What Contributions to Protein Side-chain Dynamics are Probed by NMR Experiments? A Molecular Dynamics Simulation Analysis

Unraveling motion in proteins by combining NMR relaxometry and molecular dynamics simulations: A case study on ubiquitin

Nuclear magnetic resonance (NMR) relaxation experiments shine light onto the dynamics of molecular systems in the picosecond to millisecond timescales. As these methods cannot provide an atomically resolved view of the motion of atoms, functional groups, or domains giving rise to such signals, relaxation techniques have been combined with molecular dynamics (MD) simulations to obtain mechanistic descriptions and gain insights into the functional role of side chain or domain motion. In this work, we present a comparison of five computational methods that permit the joint analysis of MD simulations and NMR relaxation experiments. We discuss their relative strengths and areas of applicability and demonstrate how they may be utilized to interpret the dynamics in MD simulations with the small protein ubiquitin as a test system. We focus on the aliphatic side chains given the rigidity of the backbone of this protein. We find encouraging agreement between experiment, Markov state models built in the χ1/χ2 rotamer space of isoleucine residues, explicit rotamer jump models, and a decomposition of the motion using ROMANCE. These methods allow us to ascribe the dynamics to specific rotamer jumps. Simulations with eight different combinations of force field and water model highlight how the different metrics may be employed to pinpoint force field deficiencies. Furthermore, the presented comparison offers a perspective on the utility of NMR relaxation to serve as validation data for the prediction of kinetics by state-of-the-art biomolecular force fields.

How Much Entropy Is Contained in NMR Relaxation Parameters?

Solution-state NMR relaxation experiments are the cornerstone to study internal protein dynamics at an atomic resolution on time scales that are faster than the overall rotational tumbling time τ_R. Since the motions described by NMR relaxation parameters are connected to thermodynamic quantities like conformational entropies, the question arises how much of the total entropy is contained within this tumbling time. Using all-atom molecular dynamics simulations of the T4 lysozyme, we found that entropy buildup is rather fast for the backbone, such that the majority of the entropy is indeed contained in the short-time dynamics. In contrast, the contribution of the slow dynamics of side chains on time scales beyond τ_R on the side-chain conformational entropy is significant and should be taken into account for the extraction of accurate thermodynamic properties.

Correlated Response of Protein Side-Chain Fluctuations and Conformational Entropy to Ligand Binding

The heterogeneous fast side-chain dynamics of proteins plays crucial roles in molecular recognition and binding. Site-specific NMR experiments quantify these motions by measuring the model-free order parameter (O_axis²) on a scale of 0 (most flexible) to 1 (least flexible) for each methyl-containing residue of proteins. Here, we have examined ligand-induced variations in the fast side-chain dynamics and conformational entropy of calmodulin (CaM) using five different CaM-peptide complexes. O_axis² of CaM in the ligand-free (O_axis,U²) and ligand-bound (O_axis,B²) states are calculated from molecular dynamics trajectories and conformational energy surfaces obtained using the adaptive biasing force (ABF) method. ΔO_axis² = O_axis,B² - O_axis,U² follows a Gaussian-like unimodal distribution whose second moment is a potential indicator of the binding affinity of these complexes. The probability for the binding-induced O_axis,U² → O_axis,B² transition decreases with increasing magnitude of ΔO_axis², indicating that large flexibility changes are improbable for side chains of CaM after ligand binding. A linear correlation established between ΔO_axis² and the conformational entropy change of the protein makes possible the determination of the conformational entropy of binding of protein-ligand complexes. The results not only underscore the functional importance of fast side-chain fluctuations but also highlight key motional and thermodynamic correlates of protein-ligand binding.

Toho-1 β-lactamase: backbone chemical shift assignments and changes in dynamics upon binding with avibactam

Backbone chemical shift assignments for the Toho-1 β-lactamase (263 amino acids, 28.9 kDa) are reported based on triple resonance solution-state NMR experiments performed on a uniformly ²H,¹³C,¹⁵N-labeled sample. These assignments allow for subsequent site-specific characterization at the chemical, structural, and dynamical levels. At the chemical level, titration with the non-β-lactam β-lactamase inhibitor avibactam is found to give chemical shift perturbations indicative of tight covalent binding that allow for mapping of the inhibitor binding site. At the structural level, protein secondary structure is predicted based on the backbone chemical shifts and protein residue sequence using TALOS-N and found to agree well with structural characterization from X-ray crystallography. At the dynamical level, model-free analysis of ¹⁵N relaxation data at a single field of 16.4 T reveals well-ordered structures for the ligand-free and avibactam-bound enzymes with generalized order parameters of ~ 0.85. Complementary relaxation dispersion experiments indicate that there is an escalation in motions on the millisecond timescale in the vicinity of the active site upon substrate binding. The combination of high rigidity on short timescales and active site flexibility on longer timescales is consistent with hypotheses for achieving both high catalytic efficiency and broad substrate specificity: the induced active site dynamics allows variously sized substrates to be accommodated and increases the probability that the optimal conformation for catalysis will be sampled.

Fitting Side-Chain NMR Relaxation Data Using Molecular Simulations

Proteins display a wealth of dynamical motions that can be probed using both experiments and simulations. We present an approach to integrate side-chain NMR relaxation measurements with molecular dynamics simulations to study the structure and dynamics of these motions. The approach, which we term ABSURDer (average block selection using relaxation data with entropy restraints), can be used to find a set of trajectories that are in agreement with relaxation measurements. We apply the method to deuterium relaxation measurements in T4 lysozyme and show how it can be used to integrate the accuracy of the NMR measurements with the molecular models of protein dynamics afforded by the simulations. We show how fitting of dynamic quantities leads to improved agreement with static properties and highlight areas needed for further improvements of the approach.

Validating the CHARMM36m protein force field with LJ-PME reveals altered hydrogen bonding dynamics under elevated pressures

The pressure-temperature phase diagram is important to our understanding of the physics of biomolecules. Compared to studies on temperature effects, studies of the pressure dependence of protein dynamic are rather limited. Molecular dynamics (MD) simulations with fine-tuned force fields (FFs) offer a powerful tool to explore the influence of thermodynamic conditions on proteins. Here we evaluate the transferability of the CHARMM36m (C36m) protein force field at varied pressures compared with NMR data using ubiquitin as a model protein. The pressure dependences of J couplings for hydrogen bonds and order parameters for internal motion are in good agreement with experiment. We demonstrate that the C36m FF combined with the Lennard-Jones particle-mesh Ewald (LJ-PME) method is suitable for simulations in a wide range of temperature and pressure. As the ubiquitin remains stable up to 2500 bar, we identify the mobility and stability of different hydrogen bonds in response to pressure. Based on those results, C36m is expected to be applied to more proteins in the future to further investigate protein dynamics under elevated pressures.

Molecular Simulations Guidelines for Biological Nanomaterials: From Peptides to Membranes

In studying biological processes and focusing on the molecular mechanisms at the basis of these, molecular dynamics (MD) simulations have demonstrated to be a very useful tool for the past 50 years. This suite of computational methods calculates the time-dependent evolution of a molecular system using physics-based first principles. In this chapter, we give a brief introduction to the theory and practical use of molecular dynamics simulations, highlighting the different models and algorithms that have been developed to tackle specific problems, with a special focus on classical force fields. Some examples of how simulations have been used in the past will help the reader in discerning their power, limitations, and significance.

Backbone assignments and conformational dynamics in the S. typhimurium tryptophan synthase α-subunit from solution-state NMR

Backbone assignments for the isolated α-subunit of Salmonella typhimurium tryptophan synthase (TS) are reported based on triple resonance solution-state NMR experiments on a uniformly 2H,13C,15N-labeled sample. From the backbone chemical shifts, secondary structure and random coil index order parameters (RCI-S2) are predicted. Titration with the 3-indole-D-glycerol 3'-phosphate analog, N-(4'-trifluoromethoxybenzenesulfonyl)-2-aminoethyl phosphate (F9), leads to chemical shift perturbations indicative of conformational changes from which an estimate of the dissociation constant is obtained. Comparisons of the backbone chemical-shifts, RCI-S2 values, and site-specific relaxation times with and without F9 reveal allosteric changes including modulation in secondary structures and loop rigidity induced upon ligand binding. A comparison is made to the X-ray crystal structure of the α-subunit in the full TS αββα bi-enzyme complex and to two new X-ray crystal structures of the isolated TS α-subunit reported in this work.

Combining Molecular and Spin Dynamics Simulations with Solid-State NMR: A Case Study of Amphiphilic Lysine-Leucine Repeat Peptide Aggregates

Interpreting dynamics in solid-state molecular systems requires characterization of the potentially heterogeneous environmental contexts of molecules. In particular, the analysis of solid-state nuclear magnetic resonance (ssNMR) data to elucidate molecular dynamics (MD) involves modeling the restriction to overall tumbling by neighbors, as well as the concentrations of water and buffer. In this exploration of the factors that influence motion, we utilize atomistic MD trajectories of peptide aggregates with varying hydration to mimic an amorphous solid-state environment and predict ssNMR relaxation rates. We also account for spin diffusion in multiply spin-labeled (up to 19 nuclei) residues, with several models of dipolar-coupling networks. The framework serves as a general approach to determine essential spin couplings affecting relaxation, benchmark MD force fields, and reveal the hydration dependence of dynamics in a crowded environment. We demonstrate the methodology on a previously characterized amphiphilic 14-residue lysine-leucine repeat peptide, LKα14 (Ac-LKKLLKLLKKLLKL-c), which has an α-helical secondary structure and putatively forms leucine-burying tetramers in the solid state. We measure the R₁ relaxation rates of uniformly ¹³C-labeled and site-specific ²H-labeled leucines in the hydrophobic core of LKα14 at multiple hydration levels. Studies of 9 and 18 tetramer bundles reveal the following: (a) for the incoherent component of ¹³C relaxation, the nearest-neighbor spin interactions dominate, while the ¹H-¹H interactions have minimal impact; (b) the AMBER ff14SB dihedral barriers for the leucine C_γ-C_δ bond ("methyl rotation barriers") must be lowered by a factor of 0.7 to better match the ²H data; (c) proton-driven spin diffusion explains some of the discrepancy between experimental and simulated rates for the C_β and C_α nuclei; and (d) ¹³C relaxation rates are mostly underestimated in the MD simulations at all hydrations, and the discrepancies identify likely motions missing in the 50 ns MD trajectories.

A Quasielastic Neutron Scattering Investigation on the Molecular Self-Dynamics of Human Myelin Protein P2

The human myelin protein P2 is a membrane binding protein believed to maintain correct lipid composition and organization in peripheral nerve myelin. Its function is related to its ability to stack membranes, and this function can be enhanced by the P38G mutation, whereby the overall protein structure does not change but the molecular dynamics increase. Mutations in P2 are linked to human peripheral neuropathy. Here, the dynamics of wild-type P2 and the P38G variant were studied using quasielastic neutron scattering on time scales from 10 ps to 1 ns at 300 K. The results suggest that the mutant protein dynamics are increased on both the fastest and the slowest measured time scales, by increasing the dynamics amplitude and/or the portion of atoms participating in the movement.

Narrowing the gap between experimental and computational determination of methyl group dynamics in proteins

A synergistic analysis of methyl NMR relaxation data and MD simulations identifies ways to improve studies of protein dynamics.

Micelles of the chiral biocompatible surfactant (1R,2S)-dodecyl(2-hydroxy-1-methyl-2-phenylethyl)dimethylammonium bromide (DMEB): molecular dynamics and fragmentation patterns in the gas phase

RATIONALE

The study of self-assembly processes of surfactant molecules in the gas phase is of great interest for several theoretical and technological reasons related to their possible exploitation as drug carriers, protein shields and cleaning agents in the gas phase.

METHODS

The stability and fragmentation patterns of singly and multiply charged (either positively or negatively) aggregates of the surfactant (1R,2S)-dodecyl(2-hydroxy-1-methyl-2-phenylethyl)dimethyl ammonium bromide (DMEB) in the gas phase have been studied by ion mobility mass spectrometry and tandem mass spectrometry. Molecular dynamics (MD) simulations of positively and negatively singly and multiply charged DMEB aggregates have been performed to obtain structural and energetics information. Finally, in order to ascertain some clues on the DMEB growth mechanism, quantum mechanics calculations were carried out.

RESULTS

It has been evidenced that positively and negatively singly charged aggregates at low collision energy decompose preferentially by loss of only one DMEB molecule. Increasing the collision energy, the loss of neutrals becomes increasingly abundant. Multiply charged DMEB aggregates are unstable and decompose forming singly charged monomers or dimers. MD simulations show reverse micelle-like structures with polar heads somewhat segregated into the aggregate interior. Finally, a good correlation between experimental and calculated collisional cross sections (CCS) was found.

CONCLUSIONS

The fragmentation pathways of DMEB charged species evidenced for singly charged aggregates exhibit features similar to that of other detergent aggregates, but multiply charged aggregates showed a system-specific behavior. QM calculations on the optimized structures (2¹⁺ , 3¹⁺ , 1^1- and 2^1- ) indicate that the most determinant interactions are due to an OH---Br hydrogen bonding that is also involved in the link between monomeric DMEB units. The MD models gave CCS values in good agreement with experimental ones, evidenced by a less strict reverse micelle-like structure and a reasonably spread bromine anion distribution Copyright © 2017 John Wiley & Sons, Ltd.

Direct Determination of Site-Specific Noncovalent Interaction Strengths of Proteins from NMR-Derived Fast Side Chain Motional Parameters

A novel approach to accurately determine residue-specific noncovalent interaction strengths (ξ) of proteins from NMR-measured fast side chain motional parameters (O_axis²) is presented. By probing the environmental sensitivity of side chain conformational energy surfaces of individual residues of a diverse set of proteins, the microscopic connections between ξ, O_axis², conformational entropy (S_conf), conformational barriers, and rotamer stabilities established here are found to be universal among proteins. The results reveal that side chain flexibility and conformational entropy of each residue decrease with increasing ξ and that for each residue type there exists a critical range of ξ, determined primarily by the mean side chain conformational barriers, within which flexibility of any residue can be reversibly tuned from highly flexible (with O_axis² ∼ 0) to highly restricted (with O_axis² ∼ 1) by increasing ξ by ∼3 kcal/mol. Beyond this critical range of ξ, both side chain flexibility and conformational entropy are insensitive to ξ. The interrelationships between conformational dynamics, conformational entropy, and noncovalent interactions of protein side chains established here open up new avenues to probe perturbation-induced (for example, ligand-binding, temperature, pressure) changes in fast side chain dynamics and thermodynamics of proteins by comparing their conformational energy surfaces in the native and perturbed states.

Picosecond to nanosecond dynamics provide a source of conformational entropy for protein folding

Myoglobin can be trapped in fully folded structures, partially folded molten globules, and unfolded states under stable equilibrium conditions.

How Efficient Is Replica Exchange Molecular Dynamics? An Analytic Approach

Replica exchange molecular dynamics (REMD) has become a standard technique for accelerating relaxation in biosimulations. Despite its widespread use, questions remain about its efficiency compared with conventional, constant temperature molecular dynamics (MD). An analytic approach is taken to describe the relative efficiency of REMD with respect to MD. This is applied to several simple two-state models and to several real proteins-protein L and the B domain of protein A-to predict the relative efficiency of REMD with respect to MD in actual applications. In agreement with others, we find the following: as long as there is a positive activation energy for folding, REMD is more efficient than MD; the effectiveness of REMD is strongly dependent on the activation enthalpy; and the efficiency of REMD for actual proteins is a strong function of the maximum temperature. Choosing the maximum temperature too high can result in REMD becoming significantly less efficient than conventional MD. A good rule of thumb appears to be to choose the maximum temperature of the REMD simulation slightly above the temperature at which the enthalpy for folding vanishes. Additionally, we find that the number of replicas in REMD, while important for simulations shorter than one or two relaxation times, has a minimal effect on the asymptotic efficiency of the method.

Slowdown of Interhelical Motions Induces a Glass Transition in RNA

RNA function depends crucially on the details of its dynamics. The simplest RNA dynamical unit is a two-way interhelical junction. Here, for such a unit--the transactivation response RNA element--we present evidence from molecular dynamics simulations, supported by nuclear magnetic resonance relaxation experiments, for a dynamical transition near 230 K. This glass transition arises from the freezing out of collective interhelical motional modes. The motions, resolved with site-specificity, are dynamically heterogeneous and exhibit non-Arrhenius relaxation. The microscopic origin of the glass transition is a low-dimensional, slow manifold consisting largely of the Euler angles describing interhelical reorientation. Principal component analysis over a range of temperatures covering the glass transition shows that the abrupt slowdown of motion finds its explanation in a localization transition that traps probability density into several disconnected conformational pools over the low-dimensional energy landscape. Upon temperature increase, the probability density pools then flood a larger basin, akin to a lakes-to-sea transition. Simulations on transactivation response RNA are also used to backcalculate inelastic neutron scattering data that match previous inelastic neutron scattering measurements on larger and more complex RNA structures and which, upon normalization, give temperature-dependent fluctuation profiles that overlap onto a glass transition curve that is quasi-universal over a range of systems and techniques.

Dynamics of the Peripheral Membrane Protein P2 from Human Myelin Measured by Neutron Scattering--A Comparison between Wild-Type Protein and a Hinge Mutant

Myelin protein P2 is a fatty acid-binding structural component of the myelin sheath in the peripheral nervous system, and its function is related to its membrane binding capacity. Here, the link between P2 protein dynamics and structure and function was studied using elastic incoherent neutron scattering (EINS). The P38G mutation, at the hinge between the β barrel and the α-helical lid, increased the lipid stacking capacity of human P2 in vitro, and the mutated protein was also functional in cultured cells. The P38G mutation did not change the overall structure of the protein. For a deeper insight into P2 structure-function relationships, information on protein dynamics in the 10 ps to 1 ns time scale was obtained using EINS. Values of mean square displacements mainly from protein H atoms were extracted for wild-type P2 and the P38G mutant and compared. Our results show that at physiological temperatures, the P38G mutant is more dynamic than the wild-type P2 protein, especially on a slow 1-ns time scale. Molecular dynamics simulations confirmed the enhanced dynamics of the mutant variant, especially within the portal region in the presence of bound fatty acid. The increased softness of the hinge mutant of human myelin P2 protein is likely related to an enhanced flexibility of the portal region of this fatty acid-binding protein, as well as to its interactions with the lipid bilayer surface requiring conformational adaptations.

Balanced Protein-Water Interactions Improve Properties of Disordered Proteins and Non-Specific Protein Association

Some frequently encountered deficiencies in all-atom molecular simulations, such as nonspecific protein-protein interactions being too strong, and unfolded or disordered states being too collapsed, suggest that proteins are insufficiently well solvated in simulations using current state-of-the-art force fields. To address these issues, we make the simplest possible change, by modifying the short-range protein-water pair interactions, and leaving all the water-water and protein-protein parameters unchanged. We find that a modest strengthening of protein-water interactions is sufficient to recover the correct dimensions of intrinsically disordered or unfolded proteins, as determined by direct comparison with small-angle X-ray scattering (SAXS) and Förster resonance energy transfer (FRET) data. The modification also results in more realistic protein-protein affinities, and average solvation free energies of model compounds which are more consistent with experiment. Most importantly, we show that this scaling is small enough not to affect adversely the stability of the folded state, with only a modest effect on the stability of model peptides forming α-helix and β-sheet structures. The proposed adjustment opens the way to more accurate atomistic simulations of proteins, particularly for intrinsically disordered proteins, protein-protein association, and crowded cellular environments.

Banding of NMR-derived methyl order parameters: implications for protein dynamics

Our understanding of protein folding, stability, and function has begun to more explicitly incorporate dynamical aspects. Nuclear magnetic resonance has emerged as a powerful experimental method for obtaining comprehensive site-resolved insight into protein motion. It has been observed that methyl-group motion tends to cluster into three "classes" when expressed in terms of the popular Lipari-Szabo model-free squared generalized order parameter. Here the origins of the three classes or bands in the distribution of order parameters are examined. As a first step, a Bayesian based approach, which makes no a priori assumption about the existence or number of bands, is developed to detect the banding of Oaxis2 values derived either from NMR experiments or molecular dynamics simulations. The analysis is applied to seven proteins with extensive molecular dynamics simulations of these proteins in explicit water to examine the relationship between O2 and fine details of the motion of methyl bearing side chains. All of the proteins studied display banding, with some subtle differences. We propose a very simple yet plausible physical mechanism for banding. Finally, our Bayesian method is used to analyze the measured distributions of methyl group motions in the catabolite activating protein and several of its mutants in various liganded states and discuss the functional implications of the observed banding to protein dynamics and function.

A simple method to measure protein side-chain mobility using NMR chemical shifts

Protein side-chain motions are involved in many important biological processes including enzymatic catalysis, allosteric regulation, and the mediation of protein-protein, protein-DNA, protein-RNA, and protein-cofactor interactions. NMR spectroscopy has long been used to provide insights into the motions of side-chain groups. Currently, the method of choice for studying side-chain dynamics by NMR is the measurement of methyl (2)H autorelaxation. Methyl (2)H autorelaxation exhibits simple relaxation mechanisms and can be straightforwardly converted to meaningful dynamic parameters. However, methyl groups can only be found in 6 of 19 side-chain bearing amino acids. Consequently, only a sparse assessment of protein side-chain dynamics is possible. Therefore, there is a significant interest in developing novel methods of studying side-chain motions that can be applied to all types of side-chains. Here, we show how side-chain chemical shifts can be used to determine the magnitude of fast side-chain motions in proteins. The chemical shift method is applicable to all side-chain bearing residues and does not require any additional measurements beyond standard NMR experiments for backbone and side-chain assignments.

CHARMM36 all-atom additive protein force field: validation based on comparison to NMR data

Protein structure and dynamics can be characterized on the atomistic level with both nuclear magnetic resonance (NMR) experiments and molecular dynamics (MD) simulations. Here, we quantify the ability of the recently presented CHARMM36 (C36) force field (FF) to reproduce various NMR observables using MD simulations. The studied NMR properties include backbone scalar couplings across hydrogen bonds, residual dipolar couplings (RDCs) and relaxation order parameter, as well as scalar couplings, RDCs, and order parameters for side-chain amino- and methyl-containing groups. It is shown that the C36 FF leads to better correlation with experimental data compared to the CHARMM22/CMAP FF and suggest using C36 in protein simulations. Although both CHARMM FFs contains the same nonbond parameters, our results show how the changes in the internal parameters associated with the peptide backbone via CMAP and the χ1 and χ2 dihedral parameters leads to improved treatment of the analyzed nonbond interactions. This highlights the importance of proper treatment of the internal covalent components in modeling nonbond interactions with molecular mechanics FFs.

Conformational contribution to thermodynamics of binding in protein-peptide complexes through microscopic simulation

We extract the thermodynamics of conformational changes in biomacromolecular complexes from the distributions of the dihedral angles of the macromolecules. These distributions are obtained from the equilibrium configurations generated via all-atom molecular dynamics simulations. The conformational thermodynamics data we obtained for calmodulin-peptide complexes using our methodology corroborate well with the experimentally observed conformational and binding entropies. The conformational free-energy changes and their contributions for different peptide-binding regions of calmodulin are evaluated microscopically.

Will molecular dynamics simulations of proteins ever reach equilibrium?

We show that conformational entropies calculated for five proteins and protein-ligand complexes with dihedral-distribution histogramming, the von Mises approach, or quasi-harmonic analysis do not converge to any useful precision even if molecular dynamics (MD) simulations of 380-500 ns length are employed (the uncertainty is 12-89 kJ mol(-1)). To explain this, we suggest a simple protein model involving dihedrals with effective barriers forming a uniform distribution and show that for such a model, the entropy increases logarithmically with time until all significantly populated dihedral states have been sampled, in agreement with the simulations (during the simulations, 52-70% of the available dihedral phase space has been visited). This is also confirmed by the analysis of the trajectories of a 1 ms simulation of bovine pancreatic trypsin inhibitor (31 kJ mol(-1) difference in the entropy between the first and second part of the simulation). Strictly speaking, this means that it is practically impossible to equilibrate MD simulations of proteins. We discuss the implications of such a lack of strict equilibration of protein MD simulations and show that ligand-binding free energies estimated with the MM/GBSA method (molecular mechanics with generalised Born and surface-area solvation) vary by 3-15 kJ mol(-1) during a 500 ns simulation (the higher estimate is caused by rare conformational changes), although they involve a questionable but well-converged normal-mode entropy estimate, whereas free energies estimated by free-energy perturbation vary by less than 0.6 kJ mol(-1) for the same simulation.

Reconstruction of protein side-chain conformational free energy surfaces from NMR-derived methyl axis order parameters

An analytical approach is developed for reconstructing site-specific methyl-bearing protein side-chain conformational energy surfaces from NMR methyl axis order parameters (O(axis)(2)). Application of an enhanced sampling algorithm (adaptive biasing force) to molecular dynamics simulation of a protein, calcium-bound calmodulin, reveals a nonlinear correlation between O(axis)(2) and the populations of rotamer states of protein side-chains, permitting the rotamer populations to be extracted directly from O(axis)(2). The analytical approach yields side-chain conformational distributions that are in excellent agreement with those obtained from the enhanced-sampling MD results.

Combining NMR and molecular dynamics studies for insights into the allostery of small GTPase-protein interactions

Combinations of experimentally derived data from nuclear magnetic resonance spectroscopy and analyses of molecular dynamics trajectories increasingly allow us to obtain a detailed description of the molecular mechanisms by which proteins function in signal transduction. This chapter provides an introduction into these two methodologies, illustrated by example of a small GTPase-effector interaction. It is increasingly becoming clear that new insights are provided by the combination of experimental and computational methods. Understanding the structural and protein dynamical contributions to allostery will be useful for the engineering of new binding interfaces and protein functions, as well as for the design/in silico screening of chemical agents that can manipulate the function of small GTPase-protein interactions in diseases such as cancer.

Vinculin activation is necessary for complete talin binding

Focal adhesions are critical to a number of cellular processes that involve mechanotransduction and mechanical interaction with the cellular environment. The growth and strengthening of these focal adhesions is dependent on the interaction between talin and vinculin. This study investigates said interaction and how vinculin activation influences it. Using molecular dynamics, the interaction between talin's vinculin binding site (VBS) and vinculin's domain 1 (D1) is simulated both before and after vinculin activation. The simulations of VBS binding to vinculin before activation suggest the proximity of the vinculin tail to D1 prevents helical movement in D1 and thus prevents binding of VBS. In contrast, interaction of VBS with activated vinculin shows the possibility of complete VBS insertion into D1. In the simulations of both activated and autoinhibited vinculin where VBS fails to fully bind, VBS demonstrates significant hydrophobic interaction with surface residues in D1. These interactions link VBS to D1 even without its proper insertion into the hydrophobic core. Together these simulations suggest VBS binds to vinculin with the following mechanism: 1), VBS links to D1 via surface hydrophobic interactions; 2), vinculin undergoes activation and D1 is moved away from the vinculin tail; 3), helices in D1 undergo conformational change to allow VBS binding; and 4), VBS inserts itself into the hydrophobic core of D1.

Evidence of protein collective motions on the picosecond timescale

We investigate the presence of structural collective motions on a picosecond timescale for the heme protein, cytochrome c, as a function of oxidation and hydration, using terahertz (THz) time domain spectroscopy and molecular dynamics simulations. The THz response dramatically increases with oxidation, with the largest increase for lowest hydrations, and highest frequencies. For both oxidation states the THz response rapidly increases with hydration saturating above ∼25% (g H(2)O/g protein). Quasiharmonic vibrational modes and dipole-dipole correlation functions were calculated from molecular dynamics trajectories. The collective mode density of states alone reproduces the measured hydration dependence, providing strong evidence of the existence of these motions. The large oxidation dependence is reproduced only by the dipole-dipole correlation function, indicating the contrast arises from diffusive motions consistent with structural changes occurring in the vicinity of buried internal water molecules. This source for the observed oxidation dependence is consistent with the lack of an oxidation dependence in nuclear resonant vibrational spectroscopy measurements.

Residue-specific side-chain packing determines the backbone dynamics of transmembrane model helices

The transmembrane domains (TMDs) of membrane-fusogenic proteins contain an overabundance of β-branched residues. In a previous effort to systematically study the relation among valine content, fusogenicity, and helix dynamics, we developed model TMDs that we termed LV-peptides. The content and position of valine in LV-peptides determine their fusogenicity and backbone dynamics, as shown experimentally. Here, we analyze their conformational dynamics and the underlying molecular forces using molecular-dynamics simulations. Our study reveals that backbone dynamics is correlated with the efficiency of side-chain to side-chain van der Waals packing between consecutive turns of the helix. Leu side chains rapidly interconvert between two rotameric states, thus favoring contacts to its i±3 and i±4 neighbors. Stereochemical restraints acting on valine side chains in the α-helix force both β-substituents into an orientation where i,i±3 interactions are less favorable than i,i±4 interactions, thus inducing a local packing deficiency at VV3 motifs. We provide a quantitative molecular model to explain the relationship among chain connectivity, side-chain mobility, and backbone flexibility. We expect that this mechanism also defines the backbone flexibility of natural TMDs.

Methyl dynamics of a Ca2+-calmodulin-peptide complex from NMR/SRLS

We developed the slowly relaxing local structure (SRLS) approach for analyzing NMR spin relaxation in proteins. SRLS accounts for dynamical coupling between the tumbling of the protein and the local motion of the probe and for general tensorial properties. It is the generalization of the traditional model-free (MF) method, which does not account for mode-coupling and treats only simple tensorial properties. SRLS is applied herein to ²H relaxation of ¹³CDH₂ groups in the complex of Ca(2+)-calmodulin with the peptide smMLCKp. Literature data comprising ²H T₁ and T₂ acquired at 14.1 and 17.6 T, and 288, 295, 308, and 320 K, are used. We find that mode-coupling is a small effect for methyl dynamics. On the other hand, general tensorial properties are important. In particular, it is important to allow for the asymmetry of the local spatial restrictions, which can be represented in SRLS by a rhombic local ordering tensor with components S(0)(2) and S(2)(2). The principal axes frame of this tensor is obviously different from the axial frames of the magnetic tensors. Here, we find that -0.2 ≤ S(0)(2) ≤ 0.5 and -0.4 ≤ S(2)(2) ≤ 0. MF features a single "generalized" order parameter, S, confined to the 0-0.316 range; the local geometry is inherently simple. The parameter S is inaccurate, having absorbed unaccounted for effects, notably S(2)(2) ≠ 0. We find that the methionine methyls (the other methyl types) reorient with rates of 8.6 × 10⁹ to 21.4 × 10⁹ (0.67 × 10⁹ to 6.5 × 10⁹) 1/s. The corresponding activation energies are 10 (10-27) kJ/mol. By contrast, MF yields inaccurate effective local motional correlation times, τ(e), with nonphysical temperature dependence. Thus, the problematic S- and τ(e)-based MF picture of methyl dynamics has been replaced with an insightful physical picture based on a local ordering tensor related to structural features, and a local diffusion tensor that yields accurate activation energies.

Side-chain conformational changes of transcription factor PhoB upon DNA binding: a population-shift mechanism

Using molecular dynamics (MD) simulations and analyses of NMR relaxation order parameters, we investigated conformational changes of side chains in hydrophobic cores upon DNA binding for the DNA binding/transactivation domain of the transcription factor PhoB, in which backbone conformational changes upon DNA binding are small. The simulation results correlated well with experimental order parameters for the backbone and side-chain methyl groups, showing that the order parameters generally represent positional fluctuations of the backbone and side-chain methyl groups. However, topological effects of the side chains on the order parameters were also found and could be eliminated using normalized order parameters for each amino acid type. Consistent with the NMR experiments, the normalized order parameters from the MD simulations showed that the side chains in one of the two hydrophobic cores (the soft core) were highly flexible in comparison with those in the other hydrophobic core (the hard core) before DNA binding and that the flexibility of the hydrophobic cores, particularly of the soft core, was reduced upon DNA binding. Principal component analysis of methyl group configurations revealed strikingly different side-chain dynamics for the soft and hard cores. In the hard core, side-chain configurations were simply distributed around one or two average configurations. In contrast, the side chains in the soft core dynamically varied their configurations in an equilibrium ensemble that included binding configurations as minor components before DNA binding. DNA binding led to a restriction of the side-chain dynamics and a shift in the equilibrium toward binding configurations, in clear correspondence with a population-shift model.

A molecular dynamics investigation of vinculin activation

Vinculin activation plays a critical role in focal adhesion initiation and formation. In its native state, vinculin is in an autoinhibitory conformation in which domain 1 prevents interaction of the vinculin tail domain with actin by steric hindrance. Once activated, vinculin is able to interact with both actin and talin. Several hypotheses have been put forth addressing the mechanisms of vinculin activation. One set of studies suggests that vinculin interaction with talin is sufficient to cause activation, whereas another set of studies suggests that a simultaneous interaction with several binding partners is necessary to achieve vinculin activation. Using molecular-dynamics (MD) simulations, we investigate the mechanisms of vinculin activation and suggest both a trajectory of conformational changes leading to vinculin activation, and key structural features that are likely involved in stabilizing the autoinhibited conformation. Assuming that the simultaneous interaction of vinculin with both actin and talin causes a stretching force on vinculin, and that vinculin activation results from a removal of steric hindrance blocking the actin-binding sites, we simulate with MD the stretching and activation of vinculin. The MD simulations are further confirmed by normal-mode analysis and simulation after residue modification. Taken together, the results of these simulations suggest that bending of the vinculin-binding-site region in vinculin away from the vinculin tail is the likely trajectory of vinculin activation.

PCDB: a database of protein conformational diversity

PCDB (http://www.pcdb.unq.edu.ar) is a database of protein conformational diversity. For each protein, the database contains the redundant compilation of all the corresponding crystallographic structures obtained under different conditions. These structures could be considered as different instances of protein dynamism. As a measure of the conformational diversity we use the maximum RMSD obtained comparing the structures deposited for each domain. The redundant structures were extracted following CATH structural classification and cross linked with additional information. In this way it is possible to relate a given amount of conformational diversity with different levels of information, such as protein function, presence of ligands and mutations, structural classification, active site information and organism taxonomy among others. Currently the database contains 7989 domains with a total of 36581 structures from 4171 different proteins. The maximum RMSD registered is 26.7 Å and the average of different structures per domain is 4.5.

Comparison of entropic contributions to binding in a "hydrophilic" versus "hydrophobic" ligand-protein interaction

In the present study we characterize the thermodynamics of binding of histamine to recombinant histamine-binding protein (rRaHBP2), a member of the lipocalin family isolated from the brown-ear tick Rhipicephalus appendiculatus. The binding pocket of this protein contains a number of charged residues, consistent with histamine binding, and is thus a typical example of a "hydrophilic" binder. In contrast, a second member of the lipocalin family, the recombinant major urinary protein (rMUP), binds small hydrophobic ligands, with a similar overall entropy of binding in comparison with rRaHBP2. Having extensively studied ligand binding thermodynamics for rMUP previously, the data we obtained in the present study for HBP enables a comparison of the driving forces for binding between these classically distinct binding processes in terms of entropic contributions from ligand, protein, and solvent. In the case of rRaHBP2, we find favorable entropic contributions to binding from desolvation of the ligand; however, the overall entropy of binding is unfavorable due to a dominant unfavorable contribution arising from the loss of ligand degrees of freedom, together with the sequestration of solvent water molecules into the binding pocket in the complex. This contrasts with binding in rMUP where desolvation of the protein binding pocket makes a minor contribution to the overall entropy of binding given that the pocket is substantially desolvated prior to binding.

The low-temperature inflection observed in neutron scattering measurements of proteins is due to methyl rotation: direct evidence using isotope labeling and molecular dynamics simulations

There is increasing interest in the contribution of methyl groups to the overall dynamics measured by neutron scattering experiments of proteins. In particular an inflection observed in atomic mean square displacements measured as a function of temperature on high resolution spectrometers (approximately 1 microeV) was explained by the onset of methyl group rotations. By specifically labeling a non-methyl-containing side-chain in a native protein system, the purple membrane, and performing neutron scattering measurements, we here provide direct experimental evidence that the observed inflection is indeed due to methyl group rotations. Molecular dynamics simulations reproduce the experimental data, and their analysis suggests that the apparent transition is due to methyl group rotation entering the finite instrumental resolution of the spectrometer. Methyl group correlation times measured by solid state NMR in the purple membrane, taken from previous work, support the interpretation.

Detection of nanosecond time scale side-chain jumps in a protein dissolved in water/glycerol solvent

In solution, the correlation time of the overall protein tumbling, tau(R), plays a role of a natural dynamics cutoff-internal motions with correlation times on the order of tau ( R ) or longer cannot be reliably identified on the basis of spin relaxation data. It has been proposed some time ago that the 'observation window' of solution experiments can be expanded by changing the viscosity of solvent to raise the value of tau(R). To further explore this concept, we prepared a series of samples of alpha-spectrin SH3 domain in solvent with increasing concentration of glycerol. In addition to the conventional (15)N labeling, the protein was labeled in the Val, Leu methyl positions ((13)CHD(2) on a deuterated background). The collected relaxation data were used in asymmetric fashion: backbone (15)N relaxation rates were used to determine tau(R) across the series of samples, while methyl (13)C data were used to probe local dynamics (side-chain motions). In interpreting the results, it has been initially suggested that addition of glycerol leads only to increases in tau(R), whereas local motional parameters remain unchanged. Thus the data from multiple samples can be analyzed jointly, with tau(R) playing the role of experimentally controlled variable. Based on this concept, the extended model-free model was constructed with the intent to capture the effect of ns time-scale rotameric jumps in valine and leucine side chains. Using this model, we made a positive identification of nanosecond dynamics in Val-23 where ns motions were already observed earlier. In several other cases, however, only tentative identification was possible. The lack of definitive results was due to the approximate character of the model-contrary to what has been assumed, addition of glycerol led to a gradual 'stiffening' of the protein. This and other observations also shed light on the interaction of the protein with glycerol, which is one of the naturally occurring osmoprotectants. In particular, it has been found that the overall protein tumbling is controlled by the bulk solvent, and not by a thin solvation layer which contains a higher proportion of water.

Protein proton-proton dynamics from amide proton spin flip rates

Residue-specific amide proton spin-flip rates K were measured for peptide-free and peptide-bound calmodulin. K approximates the sum of NOE build-up rates between the amide proton and all other protons. This work outlines the theory of multi-proton relaxation, cross relaxation and cross correlation, and how to approximate it with a simple model based on a variable number of equidistant protons. This model is used to extract the sums of K-rates from the experimental data. Error in K is estimated using bootstrap methodology. We define a parameter Q as the ratio of experimental K-rates to theoretical K-rates, where the theoretical K-rates are computed from atomic coordinates. Q is 1 in the case of no local motion, but decreases to values as low as 0.5 with increasing domination of sidechain protons of the same residue to the amide proton flips. This establishes Q as a monotonous measure of local dynamics of the proton network surrounding the amide protons. The method is applied to the study of proton dynamics in Ca(2+)-saturated calmodulin, both free in solution and bound to smMLCK peptide. The mean Q is 0.81 +/- 0.02 for free calmodulin and 0.88 +/- 0.02 for peptide-bound calmodulin. This novel methodology thus reveals the presence of significant interproton disorder in this protein, while the increase in Q indicates rigidification of the proton network upon peptide binding, confirming the known high entropic cost of this process.

Mechanical signaling on the single protein level studied using steered molecular dynamics

Efficient communication between the cell and its external environment is of the utmost importance to the function of multicellular organisms. While signaling events can be generally characterized as information exchange by means of controlled energy conversion, research efforts have hitherto mainly been concerned with mechanisms involving chemical and electrical energy transfer. Here, we review recent computational efforts addressing the function of mechanical force in signal transduction. Specifically, we focus on the role of steered molecular dynamics (SMD) simulations in providing details at the atomic level on a group of protein domains, which play a fundamental role in signal exchange by responding properly to mechanical strain. We start by giving a brief introduction to the SMD technique and general properties of mechanically stable protein folds, followed by specific examples illustrating three general regimes of signal transfer utilizing mechanical energy: purely mechanical, mechanical to chemical, and chemical to mechanical. Whenever possible the physiological importance of the example at hand is stressed to highlight the diversity of the processes in which mechanical signaling plays a key role. We also provide an overview of future challenges and perspectives for this rapidly developing field.

Conservation of side-chain dynamics within a protein family

The question of protein dynamics and its relevance to function is currently a topic of great interest. Proteins are particularly dynamic at the side-chain level on the time scale of picoseconds to nanoseconds. Here, we present a comparison of NMR-monitored side-chain motion between three PDZ domains of approximately 30% sequence identity and show that the side-chain dynamics display nontrivial conservation. Methyl (2)H relaxation was carried out to determine side-chain order parameters (S(2)), which were found to be more similar than naively expected from sequence, local packing, or a combination of the two. Thus, the dynamics of a rather distant homologue appears to be an excellent predictor of a protein's side-chain dynamics and, on average, better than current structure-based methods. Fast side-chain dynamics therefore display a high level of organization associated with global fold. Beyond simple conservation, the analysis herein suggests that the pattern of side-chain flexibility has significant contributions from nonlocal elements of the PDZ fold, such as correlated motions, and that the conserved dynamics may directly support function.

Calculation of proteins' total side-chain torsional entropy and its influence on protein-ligand interactions

Despite the high density within a typical protein fold, the ensemble of sterically permissible side-chain repackings is vast. Here, we examine the extent of this variability that survives energetic biases due to van der Waals interactions, hydrogen bonding, salt bridges, and solvation. Monte Carlo simulations of an atomistic model exhibit thermal fluctuations among a diverse set of side-chain arrangements, even with the peptide backbone fixed in its crystallographic conformation. We have quantified the torsional entropy of this native-state ensemble, relative to that of a noninteracting reference system, for 12 small proteins. The reduction in entropy per rotatable bond due to each kind of interaction is remarkably consistent across this set of molecules. To assess the biophysical importance of these fluctuations, we have estimated side-chain entropy contributions to the binding affinity of several peptide ligands with calmodulin. Calculations for our fixed-backbone model correlate very well with experimentally determined binding entropies over a range spanning more than 80 kJ/(mol x 308 K).

Computational approaches for the design of peptides with anti-breast cancer properties

Background: Breast cancer is the most common cancer among women. Tamoxifen is the preferred drug for estrogen receptor-positive breast cancer treatment, yet many of these cancers are intrinsically resistant to tamoxifen or acquire resistance during treatment. Therefore, scientists are searching for breast cancer drugs that have different molecular targets. Methodology: Recently, a computational approach was used to successfully design peptides that are new lead compounds against breast cancer. We used replica exchange molecular dynamics to predict the structure and dynamics of active peptides, leading to the discovery of smaller bioactive peptides. Conclusions: These analogs inhibit estrogen-dependent cell growth in a mouse uterine growth assay, a test showing reliable correlation with human breast cancer inhibition. We outline the computational methods that were tried and used along with the experimental information that led to the successful completion of this research.