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

Towards an optimal monoclonal antibody with higher binding affinity to the receptor-binding domain of SARS-CoV-2 spike proteins from different variants

A highly efficient and robust multiple scales in silico protocol, consisting of atomistic Molecular Dynamics (MD), coarse-grain (CG) MD, and constant-pH CG Monte Carlo (MC), has been developed and used to study the binding affinities of selected antigen-binding fragments of the monoclonal antibody (mAbs) CR3022 and several of its here optimized versions against 11 SARS-CoV-2 variants including the wild type. Totally 235,000 mAbs structures were initially generated using the RosettaAntibodyDesign software, resulting in top 10 scored CR3022-like-RBD complexes with critical mutations and compared to the native one, all having the potential to block virus-host cell interaction. Of these 10 finalists, two candidates were further identified in the CG simulations to be the best against all SARS-CoV-2 variants. Surprisingly, all 10 candidates and the native CR3022 exhibited a higher affinity for the Omicron variant despite its highest number of mutations. The multiscale protocol gives us a powerful rational tool to design efficient mAbs. The electrostatic interactions play a crucial role and appear to be controlling the affinity and complex building. Studied mAbs carrying a more negative total net charge show a higher affinity. Structural determinants could be identified in atomistic simulations and their roles are discussed in detail to further hint at a strategy for designing the best RBD binder. Although the SARS-CoV-2 was specifically targeted in this work, our approach is generally suitable for many diseases and viral and bacterial pathogens, leukemia, cancer, multiple sclerosis, rheumatoid, arthritis, lupus, and more.

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.

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.

Reformulation of the self-guided molecular simulation method

Self-guided molecular/Langevin dynamics (SGMD/SGLD) simulation methods were developed to enhance conformational sampling through promoting low frequency motion of molecular systems and have been successfully applied in many simulation studies. Quantitative understanding of conformational distribution in SGLD has been achieved by separating microscopic properties according to frequency. However, a missing link between the guiding factors and conformational distributions makes it highly empirical and system dependent when choosing the values of the guiding parameters. Based on the understanding that molecular interactions are the source of energy barriers and diffusion friction, this work reformulates the equation of the low frequency motion to resemble Langevin dynamics. This reformulation leads to new forms of guiding forces and establishes a relation between the guiding factors and conformational distributions. We call simulations with these new guiding forces the generalized self-guided molecular/Langevin dynamics (SGMDg/SGLDg). In addition, we present a new way to calculate low frequency properties and an efficient algorithm to implement SGMDg/SGLDg that minimizes memory usage and inter-processor communication. Through example simulations with a skewed double well system, an argon fluid, and a cryo-EM map flexible fitting case, we demonstrate the guiding effects on conformational distributions and conformational searching.

q-Canonical Monte Carlo Sampling for Modeling the Linkage between Charge Regulation and Conformational Equilibria of Peptides

The overall charge content and the patterning of charged residues have a profound impact on the conformational ensembles adopted by intrinsically disordered proteins. These parameters can be altered by charge regulation, which refers to the effects of post-translational modifications, pH-dependent changes to charge, and conformational fluctuations that modify the pKa values of ionizable residues. Although atomistic simulations have played a prominent role in uncovering the major sequence-ensemble relationships of IDPs, most simulations assume fixed charge states for ionizable residues. This may lead to erroneous estimates for conformational equilibria if they are linked to charge regulation. Here, we report the development of a new method we term q-canonical Monte Carlo sampling for modeling the linkage between charge regulation and conformational equilibria. The method, which is designed to be interoperable with the ABSINTH implicit solvation model, operates as follows: For a protein sequence with n ionizable residues, we start with all 2n charge microstates and use a criterion based on model compound pKa values to prune down to a subset of thermodynamically relevant charge microstates. This subset is then grouped into mesostates, where all microstates that belong to a mesostate have the same net charge. Conformational distributions, drawn from a canonical ensemble, are generated for each of the charge microstates that make up a mesostate using a method we designate as proton walk sampling. This method combines Metropolis Monte Carlo sampling in conformational space with an auxiliary Markov process that enables interconversions between charge microstates along a mesostate. Proton walk sampling helps identify the most likely charge microstate per mesostate. We then use thermodynamic integration aided by the multistate Bennett acceptance ratio method to estimate the free energies for converting between mesostates. These free energies are then combined with the per-microstate weights along each mesostate to estimate standard state free energies and pH-dependent free energies for all thermodynamically relevant charge microstates. The results provide quantitative estimates of the probabilities and preferred conformations associated with every thermodynamically accessible charge microstate. We showcase the application of q-canonical sampling using two model systems. The results establish the soundness of the method and the importance of charge regulation in systems characterized by conformational heterogeneity.

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.

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.

Enhanced Sampling of an Atomic Model with Hybrid Nonequilibrium Molecular Dynamics-Monte Carlo Simulations Guided by a Coarse-Grained Model

Molecular dynamics (MD) trajectories based on a classical equation of motion provide a straightforward, albeit somewhat inefficient approach, to explore and sample the configurational space of a complex molecular system. While a broad range of techniques can be used to accelerate and enhance the sampling efficiency of classical simulations, only algorithms that are consistent with the Boltzmann equilibrium distribution yield a proper statistical mechanical computational framework. Here, a multiscale hybrid algorithm relying simultaneously on all-atom fine-grained (FG) and coarse-grained (CG) representations of a system is designed to improve sampling efficiency by combining the strength of nonequilibrium molecular dynamics (neMD) and Metropolis Monte Carlo (MC). This CG-guided hybrid neMD-MC algorithm comprises six steps: (1) a FG configuration of an atomic system is dynamically propagated for some period of time using equilibrium MD; (2) the resulting FG configuration is mapped onto a simplified CG model; (3) the CG model is propagated for a brief time interval to yield a new CG configuration; (4) the resulting CG configuration is used as a target to guide the evolution of the FG system; (5) the FG configuration (from step 1) is driven via a nonequilibrium MD (neMD) simulation toward the CG target; (6) the resulting FG configuration at the end of the neMD trajectory is then accepted or rejected according to a Metropolis criterion before returning to step 1. A symmetric two-ends momentum reversal prescription is used for the neMD trajectories of the FG system to guarantee that the CG-guided hybrid neMD-MC algorithm obeys microscopic detailed balance and rigorously yields the equilibrium Boltzmann distribution. The enhanced sampling achieved with the method is illustrated with a model system with hindered diffusion and explicit-solvent peptide simulations. Illustrative tests indicate that the method can yield a speedup of about 80 times for the model system and up to 21 times for polyalanine and (AAQAA)₃ in water.

A Virtual Mixture Approach to the Study of Multistate Equilibrium: Application to Constant pH Simulation in Explicit Water

Chemical and thermodynamic equilibrium of multiple states is a fundamental phenomenon in biology systems and has been the focus of many experimental and computational studies. This work presents a simulation method to directly study the equilibrium of multiple states. This method constructs a virtual mixture of multiple states (VMMS) to sample the conformational space of all chemical states simultaneously. The VMMS system consists of multiple subsystems, one for each state. The subsystem contains a solute and a solvent environment. The solute molecules in all subsystems share the same conformation but have their own solvent environments. Transition between states is implicated by the change of their molar fractions. Simulation of a VMMS system allows efficient calculation of relative free energies of all states, which in turn determine their equilibrium molar fractions. For systems with a large number of state transition sites, an implicit site approximation is introduced to minimize the cost of simulation. A direct application of the VMMS method is for constant pH simulation to study protonation equilibrium. Applying the VMMS method to a heptapeptide of 3 ionizable residues, we calculated the pKas of those residues both with all explicit states and with implicit sites and obtained consistent results. For mouse epidermal growth factor of 9 ionizable groups, our VMMS simulations with implicit sites produced pKas of all 9 ionizable groups and the results agree qualitatively with NMR measurement. This example demonstrates the VMMS method can be applied to systems of a large number of ionizable groups and the computational cost scales linearly with the number of ionizable groups. For one of the most challenging systems in constant pH calculation, SNase Δ+PHS/V66K, our VMMS simulation shows that it is the state-dependent water penetration that causes the large deviation in lysine66’s pKa.

Computer simulation plays an important role to understand molecular systems and has been applied to problems of increasing complexity. Multistate equilibrium is a fundamental concept behind the structure and function of biological systems. Due to the limit in computing resources and lack of good alternative methods, computer simulation has been conducted for systems in a single state, sampling from one state to another to infer equilibrium properties. This sequential approach has been successful in many cases such as protonation equilibrium with implicit solvation model. However, state transition is difficult when explicit solvent is used for more accurate solvation description. Many efforts have been dedicated to overcome this difficulty. Analogous to real multistate systems, we proposed a virtual mixture of multiple states (VMMS) to directly simulate the equilibrium. State transitions are replaced by changes in state molar fractions. Mimicking a test tube environment, all states are simulated in parallel to equilibrate with each other. Application to constant pH simulation in explicit water demonstrates the capability of this method. It is expected that the VMMS method will find more applications in biological problems related to the equilibrium of competing states.

Self-guided Langevin dynamics via generalized Langevin equation

Self-guided Langevin dynamics (SGLD) is a molecular simulation method that enhances conformational search and sampling via acceleration of the low frequency motions of the system. This acceleration is produced via introduction of a guiding force which breaks down the detailed-balance property of the dynamics, implying that some reweighting is necessary to perform equilibrium sampling. Here, we eliminate the need of reweighing and show that the NVT and NPT ensembles are sampled exactly by a new version of self-guided motion involving a generalized Langevin equation (GLE) in which the random force is modified so as to restore detailed-balance. Through the examples of alanine dipeptide and argon liquid, we show that this SGLD-GLE method has enhanced conformational sampling capabilities compared with regular Langevin dynamics (LD) while being of comparable computational complexity. In particular, SGLD-GLE is fully size extensive and can be used in arbitrarily large systems, making it an appealing alternative to LD. © 2015 Wiley Periodicals, Inc.

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.

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.

Bayesian model aggregation for ensemble-based estimates of protein pKa values

This article investigates an ensemble-based technique called Bayesian Model Averaging (BMA) to improve the performance of protein amino acid pKa predictions. Structure-based pKa calculations play an important role in the mechanistic interpretation of protein structure and are also used to determine a wide range of protein properties. A diverse set of methods currently exist for pKa prediction, ranging from empirical statistical models to ab initio quantum mechanical approaches. However, each of these methods are based on a set of conceptual assumptions that can effect a model's accuracy and generalizability for pKa prediction in complicated biomolecular systems. We use BMA to combine eleven diverse prediction methods that each estimate pKa values of amino acids in staphylococcal nuclease. These methods are based on work conducted for the pKa Cooperative and the pKa measurements are based on experimental work conducted by the García-Moreno lab. Our cross-validation study demonstrates that the aggregated estimate obtained from BMA outperforms all individual prediction methods with improvements ranging from 45 to 73% over other method classes. This study also compares BMA's predictive performance to other ensemble-based techniques and demonstrates that BMA can outperform these approaches with improvements ranging from 27 to 60%. This work illustrates a new possible mechanism for improving the accuracy of pKa prediction and lays the foundation for future work on aggregate models that balance computational cost with prediction accuracy.

Targeted conformational search with map-restrained self-guided Langevin dynamics: application to flexible fitting into electron microscopic density maps

We present a map-restrained self-guided Langevin dynamics (MapSGLD) simulation method for efficient targeted conformational search. The targeted conformational search represents simulations under restraints defined by experimental observations and/or by user specified structural requirements. Through map-restraints, this method provides an efficient way to maintain substructures and to set structure targets during conformational searching. With an enhanced conformational searching ability of self-guided Langevin dynamics, this approach is suitable for simulating large-scale conformational changes, such as the formation of macromolecular assemblies and transitions between different conformational states. Using several examples, we illustrate the application of this method in flexible fitting of atomic structures into density maps derived from cryo-electron microscopy.

Understanding the basis of a class of paradoxical mutations in AraC through simulations

Most mutations at position 15 in the N-terminal arm of the regulatory protein AraC leave the protein incapable of responding to arabinose and inducing the proteins required for arabinose catabolism. Mutations at other positions of the arm do not have this behavior. Simple energetic analysis of the interactions between the arm and bound arabinose do not explain the uninducibility of AraC with mutations at position 15. Extensive molecular dynamics (MD) simulations, carried out largely on the Open Science Grid, were done of the wild-type protein with and without bound arabinose and of all possible mutations at position 15, many of which were constructed and measured for this work. Good correlation was found for deviation of arm position during the simulations and inducibility as measured in vivo of the same mutant proteins. Analysis of the MD trajectories revealed that preservation of the shape of the arm is critical to inducibility. To maintain the correct shape of the arm, the strengths of three interactions observed to be strong in simulations of the wild-type AraC protein need to be preserved. These interactions are between arabinose and residue 15, arabinose and residues 8-9, and residue 13 and residue 15. The latter interaction is notable because residues L9, Y13, F15, W95, and Y97 form a hydrophobic cluster which needs to be preserved for retention of the correct shape.

Describing sequence-ensemble relationships for intrinsically disordered proteins

Intrinsically disordered proteins participate in important protein-protein and protein-nucleic acid interactions and control cellular phenotypes through their prominence as dynamic organizers of transcriptional, post-transcriptional and signalling networks. These proteins challenge the tenets of the structure-function paradigm and their functional mechanisms remain a mystery given that they fail to fold autonomously into specific structures. Solving this mystery requires a first principles understanding of the quantitative relationships between information encoded in the sequences of disordered proteins and the ensemble of conformations they sample. Advances in quantifying sequence-ensemble relationships have been facilitated through a four-way synergy between bioinformatics, biophysical experiments, computer simulations and polymer physics theories. In the present review we evaluate these advances and the resultant insights that allow us to develop a concise quantitative framework for describing the sequence-ensemble relationships of intrinsically disordered proteins.

Replica exchanging self-guided Langevin dynamics for efficient and accurate conformational sampling

This work presents a replica exchanging self-guided Langevin dynamics (RXSGLD) simulation method for efficient conformational searching and sampling. Unlike temperature-based replica exchanging simulations, which use high temperatures to accelerate conformational motion, this method uses self-guided Langevin dynamics (SGLD) to enhance conformational searching without the need to elevate temperatures. A RXSGLD simulation includes a series of SGLD simulations, with simulation conditions differing in the guiding effect and/or temperature. These simulation conditions are called stages and the base stage is one with no guiding effect. Replicas of a simulation system are simulated at the stages and are exchanged according to the replica exchanging probability derived from the SGLD partition function. Because SGLD causes less perturbation on conformational distribution than high temperatures, exchanges between SGLD stages have much higher probabilities than those between different temperatures. Therefore, RXSGLD simulations have higher conformational searching ability than temperature based replica exchange simulations. Through three example systems, we demonstrate that RXSGLD can generate target canonical ensemble distribution at the base stage and achieve accelerated conformational searching. Especially for large systems, RXSGLD has remarkable advantages in terms of replica exchange efficiency, conformational searching ability, and system size extensiveness.

pH-Dependent conformational changes in proteins and their effect on experimental pK(a)s: the case of Nitrophorin 4

The acid-base behavior of amino acids is an important subject of study due to their prominent role in enzyme catalysis, substrate binding and protein structure. Due to interactions with the protein environment, their pK_as can be shifted from their solution values and, if a protein has two stable conformations, it is possible for a residue to have different “microscopic”, conformation-dependent pK_a values. In those cases, interpretation of experimental measurements of the pK_a is complicated by the coupling between pH, protonation state and protein conformation. We explored these issues using Nitrophorin 4 (NP4), a protein that releases NO in a pH sensitive manner. At pH 5.5 NP4 is in a closed conformation where NO is tightly bound, while at pH 7.5 Asp30 becomes deprotonated, causing the conformation to change to an open state from which NO can easily escape. Using constant pH molecular dynamics we found two distinct microscopic Asp30 pK_as: 8.5 in the closed structure and 4.3 in the open structure. Using a four-state model, we then related the obtained microscopic values to the experimentally observed “apparent” pK_a, obtaining a value of 6.5, in excellent agreement with experimental data. This value must be interpreted as the pH at which the closed to open population transition takes place. More generally, our results show that it is possible to relate microscopic structure dependent pKa values to experimentally observed ensemble dependent apparent pK_as and that the insight gained in the relatively simple case of NP4 can be useful in several more complex cases involving a pH dependent transition, of great biochemical interest.

The interaction of an amino acid with its protein environment can result in an acid-base behavior that is very different from what would be observed in solution. This environment can be greatly altered when the protein changes conformation. As a result, the amino acid will have two different “microscopic” pK_a values. Nitrophorin 4 is a good case study to explore this behavior, because it undergoes a pH-dependent conformational change that is well characterized experimentally. Using computer simulation tools, we found that the key titratable Aspartic acid 30, has two very different microscopic pK_as: 4.3 and 8.5, which are significantly different to the observed transition pK_a in solution. However, using a simple model, we were able to understand how this causes the conformational change to take place at pH∼6.5, as measured experimentally. The insight gained in this relatively simple case can be useful in other more complex cases where the apparent pK_a is also a result of the interplay of different conformations where some amino acids experience very different environments.

Enhanced Sampling in Free Energy Calculations: Combining SGLD with the Bennett's Acceptance Ratio and Enveloping Distribution Sampling Methods

One of the key requirements for the accurate calculation of free energy differences is proper sampling of conformational space. Especially in biological applications, molecular dynamics simulations are often confronted with rugged energy surfaces and high energy barriers, leading to insufficient sampling and, in turn, poor convergence of the free energy results. In this work, we address this problem by employing enhanced sampling methods. We explore the possibility of using self-guided Langevin dynamics (SGLD) to speed up the exploration process in free energy simulations. To obtain improved free energy differences from such simulations, it is necessary to account for the effects of the bias due to the guiding forces. We demonstrate how this can be accomplished for the Bennett's acceptance ratio (BAR) and the enveloping distribution sampling (EDS) methods. While BAR is considered among the most efficient methods available for free energy calculations, the EDS method developed by Christ and van Gunsteren is a promising development that reduces the computational costs of free energy calculations by simulating a single reference state. To evaluate the accuracy of both approaches in connection with enhanced sampling, EDS was implemented in CHARMM. For testing, we employ benchmark systems with analytical reference results and the mutation of alanine to serine. We find that SGLD with reweighting can provide accurate results for BAR and EDS where conventional molecular dynamics simulations fail. In addition, we compare the performance of EDS with other free energy methods. We briefly discuss the implications of our results and provide practical guidelines for conducting free energy simulations with SGLD.

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.

Efficient and Unbiased Sampling of Biomolecular Systems in the Canonical Ensemble: A Review of Self-Guided Langevin Dynamics

This review provides a comprehensive description of the self-guided Langevin dynamics (SGLD) and the self-guided molecular dynamics (SGMD) methods and their applications. Example systems are included to provide guidance on optimal application of these methods in simulation studies. SGMD/SGLD has enhanced ability to overcome energy barriers and accelerate rare events to affordable time scales. It has been demonstrated that with moderate parameters, SGLD can routinely cross energy barriers of 20 kT at a rate that molecular dynamics (MD) or Langevin dynamics (LD) crosses 10 kT barriers. The core of these methods is the use of local averages of forces and momenta in a direct manner that can preserve the canonical ensemble. The use of such local averages results in methods where low frequency motion "borrows" energy from high frequency degrees of freedom when a barrier is approached and then returns that excess energy after a barrier is crossed. This self-guiding effect also results in an accelerated diffusion to enhance conformational sampling efficiency. The resulting ensemble with SGLD deviates in a small way from the canonical ensemble, and that deviation can be corrected with either an on-the-fly or a post processing reweighting procedure that provides an excellent canonical ensemble for systems with a limited number of accelerated degrees of freedom. Since reweighting procedures are generally not size extensive, a newer method, SGLDfp, uses local averages of both momenta and forces to preserve the ensemble without reweighting. The SGLDfp approach is size extensive and can be used to accelerate low frequency motion in large systems, or in systems with explicit solvent where solvent diffusion is also to be enhanced. Since these methods are direct and straightforward, they can be used in conjunction with many other sampling methods or free energy methods by simply replacing the integration of degrees of freedom that are normally sampled by MD or LD.

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.

Force-momentum-based self-guided Langevin dynamics: a rapid sampling method that approaches the canonical ensemble

The self-guided Langevin dynamics (SGLD) is a method to accelerate conformational searching. This method is unique in the way that it selectively enhances and suppresses molecular motions based on their frequency to accelerate conformational searching without modifying energy surfaces or raising temperatures. It has been applied to studies of many long time scale events, such as protein folding. Recent progress in the understanding of the conformational distribution in SGLD simulations makes SGLD also an accurate method for quantitative studies. The SGLD partition function provides a way to convert the SGLD conformational distribution to the canonical ensemble distribution and to calculate ensemble average properties through reweighting. Based on the SGLD partition function, this work presents a force-momentum-based self-guided Langevin dynamics (SGLDfp) simulation method to directly sample the canonical ensemble. This method includes interaction forces in its guiding force to compensate the perturbation caused by the momentum-based guiding force so that it can approximately sample the canonical ensemble. Using several example systems, we demonstrate that SGLDfp simulations can approximately maintain the canonical ensemble distribution and significantly accelerate conformational searching. With optimal parameters, SGLDfp and SGLD simulations can cross energy barriers of more than 15 kT and 20 kT, respectively, at similar rates for LD simulations to cross energy barriers of 10 kT. The SGLDfp method is size extensive and works well for large systems. For studies where preserving accessible conformational space is critical, such as free energy calculations and protein folding studies, SGLDfp is an efficient approach to search and sample the conformational space.

The high dielectric constant of staphylococcal nuclease is encoded in its structural architecture

The pK(a) values of Lys-66, Glu-66, and Asp-66 buried in the interior of the staphylococcal nuclease Δ+PHS variant were reported to be shifted by as much as 5 pK(a) units from their normal values. Reproducing the pK(a) of these buried ionizable residues using continuum electrostatic calculations required the use of a high protein dielectric constant of 10 or higher. The apparent high dielectric constant has been rationalized as a consequence of a local structural reorganization or increased fluctuations in the microenvironment of the mutation site (Chimenti, M. S., et al. J. Mol. Biol. 2011, 405, 361-377). We have calculated the dielectric constant of Δ+PHS and the Lys-66, Asp-66, and Glu-66 mutants from first principles using the Kirkwood-Fröhlich equation and discovered that staphylococcal nuclease has a naturally high dielectric constant ranging from 20 to 30. This high dielectric constant does not change significantly with the mutation of residue 66 or with the ionization of the mutated residues. Calculation of the spatial dependence of the dielectric constant for the microenvironment of residue-66 produces a value of about 10, which matches well with the apparent dielectric constant needed to reproduce pK(a) values from continuum electrostatic calculations. Our results suggest an alternative explanation that the high dielectric constant of staphylococcal nuclease is a property resulting from the intrinsic backbone fluctuations originating from its structural architecture.

pH replica-exchange method based on discrete protonation states

We propose a new algorithm for obtaining proton titration curves of ionizable residues. The algorithm is a pH replica-exchange method (PHREM), which is based on the constant pH algorithm of Mongan et al. (J Comput Chem 2004;25:2038-2048). In the original replica-exchange method, simulations of different replicas are performed at different temperatures, and the temperatures are exchanged between the replicas. In our PHREM, simulations of different replicas are performed at different pH values, and the pHs are exchanged between the replicas. The PHREM was applied to a blocked amino acid and to two protein systems (snake cardiotoxin and turkey ovomucoid third domain), in conjunction with a generalized Born implicit solvent. The performance and accuracy of this algorithm and the original constant pH method (PHMD) were compared. For a single set of simulations at different pHs, the use of PHREM yields more accurate Hill coefficients of titratable residues. By performing multiple sets of constant pH simulations started with different initial states, the accuracy of predicted pK(a) values and Hill coefficients obtained with PHREM and PHMD methods becomes comparable. However, the PHREM algorithm exhibits better samplings of the protonation states of titratable residues and less scatter of the titration points and thus better precision of measured pK(a) values and Hill coefficients. In addition, PHREM exhibits faster convergence of individual simulations than the original constant pH algorithm.

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.

Toward canonical ensemble distribution from self-guided Langevin dynamics simulation

This work derives a quantitative description of the conformational distribution in self-guided Langevin dynamics (SGLD) simulations. SGLD simulations employ guiding forces calculated from local average momentums to enhance low-frequency motion. This enhancement in low-frequency motion dramatically accelerates conformational search efficiency, but also induces certain perturbations in conformational distribution. Through the local averaging, we separate properties of molecular systems into low-frequency and high-frequency portions. The guiding force effect on the conformational distribution is quantitatively described using these low-frequency and high-frequency properties. This quantitative relation provides a way to convert between a canonical ensemble and a self-guided ensemble. Using example systems, we demonstrated how to utilize the relation to obtain canonical ensemble properties and conformational distributions from SGLD simulations. This development makes SGLD not only an efficient approach for conformational searching, but also an accurate means for conformational sampling.

Toward accurate prediction of pKa values for internal protein residues: the importance of conformational relaxation and desolvation energy

Proton uptake or release controls many important biological processes, such as energy transduction, virus replication, and catalysis. Accurate pK(a) prediction informs about proton pathways, thereby revealing detailed acid-base mechanisms. Physics-based methods in the framework of molecular dynamics simulations not only offer pK(a) predictions but also inform about the physical origins of pK(a) shifts and provide details of ionization-induced conformational relaxation and large-scale transitions. One such method is the recently developed continuous constant pH molecular dynamics (CPHMD) method, which has been shown to be an accurate and robust pK(a) prediction tool for naturally occurring titratable residues. To further examine the accuracy and limitations of CPHMD, we blindly predicted the pK(a) values for 87 titratable residues introduced in various hydrophobic regions of staphylococcal nuclease and variants. The predictions gave a root-mean-square deviation of 1.69 pK units from experiment, and there were only two pK(a)'s with errors greater than 3.5 pK units. Analysis of the conformational fluctuation of titrating side-chains in the context of the errors of calculated pK(a) values indicate that explicit treatment of conformational flexibility and the associated dielectric relaxation gives CPHMD a distinct advantage. Analysis of the sources of errors suggests that more accurate pK(a) predictions can be obtained for the most deeply buried residues by improving the accuracy in calculating desolvation energies. Furthermore, it is found that the generalized Born implicit-solvent model underlying the current CPHMD implementation slightly distorts the local conformational environment such that the inclusion of an explicit-solvent representation may offer improvement of accuracy.

Developing hybrid approaches to predict pKa values of ionizable groups

Accurate predictions of pKa values of titratable groups require taking into account all relevant processes associated with the ionization/deionization. Frequently, however, the ionization does not involve significant structural changes and the dominating effects are purely electrostatic in origin allowing accurate predictions to be made based on the electrostatic energy difference between ionized and neutral forms alone using a static structure and the subtle structural changes be accounted by using dielectric constant larger than two. On another hand, if the change of the charge state is accompanied by a large structural reorganization of the target protein, then the relevant conformational changes have to be explicitly taken into account in the pKa calculations. Here we report a hybrid approach that first predicts the titratable groups whose ionization is expected to cause large conformational changes, termed "problematic" residues, and then applies a special protocol on them, while the rest of the pK(a)s are predicted with rigid backbone approach as implemented in multi-conformation continuum electrostatics (MCCE) method. The backbone representative conformations for "problematic" groups are generated with either molecular dynamics simulations with charged and uncharged amino acid or with ab-initio local segment modeling. The corresponding ensembles are then used to calculate the titration curves of the "problematic" residues and then the results are averaged to obtain the corresponding pKa.

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.

High-pressure SAXS study of folded and unfolded ensembles of proteins

A structural interpretation of the thermodynamic stability of proteins requires an understanding of the structural properties of the unfolded state. High-pressure small-angle x-ray scattering was used to measure the effects of temperature, pressure, denaturants, and stabilizing osmolytes on the radii of gyration of folded and unfolded state ensembles of staphylococcal nuclease. A set of variants with the internal Val-66 replaced with Ala, Tyr, or Arg was used to examine how changes in the volume and polarity of an internal microcavity affect the dimensions of the native state and the pressure sensitivity of the ensemble. The unfolded state ensembles achieved for these proteins with high pressure were more compact than those achieved at high temperature, and were all very sensitive to the presence of urea and glycerol. Substitutions at the hydrophobic core detectably altered the conformation of the protein, even in the folded state. The introduction of a charged residue, such as Arg, inside the hydrophobic interior of a protein could dramatically alter the structural properties, even those of the unfolded state. The data suggest that a charge at an internal position can interfere with the formation of transient hydrophobic clusters in the unfolded state, and ensure that the pressure-unfolded form of a protein occupies the maximum volume possible. Only at high temperatures does the radius of gyration of the unfolded state ensemble approach the value for a statistical random coil.

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.

Probing the periplasmic-open state of lactose permease in response to sugar binding and proton translocation

Based on the crystal structure of lactose permease (LacY) open to the cytoplasm, a hybrid molecular simulation approach with self-guided Langevin dynamics is used to describe conformational changes that lead to a periplasmic-open state. This hybrid approach consists of implicit (IM) and explicit (EX) membrane simulations and requires self-guided Langevin dynamics to enhance protein motions during the IM simulations. The pore radius of the lumen increases by 3.5 Å on the periplasmic side and decreases by 2.5 Å on the cytoplasmic side (relative to the crystal structure), suggesting a lumen that is fully open to the periplasm to allow for extracellular sugar transport and closed to the cytoplasm. Based on our simulations, the mechanism that triggers this conformational change to the periplasmic-open state is the protonation of Glu269 and binding of the disaccharide. Then, helix packing is destabilized by breaking of several side chains involved in hydrogen bonding (Asn245, Ser41, Glu374, Lys42, and Gln242). For the periplasmic-open conformations obtained from our simulations, helix-helix distances agree well with experimental measurements using double electron-electron resonance, fluorescence resonance energy transfer, and varying sized cross-linkers. The periplasmic-open conformations are also in compliance with various substrate accessibility/reactivity measurements that indicate an opening of the protein lumen on the periplasmic side on sugar binding. The comparison with these measurements suggests a possible incomplete closure of the cytoplasmic half in our simulations. However, the closure is sufficient to prevent the disaccharide from transporting to the cytoplasm, which is in accordance with the well-established alternating access model. Ser53, Gln60, and Phe354 are determined to be important in sugar transport during the periplasmic-open stage of the sugar transport cycle and the sugar is found to undergo an orientational change in order to escape the protein lumen.

Self-guided Langevin dynamics study of regulatory interactions in NtrC

Multiple self-guided Langevin dynamics (SGLD) simulations were performed to examine structural and dynamical properties of the receiver domain of nitrogen regulatory protein C (NtrC(r)). SGLD and MD simulations of the phosphorylated active form structure suggest a mostly stable but broad structural ensemble of this protein. The finite difference Poisson-Boltzmann calculations of the pK(a) values of the active site residues suggest an increase in the pK(a) of His-84 on phosphorylation of Asp-54. In SGLD simulations of the phosphorylated active form with charged His-84, the average position of the regulatory helix alpha4 is found closer to the starting structure than in simulations with the neutral His-84. To model the transition pathway, the phosphate group was removed from the simulations. After 7 ns of simulations, the regulatory helix alpha4 was found approximately halfway between positions in the NMR structures of the active and inactive forms. Removal of the phosphate group stimulated loss of helix alpha4, suggesting that the pathway of conformational transition may involve partial unfolding mechanism. The study illustrates the potential utility of the SGLD method in studies of the coupling between ligand binding and conformational transitions.

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.

Dynamics of tRNA at different levels of hydration

The influence of hydration on the nanosecond timescale dynamics of tRNA is investigated using neutron scattering spectroscopy. Unlike protein dynamics, the dynamics of tRNA is not affected by methyl group rotation. This allows for a simpler analysis of the influence of hydration on the conformational motions in RNA. We find that hydration affects the dynamics of tRNA significantly more than that of lysozyme. Both the characteristic length scale and the timescale of the conformational motions in tRNA depend strongly on hydration. Even the characteristic temperature of the so-called "dynamical transition" appears to be hydration-dependent in tRNA. The amplitude of the conformational motions in fully hydrated tRNA is almost twice as large as in hydrated lysozyme. We ascribe these differences to a more open and flexible structure of hydrated RNA, and to a larger fraction and different nature of hydrophilic sites. The latter leads to a higher density of water that makes the biomolecule more flexible. All-atom molecular-dynamics simulations are used to show that the extent of hydration is greater in tRNA than in lysozyme. We propose that water acts as a "lubricant" in facilitating enhanced motion in solvated RNA molecules.

The pK(a) values of acidic and basic residues buried at the same internal location in a protein are governed by different factors

The pK(a) values of internal ionizable groups are usually very different from the normal pK(a) values of ionizable groups in water. To examine the molecular determinants of pK(a) values of internal groups, we compared the properties of Lys, Asp, and Glu at internal position 38 in staphylococcal nuclease. Lys38 titrates with a normal or elevated pK(a), whereas Asp38 and Glu38 titrate with elevated pK(a) values of 7.0 and 7.2, respectively. In the structure of the L38K variant, the buried amino group of the Lys38 side chain makes an ion pair with Glu122, whereas in the structure of the L38E variant, the buried carboxyl group of Glu38 interacts with two backbone amides and has several nearby carboxyl oxygen atoms. Previously, we showed that the pK(a) of Lys38 is normal owing to structural reorganization and water penetration concomitant with ionization of the Lys side chain. In contrast, the pK(a) values of Asp38 and Glu38 are perturbed significantly owing to an imbalance between favorable polar interactions and unfavorable contributions from dehydration and from Coulomb interactions with surface carboxylic groups. Their ionization is also coupled to subtle structural reorganization. These results illustrate the complex interplay between local polarity, Coulomb interactions, and structural reorganization as determinants of pK(a) values of internal groups in proteins. This study suggests that improvements to computational methods for pK(a) calculations will require explicit treatment of the conformational reorganization that can occur when internal groups ionize.