A constant entropy increase model for the selection of parallel tempering ensembles

The present paper explores a simple approach to the question of parallel tempering temperature selection. We argue that to optimize the performance of parallel tempering it is reasonable to require that the increase in entropy between successive temperatures be uniform over the entire ensemble. An estimate of the system's heat capacity, obtained either from experiment, a preliminary simulation, or a suitable physical model, thus provides a means for generating the desired tempering ensemble. Applications to the two-dimensional Ising problem indicate that the resulting method is effective, simple to implement, and robust with respect to its sensitivity to the quality of the underlying heat capacity model.     

无机热化学数据库中卤化物高温熵的计算机预报

在W. M. Latimer估算化合物标准熵的方法的基础上,建立了卤化物高温熵的计算机预报方法。作为试验,未参加训练的18个卤化物高温熵的预报值与实验值作了对照,其偏差均小于20焦耳/度·摩尔,即与若干卤化物标准熵的实验误差相近。     

Configurational entropy: an improvement of the quasiharmonic approximation using configurational temperature

One challenge in computational biophysics and biology is to develop methodologies able to estimate accurately the configurational entropy of macromolecules. Among many methods, the quasiharmonic approximation (QH) is most widely used as it is simple in both theory and implementation. However, it has been shown that this method becomes inaccurate by overestimating entropy for systems with rugged free energy landscapes. Here, we propose a simple method to improve the QH approximation, i.e., to reduce QH entropy. We approximate the potential energy landscape of the system by an effective harmonic potential, and request that this potential must produce exactly the configurational temperature of the system. Due to this constraint, the force constants associated with the effective harmonic potential are increased, or equivalently, entropy of motion governed by this effective harmonic potential is reduced. We also introduce the effective configurational temperature concept which can be used as an indicator to check the anharmonicity of the free energy landscape. To validate the new method we compare it with the recently developed expansion approximate method by calculating entropy of one simple model system and two peptides with 3 and 16 amino acids either in gas phase or in explicit solvent. We show that the new method appears to be a good choice in practice as it is a compromise between accuracy and computational speed. A modification of the expansion approximate method is also introduced and advantages are discussed in some detail.     

Replica-exchange extensions of simulated tempering method

In this paper we consider combinations of two well-known generalized-ensemble algorithms, namely, simulated tempering and replica-exchange method. We discuss two examples of such combinations. One is the replica-exchange simulated tempering and the other is the simulated tempering replica-exchange method. In the former method, a short replica-exchange simulation is first performed and the simulated tempering weight factor is obtained by the multiple-histogram reweighting techniques. This process of simulated tempering weight factor determination is faster and simpler than that in the usual iterative process. A long simulated tempering production run is then performed with this weight factor. The latter method is a further extension of the former in which a simulated tempering replica-exchange simulation is performed with a small number of replicas. These algorithms are particularly useful for studying frustrated systems with rough energy landscape. We give the formulations of these two methods in detail and demonstrate their effectiveness taking the example of the system of a 17-residue helical peptide.     

The incomplete beta function law for parallel tempering sampling of classical canonical systems

We show that the acceptance probability for swaps in the parallel tempering Monte Carlo method for classical canonical systems is given by a universal function that depends on the average statistical fluctuations of the potential and on the ratio of the temperatures. The law, called the incomplete beta function law, is valid in the limit that the two temperatures involved in swaps are close to one another. An empirical version of the law, which involves the heat capacity of the system, is developed and tested on a Lennard-Jones cluster. We argue that the best initial guess for the distribution of intermediate temperatures for parallel tempering is a geometric progression and we also propose a technique for the computation of optimal temperature schedules. Finally, we demonstrate that the swap efficiency of the parallel tempering method for condensed-phase systems decreases naturally to zero at least as fast as the inverse square root of the dimensionality of the physical system.     

Optimal use of data in parallel tempering simulations for the construction of discrete-state Markov models of biomolecular dynamics

Parallel tempering (PT) molecular dynamics simulations have been extensively investigated as a means of efficient sampling of the configurations of biomolecular systems. Recent work has demonstrated how the short physical trajectories generated in PT simulations of biomolecules can be used to construct the Markov models describing biomolecular dynamics at each simulated temperature. While this approach describes the temperature-dependent kinetics, it does not make optimal use of all available PT data, instead estimating the rates at a given temperature using only data from that temperature. This can be problematic, as some relevant transitions or states may not be sufficiently sampled at the temperature of interest, but might be readily sampled at nearby temperatures. Further, the comparison of temperature-dependent properties can suffer from the false assumption that data collected from different temperatures are uncorrelated. We propose here a strategy in which, by a simple modification of the PT protocol, the harvested trajectories can be reweighted, permitting data from all temperatures to contribute to the estimated kinetic model. The method reduces the statistical uncertainty in the kinetic model relative to the single temperature approach and provides estimates of transition probabilities even for transitions not observed at the temperature of interest. Further, the method allows the kinetics to be estimated at temperatures other than those at which simulations were run. We illustrate this method by applying it to the generation of a Markov model of the conformational dynamics of the solvated terminally blocked alanine peptide.     

Thermally induced gelling of oil-in-water emulsions comprising partially crystallized droplets: the impact of interfacial crystals

We produced triglyceride-in-water emulsions comprising partially crystallized droplets, stabilized by a mixture of protein and low molecular weight surfactant. The emulsions were emulsified in the melted state of the oil phase and stored at low temperature (4 degrees C) right after fabrication to induce oil crystallization. The systems were then warmed to room temperature for a short period of time and cooled again to 4 degrees C. Owing to this treatment referred to as temperature cycling or "tempering", the initially fluid emulsions turned into hard gels. We followed the bulk rheological properties of the materials during and after tempering. The storage modulus, G', exhibited a dramatic increase when tempering was applied. We showed that the systems evolved following two distinct regimes that depend on the average droplet size and on the surfactant-to-protein molar ratio. Gelling may involve partial coalescence of the droplets, i.e., film rupturing with no further shape relaxation because of the solid nature of the droplets. Alternatively, gelling may occur without film rupturing, and is reminiscent of a jamming transition induced by surface roughness. We discussed the origin of these two mechanisms in terms of the properties (size and protuberance) of the interfacial oil crystals.     

Free-energy landscape for beta hairpin folding from combined parallel tempering and metadynamics

We develop a new free-energy method, based on the combination of parallel tempering and metadynamics, and apply this method to the calculation of the free-energy landscape of the folding beta hairpin in explicit water. We show that the combined method greatly improves the performance of both parallel tempering and metadynamics. In particular, we are able to sample the high free-energy regions, which are not accessible with conventional parallel tempering. We use our results to calculate the difference in entropy and enthalpy between the folded and the unfolded state and to characterize the most populated configurations in the relevant free-energy basins.     

Dilute solution properties and phase separation of branched low-density polyethylene

Viscosity, light scattering, and precipitation temperature measurements on dilute solutions of high-density and low-density polyethylene fractions have been carried out and a theory by Flory for phase equilibrium of linear polymers has been extended to branched polymer. From the results, it is shown that the entropy parameter ψ, depends on branching; a method for the determination of long-chain branching in polymer fractions is proposed combining precipitation temperature and molecular weight measurements. The method has been applied to the evaluation of long-chain branching in low-density polyethylene.     

Freezing and folding behavior in simple off-lattice heteropolymers

We have performed parallel tempering Monte Carlo simulations using a simple continuum heteropolymer model for proteins. All 10 heteropolymer sequences which we have studied have shown first-order transitions at low temperature to ordered states dominated by single chain conformations. These results are in contrast with the theoretical predictions of the random energy model for heteropolymers, from which we would expect continuous transitions to glassy behavior at low temperatures.     

A thermodynamic approach to the fragility of glass-forming polymers

We have connected the dynamic fragility, namely, the steepness of the relaxation-time variation upon temperature reduction, to the excess entropy and heat capacity of a large number of glass-forming polymers. The connection was obtained in a natural way from the Adam-Gibbs equation, relating the structural relaxation time to the configurational entropy. We find a clear correlation for a group of polymers. For another group of polymers, for which this correlation does not work, we emphasize the role of relaxation processes unrelated to the alpha process in affecting macroscopic thermodynamic properties. Once the residual excess entropy at the Vogel temperature is removed from the total excess entropy, the correlation between dynamic fragility and thermodynamic properties is reestablished.     

Low-spin state structure of [Fe(chloroethyltetrazole)6](BF4)2 obtained from synchrotron powder diffraction data

The complex [Fe(teec)6](BF4)2 (teec = chloroethyltetrazole) shows a two-step complete spin-crossover transition in the temperature range 300-90 K. Time-resolved synchrotron powder diffraction experiments have been carried out in this temperature range, and crystal structure models have been obtained from the powder patterns by using the parallel tempering technique. Of these models, the low-spin state structure at 90 K has been refined completely with Rietveld refinement. Its structural characteristics are discussed in relation to the high-spin state model and other spin-crossover compounds. The complex shows a remarkable anisotropic unit-cell parameter contraction that is dependent on the applied cooling rate. In addition, the possible important implications for the interpretation of spin-crossover behavior in terms of structural changes are discussed.     

Modification and optimization of the united-residue (UNRES) potential energy function for canonical simulations. I. Temperature dependence of the effective energy function and tests of the optimization method with single training proteins

We report the modification and parametrization of the united-residue (UNRES) force field for energy-based protein structure prediction and protein folding simulations. We tested the approach on three training proteins separately: 1E0L (beta), 1GAB (alpha), and 1E0G (alpha + beta). Heretofore, the UNRES force field had been designed and parametrized to locate native-like structures of proteins as global minima of their effective potential energy surfaces, which largely neglected the conformational entropy because decoys composed of only lowest-energy conformations were used to optimize the force field. Recently, we developed a mesoscopic dynamics procedure for UNRES and applied it with success to simulate protein folding pathways. However, the force field turned out to be largely biased toward -helical structures in canonical simulations because the conformational entropy had been neglected in the parametrization. We applied the hierarchical optimization method, developed in our earlier work, to optimize the force field; in this method, the conformational space of a training protein is divided into levels, each corresponding to a certain degree of native-likeness. The levels are ordered according to increasing native-likeness; level 0 corresponds to structures with no native-like elements, and the highest level corresponds to the fully native-like structures. The aim of optimization is to achieve the order of the free energies of levels, decreasing as their native-likeness increases. The procedure is iterative, and decoys of the training protein(s) generated with the energy function parameters of the preceding iteration are used to optimize the force field in a current iteration. We applied the multiplexing replica-exchange molecular dynamics (MREMD) method, recently implemented in UNRES, to generate decoys; with this modification, conformational entropy is taken into account. Moreover, we optimized the free-energy gaps between levels at temperatures corresponding to a predominance of folded or unfolded structures, as well as to structures at the putative folding-transition temperature, changing the sign of the gaps at the transition temperature. This enabled us to obtain force fields characterized by a single peak in the heat capacity at the transition temperature. Furthermore, we introduced temperature dependence to the UNRES force field; this is consistent with the fact that it is a free-energy and not a potential energy function. beta     

Dynamically correlated regions and configurational entropy in supercooled liquids

When a liquid is cooled below its melting temperature, if crystallization is avoided, it forms a glass. This phenomenon, called glass transition, is characterized by a marked increase of viscosity, about 14 orders of magnitude, in a narrow temperature interval. The microscopic mechanism behind the glass transition is still poorly understood. However, recently, great advances have been made in the identification of cooperative rearranging regions, or dynamical heterogeneities, i.e., domains of the liquid whose relaxation is highly correlated. The growth of the size of these domains is now believed to be the driving mechanism for the increase of the viscosity. Recently a tool to quantify the size of these domains has been proposed. We apply this tool to a wide class of materials to investigate the correlation between the size of the heterogeneities and their configurational entropy, i.e., the number of states accessible to a correlated domain. We find that the relaxation time of a given system, apart from a material dependent prefactor, is a universal function of the configurational entropy of a correlated domain. As a consequence, we find that, at the glass transition temperature, the size of the domains and the configurational entropy per unit volume are anticorrelated, as originally predicted by the Adam-Gibbs theory. Finally, we use our data to extract some exponents defined in the framework of the random first-order theory, a recent quantitative theory of the glass transition.     

Temperature variation effects on the determination of acidity constants through the internal standard–capillary electrophoresis method

The internal standard (IS) CE (IS‐CE) method is an interesting alternative to other methods for the determination of acidity constants of compounds. Although some of the advantages of this method have been already reported, the method has not been tested yet as regards to temperature effects. This has been the aim of this work, where it is demonstrated that the method can be applied successfully for the determination of pK_as at different temperatures, if the acidity constant of the IS at the desired temperature is known. The fact of obtaining the acidity constants at different temperatures allows the calculation of some thermodynamic quantities, such as the molar standard enthalpy and the molar standard entropy in a fast way. It is also demonstrated that if the IS and the test compound have similar standard enthalpy increment, the IS compensates uncontrolled possible temperature fluctuations (e.g., due to Joule heat) inside the capillary obtaining reliable acidity constant values at the desired temperature.     

~（13）C_（60）气相统计熵及热容的计算

采用统计热力学方法及理想气体模型计算了气相~（１３）Ｃ_（６０）分子在１０１３２５Ｐａ压力及不同温度下的统计熵与热容。给出了统计熵与热力学温度Ｋ之间的关系，以及等容热容和等压热容与热力学温度Ｋ之间的关系表达式。     

Temperature effect on the selective hydration of sodium ion in nitrobenzene.

The effect of the temperature on the co-extraction of water molecules with Na+ from water to nitrobenzene (NB) in the presence of dipicrylaminate ion has been studied. The number (n) of water molecules co-extracted with a Na+ ion, as measured by the Karl Fischer method, increased from 3.1 to 5.2 with increasing temperature (6-65 degrees C). This observation is in apparent contradiction to the expectation from simple thermodynamics because hydration is generally an entropically unfavorable process. Additional 1H NMR experiments for the selective hydration of Na+ in deuterated NB have confirmed that the association constants of water with Na+ indeed decrease with increasing temperature. On the other hand, however, it has been shown that water solubility into NB substantially increases with temperature. We conclude that the latter effect overwhelms the former unfavorable entropy effect, which results in a net increase of the n-value, as observed.     

Combining smart darting with parallel tempering using Eckart space: application to Lennard-Jones clusters

The smart-darting algorithm is a Monte Carlo based simulation method used to overcome quasiergodicity problems associated with disconnected regions of configurations space separated by high energy barriers. As originally implemented, the smart-darting method works well for clusters at low temperatures with the angular momentum restricted to zero and where there are no transitions to permutational isomers. If the rotational motion of the clusters is unrestricted or if permutational isomerization becomes important, the acceptance probability of darting moves in the original implementation of the method becomes vanishingly small. In this work the smart-darting algorithm is combined with the parallel tempering method in a manner where both rotational motion and permutational isomerization events are important. To enable the combination of parallel tempering with smart darting so that the smart-darting moves have a reasonable acceptance probability, the original algorithm is modified by using a restricted space for the smart-darting moves. The restricted space uses a body-fixed coordinate system first introduced by Eckart, and moves in this Eckart space are coupled with local moves in the full 3N-dimensional space. The modified smart-darting method is applied to the calculation of the heat capacity of a seven-atom Lennard-Jones cluster. The smart-darting moves yield significant improvement in the statistical fluctuations of the calculated heat capacity in the region of temperatures where the system isomerizes. When the modified smart-darting algorithm is combined with parallel tempering, the statistical fluctuations of the heat capacity of a seven-atom Lennard-Jones cluster using the combined method are smaller than parallel tempering when used alone.     

Thermodynamics of Go-type models for protein folding

Go-type potentials, based on the inter-residue contacts present in the native structure of a protein, are frequently used to predict dynamic and structural features of the folding pathways through computer simulations. However, the mathematical form used to define the model interactions includes several arbitrary choices, whose consequences are not usually analyzed. In this work, we use a simple off-lattice protein model and a parallel tempering Monte Carlo simulation technique to carry out such analysis, centered in the thermodynamic characteristics of the folding transition. We show how the definition of a native contact has a deep impact on the presence of simple or complex transitions, with or without thermodynamic intermediates. In addition, we have checked that the width of the attractive wells has a profound effect on the free-energy barrier between the folded and unfolded states, mainly through its influence on the entropy of the denatured state.     

Melting entropy of nanocrystals: an approach from statistical physics

Considering size effect on the equations obtained from statistical mechanical theories for the entropy of crystal and liquid phases, a new model has been developed for the melting entropy of nanocrystals, including the effects of the quasi-harmonic, anharmonic and electronic components of the overall melting entropy. Then with the use of our suggested new proportionality between the melting point and the entropy temperature (θ(0)), the melting entropy of nanocrystals has been obtained in terms of their melting point. Moreover, for the first time, the size-dependency of the electronic component of the overall melting entropy, arising from the change in the electronic ground-state of the nanocrystal upon melting, has been taken into account to calculate the melting entropy of nanocrystals. Through neglecting the effect of the electronic component, the present model can corroborate the previous model for size-dependent melting entropy of crystals represented by Jiang and Shi. The present model has been validated by the available computer simulation results for Ag and V nanoparticles. Moreover, a fairly constant function has been introduced which couples the melting temperature, the entropy temperature and the atomic density of elements to each other.