Entropy‐enthalpy compensation: Perturbation and relaxation in thermodynamic systems

A van der Waals Model of Solvation Thermodynamics

Exploiting the van der Waals model of liquids, it is possible to derive analytical formulas for the thermodynamic functions governing solvation, the transfer of a solute molecule from a fixed position in the ideal gas phase to a fixed position in the liquid phase. The solvation Gibbs free energy change consists of two contributions: (a) the high number density of all liquids and the repulsive interactions due to the basic fact that each molecule has its own body leading to the need to spend free energy to produce an appropriate cavity to contain the solute molecule; (b) the ubiquitous intermolecular attractive interactions lead to a gain in free energy for switching-on attractions between the solute molecule and neighboring liquid molecules. Also the solvation entropy change consists of two contributions: (a) there is an entropy loss in all liquids because the cavity presence limits the space accessible to liquid molecules during their continuous translations; (b) there is an entropy gain in all liquids, at room temperature, due to the liquid structural reorganization as a response to the perturbation represented by solute addition. The latter entropy contribution is balanced by a corresponding enthalpy term. The scenario that emerged from the van der Waals model is in qualitative agreement with experimental results.

Structural Order in the Hydration Shell of Nonpolar Groups versus that in Bulk Water

The poor solubility of nonpolar compounds in water around room temperature is governed by a large and negative entropy change, whose molecular cause is still debated. Since the Frank and Evans original proposal in 1945, the large and negative entropy change is usually attributed to the formation of ordered structures in the hydration shell of nonpolar groups. However, the existence of such ordered structures has never been proven. The present study is aimed at providing available structural results and thermodynamic arguments disproving the existence of ordered structures in the hydration shell of nonpolar groups.

Entropy-Enthalpy Compensation in Electron-Transfer Processes

Solvent reorganization energies, free energies, and entropies are obtained for photoexcitation of three molecules that exhibit strong solvatochromism [Nile red, 5-(dimethylamino)-5'-nitro-2,2-bisthiophene, and Reichardt's dye B30] by measuring their optical absorption spectra at temperatures between 150 and 300 K in solvents with a range of polarities. Energies, free energies, and entropies of solvent reorganization are also obtained from computer simulations of three intramolecular electron-transfer reactions (charge separation and recombination in Zn-porphyrin-quinone cyclophane and charge transfer in a bis-biphenylandrostane radical anion). Entropy-enthalpy compensation in the solvent reorganization free energy for photoexcitation or electron transfer is found to be essentially complete (having nearly equal and opposite contributions from entropic and enthalpic effects) for all of the processes with solvent reorganization energies less than about 0.1 eV. Compensation becomes less complete as the reorganization energy becomes larger. A semiclassical treatment of the solvent reorganization entropy can rationalize these results.

Host-guest systems for the SAMPL9 blinded prediction challenge: phenothiazine as a privileged scaffold for binding to cyclodextrins

Model systems are widely used in biology and chemistry to gain insight into more complex systems. In the field of computational chemistry, researchers use host-guest systems, relatively simple exemplars of noncovalent binding, to train and test the computational methods used in drug discovery. Indeed, host-guest systems have been developed to support the community-wide blinded SAMPL prediction challenges for over a decade. While seeking new host-guest systems for the recent SAMPL9 binding prediction challenge, which is the focus of the present PCCP Themed Collection, we identified phenothiazine as a privileged scaffold for guests of β cyclodextrin (βCD) and its derivatives. Building on this observation, we used calorimetry and NMR spectroscopy to characterize the noncovalent association of native βCD and three methylated derivatives of βCD with five phenothiazine drugs. The strongest association observed, that of thioridazine and one of the methyl derivatives, exceeds the well-known high affinity of rimantidine with βCD. Intriguingly, however, methylation of βCD at the 3 position abolished detectible binding for all of the drugs studied. The dataset has a clear pattern of entropy-enthalpy compensation. The NMR data show that all of the drugs position at least one aromatic proton at the secondary face of the CD, and most also show evidence of deep penetration of the binding site. The results of this study were used in the SAMPL9 blinded binding affinity-prediction challenge, which are detailed in accompanying papers of the present Themed Collection. These data also open the phenothiazines and, potentially, chemically similar drugs, such as the tricyclic antidepressants, as relatively potent binders of βCD, setting the stage for future SAMPL challenge datasets and for possible applications as drug reversal agents.

Light, Water, and Melatonin: The Synergistic Regulation of Phase Separation in Dementia

The swift rise in acceptance of molecular principles defining phase separation by a broad array of scientific disciplines is shadowed by increasing discoveries linking phase separation to pathological aggregations associated with numerous neurodegenerative disorders, including Alzheimer’s disease, that contribute to dementia. Phase separation is powered by multivalent macromolecular interactions. Importantly, the release of water molecules from protein hydration shells into bulk creates entropic gains that promote phase separation and the subsequent generation of insoluble cytotoxic aggregates that drive healthy brain cells into diseased states. Higher viscosity in interfacial waters and limited hydration in interiors of biomolecular condensates facilitate phase separation. Light, water, and melatonin constitute an ancient synergy that ensures adequate protein hydration to prevent aberrant phase separation. The 670 nm visible red wavelength found in sunlight and employed in photobiomodulation reduces interfacial and mitochondrial matrix viscosity to enhance ATP production via increasing ATP synthase motor efficiency. Melatonin is a potent antioxidant that lowers viscosity to increase ATP by scavenging excess reactive oxygen species and free radicals. Reduced viscosity by light and melatonin elevates the availability of free water molecules that allow melatonin to adopt favorable conformations that enhance intrinsic features, including binding interactions with adenosine that reinforces the adenosine moiety effect of ATP responsible for preventing water removal that causes hydrophobic collapse and aggregation in phase separation. Precise recalibration of interspecies melatonin dosages that account for differences in metabolic rates and bioavailability will ensure the efficacious reinstatement of the once-powerful ancient synergy between light, water, and melatonin in a modern world.

Why Do Liquids Mix? The Mixing of Protic Ionic Liquids Sharing the Same Cation Is Apparently Driven by Enthalpy, Not Entropy

We study hydrogen bond (HB) redistribution in mixtures of two protic ionic liquids (PILs) sharing the same cation: triethylammonium methanesulfonate ([TEA][OMs]) and triethylammonium trifluoromethanesulfonate ([TEA][OTf]). The mixtures exhibit large negative energies of mixing. Based on results obtained from atomic detail molecular dynamics (MD) simulations, we derive a lattice model, discriminating between HB and nonspecific intermolecular interactions. We demonstrate that due to the ordered structure of the PILs, mostly the HB interactions contribute to the mixing energy. This allows to us to connect the equilibrium of HBs to each of the two anion species with the corresponding excess energies and entropies. The entropy associated with HB redistribution is shown to be negative, and even overcompensating the positive entropy associated with a statistical distribution of the ions in the mixture. This is strongly suggesting that the mixing process is driven by enthalpy, not entropy.

Stereoelectronic effects in stabilizing protein-N-glycan interactions revealed by experiment and machine learning

The energetics of protein-carbohydrate interactions, central to many life processes, cannot yet be manipulated predictably. This is mostly due to an incomplete quantitative understanding of the enthalpic and entropic basis of these interactions in aqueous solution. Here, we show that stereoelectronic effects contribute to stabilizing protein-N-glycan interactions in the context of a cooperatively folding protein. Double-mutant cycle analyses of the folding data from 52 electronically varied N-glycoproteins demonstrate an enthalpy-entropy compensation depending on the electronics of the interacting side chains. Linear and nonlinear models obtained using quantum mechanical calculations and machine learning explain up to 79% and 97% of the experimental interaction energy variability, as inferred from the R² value of the respective models. Notably, the protein-carbohydrate interaction energies strongly correlate with the molecular orbital energy gaps of the interacting substructures. This suggests that stereoelectronic effects must be given a greater weight than previously thought for accurately modelling the short-range dispersive van der Waals interactions between the N-glycan and the protein.

Why small proteins tend to have high denaturation temperatures

Data indicate that small globular proteins (consisting of less than about 70 residues) tend to have high denaturation temperatures. This finding is analysed by comparing experimental denaturation enthalpy and entropy changes of a selected set of small proteins with values calculated on the basis of average and common properties of globular proteins. The conclusion is that the denaturation entropy change is smaller than expected, leading to an increase in denaturation temperature. The proposed molecular rationalization considers the existence of long-wavelength, low-frequency vibrational modes in the native state of small proteins due to their large surface-to-interior ratio. The effect of decreasing the conformational entropy gain associated with denaturation on thermal stability is directly verified by means of an already devised theoretical model [G. Graziano, Phys. Chem. Chem. Phys. 2010, 12, 14245-14252; 2014, 16, 21755-21767].

Hydrophobic hydration and pairwise hydrophobic interaction of Lennard-Jones and Mie particles in different water models

The study provides a deep computational analysis of the thermodynamic and structural features associated with the hydration of xenon, Xe, and its pairwise hydrophobic interaction (i.e., the potential of mean force, PMF), over a large temperature range. Xe is described both as a Lennard-Jones particle, LJ-Xe, and as a Mie particle, Mie-Xe (pseudo hard sphere). Three different water models are used: TIP3P-Ew, SPCE and TIP4P-2005. Mie-Xe is more hydrophobic than LJ-Xe due to the lack of the attractive energetic interactions with water molecules; its hydration, around room temperature, is opposed by a large and negative entropy change and a positive enthalpy change. The PMF of Mie-Xe is characterized by a deep minimum at contact distance whose depth increases with temperature, and whose magnitude is significantly larger than that obtained for LJ-Xe. The contact minimum configuration of Mie-Xe is favoured by a large positive entropy change and contrasted by a positive enthalpy change. These results are qualitatively the same regardless of the water model used. There is no clear connection between the values determined for the thermodynamic functions and the structural features of the hydration shells surrounding the single Mie-Xe and the couple of Mie-Xe particles in the contact minimum configuration. This confirms that the structural reorganization of water associated with such processes is characterized by an almost complete enthalpy-entropy compensation.

A Rational Study of the Origin and Generality of Anti-Enthalpy–Entropy Compensation (AEEC) Phenomenon

In addition to enthalpy–entropy compensation (EEC), anti-enthalpy–entropy compensation (AEEC) phenomenon is also found in literature. The reports on the latter are limited, and analyses and justifications are so far unclear. Herein we present demonstration on the nature and possibility of the AEEC phenomenon. Although literature reports so far have mostly shown linear AEEC, we have found both linear and non-linear dependences. The non-linearity we consider arises from large “free energy window” (FEW) like EEC, recently presented and discussed. Attempts have been made to rationalize the observations in terms of solvation–desolvation phenomenon of the involved processes anticipated in previous studies. We have found that enthalpy and entropy of formation of gaseous and solid materials may also exhibit AEEC, it can be thus classified as a global phenomenon. In addition to AEEC, the phenomenon of no-enthalpy–entropy compensation (NEEC) is also reported. Thus, the phenomena EEC, AEEC and NEEC are thermodynamic puzzles that require close attention and analysis. With the help of wide range of physical chemical processes, an elaborate general understanding of the linear and non-linear AEEC phenomena has been attempted. The experimental data herein used are collected from literature reports, new measurements were not done. A variety of examples have supported possible generality of AEEC.

Entropy production in mesoscopic stochastic thermodynamics: nonequilibrium kinetic cycles driven by chemical potentials, temperatures, and mechanical forces

Nonequilibrium thermodynamics (NET) investigates processes in systems out of global equilibrium. On a mesoscopic level, it provides a statistical dynamic description of various complex phenomena such as chemical reactions, ion transport, diffusion, thermochemical, thermomechanical and mechanochemical fluxes. In the present review, we introduce a mesoscopic stochastic formulation of NET by analyzing entropy production in several simple examples. The fundamental role of nonequilibrium steady-state cycle kinetics is emphasized. The statistical mechanics of Onsager's reciprocal relations in this context is elucidated. Chemomechanical, thermomechanical, and enzyme-catalyzed thermochemical energy transduction processes are discussed. It is argued that mesoscopic stochastic NET in phase space provides a rigorous mathematical basis of fundamental concepts needed for understanding complex processes in chemistry, physics and biology. This theory is also relevant for nanoscale technological advances.

Resolution and Characterization of Chemical Steps in Enzyme Catalytic Sequences by Using Low-Temperature and Time-Resolved, Full-Spectrum EPR Spectroscopy in Fluid Cryosolvent and Frozen Solution Systems

Approaches to the resolution and characterization of individual chemical steps in enzyme catalytic sequences, by using temperatures in the cryogenic range of 190-250 K, and kinetics measured by time-resolved, full-spectrum electron paramagnetic resonance spectroscopy in fluid cryosolvent and frozen solution systems, are described. The preparation and performance of the adenosylcobalamin-dependent ethanolamine ammonia-lyase enzyme from Salmonella typhimurium in the two systems exemplifies the biochemical and spectroscopic methods. General advantages of low-temperature studies are (1) slowing of reaction steps, so that measurements can be made by using straightforward T-step kinetic methods and commercial instrumentation, (2) resolution of individual reaction steps, so that first-order kinetic analysis can be applied, and (3) accumulation of intermediates that are not detectable at room temperatures. The broad temperature range from room temperature to 190 K encompasses three regimes: (1) temperature-independent mean free energy surface (corresponding to native behavior); (2) the narrow temperature region of a glass-like transition in the protein, over which the free energy surface changes, revealing dependence of the native reaction on collective protein/solvent motions; and (3) the temperature range below the glass transition region, for which persistent reaction corresponds to nonnative, alternative reaction pathways, in the vicinity of the native configurational envelope. Representative outcomes of low-temperature kinetics studies are portrayed on Eyring and free energy surface (landscape) plots, and guidelines for interpretations are presented.

Thermodynamic and Structural Evidence for Reduced Hydrogen Bonding among Water Molecules near Small Hydrophobic Solutes

The structure of water molecules near a hydrophobic solute remains elusive despite a long history of scrutiny. Here, we re-examine the subtle issue by a combination of thermodynamic analysis for Henry's constants of several nonpolar gases over a broad range of temperatures and molecular dynamic simulations for the water structure in the hydration shell using several popular semiempirical models of liquid water. Both the structural and thermodynamic data indicate that hydrophobic hydration reduces the degree of the hydrogen bonding among water molecules, and the effect becomes more prominent at high temperatures. Hydrogen-bond formation is slightly hindered near a hydrophobic solute due to the restriction of the degree of freedom for water molecules in the solvation shell, and the confinement effect becomes more significant as temperature increases. Reduction in the extent of hydrogen bonding is fully consistent with a positive contribution of a small hydrophobic solute to the solution heat capacity. As predicted by the scaled-particle theory, both Henry's constants and simulation results suggest that the hydration entropy is determined primarily by cavity formation in liquid water, with its magnitude rising with the solute size but declining with temperature.

On the mechanism of cold denaturation

A theoretical rationalization of the occurrence of cold denaturation for globular proteins was devised, assuming that the effective size of water molecules depends upon temperature [G. Graziano, Phys. Chem. Chem. Phys., 2010, 12, 14245-14252]. In the present work, it is shown that the latter assumption is not necessary. By performing the same type of calculations in water, 40% (by weight) methanol, methanol, and carbon tetrachloride, it emerges that cold denaturation occurs only in water due to the special temperature dependence of its density and the small size of its molecules. These two coupled factors determine the magnitude and the temperature dependence of the stabilizing term that measures the gain in configurational/translational entropy of water molecules upon folding of the protein. This term has to be contrasted with the destabilizing contribution measuring the loss in conformational entropy of the polypeptide chain upon folding.

A fundamental view of enthalpy–entropy compensation

There is no fundamental difference in enthalpy–entropy compensation between dispersion and electrostatics or between quantum and molecular mechanics.

Large scale affinity calculations of cyclodextrin host-guest complexes: Understanding the role of reorganization in the molecular recognition process

Host-guest inclusion complexes are useful models for understanding the structural and energetic aspects of molecular recognition. Due to their small size relative to much larger protein-ligand complexes, converged results can be obtained rapidly for these systems thus offering the opportunity to more reliably study fundamental aspects of the thermodynamics of binding. In this work, we have performed a large scale binding affinity survey of 57 β-cyclodextrin (CD) host guest systems using the binding energy distribution analysis method (BEDAM) with implicit solvation (OPLS-AA/AGBNP2). Converged estimates of the standard binding free energies are obtained for these systems by employing techniques such as parallel Hamitionian replica exchange molecular dynamics, conformational reservoirs and multistate free energy estimators. Good agreement with experimental measurements is obtained in terms of both numerical accuracy and affinity rankings. Overall, average effective binding energies reproduce affinity rank ordering better than the calculated binding affinities, even though calculated binding free energies, which account for effects such as conformational strain and entropy loss upon binding, provide lower root mean square errors when compared to measurements. Interestingly, we find that binding free energies are superior rank order predictors for a large subset containing the most flexible guests. The results indicate that, while challenging, accurate modeling of reorganization effects can lead to ligand design models of superior predictive power for rank ordering relative to models based only on ligand-receptor interaction energies.

Dissipation, generalized free energy, and a self-consistent nonequilibrium thermodynamics of chemically driven open subsystems

Nonequilibrium thermodynamics of a system situated in a sustained environment with influx and efflux is usually treated as a subsystem in a larger, closed "universe." A question remains with regard to what the minimally required description for the surrounding of such an open driven system is so that its nonequilibrium thermodynamics can be established solely based on the internal stochastic kinetics. We provide a solution to this problem using insights from studies of molecular motors in a chemical nonequilibrium steady state (NESS) with sustained external drive through a regenerating system or in a quasisteady state (QSS) with an excess amount of adenosine triphosphate (ATP), adenosine diphosphate (ADP), and inorganic phosphate (Pi). We introduce the key notion of minimal work that is needed, W(min), for the external regenerating system to sustain a NESS (e.g., maintaining constant concentrations of ATP, ADP and Pi for a molecular motor). Using a Markov (master-equation) description of a motor protein, we illustrate that the NESS and QSS have identical kinetics as well as the second law in terms of the same positive entropy production rate. The heat dissipation of a NESS without mechanical output is exactly the W(min). This provides a justification for introducing an ideal external regenerating system and yields a free-energy balance equation between the net free-energy input F(in) and total dissipation F(dis) in an NESS: F(in) consists of chemical input minus mechanical output; F(dis) consists of dissipative heat, i.e. the amount of useful energy becoming heat, which also equals the NESS entropy production. Furthermore, we show that for nonstationary systems, the F(dis) and F(in) correspond to the entropy production rate and housekeeping heat in stochastic thermodynamics and identify a relative entropy H as a generalized free energy. We reach a new formulation of Markovian nonequilibrium thermodynamics based on only the internal kinetic equation without further reference to the intrinsic degree of freedom within each Markov state. It includes an extended free-energy balance and a second law which are valid for driven stochastic dynamics with an ideal external regenerating system. Our result suggests new ingredients for a generalized thermodynamics of self-organization in driven systems.

Entropy-enthalpy compensation: role and ramifications in biomolecular ligand recognition and design

Recent calorimetric studies of interactions between small molecules and biomolecular targets have generated renewed interest in the phenomenon of entropy-enthalpy compensation. In these studies, entropic and enthalpic contributions to binding are observed to vary substantially and in an opposing manner as the ligand or protein is modified, whereas the binding free energy varies little. In severe examples, engineered enthalpic gains can lead to completely compensating entropic penalties, frustrating ligand design. Here, we examine the evidence for compensation, as well as its potential origins, prevalence, severity, and ramifications for ligand engineering. We find the evidence for severe compensation to be weak in light of the large magnitude of and correlation between errors in experimental measurements of entropic and enthalpic contributions to binding, though a limited form of compensation may be common. Given the difficulty of predicting or measuring entropic and enthalpic changes to useful precision, or using this information in design, we recommend ligand engineering efforts instead focus on computational and experimental methodologies to directly assess changes in binding free energy.

Entropy-enthalpy transduction caused by conformational shifts can obscure the forces driving protein-ligand binding

Molecular dynamics simulations of unprecedented duration now can provide new insights into biomolecular mechanisms. Analysis of a 1-ms molecular dynamics simulation of the small protein bovine pancreatic trypsin inhibitor reveals that its main conformations have different thermodynamic profiles and that perturbation of a single geometric variable, such as a torsion angle or interresidue distance, can select for occupancy of one or another conformational state. These results establish the basis for a mechanism that we term entropy-enthalpy transduction (EET), in which the thermodynamic character of a local perturbation, such as enthalpic binding of a small molecule, is camouflaged by the thermodynamics of a global conformational change induced by the perturbation, such as a switch into a high-entropy conformational state. It is noted that EET could occur in many systems, making measured entropies and enthalpies of folding and binding unreliable indicators of actual thermodynamic driving forces. The same mechanism might also account for the high experimental variance of measured enthalpies and entropies relative to free energies in some calorimetric studies. Finally, EET may be the physical mechanism underlying many cases of entropy-enthalpy compensation.

Importance of van der Waals Interactions in QM/MM Simulations

The importance of accurately treating van der Waals interactions between the quantum mechanical (QM) and molecular mechanical (MM) atoms in hybrid QM/MM simulations has been investigated systematically. First, a set of van der Waals (vdW) parameters was optimized for an approximate density functional method, the self-consistent charge-tight binding density functional (SCC-DFTB) approach, based on small hydrogen-bonding clusters. The sensitivity of condensed phase observables to the SCC-DFTB vdW parameters was then quantitatively investigated by SCC-DFTB/MM simulations of several model systems using the optimized set and two sets of extreme vdW parameters selected from the CHARMM22 forcefield. The model systems include a model FAD molecule in solution and a solvated enediolate, and the properties studied include the radial distribution functions of water molecules around the solute (model FAD and enediolate), the reduction potential of the model FAD and the potential of mean force for an intramolecular proton transfer in the enediolate. Although there are noticeable differences between parameter sets for gas-phase clusters and solvent structures around the solute, thermodynamic quantities in the condensed phase (e.g., reduction potential and potential of mean force) were found to be less sensitive to the numerical values of vdW parameters. The differences between SCC-DFTB/MM results with the three vdW parameter sets for SCC-DFTB atoms were explained in terms of the effects of the parameter set on solvation. The current study has made it clear that efforts in improving the reliability of QM/MM methods for energetical properties in the condensed phase should focus on components other than van der Waals interactions between QM and MM atoms.

Entropy-enthalpy Compensation of Biomolecular Systems in Aqueous Phase: a Dry Perspective

We survey thermodynamic measurements on processes involving biological macromolecules in aqueous solution, which illustrate well the ubiquitous phenomenon of entropy-enthalpy compensation. The processes include protein folding/unfolding and ligand binding/unbinding, with compensation temperatures varying by about 50 K around an average near 293 K. We show that incorporating both near-exact entropy-enthalpy compensation (due to solvent relaxation) and multi-excitation entropy (from vibrational quanta) leads to a compensation temperature in water of about 230 K. We illustrate a general procedure for subtracting solvent and environment-related terms to determine the bare Gibbs free energy changes of chemical processes.

Hill's small systems nanothermodynamics: a simple macromolecular partition problem with a statistical perspective

Using a simple example of biological macromolecules which are partitioned between bulk solution and membrane, we investigate T.L. Hill's phenomenological nanothermodynamics for small systems. By introducing a system size-dependent equilibrium constant for the bulk-membrane partition, we obtain Hill's results on differential and integral chemical potentials μ and [Formula: see text] from computations based on standard Gibbsian equilibrium statistical mechanics. It is shown that their difference can be understood from an equilibrium re-partitioning between bulk and membrane fractions upon a change in the system's size; it is closely related to the system's fluctuations and inhomogeneity. These results provide a better understanding of nanothermodynamics and clarify its logical relation with the theory of statistical mechanics.

How does sucrose stabilize the native state of globular proteins?

It is well known that sucrose stabilizes the native state of globular proteins against both chemical denaturants and temperature. A largely accepted explanation of sucrose-induced stabilization is not yet emerged. It is shown that the same theoretical approach able to rationalize the occurrence of cold denaturation, the contrasting role of GdmCl and Gdm(2)SO(4), and the TMAO counteraction of urea denaturing activity [PCCP 12 (2010) 14245; PCCP 13 (2011) 12008; PCCP 13 (2011) 17689] works well also in the case of sucrose. The solvent-excluded volume effect plays the fundamental role because sucrose addition to water causes a marked increase in volume packing density due to the large size of sucrose molecules, that act as crowding agents.

How does trimethylamine N-oxide counteract the denaturing activity of urea?

Trimethylamine N-oxide, TMAO, stabilizes globular proteins and is able to counteract the denaturing activity of urea. The mechanism of this counteraction has remained elusive up to now. A rationalization is proposed grounded on the same theoretical model used to clarify the origin of cold denaturation, and the denaturing activity of GdmCl versus the stabilizing one of Gdm(2)SO(4) [G. Graziano, Phys. Chem. Chem. Phys., 2010, 12, 14245-14252; G. Graziano, Phys. Chem. Chem. Phys., 2011, 13, 12008-12014]. The fundamental quantities are: (a) the difference in the solvent-excluded volume on passing from the N-state to the D-state, calculated in water and in aqueous osmolyte solution; (b) the difference in energetic attractions of the N-state and the D-state with the surrounding solvent molecules, calculated in water and in aqueous osmolyte solution. In aqueous 8 M urea + 4 M TMAO solution, the first quantity is so large and positive to counteract the second one that is large and negative due to preferential binding of urea molecules to the protein surface. This happens because aqueous 8 M urea + 4 M TMAO solution has a volume packing density markedly larger than that of water, rendering the cavity creation process much more costly. The volume packing density increase reflects the strength of the attractions of water molecules with both urea and TMAO molecules. This mechanism readily explains why TMAO counteraction is operative even though urea molecules are preferentially located on the protein surface.

Extent of enthalpy-entropy compensation in protein-ligand interactions

The extent of enthalpy-entropy compensation in protein-ligand interactions has long been disputed because negatively correlated enthalpy (ΔH) and entropy (TΔS) changes can arise from constraints imposed by experimental and analytical procedures as well as through a physical compensation mechanism. To distinguish these possibilities, we have created quantitative models of the effects of experimental constraints on isothermal titration calorimetry (ITC) measurements. These constraints are found to obscure any compensation that may be present in common data representations and regression analyses (e.g., in ΔH vs. -TΔS plots). However, transforming the thermodynamic data into ΔΔ-plots of the differences between all pairs of ligands that bind each protein diminishes the influence of experimental constraints and representational bias. Statistical analysis of data from 32 diverse proteins shows a significant and widespread tendency to compensation. ΔΔH versus ΔΔG plots reveal a wide variation in the extent of compensation for different ligand modifications. While strong compensation (ΔΔH and -TΔΔS opposed and differing by < 20% in magnitude) is observed for 22% of modifications (twice that expected without compensation), 15% of modifications result in reinforcement (ΔΔH and -TΔΔS of the same sign). Because both enthalpy and entropy changes arise from changes to the distribution of energy states on binding, there is a general theoretical expectation of compensated behavior. However, prior theoretical studies have focussed on explaining a stronger tendency to compensation than actually found here. These results, showing strong but imperfect compensation, will act as a benchmark for future theoretical models of the thermodynamic consequences of ligand modification.

Irreversible thermodynamics in multiscale stochastic dynamical systems

This work extends the results of a recently developed theory of a rather complete thermodynamic formalism for discrete-state, continuous-time Markov processes with and without detailed balance. We investigate whether and in what way the thermodynamic structure is invariant in a multiscale stochastic system, that is, whether the relations between thermodynamic functions of state and process variables remain unchanged when the system is viewed at different time scales and resolutions. Our results show that the dynamics on a fast time scale contribute an entropic term to the internal energy function u(S)(x) for the slow dynamics. Based on the conditional free energy u(S)(x), we can then treat the slow dynamics as if the fast dynamics is nonexistent. Furthermore, we show that the free energy, which characterizes the spontaneous organization in a system without detailed balance, is invariant with or without the fast dynamics: The fast dynamics is assumed to reach stationarity instantaneously on the slow time scale; it has no effect on the system's free energy. The same cannot be said for the entropy and the internal energy, both of which contain the same contribution from the fast dynamics. We also investigate the consequences of time-scale separation in connection to the concepts of quasi-stationarity and steady adiabaticity introduced in the phenomenological steady-state thermodynamics.