Quasi-harmonic Analysis Research Articles

Functional Dynamics of Substrate Recognition in TEM Beta-Lactamase

The beta-lactamase enzyme provides effective resistance to beta-lactam antibiotics due to substrate recognition controlled by point mutations. Recently, extended-spectrum and inhibitor-resistant mutants have become a global health problem. Here, the functional dynamics that control substrate recognition in TEM beta-lactamase are investigated using all-atom molecular dynamics simulations. Comparisons are made between wild-type TEM-1 and TEM-2 and the extended-spectrum mutants TEM-10 and TEM-52, both in apo form and in complex with four different antibiotics (ampicillin, amoxicillin, cefotaxime and ceftazidime). Dynamic allostery is predicted based on a quasi-harmonic normal mode analysis using a perturbation scan. An allosteric mechanism known to inhibit enzymatic function in TEM beta-lactamase is identified, along with other allosteric binding targets. Mechanisms for substrate recognition are elucidated using multivariate comparative analysis of molecular dynamics trajectories to identify changes in dynamics resulting from point mutations and ligand binding, and the conserved dynamics, which are functionally important, are extracted as well. The results suggest that the H10-H11 loop (residues 214-221) is a secondary anchor for larger extended spectrum ligands, while the H9-H10 loop (residues 194-202) is distal from the active site and stabilizes the protein against structural changes. These secondary non-catalytically-active loops offer attractive targets for novel noncompetitive inhibitors of TEM beta-lactamase.

Exploring the Structural Rearrangements of the Human Insulin-Degrading Enzyme through Molecular Dynamics Simulations.

Insulin-degrading enzyme (IDE) is a ubiquitously expressed metallopeptidase that degrades insulin and a large panel of amyloidogenic peptides. IDE is thought to be a potential therapeutic target for type-2 diabetes and neurodegenerative diseases, such as Alzheimer’s disease. IDE catalytic chamber, known as a crypt, is formed, so that peptides can be enclosed and degraded. However, the molecular mechanism of the IDE function and peptide recognition, as well as its conformation changes, remains elusive. Our study elucidates IDE structural changes and explains how IDE conformational dynamics is important to modulate the catalytic cycle of IDE. In this aim, a free-substrate IDE crystallographic structure (PDB ID: 2JG4) was used to model a complete structure of IDE. IDE stability and flexibility were studied through molecular dynamics (MD) simulations to witness IDE conformational dynamics switching from a closed to an open state. The description of IDE structural changes was achieved by analysis of the cavity and its expansion over time. Moreover, the quasi-harmonic analysis of the hinge connecting IDE domains and the angles formed over the simulations gave more insights into IDE shifts. Overall, our results could guide toward the use of different approaches to study IDE with different substrates and inhibitors, while taking into account the conformational states resolved in our study.

Pressure Adaptations in Deep-Sea Moritella Dihydrofolate Reductases: Compressibility versus Stability.

Simple SummaryDeep-sea organisms must have proteins that function under high hydrostatic pressure to survive. Adaptations used in proteins from “pressure-loving” piezophiles may include greater compressibility or greater stability against pressure-induced destabilization. However, while greater compressibility can be accomplished by greater void volume, larger cavities in a protein have been associated with greater destabilization and even unfolding as pressure is increased. Here, computer simulations of dihydrofolate reductase from a moderate piezophile and a hyperpiezophile were performed to understand the balance between adaptations for greater compressibility and those against pressure destabilization and unfolding. The results indicate that while compressibility appears to be important for deep-sea microbes, adaptation for the greatest depths may be to prevent water penetration into the interior.Proteins from “pressure-loving” piezophiles appear to adapt by greater compressibility via larger total cavity volume. However, larger cavities in proteins have been associated with lower unfolding pressures. Here, dihydrofolate reductase (DHFR) from a moderate piezophile Moritella profunda (Mp) isolated at ~2.9 km in depth and from a hyperpiezophile Moritella yayanosii (My) isolated at ~11 km in depth were compared using molecular dynamics simulations. Although previous simulations indicate that MpDHFR is more compressible than a mesophile DHFR, here the average properties and a quasiharmonic analysis indicate that MpDHFR and MyDHFR have similar compressibilities. A cavity analysis also indicates that the three unique mutations in MyDHFR are near cavities, although the cavities are generally similar in size in both. However, while a cleft overlaps an internal cavity, thus forming a pathway from the surface to the interior in MpDHFR, the unique residue Tyr103 found in MyDHFR forms a hydrogen bond with Leu78, and the sidechain separates the cleft from the cavity. Thus, while Moritella DHFR may generally be well suited to high-pressure environments because of their greater compressibility, adaptation for greater depths may be to prevent water entry into the interior cavities.

Multibasin Quasi-Harmonic Approach for the Calculation of the Configurational Entropy of Small Molecules in Solution.

Entropy is a key thermodynamic property governing most biomolecular processes, including binding. Nonetheless, quantification of the configurational entropy of a single molecule in solution remains a grand challenge. Here, we present an original approach for the calculation of absolute molecular entropies based on the analysis of converged molecular dynamics (MD) simulations. Our method, named quasi-harmonic multibasin (QHMB), relies on a multibasin decomposition of the simulated trajectory by root-mean-square deviation clustering and subsequent quasi-harmonic analysis (QHA) of extracted sub-trajectories. Last, the entropy of the landscape is evaluated using the Gibbs formula. Because of the nature of QHA, this method is directly applicable to explicit-solvent simulations to access configurational entropies in solution. When compared with calorimetric data from NIST, QHMB is shown to predict absolute entropies in the gas phase for 23 small molecules with a root-mean-squared error of 0.36 kcal/mol from the experiments. In addition, the introduction of a QHMB correction in MM/GBSA calculations to account for the ligand configurational entropy loss on binding is shown to improve the correlation between calculated and experimental binding affinities with R2 increasing from 0.67 to 0.78. Because this entropy correction penalizes large and flexible ligands more strongly, it might be useful to reduce the false-positive rate in virtual screening. The availability of an automatic procedure to compute QHMB entropies makes it a new available tool in the field of drug discovery.

Entropy of Proteins Using Multiscale Cell Correlation.

A new multiscale method is presented to calculate the entropy of proteins from molecular dynamics simulations. Termed Multiscale Cell Correlation (MCC), the method decomposes the protein into sets of rigid-body units based on their covalent-bond connectivity at three levels of hierarchy: molecule, residue, and united atom. It evaluates the vibrational and topographical entropy from forces, torques, and dihedrals at each level, taking into account correlations between sets of constituent units that together make up a larger unit at the coarser length scale. MCC gives entropies in close agreement with normal-mode analysis and smaller than those using quasiharmonic analysis as well as providing much faster convergence. Moreover, MCC provides an insightful decomposition of entropy at each length scale and for each type of amino acid according to their solvent exposure and whether they are terminal residues. While the residue entropy depends weakly on solvent exposure, there is greater variation in entropy components for larger, more polar amino acids, which have increased conformational entropy but reduced vibrational entropy with greater solvent exposure.

Thermodynamic stability and vibrational anharmonicity of black phosphorene—beyond quasi-harmonic analysis

Thermodynamic stability and vibrational anharmonicity of single layer black phosphorene (SLBP) are studied using a spectral energy density (SED) method. At finite temperatures, SLBP sheet undergoes structural deformation due to the formation of thermally excited ripples. Thermal stability of deformed SLBP sheet is analyzed by computing finite temperature phonon dispersion, which shows that SLBP sheet is thermodynamically stable and survives the crumpling transition. To analyze the vibrational anharmonicity, temperature evolution of all zone center optic phonon modes are extracted, including experimentally forbidden IR and Raman active modes. Mode resolved phonon spectra exhibits red-shift in mode frequencies with temperature. The strong anharmonic phonon–phonon coupling is the predominant reason for the observed red-shift of phonon modes, the contribution of thermal expansion is marginal. Further, temperature sensitivity of all optic modes are analyzed by computing their first order temperature co-efficient (χ), and it can be expressed as B 2g > > > > B 1g > & B 2u > B 1u for Raman and IR active modes, respectively. The quasi-harmonic χ values are much smaller than the SED and experimental values; which substantiate that quasi-harmonic methods are inadequate, and a full anharmonic analysis is essential to explain structure and dynamics of SLBP at finite temperatures.

An Efficient Timer and Sizer of Biomacromolecular Motions

Life ticks as fast as how proteins move. Computationally expensive molecular dynamics simulation has been the only theoretical tool to gauge the time and sizes of these motions, though barely to their slowest ends. Here, we convert a computationally cheap elastic network model (ENM) into a molecular timer and sizer to gauge the slowest functional motions of structured biomolecules. Quasi-harmonic analysis, fluctuation profile matching, and the Wiener-Khintchine theorem are used to define the "time periods," t, for anharmonic principal components (PCs), which are validated by nuclear magnetic resonance (NMR) order parameters. The PCs with their respective "time periods" are mapped to the eigenvalues (λENM) of the corresponding ENM modes. Thus, the power laws t(ns)= 56.1λENM-1.6 and σ2(Å2)= 32.7λENM-3.0 can be established allowing the characterization of the timescales of NMR-resolved conformers, crystallographic anisotropic displacement parameters, and important ribosomal motions, as well as motional sizes of the latter.

Calculating free energies from the vibrational density of states function: Validation and critical assessment.

We explore and show the usefulness of the density of states function for computing vibrational free energies and free energy differences between small systems. Therefore, we compare this density of states integration method (DSI) to more established schemes such as Bennett's Acceptance Ratio method (BAR), the Normal Mode Analysis (NMA), and the Quasiharmonic Analysis (QHA). The strengths and shortcomings of all methods are highlighted with three numerical examples. Furthermore, the free energy of the ionization of ammonia and the mutation from serine to cysteine are computed using extensive ab initio molecular dynamics simulations. We conclude that DSI improves upon the other frequency-based methods (NMA and QHA) regarding the treatment of anharmonicity and yielding results comparable to BAR in all cases without the need for alchemical transformations. Low-frequency modes lead to larger errors indicating that long simulation times might be required for larger systems. In addition, we introduce the use of DSI for the localization of the vibrational free energy to specific atoms or residues, leading to insights into the underlying process, a unique feature that is only offered by this method.

Molecular dynamics simulations and linear response theories jointly describe biphasic responses of myoglobin relaxation and reveal evolutionarily conserved frequent communicators.

In this study, we provide a time-dependent mechanical model, taking advantage of molecular dynamics simulations, quasiharmonic analysis of molecular dynamics trajectories, and time-dependent linear response theories to describe vibrational energy redistribution within the protein matrix. The theoretical description explained the observed biphasic responses of specific residues in myoglobin to CO-photolysis and photoexcitation on heme. The fast responses were found to be triggered by impulsive forces and propagated mainly by principal modes <40 cm−1. The predicted fast responses for individual atoms were then used to study signal propagation within the protein matrix and signals were found to propagate ~8 times faster across helices (4076 m/s) than within the helices, suggesting the importance of tertiary packing in the sensitivity of proteins to external perturbations. We further developed a method to integrate multiple intramolecular signal pathways and discover frequent “communicators”. These communicators were found to be evolutionarily conserved including those distant from the heme.

Tuning Free Energy by Backbone Conformational Entropy: A Strategy from Disordered Proteins

Tuning Free Energy by Backbone Conformational Entropy: A Strategy from Disordered Proteins

Quasiharmonic Analysis of the Energy Landscapes of Dihydrofolate Reductase from Piezophiles and Mesophiles.

A quasiharmonic analysis (QHA) method is used to compare the potential energy landscapes of dihydrofolate reductase (DHFR) from a piezophile (pressure-loving organism), Moritella profunda (Mp), and a mesophile, Escherichia coli (Ec). The QHA method considers atomic fluctuations of the protein as motions of an atom in a local effective potential created by neighboring atoms and quantitates it in terms of effective force constants, isothermal compressibilities, and thermal expansivities. The analysis indicates that the underlying potential energy surface of MpDHFR is inherently softer than that of EcDHFR. In addition, on picosecond time scales, the energy surfaces become more similar under the growth conditions of Mp and Ec. On these time scales, DHFR behaves as expected; namely, increasing temperature makes the effective energy minimum less steep because thermal fluctuations increase the available volume, whereas increasing pressure steepens it because compression reduces the available volume. Our longer simulations show that, on nanosecond time scales, increasing temperature has a similar effect as on picosecond time scales because thermal fluctuations increase the volume even more on a longer time scale. However, these simulations also indicate that, on nanosecond time scales, pressure makes the local potential less steep, contrary to picosecond time scales. Further examination of the QHA indicates the nanosecond pressure response may originate at picosecond time scales at the exterior of the protein, which suggests that protein-water interactions may be involved. The results may lead to understanding adaptations in enzymes made by piezophiles that enable them to function at higher pressures.

Zeolite Adsorption Free Energies from ab Initio Potentials of Mean Force.

The ability of metal-exchanged zeolites to chemisorb small gas molecules is key to their performance as heterogeneous catalysts and gas-separating agents. Here, we propose and evaluate an ab initio potential of mean force (PMF) method for computing adsorption free energies of representative small molecules to Cu-exchanged sites in SSZ-13 zeolite. We show that Cu ions are mobilized by adsorbates and, as a result, computed free energies are significantly more negative than those obtained from a conventional harmonic oscillator model. PMF-derived free energies are consistent with available experiment and, in many cases, with a dynamics-based quasi-harmonic analysis (QHA). The PMF approach avoids the artificial partitioning of degrees of freedom intrinsic to the QHA. On the basis of the PMF results, we propose a simple correlation to estimate free energies from computed adsorption energies and gas-phase entropies.

Transition state-based ST6Gal I inhibitors: Mimicking the phosphodiester linkage with a triazole or carbamate through an enthalpy-entropy compensation

Human β-galactoside α-2,6-sialyltransferase I (ST6Gal I) catalyses the synthesis of sialylated glycoconjugates. Overexpression of ST6Gal I is observed in many cancers, where it promotes metastasis through altered cell surface sialylation. A wide range of sialyltransferase inhibitors have been developed, with analogues structurally similar to the transition state exhibiting the highest inhibitory activity. To improve synthetic accessibility and pharmacokinetics of previously reported inhibitors, the replacement of the charged phosphodiester linker with a potential neutral isostere such as a carbamate or a 1,2,3-triazole has been investigated. Extensive molecular dynamics simulations have demonstrated that compounds with the alternate linkers could maintain key interactions with the human ST6Gal I active site, demonstrating the potential of a carbamate or a 1,2,3-triazole as a phosphodiester isostere. Free energy perturbation calculations provided energetic evidence suggesting that the carbamate and 1,2,3-triazole were slightly more favourable than the phosphodiester. Further exploration with free energy component, quasi-harmonic and cluster analysis suggested that there is an enthalpy-entropy compensation accounting for the replacement of the flexible charged phosphodiester with a neutral and rigid isostere. Overall, these simulations provide a strong rationale for the use of a carbamate or 1,2,3-triazole as a phosphodiester isostere in the development of novel inhibitors of human ST6Gal I.

Quasiharmonic analysis of protein energy landscapes from pressure-temperature molecular dynamics simulations

Positional fluctuations of an atom in a protein can be described as motion in an effective local energy minimum created by the surrounding protein atoms. The dependence of atomic fluctuations on both temperature (T) and pressure (P) has been used to probe the nature of these minima, which are generally described as harmonic in experiments such as x-ray crystallography and neutron scattering. Here, a quasiharmonic analysis method is presented in which the P-T dependence of atomic fluctuations is in terms of an intrinsic isobaric thermal expansivity αP and an intrinsic isothermal compressibility κT. The method is tested on previously reported mean-square displacements from P-T molecular dynamics simulations of lysozyme, which were interpreted to have a pressure-independent dynamical transition Tg near 200 K and a change in the pressure dependence near 480 MPa. Our quasiharmonic analysis of the same data shows that the P-T dependence can be described in terms of αP and κT where below Tg, the temperature dependence is frozen at the Tg value. In addition, the purported transition at 480 MPa is reinterpreted as a consequence of the pressure dependence of Tg and the quasiharmonic frequencies. The former also indicates that barrier heights between substates are pressure dependent in these data. Furthermore, the insights gained from this quasiharmonic analysis, which was of the energy landscape near the native state of a protein, suggest that similar analyses of other simulations may be useful in understanding such phenomena as pressure-induced protein unfolding.

Let it bind: cyclization of Mig-6 segment 2 to target EGFR signaling in lung cancer

Activation of epidermal growth factor receptor signaling by kinase dimerization plays a crucial role in the development, progression, and metastasis of lung cancer. Tumor suppressor Mig-6 is a natural inhibitory protein of epidermal growth factor receptor signaling; the protein uses its two regions, namely segments 1 and 2, to directly interact with kinase dimerization interface and then inactivates the kinases. Here, we attempted to improve the binding capability of isolated segment 2 peptide to epidermal growth factor receptor family kinases by cyclizing the peptide. In the procedure, a disulfide bond was introduced across two ends of the peptide to constrain the peptide conformation in an antiparallel, double-stranded β-sheet. Molecular dynamics simulations indicated high-structural flexibility and intrinsic disorder associated with the linear peptide of Mig-6 segment 2, whereas its cyclized version exhibited a considerable rigidity and low mobility. Molecular mechanics/Poisson–Boltzmann surface area calculations and quasiharmonic analysis revealed that the cyclization influences kinase–peptide interaction enthalpy modestly, but can largely minimize entropy penalty upon the interaction, thus effectively restoring peptide binding free energy. Fluorescence polarization assays found no affinity of linear peptide to epidermal growth factor receptor family kinases, while a weak or moderate affinity can be observed for cyclic peptide binding to the kinases.

Importance of Protein Vibration Directionality on Function

Global protein vibrations have long been associated with protein functionality. Long-range intramolecular vibrations have been measured in proteins using anisotropic absorption in the terahertz frequency range [1,2]. These measurements directly correspond to the directionality of vibrations and show large changes in the directionality of the vibrational displacements for free chicken egg white lysozyme (CEWL) and inhibitor bound CEWL. Normal mode ensemble analysis (NMEA) and quasiharmonic analysis (QHA) calculations of the free and tri-acetylglucosamine (3NAG) bound CEWL dynamics were performed and also show large changes in vibration directionality with binding. This in spite of the calculated energy distribution showing very little change, in agreement with neutron scattering measurements. We investigate the importance of the protein directionality by extending the calculations to a double deletion mutant (DD CEWL) with an activity rate 1.4 times that of WT [3]. The deletions are far from the active site, indicating that the increased activity arises from changes in the dynamics. The calculated anisotropic spectra show large changes with mutation, whereas the energy distribution show practically no change from the WT. Similarities in the bound WT, free DD, and bound DD CEWL NMEA spectra indicate the mutation may be changing the directionality of the vibrations toward more efficient motions. Projections of the low frequency vibrations, from QHA, on the functional displacement show higher overlap of residues around Glu35 and Asp52 in the mutant system. These residues are known to be critical in CEWL functionality. The results reveal that the mutation may be steering the protein toward more functional dynamics without significantly affecting the energy distribution. [1] K.A. Niessen, et al. (2015) DOI: 10.1007/s12551-015-0168-4[2] G. Acbas, et al. (2014) DOI: 10.1038/ncomms4076[3] S. Mine, et al. (1999) DOI: 10.1006/jmbi.1999.2572. Supported by NSF (DBI 1556359, MCB 1616529) and DOE (DE-SC0016317).

Full-Band Quasi-Harmonic Analysis and Synthesis of Musical Instrument Sounds with Adaptive Sinusoids

Sinusoids are widely used to represent the oscillatory modes of musical instrument sounds in both analysis and synthesis. However, musical instrument sounds feature transients and instrumental noise that are poorly modeled with quasi-stationary sinusoids, requiring spectral decomposition and further dedicated modeling. In this work, we propose a full-band representation that fits sinusoids across the entire spectrum. We use the extended adaptive Quasi-Harmonic Model (eaQHM) to iteratively estimate amplitude- and frequency-modulated (AM–FM) sinusoids able to capture challenging features such as sharp attacks, transients, and instrumental noise. We use the signal-to-reconstruction-error ratio (SRER) as the objective measure for the analysis and synthesis of 89 musical instrument sounds from different instrumental families. We compare against quasi-stationary sinusoids and exponentially damped sinusoids. First, we show that the SRER increases with adaptation in eaQHM. Then, we show that full-band modeling with eaQHM captures partials at the higher frequency end of the spectrum that are neglected by spectral decomposition. Finally, we demonstrate that a frame size equal to three periods of the fundamental frequency results in the highest SRER with AM–FM sinusoids from eaQHM. A listening test confirmed that the musical instrument sounds resynthesized from full-band analysis with eaQHM are virtually perceptually indistinguishable from the original recordings.

Rigid Residue Scan Simulations Systematically Reveal Residue Entropic Roles in Protein Allostery.

Intra-protein information is transmitted over distances via allosteric processes. This ubiquitous protein process allows for protein function changes due to ligand binding events. Understanding protein allostery is essential to understanding protein functions. In this study, allostery in the second PDZ domain (PDZ2) in the human PTP1E protein is examined as model system to advance a recently developed rigid residue scan method combining with configurational entropy calculation and principal component analysis. The contributions from individual residues to whole-protein dynamics and allostery were systematically assessed via rigid body simulations of both unbound and ligand-bound states of the protein. The entropic contributions of individual residues to whole-protein dynamics were evaluated based on covariance-based correlation analysis of all simulations. The changes of overall protein entropy when individual residues being held rigid support that the rigidity/flexibility equilibrium in protein structure is governed by the La Châtelier’s principle of chemical equilibrium. Key residues of PDZ2 allostery were identified with good agreement with NMR studies of the same protein bound to the same peptide. On the other hand, the change of entropic contribution from each residue upon perturbation revealed intrinsic differences among all the residues. The quasi-harmonic and principal component analyses of simulations without rigid residue perturbation showed a coherent allosteric mode from unbound and bound states, respectively. The projection of simulations with rigid residue perturbation onto coherent allosteric modes demonstrated the intrinsic shifting of ensemble distributions supporting the population-shift theory of protein allostery. Overall, the study presented here provides a robust and systematic approach to estimate the contribution of individual residue internal motion to overall protein dynamics and allostery.

Dissociation of a Dynamic Protein Complex Studied by All-Atom Molecular Simulations

The process of protein complex dissociation remains to be understood at the atomic level of detail. Computers now allow microsecond timescale molecular-dynamics simulations, which make the visualization of such processes possible. Here, we investigated the dissociation process of the EphA2-SHIP2 SAM-SAM domain heterodimer complex using unrestrained all-atom molecular-dynamics simulations. Previous studies on this system have shown that alternate configurations are sampled, that their interconversion can be fast, and that the complex is dynamic by nature. Starting from different NMR-derived structures, mutants were designed to stabilize a subset of configurations by swapping ion pairs across the protein-protein interface. We focused on two mutants, K956D/D1235K and R957D/D1223R, with attenuated binding affinity compared with the wild-type proteins. In contrast to calculations on the wild-type complexes, the majority of simulations of these mutants showed protein dissociation within 2.4 μs. During the separation process, we observed domain rotation and pivoting as well as a translation and simultaneous rolling, typically to alternate and weaker binding interfaces. Several unsuccessful recapturing attempts occurred once the domains were moderately separated. An analysis of protein solvation suggests that the dissociation process correlates with a progressive loss of protein-protein contacts. Furthermore, an evaluation of internal protein dynamics using quasi-harmonic and order parameter analyses indicates that changes in protein internal motions are expected to contribute significantly to the thermodynamics of protein dissociation. Considering protein association as the reverse of the separation process, the initial role of charged/polar interactions is emphasized, followed by changes in protein and solvent dynamics. The trajectories show that protein separation does not follow a single distinct pathway, but suggest that the mechanism of dissociation is common in that it initially involves transitions to surfaces with fewer, less favorable contacts compared with those seen in the fully formed complex.

Rate turnover in mechano-catalytic coupling: A model and its microscopic origin.

A novel aspect in the area of mechano-chemistry concerns the effect of external forces on enzyme activity, i.e., the existence of mechano-catalytic coupling. Recent experiments on enzyme-catalyzed disulphide bond reduction in proteins under the effect of a force applied on the termini of the protein substrate reveal an unexpected biphasic force dependence for the bond cleavage rate. Here, using atomistic molecular dynamics simulations combined with Smoluchowski theory, we propose a model for this behavior. For a broad range of forces and systems, the model reproduces the experimentally observed rates by solving a reaction-diffusion equation for a "protein coordinate" diffusing in a force-dependent effective potential. The atomistic simulations are used to compute, from first principles, the parameters of the model via a quasiharmonic analysis. Additionally, the simulations are also used to provide details about the microscopic degrees of freedom that are important for the underlying mechano-catalysis.