disorder in the isomerization dynamics of the protein BPTI

Understanding the dynamic disorder behind a process, i.e., the dynamic effect of fluctuations that occur on a timescale slower or comparable with the timescale of the process, is essential for elucidating the dynamics and kinetics of complicated molecular processes in biomolecules and liquids. Despite numerous theoretical studies of single-molecule kinetics, our microscopic understanding of dynamic disorder remains limited. In the present study, we investigate the microscopic aspects of dynamic disorder in the isomerization dynamics of the Cys14-Cys38 disulfide bond in the protein bovine pancreatic trypsin inhibitor, which has been observed by nuclear magnetic resonance. We use a theoretical model with a stochastic transition rate coefficient, which is calculated from the 1-ms-long time molecular dynamics trajectory obtained by Shaw et al. [Science 330, 341-346 (2010)]. The isomerization dynamics are expressed by the transitions between coarse-grained states consisting of internal states, i.e., conformational sub-states. In this description, the rate for the transition from the coarse-grained states is stochastically modulated due to fluctuations between internal states. We examine the survival probability for the conformational transitions from a coarse-grained state using a theoretical model, which is a good approximation to the directly calculated survival probability. The dynamic disorder changes from a slow modulation limit to a fast modulation limit depending on the aspects of the coarse-grained states. Our analysis of the rate modulations behind the survival probability, in relation to the fluctuations between internal states, reveals the microscopic origin of dynamic disorder.

Applications of water molecules for analysis of macromolecule properties

Water molecules maintain proteins' structures, functions, stabilities and dynamics. They can occupy certain positions or pass quickly via a protein's interior. Regardless of their behaviour, water molecules can be used for the analysis of proteins' structural features and biochemical properties. Here, we present a list of several software programs that use the information provided by water molecules to: i) analyse protein structures and provide the optimal positions of water molecules for protein hydration, ii) identify high-occupancy water sites in order to analyse ligand binding modes, and iii) detect and describe tunnels and cavities. The analysis of water molecules' distribution and trajectories sheds a light on proteins' interactions with small molecules, on the dynamics of tunnels and cavities, on protein composition and also on the functionality, transportation network and location of functionally relevant residues. Finally, the correct placement of water molecules in protein crystal structures can significantly improve the reliability of molecular dynamics simulations.

Point processes with Gaussian boson sampling

Random point patterns are ubiquitous in nature, and statistical models such as point processes, i.e., algorithms that generate stochastic collections of points, are commonly used to simulate and interpret them. We propose an application of quantum computing to statistical modeling by establishing a connection between point processes and Gaussian boson sampling, an algorithm for photonic quantum computers. We show that Gaussian boson sampling can be used to implement a class of point processes based on hard-to-compute matrix functions which, in general, are intractable to simulate classically. We also discuss situations where polynomial-time classical methods exist. This leads to a family of efficient quantum-inspired point processes, including a fast classical algorithm for permanental point processes. We investigate the statistical properties of point processes based on Gaussian boson sampling and reveal their defining property: like bosons that bunch together, they generate collections of points that form clusters. Finally, we analyze properties of these point processes for homogeneous and inhomogeneous state spaces, describe methods to control cluster location, and illustrate how to encode correlation matrices.

Water in protein hydration and ligand recognition

This review describes selected basics of water in biomolecular recognition. We focus on a qualitative understanding of the most important physical aspects, how these change in magnitude between bulk water and protein environment, and how the roles that water plays for proteins arise from them. These roles include mechanical support, thermal coupling, dielectric screening, mass and charge transport, and the competition with a ligand for the occupation of a binding site. The presence or absence of water has ramifications that range from the thermodynamic binding signature of a single ligand up to cellular survival. The large inhomogeneity in water density, polarity and mobility around a solute is hard to assess in experiment. This is a source of many difficulties in the solvation of protein models and computational studies that attempt to elucidate or predict ligand recognition. The influence of water in a protein binding site on the experimental enthalpic and entropic signature of ligand binding is still a point of much debate. The strong water‐water interaction in enthalpic terms is counteracted by a water molecule's high mobility in entropic terms. The complete arrest of a water molecule's mobility sets a limit on the entropic contribution of a water displacement process, while the solvent environment sets limits on ligand reactivity.

Distant Non-Obvious Mutations Influence the Activity of a Hyperthermophilic Pyrococcus furiosus Phosphoglucose Isomerase

The cupin-type phosphoglucose isomerase (PfPGI) from the hyperthermophilic archaeon Pyrococcus furiosus catalyzes the reversible isomerization of glucose-6-phosphate to fructose-6-phosphate. We investigated PfPGI using protein-engineering bioinformatics tools to select functionally-important residues based on correlated mutation analyses. A pair of amino acids in the periphery of PfPGI was found to be the dominant co-evolving mutation. The position of these selected residues was found to be non-obvious to conventional protein engineering methods. We designed a small smart library of variants by substituting the co-evolved pair and screened their biochemical activity, which revealed their functional relevance. Four mutants were further selected from the library for purification, measurement of their specific activity, crystal structure determination, and metal cofactor coordination analysis. Though the mutant structures and metal cofactor coordination were strikingly similar, variations in their activity correlated with their fine-tuned dynamics and solvent access regulation. Alternative, small smart libraries for enzyme optimization are suggested by our approach, which is able to identify non-obvious yet beneficial mutations.

NMR shutter-speed elucidates apparent population inversion of 1 H2 O signals due to active transmembrane water cycling

Purpose

The desire to quantitatively discriminate the extra‐ and intracellular tissue ¹H₂O MR signals has gone hand‐in‐hand with the continual, historic increase in MRI instrument magnetic field strength [B₀]. However, recent studies have indicated extremely valuable, novel metabolic information can be readily accessible at ultra–low B₀. The two signals can be distinguished, and the homeostatic activity of the cell membrane sodium/potassium pump (Na⁺,K⁺,ATPase) detected. The mechanism allowing ¹H₂O MRI to do this is the newly discovered active transmembrane water cycling (AWC) phenomenon, which we found using paramagnetic extracellular contrast agents at clinical B₀ values. AWC is important because Na⁺,K⁺,ATPase can be considered biology’s most vital enzyme, and its in vivo steady‐state activity has not before been measurable, let alone amenable to mapping with high spatial resolution. Recent reports indicate AWC correlates with neuronal firing rate, with malignant tumor metastatic potential, and inversely with cellular reducing equivalent fraction. We wish to systematize the ways AWC can be precisely measured.

Methods

We present a theoretical longitudinal relaxation analysis of considerable scope: it spans the low‐ and high–field situations.

Results

We show the NMR shutter‐speed organizing principle is pivotal in understanding how trans–membrane steady–state water exchange kinetics are manifest throughout the range. Our findings illuminate an aspect, apparent population inversion, which is crucial in understanding ultra‐low field results.

Conclusions

Without an appreciation of apparent population inversion, significant misinterpretations of future data are likely. These could have unfortunate diagnostic consequences.

Exploring Solanum tuberosum Epoxide Hydrolase Internal Architecture by Water Molecules Tracking

Several different approaches are used to describe the role of protein compartments and residues in catalysis and to identify key residues suitable for the modification of the activity or selectivity of the desired enzyme. In our research, we applied a combination of molecular dynamics simulations and a water tracking approach to describe the water accessible volume of Solanum tuberosum epoxide hydrolase. Using water as a molecular probe, we were able to identify small cavities linked with the active site: (i) one made up of conserved amino acids and indispensable for the proper positioning of catalytic water and (ii) two others in which modification can potentially contribute to enzyme selectivity and activity. Additionally, we identified regions suitable for de novo tunnel design that could also modify the catalytic properties of the enzyme. The identified hot-spots extend the list of the previously targeted residues used for modification of the regioselectivity of the enzyme. Finally, we have provided an example of a simple and elegant process for the detailed description of the network of cavities and tunnels, which can be used in the planning of enzyme modifications and can be easily adapted to the study of any other protein.

Characterization of low-lying excited states of proteins by high-pressure NMR

Hydrostatic pressure alters the free energy of proteins by a few kJ mol^-1, with the amount depending on their partial molar volumes. Because the folded ground state of a protein contains cavities, it is always a state of large partial molar volume. Therefore pressure always destabilises the ground state and increases the population of partially and completely unfolded states. This is a mild and reversible conformational change, which allows the study of excited states under thermodynamic equilibrium conditions. Many of the excited states studied in this way are functionally relevant; they also seem to be very similar to kinetic folding intermediates, thus suggesting that evolution has made use of the 'natural' dynamic energy landscape of the protein fold and sculpted it to optimise function. This includes features such as ligand binding, structural change during the catalytic cycle, and dynamic allostery.

Water-Protein Interactions Coupled with Protein Conformational Transition

Conformational fluctuations of proteins are crucially important for their functions. However, changes in the location and dynamics of hydrated water in many proteins accompanied by the conformational transition have not been fully understood. Here, we used phase-modulated clean chemical exchange NMR approach to investigate pressure-induced changes in water-to-amide proton exchange occurring at sub-second time scale. With the transition of ubiquitin from its native conformation (N1) to an alternative conformation (N2) at 250 MPa, proton exchange rates of residues 32-35, 40-41, and 71, which are located at the C-terminal side of the protein, were significantly increased. These observations can be explained by the destabilization of the hydrogen bonds in the backbone and partial exposure of those amide groups to solvent in N2. We conclude that phase-modulated clean chemical exchange NMR approach coupled with pressure perturbation will be a useful tool for investigations of more open and hydrated protein structures.

How proteins modify water dynamics

Much of biology happens at the protein-water interface, so all dynamical processes in this region are of fundamental importance. Local structural fluctuations in the hydration layer can be probed by ¹⁷O magnetic relaxation dispersion (MRD), which, at high frequencies, measures the integral of a biaxial rotational time correlation function (TCF)-the integral rotational correlation time. Numerous ¹⁷O MRD studies have demonstrated that this correlation time, when averaged over the first hydration shell, is longer than in bulk water by a factor 3-5. This rotational perturbation factor (RPF) has been corroborated by molecular dynamics simulations, which can also reveal the underlying molecular mechanisms. Here, we address several outstanding problems in this area by analyzing an extensive set of molecular dynamics data, including four globular proteins and three water models. The vexed issue of polarity versus topography as the primary determinant of hydration water dynamics is resolved by establishing a protein-invariant exponential dependence of the RPF on a simple confinement index. We conclude that the previously observed correlation of the RPF with surface polarity is a secondary effect of the correlation between polarity and confinement. Water rotation interpolates between a perturbed but bulk-like collective mechanism at low confinement and an exchange-mediated orientational randomization (EMOR) mechanism at high confinement. The EMOR process, which accounts for about half of the RPF, was not recognized in previous simulation studies, where only the early part of the TCF was examined. Based on the analysis of the experimentally relevant TCF over its full time course, we compare simulated and measured RPFs, finding a 30% discrepancy attributable to force field imperfections. We also compute the full ¹⁷O MRD profile, including the low-frequency dispersion produced by buried water molecules. Computing a local RPF for each hydration shell, we find that the perturbation decays exponentially with a decay "length" of 0.3 shells and that the second and higher shells account for a mere 3% of the total perturbation measured by ¹⁷O MRD. The only long-range effect is a weak water alignment in the electric field produced by an electroneutral protein (not screened by counterions), but this effect is negligibly small for ¹⁷O MRD. By contrast, we find that the ¹⁷O TCF is significantly more sensitive to the important short-range perturbations than the other two TCFs examined here.

Enhancing Structure Prediction and Design of Soluble and Membrane Proteins with Explicit Solvent-Protein Interactions

Solvent molecules interact intimately with proteins and can profoundly regulate their structure and function. However, accurately and efficiently modeling protein solvation effects at the molecular level has been challenging. Here, we present a method that improves the atomic-level modeling of soluble and membrane protein structures and binding by efficiently predicting de novo protein-solvent molecule interactions. The method predicted with unprecedented accuracy buried water molecule positions, solvated protein conformations, and challenging mutational effects on protein binding. When applied to homology modeling, solvent-bound membrane protein structures, pockets, and cavities were recapitulated with near-atomic precision even from distant homologs. Blindly refined atomic-level structures of evolutionary distant G protein-coupled receptors imply strikingly different functional roles of buried solvent between receptor classes. The method should prove useful for refining low-resolution protein structures, accurately modeling drug-binding sites in structurally uncharacterized receptors, and designing solvent-mediated protein catalysis, recognition, ligand binding, and membrane protein signaling.

Water Dynamics in the Hydration Shells of Biomolecules

The structure and function of biomolecules are strongly influenced by their hydration shells. Structural fluctuations and molecular excitations of hydrating water molecules cover a broad range in space and time, from individual water molecules to larger pools and from femtosecond to microsecond time scales. Recent progress in theory and molecular dynamics simulations as well as in ultrafast vibrational spectroscopy has led to new and detailed insight into fluctuations of water structure, elementary water motions, electric fields at hydrated biointerfaces, and processes of vibrational relaxation and energy dissipation. Here, we review recent advances in both theory and experiment, focusing on hydrated DNA, proteins, and phospholipids, and compare dynamics in the hydration shells to bulk water.

Perspective: Structure and ultrafast dynamics of biomolecular hydration shells

The structure and function of biomolecules can be strongly influenced by their hydration shells. A key challenge is thus to determine the extent to which these shells differ from bulk water, since the structural fluctuations and molecular excitations of hydrating water molecules within these shells can cover a broad range in both space and time. Recent progress in theory, molecular dynamics simulations, and ultrafast vibrational spectroscopy has led to new and detailed insight into the fluctuations of water structure, elementary water motions, and electric fields at hydrated biointerfaces. Here, we discuss some central aspects of these advances, focusing on elementary molecular mechanisms and processes of hydration on a femto- to picosecond time scale, with some special attention given to several issues subject to debate.

Water is an active matrix of life for cell and molecular biology

Szent-Győrgi called water the "matrix of life" and claimed that there was no life without it. This statement is true, as far as we know, on our planet, but it is not clear whether it must hold throughout the cosmos. To evaluate that question requires a close consideration of the many varied and subtle roles that water plays in living cells-a consideration that must be free of both an assumed essentialism that gives water an almost mystical life-giving agency and a traditional tendency to see it as a merely passive solvent. Water is a participant in the "life of the cell," and here I describe some of the features of that active agency. Water's value for molecular biology comes from both the structural and dynamic characteristics of its status as a complex, structured liquid as well as its nature as a polar, protic, and amphoteric reagent. Any discussion of water as life's matrix must, however, begin with an acknowledgment that our understanding of it as both a liquid and a solvent is still incomplete.

Proton Wire Dynamics in the Green Fluorescent Protein

Inside proteins, protons move on proton wires (PWs). Starting from the highest resolution X-ray structure available, we conduct a 306 ns molecular dynamics simulation of the (A-state) wild-type (wt) green fluorescent protein (GFP) to study how its PWs change with time. We find that the PW from the chromophore via Ser205 to Glu222, observed in all X-ray structures, undergoes rapid water molecule insertion between Ser205 and Glu222. Sometimes, an alternate Ser205-bypassing PW exists. Side chain rotations of Thr203 and Ser205 play an important role in shaping the PW network in the chromophore region. Thr203, with its bulkier side chain, exhibits slower transitions between its three rotameric states. Ser205 experiences more frequent rotations, slowing down when the Thr203 methyl group is close by. The combined states of both residues affect the PW probabilities. A random walk search for PWs from the chromophore reveals several exit points to the bulk, one being a direct water wire (WW) from the chromophore to the bulk. A longer WW connects the "bottom" of the GFP barrel with a "water pool" (WP1) situated below Glu222. These two WWs were not observed in X-ray structures of wt-GFP, but their analogues have been reported in related fluorescent proteins. Surprisingly, the high-resolution X-ray structure utilized herein shows that Glu222 is protonated at low temperatures. At higher temperatures, we suggest ion pairing between anionic Glu222 and a proton hosted in WP1. Upon photoexcitation, these two recombine, while a second proton dissociates from the chromophore and either exits the protein using the short WW or migrates along the GFP-barrel axis on the long WW. This mechanism reconciles the conflicting experimental and theoretical data on proton motion within GFP.

Water Determines the Structure and Dynamics of Proteins

Water is an essential participant in the stability, structure, dynamics, and function of proteins and other biomolecules. Thermodynamically, changes in the aqueous environment affect the stability of biomolecules. Structurally, water participates chemically in the catalytic function of proteins and nucleic acids and physically in the collapse of the protein chain during folding through hydrophobic collapse and mediates binding through the hydrogen bond in complex formation. Water is a partner that slaves the dynamics of proteins, and water interaction with proteins affect their dynamics. Here we provide a review of the experimental and computational advances over the past decade in understanding the role of water in the dynamics, structure, and function of proteins. We focus on the combination of X-ray and neutron crystallography, NMR, terahertz spectroscopy, mass spectroscopy, thermodynamics, and computer simulations to reveal how water assist proteins in their function. The recent advances in computer simulations and the enhanced sensitivity of experimental tools promise major advances in the understanding of protein dynamics, and water surely will be a protagonist.

Nuclear magnetic relaxation by the dipolar EMOR mechanism: General theory with applications to two-spin systems

In aqueous systems with immobilized macromolecules, including biological tissue, the longitudinal spin relaxation of water protons is primarily induced by exchange-mediated orientational randomization (EMOR) of intra- and intermolecular magnetic dipole-dipole couplings. We have embarked on a systematic program to develop, from the stochastic Liouville equation, a general and rigorous theory that can describe relaxation by the dipolar EMOR mechanism over the full range of exchange rates, dipole coupling strengths, and Larmor frequencies. Here, we present a general theoretical framework applicable to spin systems of arbitrary size with symmetric or asymmetric exchange. So far, the dipolar EMOR theory is only available for a two-spin system with symmetric exchange. Asymmetric exchange, when the spin system is fragmented by the exchange, introduces new and unexpected phenomena. Notably, the anisotropic dipole couplings of non-exchanging spins break the axial symmetry in spin Liouville space, thereby opening up new relaxation channels in the locally anisotropic sites, including longitudinal-transverse cross relaxation. Such cross-mode relaxation operates only at low fields; at higher fields it becomes nonsecular, leading to an unusual inverted relaxation dispersion that splits the extreme-narrowing regime into two sub-regimes. The general dipolar EMOR theory is illustrated here by a detailed analysis of the asymmetric two-spin case, for which we present relaxation dispersion profiles over a wide range of conditions as well as analytical results for integral relaxation rates and time-dependent spin modes in the zero-field and motional-narrowing regimes. The general theoretical framework presented here will enable a quantitative analysis of frequency-dependent water-proton longitudinal relaxation in model systems with immobilized macromolecules and, ultimately, will provide a rigorous link between relaxation-based magnetic resonance image contrast and molecular parameters.

Unraveling Entropic Rate Acceleration Induced by Solvent Dynamics in Membrane Enzymes

Enzyme catalysis evolved in an aqueous environment. The influence of solvent dynamics on catalysis is, however, currently poorly understood and usually neglected. The study of water dynamics in enzymes and the associated thermodynamical consequences is highly complex and has involved computer simulations, nuclear magnetic resonance (NMR) experiments, and calorimetry. Water tunnels that connect the active site with the surrounding solvent are key to solvent displacement and dynamics. The protocol herein allows for the engineering of these motifs for water transport, which affects specificity, activity and thermodynamics. By providing a biophysical framework founded on theory and experiments, the method presented herein can be used by researchers without previous expertise in computer modeling or biophysical chemistry. The method will advance our understanding of enzyme catalysis on the molecular level by measuring the enthalpic and entropic changes associated with catalysis by enzyme variants with obstructed water tunnels. The protocol can be used for the study of membrane-bound enzymes and other complex systems. This will enhance our understanding of the importance of solvent reorganization in catalysis as well as provide new catalytic strategies in protein design and engineering.

Stay Wet, Stay Stable? How Internal Water Helps the Stability of Thermophilic Proteins

We present a systematic computational investigation of the internal hydration of a set of homologous proteins of different stability content and molecular complexities. The goal of the study is to verify whether structural water can be part of the molecular mechanisms ensuring enhanced stability in thermophilic enzymes. Our free-energy calculations show that internal hydration in the thermophilic variants is generally more favorable, and that the cumulated effect of wetting multiple sites results in a meaningful contribution to stability. Moreover, thanks to a more effective capability to retain internal water, some thermophilic proteins benefit by a systematic gain from internal wetting up to their optimal working temperature. Our work supports the idea that internal wetting can be viewed as an alternative molecular variable to be tuned for increasing protein stability.

Statistical survey of the buried waters in the Protein Data Bank

The structures of buried water molecules were studied in an ensemble of high-quality and non-redundant protein crystal structures. Buried water molecules were clustered and classified in lake-like clusters, which are completely isolated from the bulk solvent, and bay-like clusters, which are in contact with the bulk solvent through a surface water molecule. Buried water molecules are extremely common: lake-like clusters are found in 89 % of the protein crystal structures and bay-like clusters in 93 %. Clusters with only one water molecule are much more common than larger clusters. Both cluster types incline to be surrounded by loop residues, and to a minor extent by residues in extended secondary structure. Helical residues on the contrary do not tend to surround clusters of buried water molecules. One buried water molecule is found every 30-50 amino acid residues, depending on the secondary structures that are more abundant in the protein. Both main- and side-chain atoms are in contact with buried waters; they form four hydrogen bonds with the first water and 1-1.5 additional hydrogen bond for each additional water in the cluster. Consequently, buried water molecules appear to be firmly packed and rigid like the protein atoms. In this regard, it is remarkable to observe that prolines often surround water molecules buried in the protein interior. Interestingly, clusters of buried water molecules tend to be just beneath the protein surface. Moreover, water molecules tend to form a one-dimensional wire rather than more compact arrangements. This agrees with recent evidence of the mechanisms of solvent exchange between internal cavities and bulk solvent.

Pf1 bacteriophage hydration by magic angle spinning solid-state NMR

High resolution two- and three-dimensional heteronuclear correlation spectroscopy ((1)H-(13)C, (1)H-(15)N, and (1)H-(13)C-(13)C HETCOR) has provided a detailed characterization of the internal and external hydration water of the Pf1 virion. This long and slender virion (2000 nm × 7 nm) contains highly stretched DNA within a capsid of small protein subunits, each only 46 amino acid residues. HETCOR cross-peaks have been unambiguously assigned to 25 amino acids, including most external residues 1-21 as well as residues 39-40 and 43-46 deep inside the virion. In addition, the deoxyribose rings of the DNA near the virion axis are in contact with water. The sets of cross-peaks to the DNA and to all 25 amino acid residues were from the same hydration water (1)H resonance; some of the assigned residues do not have exchangeable side-chain protons. A mapping of the contacts onto structural models indicates the presence of water "tunnels" through a highly hydrophobic region of the capsid. The present results significantly extend and modify results from a lower resolution study, and yield a comprehensive hydration surface map of Pf1. In addition, the internal water could be distinguished from external hydration water by means of paramagnetic relaxation enhancement. The internal water population may serve as a conveniently localized magnetization reservoir for structural studies.

How amide hydrogens exchange in native proteins

Amide hydrogen exchange (HX) is widely used in protein biophysics even though our ignorance about the HX mechanism makes data interpretation imprecise. Notably, the open exchange-competent conformational state has not been identified. Based on analysis of an ultralong molecular dynamics trajectory of the protein BPTI, we propose that the open (O) states for amides that exchange by subglobal fluctuations are locally distorted conformations with two water molecules directly coordinated to the N-H group. The HX protection factors computed from the relative O-state populations agree well with experiment. The O states of different amides show little or no temporal correlation, even if adjacent residues unfold cooperatively. The mean residence time of the O state is ∼100 ps for all examined amides, so the large variation in measured HX rate must be attributed to the opening frequency. A few amides gain solvent access via tunnels or pores penetrated by water chains including native internal water molecules, but most amides access solvent by more local structural distortions. In either case, we argue that an overcoordinated N-H group is necessary for efficient proton transfer by Grotthuss-type structural diffusion.

Information flow and protein dynamics: the interplay between nuclear magnetic resonance spectroscopy and molecular dynamics simulations

Proteins participate in information pathways in cells, both as links in the chain of signals, and as the ultimate effectors. Upon ligand binding, proteins undergo conformation and motion changes, which can be sensed by the following link in the chain of information. Nuclear magnetic resonance (NMR) spectroscopy and molecular dynamics (MD) simulations represent powerful tools for examining the time-dependent function of biological molecules. The recent advances in NMR and the availability of faster computers have opened the door to more detailed analyses of structure, dynamics, and interactions. Here we briefly describe the recent applications that allow NMR spectroscopy and MD simulations to offer unique insight into the basic motions that underlie information transfer within and between cells.

Role of Internal Water on Protein Thermal Stability: The Case of Homologous G Domains

In this work, we address the question of whether the enhanced stability of thermophilic proteins has a direct connection with internal hydration. Our model systems are two homologous G domains of different stability: the mesophilic G domain of the elongation factor thermal unstable protein from E. coli and the hyperthermophilic G domain of the EF-1α protein from S. solfataricus. Using molecular dynamics simulation at the microsecond time scale, we show that both proteins host water molecules in internal cavities and that these molecules exchange with the external solution in the nanosecond time scale. The hydration free energy of these sites evaluated via extensive calculations is found to be favorable for both systems, with the hyperthermophilic protein offering a slightly more favorable environment to host water molecules. We estimate that, under ambient conditions, the free energy gain due to internal hydration is about 1.3 kcal/mol in favor of the hyperthermophilic variant. However, we also find that, at the high working temperature of the hyperthermophile, the cavities are rather dehydrated, meaning that under extreme conditions other molecular factors secure the stability of the protein. Interestingly, we detect a clear correlation between the hydration of internal cavities and the protein conformational landscape. The emerging picture is that internal hydration is an effective observable to probe the conformational landscape of proteins. In the specific context of our investigation, the analysis confirms that the hyperthermophilic G domain is characterized by multiple states and it has a more flexible structure than its mesophilic homologue.

Reptation-induced coalescence of tunnels and cavities in Escherichia Coli XylE transporter conformers accounts for facilitated diffusion

Structural changes and xylose docking to eight conformers of Escherichia Coli XylE, a xylose transporter similar to mammalian passive glucose transporters GLUTs, have been examined. Xylose docks to inward and outward facing conformers at a high affinity central site (K_i 4–20 µM), previously identified by crystallography and additionally consistently docks to lower affinity sites in the external and internal vestibules (K_i 12–50 µM). All these sites lie within intramolecular tunnels and cavities. Several local regions in the central transmembrane zone have large positional divergences of both skeleton carbon Cα positions and side chains. One such in TM 10 is the destabilizing sequence G388-P389-V390-C391 with an average RMSD (4.5 ± 0.4 Å). Interchange between conformer poses results in coalescence of tunnels with adjacent cavities, thereby producing a transitory channel spanning the entire transporter. A fully open channel exists in one inward-facing apo-conformer, (PDB 4ja4c) as demonstrated by several different tunnel-finding algorithms. The conformer interchanges produce a gated network within a branched central channel that permits staged ligand diffusion across the transporter during the open gate periods. Simulation of this model demonstrates that small-scale conformational changes required for sequentially opening gate with frequencies in the ns-μs time domain accommodate diffusive ligand flow between adjacent sites with association–dissociation rates in the μs-ms domain without imposing delays. This current model helps to unify the apparently opposing concepts of alternate access and multisite models of ligand transport.

Chemical exchange in biomacromolecules: past, present, and future

The perspective reviews quantitative investigations of chemical exchange phenomena in proteins and other biological macromolecules using NMR spectroscopy, particularly relaxation dispersion methods. The emphasis is on techniques and applications that quantify the populations, interconversion kinetics, and structural features of sparsely populated conformational states in equilibrium with a highly populated ground state. Applications to folding, molecular recognition, catalysis, and allostery by proteins and nucleic acids are highlighted.

Quantitative analysis of the water occupancy around the selectivity filter of a K+ channel in different gating modes

Recovery in K(+) channels, that is, the transition from the inactivated nonconductive selectivity filter conformation toward the conductive conformation, occurs on a time scale of the order of seconds, which is astonishingly long, given that the structural differences among the filter conformations are faint (<1 Å). Computational studies and electrophysiological measurements suggested that buried water molecules bound behind the selectivity filter are at the origin of the slowness of recovery in K(+) channels. Using a combination of solid-state NMR spectroscopy (ssNMR) and long molecular dynamics simulations, we sketch a high-resolution map of the spatial and temporal distribution of water behind the selectivity filter of a membrane-embedded K(+) channel in two different gating modes. Our study demonstrates that buried water molecules with long residence times are spread all along the rear of the inactivated filter, which explains the recovery kinetics. In contrast, the same region of the structure appears to be dewetted when the selectivity filter is in the conductive state. Using proton-detected ssNMR on fully protonated channels, we demonstrate the presence of a pathway that allows for the interchange of buried and bulk water, as required for a functional influence of buried water on recovery and slow inactivation. Furthermore, we provide direct experimental evidence for the presence of additional ordered water molecules that surround the filter and that are modulated by the channel's gating mode.

Internal water and microsecond dynamics in myoglobin

Myoglobin (Mb) binds diatomic ligands, like O₂, CO, and NO, in a cavity that is only transiently accessible. Crystallography and molecular simulations show that the ligands can migrate through an extensive network of transiently connected cavities but disagree on the locations and occupancy of internal hydration sites. Here, we use water ²H and ¹⁷O magnetic relaxation dispersion (MRD) to characterize the internal water molecules in Mb under physiological conditions. We find that equine carbonmonoxy Mb contains 4.5 ± 1.0 ordered internal water molecules with a mean survival time of 5.6 ± 0.5 μs at 25 °C. The likely locations of these water molecules are the four polar hydration sites, including one of the xenon-binding cavities, that are fully occupied in all high-resolution crystal structures of equine Mb. The finding that water escapes from these sites, located 17–31 Å apart in the protein, on the same μs time scale suggests a global exchange mechanism. We propose that this mechanism involves transient penetration of the protein by H-bonded water chains. Such a mechanism could play a functional role by eliminating trapped ligands. In addition, the MRD results indicate that 2 or 3 of the 11 histidine residues of equine Mb undergo intramolecular hydrogen exchange on a μs time scale.

Nuclear magnetic relaxation induced by exchange-mediated orientational randomization: longitudinal relaxation dispersion for a dipole-coupled spin-1/2 pair

In complex biological or colloidal samples, magnetic relaxation dispersion (MRD) experiments using the field-cycling technique can characterize molecular motions on time scales ranging from nanoseconds to microseconds, provided that a rigorous theory of nuclear spin relaxation is available. In gels, cross-linked proteins, and biological tissues, where an immobilized macromolecular component coexists with a mobile solvent phase, nuclear spins residing in solvent (or cosolvent) species relax predominantly via exchange-mediated orientational randomization (EMOR) of anisotropic nuclear (electric quadrupole or magnetic dipole) couplings. The physical or chemical exchange processes that dominate the MRD typically occur on a time scale of microseconds or longer, where the conventional perturbation theory of spin relaxation breaks down. There is thus a need for a more general relaxation theory. Such a theory, based on the stochastic Liouville equation (SLE) for the EMOR mechanism, is available for a single quadrupolar spin I = 1. Here, we present the corresponding theory for a dipole-coupled spin-1/2 pair. To our knowledge, this is the first treatment of dipolar MRD outside the motional-narrowing regime. Based on an analytical solution of the spatial part of the SLE, we show how the integral longitudinal relaxation rate can be computed efficiently. Both like and unlike spins, with selective or non-selective excitation, are treated. For the experimentally important dilute regime, where only a small fraction of the spin pairs are immobilized, we obtain simple analytical expressions for the auto-relaxation and cross-relaxation rates which generalize the well-known Solomon equations. These generalized results will be useful in biophysical studies, e.g., of intermittent protein dynamics. In addition, they represent a first step towards a rigorous theory of water (1)H relaxation in biological tissues, which is a prerequisite for unravelling the molecular basis of soft-tissue contrast in clinical magnetic resonance imaging.