Electrostatic Energetics of Bacillus subtilis Ribonuclease P Protein Determined by Nuclear Magnetic Resonance-Based Histidine pKa Measurements.

The pKa values of ionizable groups in proteins report the free energy of site-specific proton binding and provide a direct means of studying pH-dependent stability. We measured histidine pKa values (H3, H22, and H105) in the unfolded (U), intermediate (I), and sulfate-bound folded (F) states of RNase P protein, using an efficient and accurate nuclear magnetic resonance-monitored titration approach that utilizes internal reference compounds and a parametric fitting method. The three histidines in the sulfate-bound folded protein have pKa values depressed by 0.21 ± 0.01, 0.49 ± 0.01, and 1.00 ± 0.01 units, respectively, relative to that of the model compound N-acetyl-l-histidine methylamide. In the unliganded and unfolded protein, the pKa values are depressed relative to that of the model compound by 0.73 ± 0.02, 0.45 ± 0.02, and 0.68 ± 0.02 units, respectively. Above pH 5.5, H22 displays a separate resonance, which we have assigned to I, whose apparent pKa value is depressed by 1.03 ± 0.25 units, which is ∼0.5 units more than in either U or F. The depressed pKa values we observe are consistent with repulsive interactions between protonated histidine side chains and the net positive charge of the protein. However, the pKa differences between F and U are small for all three histidines, and they have little ionic strength dependence in F. Taken together, these observations suggest that unfavorable electrostatics alone do not account for the fact that RNase P protein is intrinsically unfolded in the absence of ligand. Multiple factors encoded in the P protein sequence account for its IUP property, which may play an important role in its function.

Modeling non-harmonic behavior of materials from experimental inelastic neutron scattering and thermal expansion measurements

Based on thermodynamic principles, we derive expressions quantifying the non-harmonic vibrational behavior of materials, which are rigorous yet easily evaluated from experimentally available data for the thermal expansion coefficient and the phonon density of states. These experimentally- derived quantities are valuable to benchmark first-principles theoretical predictions of harmonic and non-harmonic thermal behaviors using perturbation theory, ab initio molecular-dynamics, or Monte-Carlo simulations. We illustrate this analysis by computing the harmonic, dilational, and anharmonic contributions to the entropy, internal energy, and free energy of elemental aluminum and the ordered compound FeSi over a wide range of temperature. Results agree well with previous data in the literature and provide an efficient approach to estimate anharmonic effects in materials.

Differential scanning calorimetry in life science: thermodynamics, stability, molecular recognition and application in drug design

All biological phenomena depend on molecular recognition, which is either intermolecular like in ligand binding to a macromolecule or intramolecular like in protein folding. As a result, understanding the relationship between the structure of proteins and the energetics of their stability and binding with others (bio)molecules is a very interesting point in biochemistry and biotechnology. It is essential to the engineering of stable proteins and to the structure-based design of pharmaceutical ligands. The parameter generally used to characterize the stability of a system (the folded and unfolded state of the protein for example) is the equilibrium constant (K) or the free energy (deltaG(o)), which is the sum of enthalpic (deltaH(o)) and entropic (deltaS(o)) terms. These parameters are temperature dependent through the heat capacity change (deltaCp). The thermodynamic parameters deltaH(o) and deltaCp can be derived from spectroscopic experiments, using the van't Hoff method, or measured directly using calorimetry. Along with isothermal titration calorimetry (ITC), differential scanning calorimetry (DSC) is a powerful method, less described than ITC, for measuring directly the thermodynamic parameters which characterize biomolecules. In this article, we summarize the principal thermodynamics parameters, describe the DSC approach and review some systems to which it has been applied. DSC is much used for the study of the stability and the folding of biomolecules, but it can also be applied in order to understand biomolecular interactions and can thus be an interesting technique in the process of drug design.

The effects of thermo-electrically induced convection in alloy solidification

The effects of a constant uniform magnetic field on thermoelectric currents during dendritic solidification were investigated using a 2-dimensional enthalpy based numerical model. Using an approximation of the dendrite growing in free space it was found that the resulting Lorentz force generates a circulating flow influencing the solidification pattern. As the magnetic field strength increases it was found that secondary growth on the clockwise side of the primary arm of the dendrite was encouraged, while the anticlockwise side is suppressed due to a reduction in local free energy. The preferred direction of growth rotated in the clockwise sense under an anti-clockwise flow for both the binary alloy and pure material. The tip velociy is significantly increased compared to growth in stagnant flow. This is due to a small recirculation that follows the tip of the dendrite; bringing in colder liquid and lower concentrations of solute. The recirculation being not normally incident on the tip is most likely the cause for the rotation. Grain growth consisting of multiple seeds with the same anisotropy growing in the same plane, gives a competition to release latent heat resulting in stunted growth. The initial growth for each dendrite is very similar to the single seed cases indicating that dendrites must become before the thermoelectric interactions are significant.

Thermoelectric MHD effects on equiaxed crystal morphology

The effects of a constant uniform magnetic field on a growing equiaxed crystal are investigated using a 3-dimensional enthalpy based numerical model. Two cases are considered: The first case looks at unconstrained growth, where the current density is generated through the thermo-electric effect and the current circulates between the tips and roots of the dendrite, the second represents an imposed potential difference across the domain. A jump in the electrical conductivity between the liquid and solid causes the current density to be non uniform. In both cases the resulting Lorentz force drives fluid flow in the liquid phase, this in turn causes advection of the thermal and solute field altering the free energy close to the interface and changing the morphology of the dendrite. In the first case the flow field is complex comprising of many circulations, the morphological changes are modelled using a 2D model with a quasi 3D approximation. The second case is comparable to classic problems involving a constant velocity boundary.

Effects of magnetic fields on crystal growth

The effects of a constant uniform magnetic field on thermoelectric currents during dendritic solidification were investigated using a two-dimensional enthalpy based numerical model. Using an approximation for three-dimensional unconstricted growth, the resulting Lorentz forces generate a circulating flow influencing the solidification pattern. Under the presence of a strong magnetic field secondary growth on the clockwise side of the primary arm of the dendrite was encouraged, whereas the anticlockwise side is suppressed due to a reduction in local free energy. The preferred direction of growth rotated in the clockwise sense under an anticlockwise flow. The tip velocity is significantly increased compared with growth in stagnant flow. This is due to a small recirculation at the tip of the dendrite; bringing in colder liquid and lowering the concentration of solute.

Determination of micelle/water partition coefficients and associated thermodynamic data for dialkyl phthalate esters

Micelle/water partition coefficients for three dialkyl phthalate esters - dimethyl phthalate ester (DMP), diethyl phthalate ester (DEP) and dipropyl phthalate ester (DPP) were obtained by micellar liquid chromatography (MLC). Experiments were conducted over a temperature range which led to calculation of a Gibbs free energy, enthalpy and entropy of transfer for the phthalate esters. In addition, small angle neutron scattering (SANS) experiments were conducted with no substantial change observed in micelle size before and after phthalate ester incorporation. Overall, a novel method for obtaining thermodynamic information, based on partitioning data, has been developed for dialkyl phthalate esters using micellar liquid chromatography.

A Phase-field Model for Computer Simulation of Lamellar Structure Formation in y-TiAI

In the present paper, a phase-field model is developed to simulate the formation and evolution of lamellar microstructure in γ-TiAl alloys. The mechanism of formation of TiAl lamellae proposed by Denquin and Naka is incorporated into the model. The model describes the formation and evolution of the face-centered cubic (fcc) stacking lamellar zone followed by the subsequent appearance and growth of the γ-phase, involving both the chemical composition change by atom transfer and the ordering of the fcc lattice. The thermodynamics of the model system and the interaction between the displacive and diffusional transformations are described by a non-equilibrium free energy formulated as a function of concentration and structural order parameter fields. The long-range elastic interactions, arising from the lattice misfit between the α, fcc (A1) and the various orientation variants of the γ-phase are taken into account by incorporating of the elastic strain energy into the total free energy. Simulation studies based on the model successfully predicted some essential features of the lamellar structure. It is found that the formation and evolution of the lamellar structure are predominantly controlled by the minimization of the elastic energy of the interfaces between the different fcc stacking groups, low-symmetry product phase γ and the high-symmetry α-phase, as well as between the various orientation variants of the product phase.

Stability of Sr adatom model structures for SrTiO3(001) surface reconstructions

We report results of first-principles calculations on the thermodynamic stability of different Sr adatom structures that have been proposed to explain some of the observed reconstructions of the (001) surface of strontium titanate (Kubo and Nozoye 2003 Surf Sci. 542 177). From surface free energy calculations, a phase diagram is constructed indicating the range of conditions over which each structure is most stable. These results are compared with Kubo and Nozoye's experimental observations. It is concluded that low Sr adatom coverage structures can only be explained if the surface is far from equilibrium. Intermediate coverage structures are stable only if the surface is in or very nearly in equilibrium with the strontium oxide.

Kinetics of phase transformations in a model with metastable fluid-fluid separation: A molecular dynamics study

By molecular dynamics (MD) simulations we study the crystallization process in a model system whose particles interact by a spherical pair potential with a narrow and deep attractive well adjacent to a hard repulsive core. The phase diagram of the model displays a solid-fluid equilibrium, with a metastable fluid-fluid separation. Our computations are restricted to fairly small systems (from 2592 to 10368 particles) and cover long simulation times, with constant energy trajectories extending up to 76x10(6) MD steps. By progressively reducing the system temperature below the solid-fluid line, we first observe the metastable fluid-fluid separation, occurring readily and almost reversibly upon crossing the corresponding line in the phase diagram. The nucleation of the crystal phase takes place when the system is in the two-fluid metastable region. Analysis of the temperature dependence of the nucleation time allows us to estimate directly the nucleation free energy barrier. The results are compared with the predictions of classical nucleation theory. The critical nucleus is identified, and its structure is found to be predominantly fcc. Following nucleation, the solid phase grows steadily across the system, incorporating a large number of localized and extended defects. We discuss the relaxation processes taking place both during and after the crystallization stage. The relevance of our simulation for the kinetics of protein crystallization under normal experimental conditions is discussed. (C) 2002 American Institute of Physics.

A dielectric continuum molecular dynamics method

We introduce a novel method to simulate hydrated macromolecules with a dielectric continuum representation of the surrounding solvent. In our approach, the interaction between the solvent and the molecular degrees of freedom is described by means of a polarization density free energy functional which is minimum at electrostatic equilibrium. After a pseudospectral expansion of the polarization and a discretization of the functional, we construct the equations of motion for the system based on a Car-Parrinello technique. In the limit of the adiabatic evolution of the polarization field variables, our method provides the solution of the dielectric continuum problem "on the fly," while the molecular coordinates are propagated. In this first study, we show how our dielectric continuum molecular dynamics method can be successfully applied to hydrated biomolecules, with low cost compared to free energy simulations with explicit solvent. To our knowledge, this is the first time that stable and conservative molecular dynamic simulations of solutes can be performed for a dielectric continuum model of the solvent. (C) 2001 American Institute of Physics.

Determining the electronic structure and chemical potentials of molecules in solution

A simulation scheme is proposed for determining the excess chemical potential of a substance in solution. First, a Monte Carlo simulation is performed with classical models for solute and solvent molecules. A representative sample of these configurations is then used in a hybrid quantum/classical (QM/MM) calculation, where the solute is treated quantum-mechanically, and the average electronic structure is used to construct an improved classical model. This procedure is iterated to self-consistency in the classical model, which in practice is attained in one or two steps, depending on the quality of the initial guess. The excess free energy of the molecule within the QM/MM approach is determined relative to the classical model using thermodynamic perturbation theory with a cumulant expansion. The procedure provides a method of constructing classical point charge models appropriate for the solution and gives a measure of the importance of solvent fluctuations.

Concertedness and solvent effects in multiple proton transfer reactions: The formic acid dimer in solution

The issue of multiple proton transfer (PT) reactions in solution is addressed by performing molecular dynamics simulations for a formic acid dimer embedded in a water cluster. The reactant species is treated quantum mechanically, within a density functional approach, while the solvent is represented by a classical model. By constraining different distances within the dimer we analyze the PT process in a variety of situations representative of more complex environments. Free energy profiles are presented, and analyzed in terms of typical solvated configurations extracted from the simulations. A decrease in the PT barrier height upon solvation is rationalized in terms of a transition state which is more polarized than the stable states. The dynamics of the double PT process is studied in a low-barrier case and correlated with solvent polarization fluctuations. Cooperative effects in the motion of the two protons are observed in two different situations: when the solvent polarization does not favor the transfer of one of the two protons and when the motion of the two protons is not synchronized. This body of observations is correlated with local structural and dynamical properties of the solvent in the vicinity of the reactant. (C) 2000 American Institute of Physics. [S0021-9606(00)51121-0].

Solvation Structure and Transport of Acidic Protons in Ionic Liquids: A First-principles Simulation Study

Ab initio simulations of a single molecule of HCl in liquid dimethyl imidazolium chloride [dmim][Cl] show that the acidic proton exists as a symmetric, linear ClHCl- species. Details of the solvation structure around this molecule are given. The proton-transfer process was investigated by applying a force along the antisymmetric stretch coordinate until the molecule broke. Changes in the free energy and local solvation structure during this process were investigated. In the reaction mechanism identified, a free chloride approaches the proton from the side. As the original ClHCl- distorts and the incoming chloride forms a new bond to the proton, one of the original chlorine atoms is expelled and a new linear molecule is formed.

Neutral and Charged 1-Butyl-3-methylimidazolium Triflate Clusters: Equilibrium Concentration in the Vapor Phase and Thermal Properties of Nanometric Droplets

Ground state energy, structure, and harmonic vibrational modes of 1-butyl-3-methylimidazolium triflate ([bmim][Tf]) clusters have been computed using an all-atom empirical potential model. Neutral and charged species have been considered up to a size (30 [bmim][Tf] pairs) well into the nanometric range. Free energy computations and thermodynamic modeling have been used to predict the equilibrium composition of the vapor phase as a function of temperature and density. The results point to a nonnegligible concentration of very small charged species at pressures (P ~ 0.01 Pa) and temperatures (T 600 K) at the boundary of the stability range of [bmim][Tf]. Thermal properties of nanometric neutral droplets have been investigated in the 0 T 700 K range. A near-continuous transition between a liquidlike phase at high T and a solidlike phase at low T takes place at T ~ 190 K in close correspondence with the bulk glass point Tg ~ 200 K. Solidification is accompanied by a transition in the dielectric properties of the droplet, giving rise to a small permanent dipole embedded into the solid cluster. The simulation results highlight the molecular precursors of several macroscopic properties and phenomena and point to the close competition of Coulomb and dispersion forces as their common origin.