Vibrational Entropy Change Research Articles

Rigidity Theory-Based Approximation of Vibrational Entropy Changes upon Binding to Biomolecules.

We introduce a computationally efficient approximation of vibrational entropy changes (ΔSvib) upon binding to biomolecules based on rigidity theory. From constraint network representations of the binding partners, ΔSvib is estimated from changes in the number of low frequency ("spongy") modes with respect to changes in the networks' coordination number. Compared to ΔSvib computed by normal-mode analysis (NMA), our approach yields significant and good to fair correlations for data sets of protein-protein and protein-ligand complexes. Our approach could be a valuable alternative to NMA-based ΔSvib computation in end-point (free) energy methods.

Dynamic Coarse-Graining of DNA Melting Kinetics: Enthalpic and Entropic Effects of Cooperative Base-Pair Dynamics

Thermodynamics and kinetics are two fundamental aspects of DNA melting and annealing. The thermodynamics of DNA duplex melting, dominated by states involving either strongly bound duplexes or widely separated strands, are well characterized and can be described by two-state models. On the other hand, kinetics involve the rarely visited intermediate states and are therefore harder to understand. Melting kinetics involve large enough time scales to prevent meaningful studies through all-atom molecular dynamics (MD) simulations, leading to the need to develop coarse-grained models. Existing coarse-grained models described well the thermodynamic melting temperature and near-equilibrium phenomena such as bubble formation and sharp phase transitions. However, the predicted kinetic rates were off by several orders of magnitude because they do not capture non-equilibrium cooperative dynamics near the transition state such as coupling among base unstacking, hydration cage vibration/breakup, and the untwisting of the helix. In this work, an MD dynamic coarse-graining approach is developed to analyze the correct melting kinetics of short DNA sequences. By projecting the dynamics onto the one-dimensional cooperative reaction coordinate based on time-scale separation, we decipher the sequential triggering of several key events that determine the successive changes in enthalpy, vibrational entropy, and configurational entropy towards the melting barrier. This results in a Fick-Jacobs “inverted-funnel” transition state theory which allows us to use all-atom MD simulations, principal component analysis, and elastic homogenization theory to identify the enthalpies and entropies at strategic locations along the reaction coordinate and to estimate the melting rate in agreement with experimental results.

Quantum Chemical Insight into the Interactions and Thermodynamics Present in Choline Chloride Based Deep Eutectic Solvents.

We report quantum chemical calculations performed on three popular deep eutectic solvents (DESs) in order to elucidate the molecular interactions, charge transfer interactions, and thermodynamics associated with these systems. The DESs studied comprise 1:2 choline chloride/urea (reline), 1:2 choline chloride/ethylene glycol (ethaline), and 1:1 choline chloride/malonic acid (maloline). The excellent correlation between calculated and experimental vibrational spectra allowed for identification of dominant interactions in the DES systems. The DESs were found to be stabilized by both conventional hydrogen bonds and C-H···O/C-H···π interactions between the components. The hydrogen-bonding network established in the DES is clearly distinct from that which exists within the neat hydrogen-bond donor dimer. Charge decomposition analysis indicates significant charge transfer from choline and chloride to the hydrogen-bond donor with a higher contribution from the cation, and a density of states analysis confirms the direction of the charge transfer. Consequently, the sum of the bond orders of the choline-Cl(-) interactions in the DESs correlates directly with the melting temperatures of the DESs, a correlation that offers insight into the effect of the tuning of the choline-Cl(-) interactions by the hydrogen-bond donors on the physical properties of the DESs. Finally, the differences in the vibrational entropy changes upon DES formation are consistent with the trend in the overall entropy changes upon DES formation.

ENCoM server: exploring protein conformational space and the effect of mutations on protein function and stability.

ENCoM is a coarse-grained normal mode analysis method recently introduced that unlike previous such methods is unique in that it accounts for the nature of amino acids. The inclusion of this layer of information was shown to improve conformational space sampling and apply for the first time a coarse-grained normal mode analysis method to predict the effect of single point mutations on protein dynamics and thermostability resulting from vibrational entropy changes. Here we present a web server that allows non-technical users to have access to ENCoM calculations to predict the effect of mutations on thermostability and dynamics as well as to generate geometrically realistic conformational ensembles. The server is accessible at: http://bcb.med.usherbrooke.ca/encom.

Uranyl (VI) and neptunyl (V) incorporation in carbonate and sulfate minerals: Insight from first-principles

The incorporation of radionuclides into low-temperature mineral hosts may strongly influence the concentration and migration of radioactive contaminants in the subsurface. One difficulty in evaluating the thermodynamics of incorporation is that experiments are often performed at high supersaturations and typically do not reach equilibrium. An alternative way to obtain the equilibrium thermodynamics is the quantum–mechanical analysis of the mineral host and the incorporated species before and after incorporation. In this contribution, density functional theory is used to calculate the energetics, resulting structures, and electronic configuration of uranyl (UO22+) and neptunyl (NpO2+) incorporation into sulfate and carbonate minerals. In each host mineral, gypsum (CaSO4·2H2O), anhydrite (CaSO4), anglesite (PbSO4), celestine (SrSO4), barite (BaSO4), calcite (CaCO3), aragonite (CaCO3), cerussite (PbCO3), strontianite (SrCO3), and witherite (BaCO3), a divalent cation is replaced with either UO22+ or NpO2+ (in the case of neptunyl, charge balance is maintained with an additional hydrogen ion). The source of the actinyl ion and the sink for the host cation are modeled as both solid and aqueous phases, the latter of which requires an expansion of previous descriptions of incorporation. By combining periodic and cluster computational methods, this newly-developed approach enables the quantum–mechanical simulation of reactions between charged, aqueous molecular species and solid mineral phases.Among the host minerals considered, gypsum and aragonite are the most favorable hosts for both uranyl and neptunyl uptake (ΔEgyp,aqU=0.19eV and ΔEarag,aqU=0.27eV for incorporation from aqueous species compared with ΔEgyp,solidU=1.88eV and ΔEgyp,solidU=1.94eV if solid sources and sinks are used; for neptunyl incorporation, ΔEgyp,aqNp=0.36eV, ΔEgyp,solidNp=3.29eV; ΔEarag,aqNp=0.10eV, and ΔEarag,solidNp=3.02eV). Incorporation into a vacancy site, for example by filling a cation–anion vacancy with a uranyl-(CO32−, SO42−) or neptunyl-(Cl−, HCO3−, HSO4−) pair, is energetically more favorable than cation substitution, mainly due to the thermodynamic instability of the defect site.Uranyl and neptunyl incorporation decreases the band gap on the order of 3–5eV by creating mid-bandgap states. The band gap for aragonite without actinyl incorporation is 4.35eV; with UO22+ incorporation the band gap decreases to 1.12eV and with NpO2+ incorporation to 1.08eV. For anhydrite, the band gap decreases from 6.39eV (no incorporation) to 2.24eV for UO22+ incorporation and to 1.04eV for NpO2+ incorporation. Vibrational entropy changes during incorporation from solid sources were calculated for selected examples; however, the entropy contribution does not significantly lower the reaction Gibbs free energy relative to the enthalpy of incorporation. TΔS ranges from 0.01eV for calcite to 0.04eV for anglesite at room temperature. This correction is relatively small compared with other sources of error, in particular variations between different approaches to calculate hydration energies. While the presented approach may still include sources of uncertainty, especially with regard to changes in entropy and hydration, this methodology has promise as a valuable complement to determine the energetics of incorporation reactions.

Application of density functional theory calculations to the statistical mechanics of normal and anomalous melting

Density functional theory (DFT) calculations reliably aid in understanding the relative stability of different crystal phases as functions of pressure and temperature. Our purpose here is to employ DFT to analyze the character of the melting process, with an emphasis on comparing normal and anomalous melting. The normal-anomalous distinction is the absence or presence, respectively, of a significant electronic structure change between crystal and liquid. We study the normal melters Na and Cu, which are metallic in both phases, and the anomalous melter Ga, which has a partially covalent crystal and a nearly free-electron liquid. We calculate free energies from lattice dynamics for the crystal and from vibration-transit (V-T) theory for the liquid, where the liquid formulation is similar to that of the crystal but has an additional term representing the diffusive transits. Internal energies $U$ and entropies $S$ calculated for both phases of Na and Cu were previously shown to be in good agreement with experiment; here we find the same agreement for Ga. The dominant theoretical terms in the melting $\ensuremath{\Delta}U$ and $\ensuremath{\Delta}S$ are the structural potential energy, the vibrational entropy, and the purely liquid transit terms in both $U$ and $S$. The melting changes in structural energy and vibrational entropy are much larger in Ga than in Na and Cu. This behavior arises from the change in electronic structure in Ga, and is the identifying characteristic of anomalous melting. We interpret our DFT results in terms of the physical effects of the relatively few covalent bonds in the otherwise metallic Ga crystal.

The role of vibrations in thermodynamic properties of Cu-Ni alloys

We report results of a systematic study for vibrational thermodynamic functions of Cu-Ni alloys, in the harmonic approximation, using interaction potentials based on the embedded atom method with improved optimization techniques. The vibrational density of states of the systems is calculated using real space Green’s function method. From an investigation of local force fields we found that increasing Ni concentration in the alloy substantially stiffens the force experienced by Cu atoms compared to that of Ni atoms. Our calculations also reveal that vibrational entropy change between ordered and disordered crystals of Cu-Ni is negligible. However, the mixing entropy of the phonons and electronic states is found to be negative and favors un-mixing, and thus contributes to the miscibility gap.

ATP-Induced Conformational Changes of Nucleotide-Binding Domains in an ABC Transporter. Importance of the Water-Mediated Entropic Force

ATP binding cassette (ABC) proteins belong to a superfamily of active transporters. Recent experimental and computational studies have shown that binding of ATP to the nucleotide binding domains (NBDs) of ABC proteins drives the dimerization of NBDs, which, in turn, causes large conformational changes within the transmembrane domains (TMDs). To elucidate the active substrate transport mechanism of ABC proteins, it is first necessary to understand how the NBD dimerization is driven by ATP binding. In this study, we selected MalKs (NBDs of a maltose transporter) as a representative NBD and calculated the free-energy change upon dimerization using molecular mechanics calculations combined with a statistical thermodynamic theory of liquids, as well as a method to calculate the translational, rotational, and vibrational entropy change. This combined method is applied to a large number of snapshot structures obtained from molecular dynamics simulations containing explicit water molecules. The results suggest that the NBD dimerization proceeds with a large gain of water entropy when ATP molecules bind to the NBDs. The energetic gain arising from direct NBD-NBD interactions is canceled by the dehydration penalty and the configurational-entropy loss. ATP hydrolysis induces a loss of the shape complementarity between the NBDs, which leads to the dissociation of the dimer, due to a decrease in the water-entropy gain and an increase in the configurational-entropy loss. This interpretation of the NBD dimerization mechanism in concert with ATP, especially focused on the water-mediated entropy force, is potentially applicable to a wide variety of the ABC transporters.

Nonharmonic phonons inα-iron at high temperatures

Phonon densities of states (DOS) of bcc $\alpha$-$^{57}$Fe were measured from room temperature through the 1044K Curie transition and the 1185K fcc $\gamma$-Fe phase transition using nuclear resonant inelastic x-ray scattering. At higher temperatures all phonons shift to lower energies (soften) with thermal expansion, but the low transverse modes soften especially rapidly above 700K, showing strongly nonharmonic behavior that persists through the magnetic transition. Interatomic force constants for the bcc phase were obtained by iteratively fitting a Born-von K\'{a}rm\'{a}n model to the experimental phonon spectra using a genetic algorithm optimization. The second-nearest-neighbor fitted axial force constants weakened significantly at elevated temperatures. An unusually large nonharmonic behavior is reported, which increases the vibrational entropy and accounts for a contribution of 35 meV/atom in the free energy at high temperatures. The nonharmonic contribution to the vibrational entropy follows the thermal trend of the magnetic entropy, and may be coupled to magnetic excitations. A small change in vibrational entropy across the $\alpha$-$\gamma$ structural phase transformation is also reported.

Elasticity of cerium up to 4.4 GPa by sound velocity measurements under hydrostatic pressure

We report here the longitudinal and shear sound velocities on polycrystalline cerium under hydrostatic pressure across the iso-structural γ-α phase transition up to 4.4 GPa. Comparing with previous methods, the pressure-density relation of Ce has been calculated by integrating with the initial travel time and pressure without any fitting. The pressure correction of the Grüneisen parameter and linear expansion coefficient are taken into account during the integration process. The sound velocities, bulk modulus, shear modulus, Debye temperature, and vibrational entropy are achieved and have been compared with previous results. The bulk modulus of cerium in α phase agrees with the previous results determined by neutron and x-ray diffraction. The Debye temperature above and below the phase transition are and , respectively. The difference of the Debye temperature from respective experiment is found and has been expounded. We consider that the vibrational entropy change per atom of 0.44 kB as the Kondo collapse of 17% volume change, and 0.70 kB as the total change from γ phase to complete α phase.

Exhaustive docking and solvated interaction energy scoring: lessons learned from the SAMPL4 challenge

We continued prospective assessments of the Wilma-solvated interaction energy (SIE) platform for pose prediction, binding affinity prediction, and virtual screening on the challenging SAMPL4 data sets including the HIV-integrase inhibitor and two host-guest systems. New features of the docking algorithm and scoring function are tested here prospectively for the first time. Wilma-SIE provides good correlations with actual binding affinities over a wide range of binding affinities that includes strong binders as in the case of SAMPL4 host-guest systems. Absolute binding affinities are also reproduced with appropriate training of the scoring function on available data sets or from comparative estimation of the change in target's vibrational entropy. Even when binding modes are known, SIE predictions lack correlation with experimental affinities within dynamic ranges below 2 kcal/mol as in the case of HIV-integrase ligands, but they correctly signaled the narrowness of the dynamic range. Using a common protein structure for all ligands can reduce the noise, while incorporating a more sophisticated solvation treatment improves absolute predictions. The HIV-integrase virtual screening data set consists of promiscuous weak binders with relatively high flexibility and thus it falls outside of the applicability domain of the Wilma-SIE docking platform. Despite these difficulties, unbiased docking around three known binding sites of the enzyme resulted in over a third of ligands being docked within 2 Å from their actual poses and over half of the ligands docked in the correct site, leading to better-than-random virtual screening results.

Changes in vibrational entropy during the early stages of chemical unmixing in fcc Cu–6% Fe

A nanocrystalline face-centered cubic (fcc) solid solution of 6% Fe in Cu was prepared by high-energy ball milling, and annealed at temperatures from 200 to 360°C to induce chemical unmixing. The chemical state of the material was characterized by three-dimensional atom probe microscopy, Mössbauer spectrometry and X-ray powder diffractometry. The unmixing was heterogeneous, with iron atoms forming iron-rich zones that thicken with further annealing. The phonon partial density of states (pDOS) of 57Fe was measured by nuclear resonant inelastic X-ray scattering, showing the pDOS of the as-prepared material to be that of an fcc crystal. The features of this pDOS became broader in the early stages of unmixing, but only small changes in average phonon frequencies occurred until the body-centered cubic (bcc) phase began to form. The vibrational entropy calculated from the pDOS underwent little change during the early stage of annealing, but decreased rapidly when the bcc phase formed in the material.

Phonons of the anomalous element cerium.

Many physical and chemical properties of the light rare-earths and actinides are governed by the active role of f electrons, and despite intensive efforts the details of the mechanisms of phase stability and transformation are not fully understood. A prominent example which has attracted a lot of interest, both experimentally and theoretically over the years is the isostructural γ - α transition in cerium. We have determined by inelastic X-ray scattering, the complete phonon dispersion scheme of elemental cerium across the γ → α transition, and compared it with theoretical results using ab initio lattice dynamics. Several phonon branches show strong changes in the dispersion shape, indicating large modifications in the interactions between phonons and conduction electrons. This is reflected as well by the lattice Grüneisen parameters, particularly around the X point. We derive a vibrational entropy change ΔS(γ-α)(vib) ≈ (0.33+/-0.03)k(B), illustrating the importance of the lattice contribution to the transition. Additionally, we compare first principles calculations with the experiments to shed light on the mechanism underlying the isostructural volume collapse in cerium under pressure.

Effects of chemical composition and B2 order on phonons in bcc Fe–Co alloys

The phonon density of states (DOS) gives insight into interatomic forces and provides the vibrational entropy, making it a key thermodynamic function for understanding alloy phase transformations. Nuclear resonant inelastic x-ray scattering and inelastic neutron scattering were used to measure the chemical dependence of the DOS of bcc Fe–Co alloys. For the equiatomic alloy, the A2→B2 (chemically disordered→chemically ordered) phase transformation caused measurable changes in the phonon spectrum. The measured change in vibrational entropy upon ordering was −0.02±0.02 kB/atom, suggesting that vibrational entropy results in a reduction in the order–disorder transition temperature by 60±60 K. The Connolly–Williams cluster inversion method was used to obtain interaction DOS (IDOS) curves that show how point and pair variables altered the phonon DOS of disordered bcc Fe–Co alloys. These IDOS curves accurately captured the change in the phonon DOS and vibrational entropy of the B2 ordering transition.

Lattice dynamics and phase transition of NiTi alloy

We have performed detailed first-principles calculations to investigate the structural and lattice dynamical properties of NiTi alloy. The calculated static structures consist well with the experimental data and other theoretical results. With quasi harmonic approximation, the phase boundary between B19′ and BCO phases can be described as a five order polynomial T = 100 − 89.28 P + 296.75 P 2 − 717.94 P 3 + 734.62 P 4 − 274.25 P 5 . The change of vibrational entropy is 0.07 k B /atom at the transition temperature 100 K under zero pressure.

Free energy calculations of glycosaminoglycan–protein interactions

Glycosaminoglycans (GAGs) are complex highly charged linear polysaccharides that have a variety of roles in biological processes. We report the first use of molecular dynamics (MD) free energy calculations using the MM/PBSA method to investigate the binding of GAGs to protein molecules, namely the platelet endothelial cell adhesion molecule 1 (PECAM-1) and annexin A2. Calculations of the free energy of the binding of heparin fragments of different sizes reveal the existence of a region of low GAG-binding affinity in domains 5-6 of PECAM-1 and a region of high affinity in domains 2-3, consistent with experimental data and ligand-protein docking studies. A conformational hinge movement between domains 2 and 3 was observed, which allows the binding of heparin fragments of increasing size (pentasaccharides to octasaccharides) with an increasingly higher binding affinity. Similar simulations of the binding of a heparin fragment to annexin A2 reveal the optimization of electrostatic and hydrogen bonding interactions with the protein and protein-bound calcium ions. In general, these free energy calculations reveal that the binding of heparin to protein surfaces is dominated by strong electrostatic interactions for longer fragments, with equally important contributions from van der Waals interactions and vibrational entropy changes, against a large unfavorable desolvation penalty due to the high charge density of these molecules.

Neutron diffraction study on γ ↔ α phase transition in Ce0.9Th0.1 alloy

Comprehensive neutron diffraction measurements were performed to study the isostructural γ ↔ α phase transition in Ce0.9Th0.1 alloy. Using Rietveld refinements, we obtained lattice and thermal parameters as a function of temperature. From the temperature slope of the thermal parameters, we determined Debye temperatures =133(1) K and =140(1) K for the γ phase and the α phase, respectively. This result implies that the vibrational entropy change is not significant at the γ ↔ α transition, contrary to that from elemental Cerium [I.-K. Jeong, T.W. Darling, M.J. Graf et al., Phys. Rev. Lett. 92 (2004) p.105702].

Large ground-state entropy changes for hydrogen atom transfer reactions of iron complexes.

Reported herein are the hydrogen atom transfer (HAT) reactions of two closely related dicationic iron tris(alpha-diimine) complexes. FeII(H2bip) (iron(II) tris[2,2'-bi-1,4,5,6-tetrahydropyrimidine]diperchlorate) and FeII(H2bim) (iron(II) tris[2,2'-bi-2-imidazoline]diperchlorate) both transfer H* to TEMPO (2,2,6,6-tetramethyl-1-piperidinoxyl) to yield the hydroxylamine, TEMPO-H, and the respective deprotonated iron(III) species, FeIII(Hbip) or FeIII(Hbim). The ground-state thermodynamic parameters in MeCN were determined for both systems using both static and kinetic measurements. For FeII(H2bip) + TEMPO, DeltaG degrees = -0.3 +/- 0.2 kcal mol-1, DeltaH degrees = -9.4 +/- 0.6 kcal mol-1, and DeltaS degrees = -30 +/- 2 cal mol-1 K-1. For FeII(H2bim) + TEMPO, DeltaG degrees = 5.0 +/- 0.2 kcal mol-1, DeltaH degrees = -4.1 +/- 0.9 kcal mol-1, and DeltaS degrees = -30 +/- 3 cal mol-1 K-1. The large entropy changes for these reactions, |TDeltaS degrees | = 9 kcal mol-1 at 298 K, are exceptions to the traditional assumption that DeltaS degrees approximately 0 for simple HAT reactions. Various studies indicate that hydrogen bonding, solvent effects, ion pairing, and iron spin equilibria do not make major contributions to the observed DeltaS degrees HAT. Instead, this effect arises primarily from changes in vibrational entropy upon oxidation of the iron center. Measurement of the electron-transfer half-reaction entropy, |DeltaS degrees Fe(H2bim)/ET| = 29 +/- 3 cal mol-1 K-1, is consistent with a vibrational origin. This conclusion is supported by UHF/6-31G* calculations on the simplified reaction [FeII(H2N=CHCH=NH2)2(H2bim)]2+...ONH2 left arrow over right arrow [FeII(H2N=CHCH=NH2)2(Hbim)]2+...HONH2. The discovery that DeltaS degrees HAT can deviate significantly from zero has important implications on the study of HAT and proton-coupled electron-transfer (PCET) reactions. For instance, these results indicate that free energies, rather than enthalpies, should be used to estimate the driving force for HAT when transition-metal centers are involved.

Theoretical insight of adsorption thermodynamics of multifunctional molecules on metal surfaces

Adsorption thermodynamics based on density functional theory (DFT) calculations are exposed for the interaction of several multifunctional molecules with Pt and Au(1 1 0)-(1 × 2) surfaces. The Gibbs free adsorption energy explicitly depends on the adsorption internal energy, which is derived from DFT adsorption energy, and the vibrational entropy change during the chemisorption process. Zero-point energy (ZPE) corrections have been systematically applied to the adsorption energy. Moreover the vibrational entropy change has been computed on the basis of DFT harmonic frequencies (gas and adsorbed phases, clean surfaces), which have been extended to all the adsorbate vibrations and the metallic surface phonons. The phase diagrams plotted in realistic conditions of temperature (from 100 to 400 K) and pressure (0.15 atm) show that the ZPE corrected adsorption energy is the main contribution. When strong chemisorption is considered on the Pt surface, the multifunctional molecules are adsorbed on the surface in the considered temperature range. In contrast for weak chemisorption on the Au surface, the thermodynamic results should be held cautiously. The systematic errors of the model (choice of the functional, configurational entropy and vibrational entropy) make difficult the prediction of the adsorption–desorption phase boundaries.

Vibrational entropy of the γ−α martensitic transformation in Fe71Ni29

The low-temperature martensitic phase transformation in Fe71Ni29 was studied by X-ray diffractometry, differential scanning calorimetry (DSC) and inelastic neutron scattering. From inelastic neutron scattering spectra, the phonon density of states of the high-temperature austenite and low-temperature martensite were obtained, showing a substantial stiffening in the martensite phase. The change in vibrational entropy associated with this stiffening was found to be . Using published results for the Fe partial density of states in disordered BCC Fe–Ni of similar composition, a Ni partial density of states was obtained, which shows a significant number of modes at much lower energies than its Fe counterpart. The martensitic and reverse-martensitic transformations occur at different temperatures and the total entropies of transformation were measured by DSC for both. From these measurements and published magnetisation results for this alloy, it is found that the change in magnetic entropy is twice as large as the phonon contribution in the reverse martensitic transformation, accounting for the inequality of the total entropies of the forward and reverse transformations.