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PubMed2004

Importance of entropy in the diastereoselectivity of 5-substituted 2-methyladamant-2-yl cations.

The diastereofacial selectivity of 2-methyl-5-X-adamant-2-yl cations IX (X = CN, Cl, Br, CH3O, COOCH3, C6H5, CH3, and (CH3)3Sn) toward methanol has been investigated in the gas phase at 750 Torr and in the 40-120 degrees C temperature range and compared with that of IF (X = F) and ISi (X = (CH3)3Si) measured previously under similar conditions. Detailed analysis of the energy surface of the IMe (X = CH3) ion reveals that the activation barrier of its syn addition to methanol is significantly lower than that of the anti attack. In the 40-100 degrees C range, such a difference is strongly reduced by adverse entropic factors which are large enough to invert the IMe diastereoselectivity from syn to anti at T > 69 degrees C. The behavior of IMe diverges markedly from that of IF and ISi. Large adverse entropic factors account for the predominant syn diastereoselectivity observed in the reaction with IF (X = F), notwithstanding the anti enthalpy barrier is lower than the syn one. Adverse entropy plays a minor role in the reaction with ISi (X = (CH3)3Si) which instead exhibits a preferred anti diastereoselectivity governed by the activation enthalpies. Depending on the electronic properties of X, the kinetic behavior of the other IX ions obeys one of the above models. The gas-phase diastereoselectivity of IX ions responds to a subtle interplay between the sigma-hyperconjugative/electrostatic effects of the X substituent and the activation entropy terms. sigma-Hyperconjugation/field effects determine the pyramidal structure and the relative stability of the syn and anti conformers of IX as well as the relative stability of their addition transition structures and their position along the reaction coordinate. The diastereoselectivity of IX in the gas phase is compared with that measured in solution and with theoretical predictions.

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PubMed2006

Can configuration entropy losses be predicted from the binding affinities of hydrogen-bonded complexes with varying numbers of single bonds?

The design of new supramolecular complexes often depends on reducing entropic contributions to improve binding. However, few studies provide reliable values for the cost of entropic contributions. Here, the binding affinities of a series of six alpha,omega-diamides to alpha,omega-dicarboxylates are calculated using a predominant states method and an implicit solvent model based upon finite difference solutions of the Poisson-Boltzmann equation. The calculations are able to reproduce the observed increase in binding free energy as the number of single bonds increases. However, calculations show that the increase in binding free energy is not due to an increase in entropy. Instead, the increase is due to the changing ability of the alpha,omega-diamides to form internal hydrogen bonds that must be disrupted to bind to the dicarboxylate receptors. This suggests that interpreting experimental free-energy trends to give rotational entropy contributions may be problematic.

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PubMed2006

How the stabilization of INK4 tumor suppressor 3D structure evaluated by quantum chemical and molecular mechanics calculations corresponds well with experimental results: interplay of association enthalpy, entropy, and solvation effects.

The folding free energy of the INK4c tumor suppressor core, consisting of 10 helices, was determined as the sum of gas-phase interaction enthalpy, gas-phase interaction entropy, and dehydration and hydration free energy. The interaction energy and the hydration free energy were determined using the nonempirical density functional theory (DFT) method, augmented by a dispersion-energy correction term, the semiempirical density-functional tight-binding method covering the dispersion energy, and the density functional theory/conductor-like screening model (DFT/COSMO) procedure, whereas the interaction entropy was calculated with the empirical Cornell et al. force field. Alternatively, all contributions were evaluated consistently using empirical methods. All the values of the interaction energy of helix pairs are stabilizing, and the dominant stabilizing terms stem from the London dispersion energy and, in the case of charged systems, the electrostatic energy. The stabilization energy of the core, determined as the difference of the energy of the core and 10 separate helices, amounts to approximately 450 kcal/mol. Systematically, the difference in the hydration free energy of a helix pair and its separate components is smaller in magnitude than the interaction energy, and it is negative for some pairs while positive for others. The average total free energy of a core formation amounts to -29.6 kcal/mol (yielded by scaled quantum-chemical methods) and +13.9 kcal/mol (resulting from empirical methods). These values are considerably smaller than their single components, which are dominated by the interaction energy. The computationally predicted interval encloses the experimental value of the folding free energy (-2.8 kcal/mol).

Amino Acid Motifs↗

PubMed2006

Hydration of dimethyldodecylamine-N-oxide: enthalpy and entropy driven processes.

Dimethyldodecylamine-N-oxide (DDAO) has only one polar atom that is able to interact with water. Still, this surfactant shows very hydrophilic properties: in mixtures with water, it forms normal liquid crystalline phases and micelles. Moreover, there is data in the literature indicating that the hydration of this surfactant is driven by enthalpy while other studies show that hydration of surfactants and lipids typically is driven by entropy. Sorption calorimetry allows resolving enthalpic and entropic contributions to the free energy of hydration at constant temperature and thus directly determines the driving forces of hydration. The results of the present sorption calorimetric study show that the hydration of liquid crystalline phases of DDAO is driven by entropy, except for the hydration of the liquid crystalline lamellar phase which is co-driven by enthalpy. The exothermic heat effect of the hydration of the lamellar phase arises from formation of strong hydrogen bonds between DDAO and water. Another issue is the driving forces of the phase transitions caused by the hydration. The sorption calorimetric results show that the transitions from the lamellar to cubic and from the cubic to the hexagonal phase are driven by enthalpy. Transitions from solid phases to the liquid crystalline lamellar phase are entropically driven, while the formation of the monohydrate from the dry surfactant is driven by enthalpy. The driving forces of the transition from the hexagonal phase to the isotropic solution are close to zero. These sorption calorimetric results are in good agreement with the analysis of the binary phase diagram based on the van der Waals differential equation. The phase diagram of the DDAO-water system determined using DSC and sorption calorimetry is presented.

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PubMed2005

Enthalpy and entropy effects in hydrogen adsorption on carbon nanotubes.

Interaction energies and entropies associated with hydrogen adsorption on the inner and outer surfaces of zigzag single-wall carbon nanotubes (SWCNT) of various diameters are analyzed by means of molecular mechanics, density functional theory, and ab initio calculations. For a single molecule the strongest interaction, which is 3.5 greater than that with the planar graphite sheet, is found inside a (8,0) nanotube. Adsorption on the outer surfaces is weaker than that on graphite. Due to the steric considerations, both processes are accompanied by an extremely strong decline in entropy. Absence of specific adsorption sites and weak attractive interaction between hydrogen molecules within carbon nanotubes results in their close packing at low temperatures. Using the calculated geometric and thermodynamic parameters in Langmuir isotherms we predict the adsorption capacity of SWCNTs at room temperature to be smaller than 1 wt % even at 100 bar.

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PubMed2001

Microscopic origins of entropy, heat capacity and the glass transition in proteins.

Internal motion is central to protein folding, to protein stability through the resulting residual entropy, and to protein function. Despite its importance, the precise nature of the internal motions of protein macromolecules remains a mystery. Here we report a survey of the temperature dependence of the fast dynamics of methyl-bearing side chains in a calmodulin-peptide complex using site-specific deuterium NMR relaxation methods. The amplitudes of motion had a markedly heterogeneous spectrum and segregated into three largely distinct classes. Other proteins studied at single temperatures tend to segregate similarly. Furthermore, a large variability in the degree of thermal activation of the dynamics in the calmodulin complex indicates a heterogeneous distribution of residual entropy and hence reveals the microscopic origins of heat capacity in proteins. These observations also point to an unexpected explanation for the low-temperature 'glass transition' of proteins. It is this transition that has been ascribed to the creation of protein motional modes that are responsible for biological activity.

Binding Sites↗

PubMed2005

Solvent effect on the adduct formation of methyltrioxorhenium (MTO) and pyridine: enthalpy and entropy contributions.

1:1 adduct formation between methyltrioxorhenium (MTO) and pyridine in different solvents (n-hexane, benzene, chloroform, ethyl acetate, dichloromethane and acetone) was studied using spectrophotometric techniques. The formation constants were determined from the absorbance change of the adduct versus pyridine concentration. The values of the formation constants vary from 114.5 to 752.5 L mol(-1) at T= 20 degrees C depending on the dielectric constant of the solvent (epsilon(r) = 1.89-20.7). Enthalpy and entropy changes during the adduct formation reactions were determined from van't Hoff plots. The measured enthalpy change of -37.0 to -22.2 kJ mol(-1) depends on epsilon(r), which is explained by Onsager's reaction field theory. The measured entropy change ranges from -71.2 to -36.6 J K(-1) mol(-1), and the dependence on the solvent is discussed in terms of the solvation effect.

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PubMed2001

The Szilard engine revisited: Entropy, macroscopic randomness, and symmetry breaking phase transitions.

The role of symmetry breaking phase transitions in the Szilard engine is analyzed. It is shown that symmetry breaking is the only necessary ingredient for the engine to work. To support this idea, we show that the Ising model behaves exactly as the Szilard engine. We design a purely macroscopic Maxwell demon from an Ising model, demonstrating that a demon can operate with information about the macrostate of the system. We finally discuss some aspects of the definition of entropy and how thermodynamics should be modified to account for the variations of entropy in second-order phase transitions. (c) 2001 American Institute of Physics.

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PubMed2004

Computing minimal entropy production trajectories: an approach to model reduction in chemical kinetics.

Advanced experimental techniques in chemistry and physics provide increasing access to detailed deterministic mass action models for chemical reaction kinetics. Especially in complex technical or biochemical systems the huge amount of species and reaction pathways involved in a detailed modeling approach call for efficient methods of model reduction. These should be automatic and based on a firm mathematical analysis of the ordinary differential equations underlying the chemical kinetics in deterministic models. A main purpose of model reduction is to enable accurate numerical simulations of even high dimensional and spatially extended reaction systems. The latter include physical transport mechanisms and are modeled by partial differential equations. Their numerical solution for hundreds or thousands of species within a reasonable time will exceed computer capacities available now and in a foreseeable future. The central idea of model reduction is to replace the high dimensional dynamics by a low dimensional approximation with an appropriate degree of accuracy. Here I present a global approach to model reduction based on the concept of minimal entropy production and its numerical implementation. For given values of a single species concentration in a chemical system all other species concentrations are computed under the assumption that the system is as close as possible to its attractor, the thermodynamic equilibrium, in the sense that all modes of thermodynamic forces are maximally relaxed except the one, which drives the remaining system dynamics. This relaxation is expressed in terms of minimal entropy production for single reaction steps along phase space trajectories.

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PubMed1995

Approximate entropy (ApEn) as a complexity measure.

Approximate entropy (ApEn) is a recently developed statistic quantifying regularity and complexity, which appears to have potential application to a wide variety of relatively short (greater than 100 points) and noisy time-series data. The development of ApEn was motivated by data length constraints commonly encountered, e.g., in heart rate, EEG, and endocrine hormone secretion data sets. We describe ApEn implementation and interpretation, indicating its utility to distinguish correlated stochastic processes, and composite deterministic/ stochastic models. We discuss the key technical idea that motivates ApEn, that one need not fully reconstruct an attractor to discriminate in a statistically valid manner-marginal probability distributions often suffice for this purpose. Finally, we discuss why algorithms to compute, e.g., correlation dimension and the Kolmogorov-Sinai (KS) entropy, often work well for true dynamical systems, yet sometimes operationally confound for general models, with the aid of visual representations of reconstructed dynamics for two contrasting processes. (c) 1995 American Institute of Physics.

Journal Article↗

PubMed1998

Note on phase space contraction and entropy production in thermostatted Hamiltonian systems.

The phase space contraction and the entropy production rates of Hamiltonian systems in an external field, thermostatted to obtain a stationary state, are considered. While for stationary states with a constant kinetic energy the two rates are formally equal for all numbers of particles N, for stationary states with constant total (kinetic and potential) energy this only obtains for large N. However, in both cases a large number of particles is required to obtain equality with the entropy production rate of Irreversible Thermodynamics. Consequences of this for the positivity of the transport coefficients and for the Onsager relations are discussed. Numerical results are presented for the special case of the Lorentz gas. (c) 1998 American Institute of Physics.

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PubMed2004

The structure of methane hydrate under geological conditions a combined Rietveld and maximum entropy analysis.

We present a study of the structure of a fully deuterated methane hydrate under the geological conditions found in the world's oceans. In situ high-resolution neutron diffraction experiments have been performed at temperatures of 220, 275, and 280 K and a pressure of 100 bar, corresponding to the conditions at 1000 m water depth. The data were analyzed with a combination of Rietveld refinement and maximum entropy methods. From the Rietveld refinement, precise atomic parameters of the host lattice could be determined, indicating increasing distortions of the structure of the cages at elevated temperatures and pressures. Debye-Waller factors of the encaged CD(4) molecules have been found to exceed the values of the Debye-Waller factors of the D(2)O molecules considerably. In the large cage of structure type I the thermal center-of-mass displacements of the guests are 5-10 times larger than those of the water molecules. From the maximum entropy analysis maps of the scattering length density have been obtained, showing details of the vibrational amplitudes of the atoms in methane hydrate. The Debye-Waller factors of all molecules have been found to deviate considerably from a simple spherical geometry.

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PubMed2005

A simple model of entropy relaxation for explaining effective activation energy behavior below the glass transition temperature.

Strong changes in relaxation rates observed at the glass transition region are frequently explained in terms of a physical singularity of the molecular motions. We show that the unexpected trends and values for activation energy and preexponential factor of the relaxation time tau, obtained at the glass transition from the analysis of the thermally stimulated current signal, result from the use of the Arrhenius law for treating the experimental data obtained in nonstationary experimental conditions. We then demonstrate that a simple model of structural relaxation based on a time dependent configurational entropy and Adam-Gibbs relaxation time is sufficient to explain the experimental behavior, without invoking a kinetic singularity at the glass transition region. The pronounced variation of the effective activation energy appears as a dynamic signature of entropy relaxation that governs the change of relaxation time in nonstationary conditions. A connection is demonstrated between the peak of apparent activation energy measured in nonequilibrium dielectric techniques, with the overshoot of the dynamic specific heat that is obtained in calorimetry techniques.

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PubMed2005

Molecular dynamics simulation of entropy driven ligand escape process in heme pocket.

Molecular dynamics simulations were performed to investigate the gate effect of protein motion on the escape of O(2) from the heme pocket. The existing geometric entropy in a spherical cavity pushes the ligand toward the cavity surface, and then the ligand escape along the cavity surface is controlled by the gate size and gate modulation, i.e., protein dynamics regulate the gating behavior, which is an inherent feature of proteins such as myoglobin. Our simulation results confirm that the ligand escape process is basically entropy driven.

Journal Article↗

PubMed2005

Statistical mechanical theory for steady state systems. II. Reciprocal relations and the second entropy.

The concept of second entropy is introduced for the dynamic transitions between macrostates. It is used to develop a theory for fluctuations in velocity, and is exemplified by deriving Onsager reciprocal relations for Brownian motion. The cases of free, driven, and pinned Brownian particles are treated in turn, and Stokes' law is derived. The second entropy analysis is applied to the general case of thermodynamic fluctuations, and the Onsager reciprocal relations for these are derived using the method. The Green-Kubo formulas for the transport coefficients emerge from the analysis, as do Langevin dynamics.

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PubMed2005

Configurational entropy of interacting particles adsorbed on one-dimensional channels arranged in a triangular structure.

The configurational entropy of interacting particles adsorbed on one-dimensional channels arranged in a triangular cross-sectional structure is studied by combining Monte Carlo simulation and thermodynamic integration method. Three different energies have been considered in the adsorption process: (1) epsilono, constant interaction energy between a monomer and an adsorption site; (2) wL, interaction energy between nearest-neighbor particles adsorbed along a single channel, and (3) wT, interaction energy between particles adsorbed across nearest-neighbor channels. Special attention is devoted to the case of repulsive transversal interactions (wT>0), for which a rich variety of ordered phases are observed in the adlayer, depending on the value of the parameters kBT/wT (being kB the Boltzmann constant) and wL/wT. The influence of each ordered structure on the configurational entropy of the adlayer has been analyzed and discussed in the context of the lattice-gas model.

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PubMed2005

Pattern formation in nonextensive thermodynamics: selection criterion based on the Renyi entropy production.

We analyze a system of two different types of Brownian particles confined in a cubic box with periodic boundary conditions. Particles of different types annihilate when they come into close contact. The annihilation rate is matched by the birth rate, thus the total number of each kind of particles is conserved. When in a stationary state, the system is divided by an interface into two subregions, each occupied by one type of particles. All possible stationary states correspond to the Laplacian eigenfunctions. We show that the system evolves towards those stationary distributions of particles which minimize the Renyi entropy production. In all cases, the Renyi entropy production decreases monotonically during the evolution despite the fact that the topology and geometry of the interface exhibit abrupt and violent changes.

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PubMed2005

Nature of the entropy versus self-diffusivity plot for simple liquids.

The empirical relation (D(*))(alpha) = a exp[S] between the self-diffusion coefficient D(*) and the excess entropy S of a liquid is studied here in the context of theoretical model calculation. The coefficient alpha is dependent on the interaction potential and shows a crossover at an intermediate density, where cooperative dynamics become more important. Around this density a departure from the Stokes-Einstein relation is also observed. The above relation between entropy and diffusion is also tested for the scaled total diffusion coefficient in a binary mixture.

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