Molecular dynamics study of water penetration in staphylococcal nuclease

The structure and dynamics of water molecule networks underlie catalytic efficiency in a glycoside exo-hydrolase

Glycoside hydrolases break glycosidic bonds by transferring a water molecule onto the glycosidic oxygen of carbohydrates, but on the nanoscale, the dynamics of water molecules remains unclear. We investigate the role of the non-nucleophilic E220 glutamate, essential for maintaining the water molecule network in a family 3 β-D-glucan glucohydrolase, but not involved directly in catalysis. Kinetic data disclose that the E220A mutant retains substrate poly-specificity but has drastically reduced catalytic efficiency compared to the wild-type. High-resolution structures in-complex with a hydrolytic product and a mechanism-based inhibitor reveal that in wild-type, the concatenated water molecules near acid/base E491 and neighbouring N219 and E220 form a harmonised network. In contrast, in the E220A mutant, this network is uncoordinated. Computational models of covalent complexes show that water flux through the wild-type protein correlates with high catalytic efficiency dissimilar to E220A, where this correlation is lost. Ancestral sequence reconstructions of family 3 enzymes divulge the evolutionary conservation of residues participating in water molecule networks, which underlie substrate-product-assisted processivity. Our findings provide a blueprint for the dynamics of catalysis mediated by hydrolytic enzymes, which could inspire bioengineering to create a sustainable bio-economy.

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.

Protein pKa Prediction by Tree-Based Machine Learning

Protonation states of ionizable protein residues modulate many essential biological processes. For correct modeling and understanding of these processes, it is crucial to accurately determine their pKa values. Here, we present four tree-based machine learning models for protein pKa prediction. The four models, Random Forest, Extra Trees, eXtreme Gradient Boosting (XGBoost), and Light Gradient Boosting Machine (LightGBM), were trained on three experimental PDB and pKa datasets, two of which included a notable portion of internal residues. We observed similar performance among the four machine learning algorithms. The best model trained on the largest dataset performs 37% better than the widely used empirical pKa prediction tool PROPKA and 15% better than the published result from the pKa prediction method DelPhiPKa. The overall root-mean-square error (RMSE) for this model is 0.69, with surface and buried RMSE values being 0.56 and 0.78, respectively, considering six residue types (Asp, Glu, His, Lys, Cys, and Tyr), and 0.63 when considering Asp, Glu, His, and Lys only. We provide pKa predictions for proteins in human proteome from the AlphaFold Protein Structure Database and observed that 1% of Asp/Glu/Lys residues have highly shifted pKa values close to the physiological pH.

Pressure Unfolding of Proteins: New Insights into the Role of Bound Water

High pressures can be detrimental for protein stability, resulting in unfolding and loss of function. This phenomenon occurs because the unfolding transition is accompanied by a decrease in volume, which is typically attributed to the elimination of cavities that are present within the native state as a result of packing defects. We present a novel computational approach that enables the study of pressure unfolding in atomistically detailed protein models in implicit solvent. We include the effect of pressure using a transfer free energy term that allows us to decouple the effect of protein residues and bound water molecules on the volume change upon unfolding. We discuss molecular dynamics simulations results using this protocol for two model proteins, Trp-cage and staphylococcal nuclease (SNase). We find that the volume reduction of bound water is the key energetic term that drives protein denaturation under the effect of pressure, for both Trp-cage and SNase. However, we note differences in unfolding mechanisms between the smaller Trp-cage and the larger SNase protein. Indeed, the unfolding of SNase, but not Trp-cage, is seen to be further accompanied by a reduction in the volume of internal cavities. Our results indicate that, for small peptides, like Trp-cage, pressure denaturation is driven by the increase in solvent accessibility upon unfolding, and the subsequent increase in the number of bound water molecules. For larger proteins, like SNase, the cavities within the native fold act as weak spots, determining the overall resistance to pressure denaturation. Our simulations display a striking agreement with the pressure-unfolding profile experimentally obtained for SNase and represent a promising approach for a computationally efficient and accurate exploration of pressure-induced denaturation of proteins.

Determinants of conductance of a bacterial voltage-gated sodium channel

Through molecular dynamics (MD) and free energy simulations in electric fields, we examine the factors influencing conductance of bacterial voltage-gated sodium channel Na_vMs. The channel utilizes four glutamic acid residues in the selectivity filter (SF). Previously, we have shown, through constant pH and free energy calculations of pKa values, that fully deprotonated, singly protonated, and doubly protonated states are all feasible at physiological pH, depending on how many ions are bound in the SF. With 173 MD simulations of 450 or 500 ns and additional free energy simulations, we determine that the conductance is highest for the deprotonated state and decreases with each additional proton bound. We also determine that the pKa value of the four glutamic residues for the transition between deprotonated and singly protonated states is close to the physiological pH and that there is a small voltage dependence. The pKa value and conductance trends are in agreement with experimental work on bacterial Na_v channels, which show a decrease in maximal conductance with lowering of pH, with pKa in the physiological range. We examine binding sites for Na⁺ in the SF, compare with previous work, and note a dependence on starting structures. We find that narrowing of the gate backbone to values lower than the crystal structure's backbone radius reduces the conductance, whereas increasing the gate radius further does not affect the conductance. Simulations with some amount of negatively charged lipids as opposed to purely neutral lipids increases the conductance, as do simulations at higher voltages.

Reservoir pH replica exchange

We present the reservoir pH replica exchange (R-pH-REM) method for constant pH simulations. The R-pH-REM method consists of a two-step procedure; the first step involves generation of one or more reservoirs of conformations. Each reservoir is obtained from a standard or enhanced molecular dynamics simulation with a constrained (fixed) protonation state. In the second step, fixed charge constraints are relaxed, as the structures from one or more reservoirs are periodically injected into a constant pH or a pH-replica exchange (pH-REM) simulation. The benefit of this two-step process is that the computationally intensive part of conformational search can be decoupled from constant pH simulations, and various techniques for enhanced conformational sampling can be applied without the need to integrate such techniques into the pH-REM framework. Simulations on blocked Lys, KK, and KAAE peptides were used to demonstrate an agreement between pH-REM and R-pH-REM simulations. While the reservoir simulations are not needed for these small test systems, the real need arises in cases when ionizable molecules can sample two or more conformations separated by a large energy barrier, such that adequate sampling is not achieved on a time scale of standard constant pH simulations. Such problems might be encountered in protein systems that exploit conformational transitions for function. A hypothetical case is studied, a small molecule with a large torsional barrier; while results of pH-REM simulations depend on the starting structure, R-pH-REM calculations on this model system are in excellent agreement with a theoretical model.

Hydronium Ions Accompanying Buried Acidic Residues Lead to High Apparent Dielectric Constants in the Interior of Proteins

Internal ionizable groups are known to play important roles in protein functions. A mystery that has attracted decades of extensive experimental and theoretical studies is the apparent dielectric constants experienced by buried ionizable groups, which are much higher than values expected for protein interiors. Many interpretations have been proposed, such as water penetration, conformational relaxation, local unfolding, protein intrinsic backbone fluctuations, etc. However, these interpretations conflict with many experimental observations. The virtual mixture of multiple states (VMMS) simulation method developed in our lab provides a direct approach for studying the equilibrium of multiple chemical states and can monitor p K_a values along simulation trajectories. Through VMMS simulations of staphylococcal nuclease (SNase) variants with internal Asp or Glu residues, we discovered that cations were attracted to buried deprotonated acidic groups and the presence of the nearby cations were essential to reproduce experimentally measured p K_a values. This finding, combined with structural analysis and validation simulations, suggests that the proton released from a deprotonation process stays near the deprotonated group inside proteins, possibly in the form of a hydronium ion. The existence of a proton near a buried charge has many implications in our understanding of protein functions.

Electrostatic Interactions in Protein Structure, Folding, Binding, and Condensation

Charged and polar groups, through forming ion pairs, hydrogen bonds, and other less specific electrostatic interactions, impart important properties to proteins. Modulation of the charges on the amino acids, e.g., by pH and by phosphorylation and dephosphorylation, have significant effects such as protein denaturation and switch-like response of signal transduction networks. This review aims to present a unifying theme among the various effects of protein charges and polar groups. Simple models will be used to illustrate basic ideas about electrostatic interactions in proteins, and these ideas in turn will be used to elucidate the roles of electrostatic interactions in protein structure, folding, binding, condensation, and related biological functions. In particular, we will examine how charged side chains are spatially distributed in various types of proteins and how electrostatic interactions affect thermodynamic and kinetic properties of proteins. Our hope is to capture both important historical developments and recent experimental and theoretical advances in quantifying electrostatic contributions of proteins.

Exploring interfacial water trapping in protein-ligand complexes with multithermal titration calorimetry

In this work, we examine the hypothesis about how trapped water molecules at the interface between triosephosphate isomerase (TIM) and either of two phosphorylated inhibitors, 2-phosphoglycolate (2PG) or phosphoglycolohydroxamate (PGH), can explain the anomalous highly negative binding heat capacities (ΔC_p,b) of both complexes, TIM-2PG and TIM-PGH. We performed fluorimetric titrations of the enzyme with PGH inhibitor under osmotic stress conditions, using various concentrations of either osmolyte: sucrose, ethylene glycol or glycine betaine. We also analyze the binding processes under various stressor concentrations using a novel calorimetric methodology that allows ΔC_p,b determinations in single experiments: Multithermal Titration Calorimetry. The binding constant of the TIM-PGH complex decreased gradually with the concentration of all osmolytes, but at diverse extents depending on the osmolyte nature. According to the osmotic stress theory, this decrease indicates that the number of water molecules associated with the enzyme increases with inhibitor binding, i.e. some solvent molecules became trapped. Additionally, the binding heat capacities became less negative at higher osmolyte concentrations, their final values depending on the osmolyte. These effects were also observed in the TIM-2PG complex using sucrose as stressor. Our results strongly suggest that some water molecules became immobilized when the TIM-inhibitor complexes were formed. A computational analysis of the hydration state of the binding site of TIM in both its free state and its complexed form with 2PG or PGH, based on molecular dynamics (MD) simulations in explicit solvent, showed that the binding site effectively immobilized additional water molecules after binding these inhibitors.

Influence of glutamic acid residues and pH on the properties of transmembrane helices

Negatively charged side chains are important for the function of particular ion channels and certain other membrane proteins. To investigate the influence of single glutamic acid side chains on helices that span lipid-bilayer membranes, we have employed GWALP23 (acetyl-GGALW⁵LALALALALALALW¹⁹LAGA-amide) as a favorable host peptide framework. We substituted individual Leu residues with Glu residues (L12E or L14E or L16E) and incorporated specific ²H-labeled alanine residues within the core helical region or near the ends of the sequence. Solid-state ²H NMR spectra reveal little change for the core labels in GWALP23-E12, -E14 and -E16 over a pH range of 4 to 12.5, with the spectra being broader for samples in DOPC compared to DLPC bilayers. The spectra for samples with deuterium labels near the helix ends on alanines 3 and 21 show modest pH-dependent changes in the extent of unwinding of the helix terminals in DLPC and DOPC bilayers. The combined results indicate minor overall responses of these transmembrane helices to changes in pH, with the most buried residue E12 showing no pH dependence. While the Glu residues E14 and E16 may have high pK_a values in the lipid bilayer environment, it is also possible that a paucity of helix response is masking the pK_a values. Interestingly, when E16 is present, spectral changes at high pH report significant local unwinding of the core helix. Our results are consistent with the expectation that buried carboxyl groups aggressively hold their protons and/or waters of hydration.

Microscopic mechanisms that govern the titration response and pKa values of buried residues in staphylococcal nuclease mutants

To probe the microscopic mechanisms that govern the titration behavior of buried ionizable groups, microsecond explicit solvent molecular dynamics simulations are carried out for several mutants of Staphylococcal nuclease using both fixed charge and polarizable force fields. While the ionization of Asp 66, Glu 66, and Lys 125 lead to enhanced structural fluctuations and partial unfolding of adjacent α-helical regions, the ionization of Lys 25 causes local unfolding of adjacent β sheets. Using the sampled conformational ensembles, good agreement with experimental pK_a values is obtained with Poisson-Boltzmann calculations using a protein dielectric constant of 2-4 for V66D/E; slightly larger dielectric constants are needed for Lys mutants especially L25K, suggesting that structural responses beyond microseconds are involved in ionization of Lys 25. Overall, the set of unbiased simulations provides insights into the spatial and temporal scales of protein and solvent motions that dictate the diverse titration behaviors of buried protein residues. Proteins 2017; 85:268-281. © 2016 Wiley Periodicals, Inc.

Origin of pKa Shifts of Internal Lysine Residues in SNase Studied Via Equal-Molar VMMS Simulations in Explicit Water

Protein internal ionizable groups can exhibit large shifts in pK_a values. Although the environment and interaction changes have been extensively studied both experimentally and computationally, direct calculation of pK_a values of these internal ionizable groups in explicit water is challenging due to energy barriers in solvent interaction and in conformational transition. The virtual mixture of multiple states (VMMS) method is a new approach designed to study chemical state equilibrium. This method constructs a virtual mixture of multiple chemical states in order to sample the conformational space of all states simultaneously and to avoid crossing energy barriers related to state transition. By applying VMMS to 25 variants of staphylococcal nuclease with lysine residues at internal positions, we obtained the pK_a values of these lysine residues and investigated the physics underlining the pK_a shifts. Our calculation results agree reasonably well with experimental measurements, validating the VMMS method for pK_a calculation and providing molecular details of the protonation equilibrium for protein internal ionizable groups. Based on our analyses of protein conformation relaxation, lysine side chain flexibility, water penetration, and the microenvironment, we conclude that the hydrophobicity of the microenvironment around the lysine side chain (which affects water penetration differently for different protonation states) plays an important role in the pK_a shifts.

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.

Enhancing constant-pH simulation in explicit solvent with a two-dimensional replica exchange method

We present a new method for enhanced sampling for constant-pH simulations in explicit water based on a two-dimensional (2D) replica exchange scheme. The new method is a significant extension of our previously developed constant-pH simulation method, which is based on enveloping distribution sampling (EDS) coupled with a one-dimensional (1D) Hamiltonian exchange method (HREM). EDS constructs a hybrid Hamiltonian from multiple discrete end state Hamiltonians that, in this case, represent different protonation states of the system. The ruggedness and heights of the hybrid Hamiltonian's energy barriers can be tuned by the smoothness parameter. Within the context of the 1D EDS-HREM method, exchanges are performed between replicas with different smoothness parameters, allowing frequent protonation-state transitions and sampling of conformations that are favored by the end-state Hamiltonians. In this work, the 1D method is extended to 2D with an additional dimension, external pH. Within the context of the 2D method (2D EDS-HREM), exchanges are performed on a lattice of Hamiltonians with different pH conditions and smoothness parameters. We demonstrate that both the 1D and 2D methods exactly reproduce the thermodynamic properties of the semigrand canonical (SGC) ensemble of a system at a given pH. We have tested our new 2D method on aspartic acid, glutamic acid, lysine, a four residue peptide (sequence KAAE), and snake cardiotoxin. In all cases, the 2D method converges faster and without loss of precision; the only limitation is a loss of flexibility in how CPU time is employed. The results for snake cardiotoxin demonstrate that the 2D method enhances protonation-state transitions, samples a wider conformational space with the same amount of computational resources, and converges significantly faster overall than the original 1D method.

Discovery of multiple hidden allosteric sites by combining Markov state models and experiments

The discovery of drug-like molecules that bind pockets in proteins that are not present in crystallographic structures yet exert allosteric control over activity has generated great interest in designing pharmaceuticals that exploit allosteric effects. However, there have only been a small number of successes, so the therapeutic potential of these pockets--called hidden allosteric sites--remains unclear. One challenge for assessing their utility is that rational drug design approaches require foreknowledge of the target site, but most hidden allosteric sites are only discovered when a small molecule is found to stabilize them. We present a means of decoupling the identification of hidden allosteric sites from the discovery of drugs that bind them by drawing on new developments in Markov state modeling that provide unprecedented access to microsecond- to millisecond-timescale fluctuations of a protein's structure. Visualizing these fluctuations allows us to identify potential hidden allosteric sites, which we then test via thiol labeling experiments. Application of these methods reveals multiple hidden allosteric sites in an important antibiotic target--TEM-1 β-lactamase. This result supports the hypothesis that there are many as yet undiscovered hidden allosteric sites and suggests our methodology can identify such sites, providing a starting point for future drug design efforts. More generally, our results demonstrate the power of using Markov state models to guide experiments.

Constant pH Molecular Dynamics in Explicit Solvent with Enveloping Distribution Sampling and Hamiltonian Exchange

We present a new computational approach for constant pH simulations in explicit solvent based on the combination of the enveloping distribution sampling (EDS) and Hamiltonian replica exchange (HREX) methods. Unlike constant pH methods based on variable and continuous charge models, our method is based on discrete protonation states. EDS generates a hybrid Hamiltonian of different protonation states. A smoothness parameter s is used to control the heights of energy barriers of the hybrid-state energy landscape. A small s value facilitates state transitions by lowering energy barriers. Replica exchange between EDS potentials with different s values allows us to readily obtain a thermodynamically accurate ensemble of multiple protonation states with frequent state transitions. The analysis is performed with an ensemble obtained from an EDS Hamiltonian without smoothing, s = ∞, which strictly follows the minimum energy surface of the end states. The accuracy and efficiency of this method is tested on aspartic acid, lysine, and glutamic acid, which have two protonation states, a histidine with three states, a four-residue peptide with four states, and snake cardiotoxin with eight states. The pKa values estimated with the EDS-HREX method agree well with the experimental pKa values. The mean absolute errors of small benchmark systems range from 0.03 to 0.17 pKa units, and those of three titratable groups of snake cardiotoxin range from 0.2 to 1.6 pKa units. This study demonstrates that EDS-HREX is a potent theoretical framework, which gives the correct description of multiple protonation states and good calculated pKa values.

Biomolecular electrostatics and solvation: a computational perspective

An understanding of molecular interactions is essential for insight into biological systems at the molecular scale. Among the various components of molecular interactions, electrostatics are of special importance because of their long-range nature and their influence on polar or charged molecules, including water, aqueous ions, proteins, nucleic acids, carbohydrates, and membrane lipids. In particular, robust models of electrostatic interactions are essential for understanding the solvation properties of biomolecules and the effects of solvation upon biomolecular folding, binding, enzyme catalysis, and dynamics. Electrostatics, therefore, are of central importance to understanding biomolecular structure and modeling interactions within and among biological molecules. This review discusses the solvation of biomolecules with a computational biophysics view toward describing the phenomenon. While our main focus lies on the computational aspect of the models, we provide an overview of the basic elements of biomolecular solvation (e.g. solvent structure, polarization, ion binding, and non-polar behavior) in order to provide a background to understand the different types of solvation models.

Capturing the energetics of water insertion in biological systems: the water flooding approach

Consistent description of the effect of internal water in proteins has been a major challenge for both simulation and experimental studies. Describing this effect has been particularly important and elusive in cases of charges in protein interiors. Here, we present a new microscopic method that provides an efficient way for simulating the energetics of water insertion. Instead of performing explicit Monte Carlo (MC) moves on the insertion process, which generally involves an enormous number of rejected attempts, our method is based on generating trial configurations with excess amount of internal water, estimating the relevant free energy by the linear response approximation, and then using a postprocessing MC treatment to filter out a limited number of configurations from a large possible set. Our approach is validated on particularly challenging test cases including the pK(a) of the V66D mutation in Staphylococcal nuclease, Glu286 in cytochrome c oxidase (CcO) and the energetics of a protonated water molecule in the D channel of CcO. The new postprocessing method allows us to reproduce the relevant energetics of highly unstable charges in protein interiors using fully microscopic calculations and provides a substantial improvement over regular microscopic free energy estimates. This advance established the effectiveness of our water insertion strategy in challenging cases that have not been addressed successfully by other microscopic methods. Furthermore, our study provides a new exciting view on the crucial effect of water penetration in key biological systems as well as a new view on the nature of the dielectric in protein interiors.

Structural reorganization triggered by charging of Lys residues in the hydrophobic interior of a protein

Structural consequences of ionization of residues buried in the hydrophobic interior of proteins were examined systematically in 25 proteins with internal Lys residues. Crystal structures showed that the ionizable groups are buried. NMR spectroscopy showed that in 2 of 25 cases studied, the ionization of an internal Lys unfolded the protein globally. In five cases, the internal charge triggered localized changes in structure and dynamics, and in three cases, it promoted partial or local unfolding. Remarkably, in 15 proteins, the ionization of the internal Lys had no detectable structural consequences. Highly stable proteins appear to be inherently capable of withstanding the presence of charge in their hydrophobic interior, without the need for specialized structural adaptations. The extent of structural reorganization paralleled loosely with global thermodynamic stability, suggesting that structure-based pK(a) calculations for buried residues could be improved by calculation of thermodynamic stability and by enhanced conformational sampling.

Thermodynamic coupling of protonation and conformational equilibria in proteins: theory and simulation

Ionization-coupled conformational phenomena are ubiquitous in biology. However, quantitative characterization of the underlying thermodynamic cycle comprised of protonation and conformational equilibria has remained an elusive goal. Here we use theory and continuous constant pH molecular dynamics (CpHMD) simulations to provide a thermodynamic description for the coupling of proton titration and conformational exchange between two distinct states of a protein. CpHMD simulations with a hybrid-solvent scheme and the pH-based replica-exchange (REX) protocol are applied to obtain the equilibrium constants and atomic details of the ionization-coupled conformational exchange between open and closed states of an engineered mutant of staphylococcal nuclease. Although the coupling of protonation and conformational equilibria is not exact in the simulation, the results are encouraging. They demonstrate that REX-CpHMD simulations can be used to study thermodynamics of ionization-coupled conformational processes--which has not possible using present experimental techniques or traditional simulations based on fixed protonation states.

The role of conserved waters in conformational transitions of Q61H K-ras

To investigate the stability and functional role of long-residence water molecules in the Q61H variant of the signaling protein K-ras, we analyzed all available Ras crystal structures and conformers derived from a series of independent explicit solvent molecular dynamics (MD) simulations totaling 1.76 µs. We show that the protein samples a different region of phase space in the presence and absence of several crystallographically conserved and buried water molecules. The dynamics of these waters is coupled with the local as well as the global motions of the protein, in contrast to less buried waters whose exchange with bulk is only loosely coupled with the motion of loops in their vicinity. Aided by two novel reaction coordinates involving the distance (d) between the C_α atoms of G60 at switch 2 and G10 at the P-loop and the N-C_α-C-O dihedral (ξ) of G60, we further show that three water molecules located in lobe1, at the interface between the lobes and at lobe2, are involved in the relative motion of residues at the two lobes of Q61H K-ras. Moreover, a d/ξ plot classifies the available Ras x-ray structures and MD-derived K-ras conformers into active GTP-, intermediate GTP-, inactive GDP-bound, and nucleotide-free conformational states. The population of these states and the transition between them is modulated by water-mediated correlated motions involving the functionally critical switch 2, P-loop and helix 3. These results suggest that water molecules act as allosteric ligands to induce a population shift among distinct switch 2 conformations that differ in effector recognition.

K-ras belongs to the Ras family of G-proteins that regulate cell proliferation and development. To execute its function, K-ras adopts different conformational states when it is active and inactive. In addition to these two states, it samples many transient intermediate conformations as it makes the transition from one state to the other. Mutations that affect the population of these states can cause cancer or developmental disorder. Using simulation approaches, here we show that a number of water molecules buried within the structure of an oncogenic K-ras protein modulate the distribution of its conformational states. Moreover, a detailed analysis based on two novel structural parameters revealed the existence of long-range water-mediated interactions that facilitate a dynamic coupling between the two lobes of the protein. These findings pave the way for a dynamics-guided strategy to inhibit abnormal Ras signaling.

The pKa Cooperative: a collaborative effort to advance structure-based calculations of pKa values and electrostatic effects in proteins

The pK(a) Cooperative (http://www.pkacoop.org) was organized to advance development of accurate and useful computational methods for structure-based calculation of pK(a) values and electrostatic energies in proteins. The Cooperative brings together laboratories with expertise and interest in theoretical, computational, and experimental studies of protein electrostatics. To improve structure-based energy calculations, it is necessary to better understand the physical character and molecular determinants of electrostatic effects. Thus, the Cooperative intends to foment experimental research into fundamental aspects of proteins that depend on electrostatic interactions. It will maintain a depository for experimental data useful for critical assessment of methods for structure-based electrostatics calculations. To help guide the development of computational methods, the Cooperative will organize blind prediction exercises. As a first step, computational laboratories were invited to reproduce an unpublished set of experimental pK(a) values of acidic and basic residues introduced in the interior of staphylococcal nuclease by site-directed mutagenesis. The pK(a) values of these groups are unique and challenging to simulate owing to the large magnitude of their shifts relative to normal pK(a) values in water. Many computational methods were tested in this first Blind Prediction Challenge and critical assessment exercise. A workshop was organized in the Telluride Science Research Center to objectively assess the performance of many computational methods tested on this one extensive data set. This volume of Proteins: Structure, Function, and Bioinformatics introduces the pK(a) Cooperative, presents reports submitted by participants in the Blind Prediction Challenge, and highlights some of the problems in structure-based calculations identified during this exercise.

Comparative void-volume analysis of psychrophilic and mesophilic enzymes: Structural bioinformatics of psychrophilic enzymes reveals sources of core flexibility

Background

Psychrophiles, cold-adapted organisms, have adapted to live at low temperatures by using a variety of mechanisms. Their enzymes are active at cold temperatures by being structurally more flexible than mesophilic enzymes. Even though, there are some indications of the possible structural mechanisms by which psychrophilic enzymes are catalytic active at cold temperatures, there is not a generalized structural property common to all psychrophilic enzymes.

Results

We examine twenty homologous enzyme pairs from psychrophiles and mesophiles to investigate flexibility as a key characteristic for cold adaptation. B-factors in protein X-ray structures are one way to measure flexibility. Comparing psychrophilic to mesophilic protein B-factors reveals that psychrophilic enzymes are more flexible in 5-turn and strand secondary structures. Enzyme cavities, identified using CASTp at various probe sizes, indicate that psychrophilic enzymes have larger average cavity sizes at probe radii of 1.4-1.5 Å, sufficient for water molecules. Furthermore, amino acid side chains lining these cavities show an increased frequency of acidic groups in psychrophilic enzymes.

Conclusions

These findings suggest that embedded water molecules may play a significant role in cavity flexibility, and therefore, overall protein flexibility. Thus, our results point to the important role enzyme flexibility plays in adaptation to cold environments.

MCCE analysis of the pKas of introduced buried acids and bases in staphylococcal nuclease

The pK(a)s of 96 acids and bases introduced into buried sites in the staphylococcal nuclease protein (SNase) were calculated using the multiconformation continuum electrostatics (MCCE) program and the results compared with experimental values. The pK(a)s are obtained by Monte Carlo sampling of coupled side chain protonation and position as a function of pH. The dependence of the results on the protein dielectric constant (ε(prot)) in the continuum electrostatics analysis and on the Lennard-Jones non-electrostatics parameters was evaluated. The pK(a)s of the introduced residues have a clear dependence on ε(prot,) whereas native ionizable residues do not. The native residues have electrostatic interactions with other residues in the protein favoring ionization, which are larger than the desolvation penalty favoring the neutral state. Increasing ε(prot) scales both terms, which for these residues leads to small changes in pK(a). The introduced residues have a larger desolvation penalty and negligible interactions with residues in the protein. For these residues, changing ε(prot) has a large influence on the calculated pK(a). An ε(prot) of 8-10 and a Lennard-Jones scaling of 0.25 is best here. The X-ray crystal structures of the mutated proteins are found to provide somewhat better results than calculations carried out on mutations made in silico. Initial relaxation of the in silico mutations by Gromacs and extensive side chain rotamer sampling within MCCE can significantly improve the match with experiment.

Continuous Constant pH Molecular Dynamics in Explicit Solvent with pH-Based Replica Exchange

A computational tool that offers accurate pKa values and atomically detailed knowledge of protonation-coupled conformational dynamics is valuable for elucidating mechanisms of energy transduction processes in biology, such as enzyme catalysis and electron transfer as well as proton and drug transport. Toward this goal we present a new technique of embedding continuous constant pH molecular dynamics within an explicit-solvent representation. In this technique we make use of the efficiency of the generalized-Born (GB) implicit-solvent model for estimating the free energy of protein solvation while propagating conformational dynamics using the more accurate explicit-solvent model. Also, we employ a pH-based replica exchange scheme to significantly enhance both protonation and conformational state sampling. Benchmark data of five proteins including HP36, NTL9, BBL, HEWL, and SNase yield an average absolute deviation of 0.53 and a root mean squared deviation of 0.74 from experimental data. This level of accuracy is obtained with 1 ns simulations per replica. Detailed analysis reveals that explicit-solvent sampling provides increased accuracy relative to the previous GB-based method by preserving the native structure, providing a more realistic description of conformational flexibility of the hydrophobic cluster, and correctly modeling solvent mediated ion-pair interactions. Thus, we anticipate that the new technique will emerge as a practical tool to capture ionization equilibria while enabling an intimate view of ionization coupled conformational dynamics that is difficult to delineate with experimental techniques alone.

Simulations of the confinement of ubiquitin in self-assembled reverse micelles

We describe the effects of confinement on the structure, hydration, and the internal dynamics of ubiquitin encapsulated in reverse micelles (RM). We performed molecular dynamics simulations of the encapsulation of ubiquitin into self-assembled protein/surfactant reverse micelles to study the positioning and interactions of the protein with the RM and found that ubiquitin binds to the RM interface at low salt concentrations. The same hydrophobic patch that is recognized by ubiquitin binding domains in vivo is found to make direct contact with the surfactant head groups, hydrophobic tails, and the iso-octane solvent. The fast backbone N-H relaxation dynamics show that the fluctuations of the protein encapsulated in the RM are reduced when compared to the protein in bulk. This reduction in fluctuations can be explained by the direct interactions of ubiquitin with the surfactant and by the reduced hydration environment within the RM. At high concentrations of excess salt, the protein does not bind strongly to the RM interface and the fast backbone dynamics are similar to that of the protein in bulk. Our simulations demonstrate that the confinement of protein can result in altered protein dynamics due to the interactions between the protein and the surfactant.

Statistical analysis of protein structures suggests that buried ionizable residues in proteins are hydrogen bonded or form salt bridges

It is well known that nonpolar residues are largely buried in the interior of proteins, whereas polar and ionizable residues tend to be more localized on the protein surface where they are solvent exposed. Such a distribution of residues between surface and interior is well understood from a thermodynamic point: nonpolar side chains are excluded from the contact with the solvent water, whereas polar and ionizable groups have favorable interactions with the water and thus are preferred at the protein surface. However, there is an increasing amount of information suggesting that polar and ionizable residues do occur in the protein core, including at positions that have no known functional importance. This is inconsistent with the observations that dehydration of polar and in particular ionizable groups is very energetically unfavorable. To resolve this, we performed a detailed analysis of the distribution of fractional burial of polar and ionizable residues using a large set of ˜2600 nonhomologous protein structures. We show that when ionizable residues are fully buried, the vast majority of them form hydrogen bonds and/or salt bridges with other polar/ionizable groups. This observation resolves an apparent contradiction: the energetic penalty of dehydration of polar/ionizable groups is paid off by favorable energy of hydrogen bonding and/or salt bridge formation in the protein interior. Our conclusion agrees well with the previous findings based on the continuum models for electrostatic interactions in proteins.

Conformational relaxation and water penetration coupled to ionization of internal groups in proteins

Molecular dynamics simulations were used to examine the effects of ionization of internal groups on the structures of eighteen variants of staphylococcal nuclease (SNase) with internal Lys, Asp, or Glu. In most cases the RMSD values of internal ionizable side chains were larger when the ionizable moieties were charged than when they were neutral. Calculations of solvent-accessible surface area showed that the internal ionizable side chains were buried in the protein interior when they were neutral and moved toward crevices and toward the protein-water interface when they were charged. The only exceptions are Lys-36, Lys-62, and Lys-103, which remained buried even after charging. With the exception of Lys-38, the number of internal water molecules surrounding the ionizable group increased upon charging: the average number of water oxygen atoms within the first hydration shell increased by 1.7 for Lys residues, by 5.2 for Asp residues, and by 3.2 for Glu residues. The polarity of the microenvironment of the ionizable group also increased when the groups were charged: the average number of polar atoms of any kind within the first hydration shell increased by 2.7 for Lys residues, by 4.8 for Asp residues, and by 4.0 for Glu residues. An unexpected correlation was observed between the absolute value of the shifts in pK(a) values measured experimentally, and several parameters of structural relaxation: the net difference in the polarity of the microenvironment of the charged and neutral forms of the ionizable groups, the net difference in hydration of the charged and neutral forms of the ionizable groups, and the difference in RMSD values of the charged and neutral forms of the ionizable groups. The effects of ionization of internal groups on the conformation of the backbone were noticeable but mostly small and localized to the area immediately next to the internal ionizable moiety. Some variants did exhibit local unfolding.

Size and sequence and the volume change of protein folding

The application of hydrostatic pressure generally leads to protein unfolding, implying, in accordance with Le Chatelier's principle, that the unfolded state has a smaller molar volume than the folded state. However, the origin of the volume change upon unfolding, ΔV(u), has yet to be determined. We have examined systematically the effects of protein size and sequence on the value of ΔV(u) using as a model system a series of deletion variants of the ankyrin repeat domain of the Notch receptor. The results provide strong evidence in support of the notion that the major contributing factor to pressure effects on proteins is their imperfect internal packing in the folded state. These packing defects appear to be specifically localized in the 3D structure, in contrast to the uniformly distributed effects of temperature and denaturants that depend upon hydration of exposed surface area upon unfolding. Given its local nature, the extent to which pressure globally affects protein structure can inform on the degree of cooperativity and long-range coupling intrinsic to the folded state. We also show that the energetics of the protein's conformations can significantly modulate their volumetric properties, providing further insight into protein stability.

Large shifts in pKa values of lysine residues buried inside a protein

Internal ionizable groups in proteins are relatively rare but they are essential for catalysis and energy transduction. To examine molecular determinants of their unusual and functionally important properties, we engineered 25 variants of staphylococcal nuclease with lysine residues at internal positions. Nineteen of the Lys residues have depressed pK(a) values, some as low as 5.3, and 20 titrate without triggering any detectable conformational reorganization. Apparently, simply by being buried in the protein interior, these Lys residues acquired pK(a) values comparable to those of naturally occurring internal ionizable groups involved in catalysis and biological H(+) transport. The pK(a) values of some of the internal Lys residues were affected by interactions with surface carboxylic groups. The apparent polarizability reported by the pK(a) values varied significantly from location to location inside the protein. These data will enable an unprecedented examination of the positional dependence of the dielectric response of a protein. This study also shows that the ability of proteins to withstand the presence of charges in their hydrophobic interior is a fundamental property inherent to all stable proteins, not a specialized adaptation unique to proteins that evolved to depend on internal charges for function.

Structural origins of high apparent dielectric constants experienced by ionizable groups in the hydrophobic core of a protein

The side chains of Lys66, Asp66, and Glu66 in staphylococcal nuclease are fully buried and surrounded mainly by hydrophobic matter, except for internal water molecules associated with carboxylic oxygen atoms. These ionizable side chains titrate with pK(a) values of 5.7, 8.8, and 8.9, respectively. To reproduce these pK(a) values with continuum electrostatics calculations, we treated the protein with high dielectric constants. We have examined the structural origins of these high apparent dielectric constants by using NMR spectroscopy to characterize the structural response to the ionization of these internal side chains. Substitution of Val66 with Lys66 and Asp66 led to increased conformational fluctuations of the microenvironments surrounding these groups, even under pH conditions where Lys66 and Asp66 are neutral. When Lys66, Asp66, and Glu66 are charged, the proteins remain almost fully folded, but resonances for a few backbone amides adjacent to the internal ionizable residues are broadened. This suggests that the ionization of the internal groups promotes a local increase in dynamics on the intermediate timescale, consistent with either partial unfolding or increased backbone fluctuations of helix 1 near residue 66, or, less likely, with increased fluctuations of the charged side chains at position 66. These experiments confirm that the high apparent dielectric constants reported by internal Lys66, Asp66, and Glu66 reflect localized changes in conformational fluctuations without incurring detectable global structural reorganization. To improve structure-based pK(a) calculations in proteins, we will need to learn how to treat this coupling between ionization of internal groups and local changes in conformational fluctuations explicitly.

Protein dynamics and pressure: what can high pressure tell us about protein structural flexibility?

After a brief overview of NMR and X-ray crystallography studies on protein flexibility under pressure, we summarize the effects of hydrostatic pressure on the native fold of azurin from Pseudomonas aeruginosa as inferred from the variation of the intrinsic phosphorescence lifetime and the acrylamide bimolecular quenching rate constants of the buried Trp residue. The pressure/temperature response of the globular fold and modulation of its dynamical structure is analyzed both in terms of a reduction of internal cavities and of the hydration of the polypeptide. The study of the effect of two single point cavity forming mutations, F110S and I7S, on the unfolding volume change (ΔV(0)) of azurin and on the internal dynamics of the protein fold under pressure demonstrate that the creation of an internal cavity will enhance the plasticity and lower the stability of the globular structure. This article is part of a Special Issue entitled: Protein Dynamics: Experimental and Computational Approaches.

Molecular dynamics free energy calculations to assess the possibility of water existence in protein nonpolar cavities

Are protein nonpolar cavities filled with water molecules? Although many experimental and theoretical investigations have been done, particularly for the nonpolar cavity of IL-1 beta, the results are still conflicting. To study this problem from the thermodynamic point of view, we calculated hydration free energies of four protein nonpolar cavities by means of the molecular dynamics thermodynamic integration method. In addition to the IL-1 beta cavity (69 A(3)), we selected the three largest nonpolar cavities of AvrPphB (81 A(3)), Trp repressor (87 A(3)), and hemoglobin (108 A(3)) from the structural database, in view of the simulation result from another study that showed larger nonpolar cavities are more likely to be hydrated. The calculations were performed with flexible and rigid protein models. The calculated free energy changes were all positive; hydration of the nonpolar cavities was energetically unfavorable for all four cases. Because hydration of smaller cavities should happen more rarely, we conclude that existing protein nonpolar cavities are not likely to be hydrated. Although a possibility remains for much larger nonpolar cavities, such cases are not found experimentally. We present a hypothesis to explain this: hydrated nonpolar cavities are quite unstable and the conformation could not be maintained.

Studying pressure denaturation of a protein by molecular dynamics simulations

Many globular proteins unfold when subjected to several kilobars of hydrostatic pressure. This "unfolding-up-on-squeezing" is counter-intuitive in that one expects mechanical compression of proteins with increasing pressure. Molecular simulations have the potential to provide fundamental understanding of pressure effects on proteins. However, the slow kinetics of unfolding, especially at high pressures, eliminates the possibility of its direct observation by molecular dynamics (MD) simulations. Motivated by experimental results-that pressure denatured states are water-swollen, and theoretical results-that water transfer into hydrophobic contacts becomes favorable with increasing pressure, we employ a water insertion method to generate unfolded states of the protein Staphylococcal Nuclease (Snase). Structural characteristics of these unfolded states-their water-swollen nature, retention of secondary structure, and overall compactness-mimic those observed in experiments. Using conformations of folded and unfolded states, we calculate their partial molar volumes in MD simulations and estimate the pressure-dependent free energy of unfolding. The volume of unfolding of Snase is negative (approximately -60 mL/mol at 1 bar) and is relatively insensitive to pressure, leading to its unfolding in the pressure range of 1500-2000 bars. Interestingly, once the protein is sufficiently water swollen, the partial molar volume of the protein appears to be insensitive to further conformational expansion or unfolding. Specifically, water-swollen structures with relatively low radii of gyration have partial molar volume that are similar to that of significantly more unfolded states. We find that the compressibility change on unfolding is negligible, consistent with experiments. We also analyze hydration shell fluctuations to comment on the hydration contributions to protein compressibility. Our study demonstrates the utility of molecular simulations in estimating volumetric properties and pressure stability of proteins, and can be potentially extended for applications to protein complexes and assemblies.

Functional impact of polar and acidic substitutions in the lactose repressor hydrophobic monomer.monomer interface with a buried lysine

Despite predicted energetic penalties, the charged K84 side chains of tetrameric lactose repressor protein (LacI) are found buried within the highly hydrophobic monomer.monomer interface that includes side chains of V94 and V96. Once inducer binding has occurred, these K84 side chains move to interact with the more solvent-exposed side chains of D88 and E100'. Previous studies demonstrated that hydrophobic substitutions for K84 increased protein stability and significantly impaired the allosteric response. These results indicated that enhanced hydrophobic interactions at the monomer.monomer interface remove the energetic driving force of the buried charges, decreasing the likelihood of a robust conformational change and stabilizing the structure. We hypothesized that creating a salt bridge network with the lysine side chains by including nearby negatively charged residues might result in a similar outcome. To that end, acidic residues, D and E, and their neutral amides, N and Q, were substituted for the valines at positions 94 and 96. These variants exhibited one or more of the following functional changes: weakened inducer binding, impaired allosteric response, and diminished protein stability. For V96D and V96E, ion pair formation with K84 appears optimal, and the loss of inducer response exceeds that of the hydrophobic K84A and -L variants. However, impacts on functional properties indicate that stabilizing the buried positive charge with polar or ion pair interactions is not functionally equivalent to structural stabilization via hydrophobic enhancement.

Backbone relaxation coupled to the ionization of internal groups in proteins: a self-guided Langevin dynamics study

Pathways of structural relaxation triggered by ionization of internal groups in staphylococcal nuclease (SNase) were studied through multiple self-guided Langevin dynamics (SGLD) simulations. Circular dichroism, steady-state Trp fluorescence, and nuclear magnetic resonance spectroscopy have shown previously that variants of SNase with internal Glu, Asp, and Lys at positions 66 or 92, and Arg at position 66, exhibit local reorganization or global unfolding when the internal ionizable group is charged. Except for Arg-66, these internal ionizable groups have unusual pKa values and are neutral at physiological pH. The structural trends observed in the simulations are in general agreement with experimental observations. The I92D variant, which unfolds globally upon ionization of Asp-92, in simulations often exhibits extensive hydration of the protein core, and sometimes also significant perturbations of the beta-barrel. In the crystal structure of the V66R variant, the beta1 strand from the beta-barrel is domain-swapped; in the simulations, the beta1 strand is sometimes partially released. The V66K variant, which in solutions shows reorganization of six residues at the C-terminus of helix alpha1 and perturbations in the beta-barrel structure, exhibits fraying of three residues of helix alpha1 in one simulation, and perturbations and partial unfolding of three beta-strands in a few other simulations. In sharp contrast, very small structural changes were observed in simulations of the wild-type protein. The simulations indicate that charging of internal groups frequently triggers penetration of water into the protein interior. The pKa values of Asp-92 and Arg-66 calculated with continuum methods on SGLD-relaxed structures reached the normal values in most simulations. Detailed analysis of accuracy and performance of SGLD demonstrates that SGLD outperforms LD in sampling of alternative protein conformations without loss of the accuracy and level of detail characteristic of regular LD.

Open science grid study of the coupling between conformation and water content in the interior of a protein

Computational grids are a promising resource for modeling complex biochemical processes such as protein folding, penetration of gases or water into proteins, or protein structural rearrangements coupled to ligand binding. We have enabled the molecular dynamics program CHARMM to run on the Open Science Grid. The implementation is general, flexible, easily modifiable for use with other molecular dynamics programs and other grids and automated in terms of job submission, monitoring, and resubmission. The usefulness of grid computing was demonstrated through the study of hydration of the Glu-66 side chain in the interior of protein staphylococcal nuclease. Multiple simulations started with and without two internal water molecules shown crystallographically to be associated with the side chain of Glu-66 yielded two distinct populations of rotameric states of Glu-66 that differed by as much as 20%. This illustrates how internal water molecules can bias protein conformations. Furthermore, there appeared to be a temporal correlation between dehydration of the side chain and conformational transitions of Glu-66. This example demonstrated how difficult it is to get convergence even in the relatively simple case of a side chain oscillating between two conformations. With grid computing, we also benchmarked the self-guided Langevin dynamics method against the Langevin dynamics method traditionally used for temperature control in molecular dynamics simulations and showed that the two methods yield comparable results.

pKa of residue 66 in Staphylococal nuclease. I. Insights from QM/MM simulations with conventional sampling

A combined quantum mechanical/molecular mechanical (QM/MM) potential function is used in a thermodynamic integration approach to calculate the pK(a) of residue 66 in two mutants (V66E, V66D) of Staphylococal nuclease relative to solution. Despite the similarity in chemical nature and experimentally measured pK(a) of the two buried titritable residues, the behaviors of the two mutants and the computed pK(a) values vary greatly in the simulations. For Glu66, the side chain is consistently observed to spontaneously flip out from the protein interior during titration, and the overall protein structure remains stable throughout the simulations. The computed pK(a) shifts using conventional sampling techniques with multiple nanoseconds per lambda window (Set A and B) are generally close to the experimental value, therefore indicating that large-scale conformational rearrangements are not as important for V66E as suggested by the recent study of Warshel and co-worker. For Asp66, by contrast, flipping of the shorter side chain is not sufficient for getting adequate solvent stabilization of the ionized state. As a result, more complex behaviors such as partial unfolding of a nearby beta-sheet region is observed, and the computed pK(a) shift is substantially higher than the experimental value unless Asp66 is biased to adopt the similar configurations as Glu66 in the V66E simulations. Collectively, these studies suggest that the lack of electronic polarization is not expected to be the dominant source of error in microscopic pK(a) shift calculations, while the need of enhanced sampling is more compelling for predicting the pK(a) of buried residues. Furthermore, the comparison between V66E and V66D also highlights that the microscopic interpretation of similar apparent pK(a) values and effective "dielectric constants" of proteins can vary greatly in terms of the residues that make key contributions and the scale of structural/hydration response to titration, the latter of which is difficult to predict a priori. Perturbative analyses of interactions that contribute to the titration free energy point to mutants that can be used to verify the microscopic mechanisms of titration in V66E/D SNase proteins.

Studying the unfolding kinetics of proteins under pressure using long molecular dynamic simulation runs

The usefulness of computational methods such as molecular dynamics simulation has been extensively established for studying systems in equilibrium. Nevertheless, its application to complex non-equilibrium biological processes such as protein unfolding has been generally regarded as producing results which cannot be interpreted straightforwardly. In the present study, we present results for the kinetics of unfolding of apomyoglobin, based on the analysis of long simulation runs of this protein in solution at 3 kbar (1 atm = 1.01325, bar = 101,325 Pa). We hereby demonstrate that the analysis of the data collected within a simulated time span of 0.18 mus suffices for producing results, which coincide remarkably with the available unfolding kinetics experimental data. This not only validates molecular dynamics simulation as a valuable alternative for studying non-equilibrium processes, but also enables a detailed analysis of the actual structural mechanism which underlies the unfolding process of proteins under elusive denaturing conditions such as high pressure.

Direct evidence for deprotonation of a lysine side chain buried in the hydrophobic core of a protein

We report direct evidence for deprotonation of a lysine side chain buried in the hydrophobic core of a protein, demonstrating heteronuclear 1H-15N NMR data on the Lys-66 side chain amine (Nzeta) group in the delta-PHS/V66K variant of staphylococcal nuclease. Previous crystallographic study has shown that the Lys-66 Nzeta group is completely buried in the hydrophobic core. On the basis of double and triple resonance experiments, we found that the 1Hzeta and 15Nzeta chemical shifts at pH 8.0 and 6 degrees C for the buried lysine are 0.81 and 23.3 ppm, respectively, which are too abnormal to correspond to the protonated (NH3+) state. Further investigations using a model system suggested that the abnormal 1H and 15N chemical shifts represent the deprotonated (NH2) state of the Lys-66 Nzeta group. More straightforward evidence for the deprotonation was obtained with 2D F1-1H-coupled 1H-15N heteronuclear correlation experiments. Observed 15N multiplets clearly indicated that the spin system for the Lys-66 Nzeta group is AX2 (NH2) rather than AX3 (NH3+). Interestingly, although the amine group is buried in the hydrophobic core, the hydrogen exchange between water and the Lys-66 Nzeta group was found to be relatively rapid (93 s(-1) at -1 degrees C), which suggests the presence of a dynamic process such as local unfolding or water penetration. The partial self-decoupling effect on 15Nzeta multiplets due to the rapid hydrogen exchange is also discussed.

Electrostatic effects in a network of polar and ionizable groups in staphylococcal nuclease

His121 and His124 are embedded in a network of polar and ionizable groups on the surface of staphylococcal nuclease. To examine how membership in a network affects the electrostatic properties of ionizable groups, the tautomeric state and the pK(a) values of these histidines were measured with NMR spectroscopy in the wild-type nuclease and in 13 variants designed to disrupt the network. In the background protein, His121 and His124 titrate with pK(a) values of 5.2 and 5.6, respectively. In the variants, where the network was disrupted, the pK(a) values range from 4.03 to 6.46 for His121, and 5.04 to 5.99 for His124. The largest decrease in a pK(a) was observed when the favorable Coulomb interaction between His121 and Glu75 was eliminated; the largest increase was observed when Tyr91 or Tyr93 was substituted with Ala or Phe. In all variants, the dominant tautomeric state at neutral pH was the N(epsilon2) state. At one level the network behaves as a rigid unit that does not readily reorganize when disrupted: crystal structures of the E75A or E75Q variants show that even when the pivotal Glu75 is removed, the overall configuration of the network was unaffected. On the other hand, a few key hydrogen bonds appear to govern the conformation of the network, and when these bonds are disrupted the network reorganizes. Coulomb interactions within the network report an effective dielectric constant of 20, whereas a dielectric constant of 80 is more consistent with the magnitude of medium to long-range Coulomb interactions in this protein. The data demonstrate that when structures are treated as static, rigid bodies, structure-based pK(a) calculations with continuum electrostatics method are not useful to treat ionizable groups in cases where pK(a) values are governed by short-range polar and Coulomb interactions.

On the Dielectric Boundary in Poisson-Boltzmann Calculations

In applying the Poisson-Boltzmann (PB) equation for calculating the electrostatic free energies of solute molecules, an open question is how to specify the boundary between the low-dielectric solute and the high-dielectric solvent. Two common specifications of the dielectric boundary, as the molecular surface (MS) or the van der Waals (vdW) surface of the solute, give very different results for the electrostatic free energy of the solute. With the same atomic radii, the solute is more solvent-exposed in the vdW specification. One way to resolve the difference is to use different sets of atomic radii for the two surfaces. The radii for the vdW surface would be larger in order to compensate for the higher solvent exposure. Here we show that radius re-parameterization required for bringing MS-based and vdW-based PB results to agreement is solute-size dependent. The difference in atomic radii for individual amino acids as solutes is only 2-5% but increases to over 20% for proteins with ~200 residues. Therefore two sets of radii that yield identical MS-based and vdW-based PB results for small solutes will give very different PB results for large solutes. This finding raises issues about two common practices. The first is the use of atomic radii, which are parameterized against either experimental solvation data or data obtained from explicit-solvent simulations on small compounds, for PB calculations on proteins. The second is the parameterization of vdW-based generalized Born models against MS-based PB results.

Crystallographic study of hydration of an internal cavity in engineered proteins with buried polar or ionizable groups

Although internal water molecules are essential for the structure and function of many proteins, the structural and physical factors that govern internal hydration are poorly understood. We have examined the molecular determinants of internal hydration systematically, by solving the crystal structures of variants of staphylococcal nuclease with Gln-66, Asn-66, and Tyr-66 at cryo (100 K) and room (298 K) temperatures, and comparing them with existing cryo and room temperature structures of variants with Glu-66, Asp-66, Lys-66, Glu-92 or Lys-92 obtained under conditions of pH where the internal ionizable groups are in the neutral state. At cryogenic temperatures the polar moieties of all these internal side chains are hydrated except in the cases of Lys-66 and Lys-92. At room temperature the internal water molecules were observed only in variants with Glu-66 and Tyr-66; water molecules in the other variants are probably present but they are disordered and therefore undetectable crystallographically. Each internal water molecule establishes between 3 and 5 hydrogen bonds with the protein or with other internal water molecules. The strength of interactions between internal polar side chains and water molecules seems to decrease from carboxylic acids to amides to amines. Low temperature, low cavity volume, and the presence of oxygen atoms in the cavity increase the positional stability of internal water molecules. This set of structures and the physical insight they contribute into internal hydration will be useful for the development and benchmarking of computational methods for artificial hydration of pockets, cavities, and active sites in proteins.

Minimizing frustration by folding in an aqueous environment

Although life as we know it evolved in an aqueous medium, the properties of water are not completely understood. In this review, we focus on the role of water in guiding protein folding and stability. Specifically, we discuss the mechanisms of protein folding in an aqueous environment, the effects of water on the folding energy landscape as well as the transition state ensemble, and interactions of water with the folded state. We show that water cannot be viewed as a passive solvent, but rather, plays a very active role in the life of a protein.

Water penetration in the low and high pressure native states of ubiquitin

Theoretical studies on the solvation of methane molecules in water have shown that the effect of increased pressure is to stabilize solvent separated contacts relative to direct contacts. This suggests that high pressure stabilizes waters that have penetrated into a protein's core, indicating a mechanism for the high pressure denaturation of proteins. We test this theory on a folded protein by studying the penetration of water into the native state of ubiquitin at low and high pressures, using molecular dynamics. An ensemble of conformations sampled in the folded state of ubiquitin has been determined by NMR at two pressures below the protein's denaturation pressure, 30 atm and 3000 atm. We find that 1-5 more waters penetrate the high pressure conformations than the low pressure conformations. Low volume configurations of the system are favored at high pressures, but different components of the system may experience increases or decreases in their specific volumes. We find that penetrating waters have a higher volume per water than bulk waters, but that the volume per protein residue may be lowered by solvation. Furthermore, we find that penetration of the protein by water at high pressures is driven by the difference in the pressure dependence of the probability of cavity opening in the protein and pressure dependence of the probability of cavity opening in the bulk solvent. The volume changes associated with cavity opening and closing indicate that each penetrating water reduces the volume of the system by about 12 mL/mol. The experimental volume change going from the low pressure to the high pressure native state of ubiquitin is 24 mL/mol. Our results indicate that this volume change can be explained by penetration of the protein by two water molecules.