Protein heat capacity reflects the dynamics of enthalpy exchange between the single macromolecule and the surroundings

Heat capacity has played a prominent role in relating macroscopic and microscopic properties of small molecules and crystals. However, its diagnostic power can also be used for macromolecules such as proteins. It is shown in the present study that the macroscopically observed protein heat capacity provides direct access to the thermodynamic state of the single protein molecule. The new model of the physical basis of protein heat capacity emphasizes the dynamic nature of protein molecules. It incorporates equilibrium fluctuations as an integral constituent and shows that the increase in the magnitude of equilibrium fluctuations is coupled to an increase in the enthalpy flux between the individual protein molecule and its surroundings. Proteins 2000;41:86–92. © 2000 Wiley‐Liss, Inc.     

The Hydrophobic Effect: A New Insight from Cold Denaturation and a Two-State Water Structure

Herein we provide a new insight into the hydrophobic effect in protein folding. Our proposition explains the molecular basis of cold denaturation, and of intermediate states in heat and their absence in cold denaturation. The exposure of non-polar surface reduces the entropy and enthalpy of the system, at low and at high temperatures. At low temperatures the favorable reduction in enthalpy overcomes the unfavorable reduction in entropy, leading to cold denaturation. At high temperatures, folding/unfolding is a two-step process: in the first, the entropy gain leads to hydrophobic collapse, in the second, the reduction in enthalpy due to protein-protein interactions leads to the native state. The different entropy and enthalpy contributions to the Gibbs energy change at each step at high, and at low, temperatures can be conveniently explained by a two-state model of the water structure. The model provides a clear view of the dominant factors in protein folding and stability. Consequently, it appears to provide a microscopic view of the hydrophobic effect and is consistently linked to macroscopic thermodynamic parameters.     

The hydrophobic effect: a new insight from cold denaturation and a two-state water structure

Herein we provide a new insight into the hydrophobic effect in protein folding. Our proposition explains the molecular basis of cold denaturation, and of intermediate states in heat and their absence in cold denaturation. The exposure of non-polar surface reduces the entropy and enthalpy of the system, at low and at high temperatures. At low temperatures the favorable reduction in enthalpy overcomes the unfavorable reduction in entropy, leading to cold denaturation. At high temperatures, folding/unfolding is a two-step process: in the first, the entropy gain leads to hydrophobic collapse, in the second, the reduction in enthalpy due to protein-protein interactions leads to the native state. The different entropy and enthalpy contributions to the Gibbs energy change at each step at high, and at low, temperatures can be conveniently explained by a two-state model of the water structure. The model provides a clear view of the dominant factors in protein folding and stability. Consequently, it appears to provide a microscopic view of the hydrophobic effect and is consistently linked to macroscopic thermodynamic parameters.     

The Glansdorff-Prigogine thermodynamic stability criterion in the light of Lyapunov's theory.

The significance of thermodynamic coupling in chemical reactions—which recently has been questioned on thermodynamic grounds—is examined from the point of view of kinetics. It is shown that considerations of stoichiometry lead to a meaningful definition of velocity for elementary and certain elementary-complex reactions, whereas the non-equilibrium thermodynamic definition of reaction velocity is ambiguous in multireaction systems. Based on rate laws which include the effects of nonideality, it is proven that elementary-type reactions are not coupled thermodynamically and concluded that thermodynamic coupling has no kinetic significance. A discussion is given to show that this result is compatible with coupling in both biochemical systems and oscillating reactions.     

The efficiency of muscle contraction

When a muscle contracts and shortens against a load, it performs work. The performance of work is fuelled by the expenditure of metabolic energy, more properly quantified as enthalpy (i.e., heat plus work). The ratio of work performed to enthalpy produced provides one measure of efficiency. However, if the primary interest is in the efficiency of the actomyosin cross-bridges, then the metabolic overheads associated with basal metabolism and excitation-contraction coupling, together with those of subsequent metabolic recovery process, must be subtracted from the total heat and work observed. By comparing the cross-bridge work component of the remainder to the Gibbs free energy of hydrolysis of ATP, a measure of thermodynamic efficiency is achieved. We describe and quantify this partitioning process, providing estimates of the efficiencies of selected steps, while discussing the errors that can arise in the process of quantification. The dependence of efficiency on animal species, fibre-type, temperature, and contractile velocity is considered. The effect of contractile velocity on energetics is further examined using a two-state, Huxley-style, mathematical model of cross-bridge cycling that incorporates filament compliance. Simulations suggest only a modest effect of filament compliance on peak efficiency, but progressively larger gains (vis-à-vis the rigid filament case) as contractile velocity approaches Vmax. This effect is attributed primarily to a reduction in the component of energy loss arising from detachment of cross-bridge heads at non-zero strain.     

Local description of surface tension through thermodynamic and mechanical definitions

For a half century, the calculation of local pressure components and surface tension along the normal to the surface have been carried out using mechanical definitions. This has led to three principal definitions: Irving and Kirkwood, Harasima and Kirkwood–Buff. Recently, thermodynamic definitions based on the energy calculation have been introduced to compute the local properties. We propose here to compare both definitions for Lennard–Jones particles interacting through a truncated and shifted potential. For this, two locations of the pairwise interaction involved in the calculation of the local pressure components and surface tension within the thermodynamic routes are investigated. For the first time, we show that the thermodynamic definition suffers, to one least degree with respect to the mechanical definition, from the same ambiguity. From a numerical standpoint, thermodynamic definition is more simple and less computationally expensive. Therefore, with the complicated potential, the thermodynamic approach appears to be most interesting to compute macroscopic and local pressure and surface tension.     

Structural and thermodynamic strategies for site-specific DNA binding proteins

BACKGROUND: Site-specific protein-DNA complexes vary greatly in structural properties and in the thermodynamic strategy for achieving an appropriate binding free energy. A better understanding of the structural and energetic engineering principles might lead to rational methods for modification or design of such proteins. RESULTS: A novel analysis of ten site-specific protein-DNA complexes reveals a striking correspondence between the degree of imposed DNA distortion and the thermodynamic parameters of each system. For complexes with relatively undistorted DNA, favorable enthalpy change drives unfavorable entropy change, whereas for complexes with highly distorted DNA, unfavorable DeltaH degrees is driven by favorable DeltaS degrees. We show for the first time that protein-DNA associations have isothermal enthalpy-entropy compensation, distinct from temperature-dependent compensation, so DeltaH degrees and DeltaS degrees do not vary independently. All complexes have favorable DeltaH degrees from direct protein-DNA recognition interactions and favorable DeltaS degrees from water release. Systems that strongly distort the DNA nevertheless have net unfavorable DeltaH degrees as the result of molecular strain, primarily associated with the base pair destacking. These systems have little coupled protein folding and the strained interface suffers less immobilization, so DeltaS degrees is net favorable. By contrast, systems with little DNA distortion have net favorable DeltaH degrees, which must be counterbalanced by net unfavorable DeltaS degrees, derived from loss of vibrational entropy (a result of isothermal enthalpy-entropy compensation) and from coupling between DNA binding and protein folding. CONCLUSIONS: Isothermal enthalpy-entropy compensation implies that a structurally optimal, unstrained fit is achieved only at the cost of entropically unfavorable immobilization, whereas an enthalpically weaker, strained interface entails smaller entropic penalties.     

Parameterization and optimization of the menthol force field for molecular dynamics simulations

Menthol’s various biological properties render it a useful component for medical and cosmetological applications, while its three centers of asymmetry mean that it can be used in a range of organic reactions. Menthol-substituted ionic liquids (ILs) have been found to exhibit promising antimicrobial and antielectrostatic properties, as well as being useful in organic catalysis and biochemical studies. However, so far, a force field designed and validated specifically for the menthol molecule has not been constructed. In the present work, the validation and optimization of force field parameters with regard to the ability to reproduce the macroscopic properties of menthol is presented. The set of optimized potentials for liquid simulations all atom (OPLS-AA) compatible parameters was tested and carefully tuned. The refinement of parameters included fitting of partial atomic charges, optimization of Lennard-Jones parameters, and recalculation of the dihedral angle parameters needed to reproduce quantum energy profiles. To validate the force field, a variety of physicochemical properties were calculated for liquid menthol. Both thermodynamic and kinetic properties were taken into account, including density, surface tension, enthalpy of vaporization, and shear viscosity. The obtained force field was proven to accurately reproduce the properties of the investigated compound while being fully compatible with the OPLS-AA force field.

     

Elucidating protein thermodynamics from the three-dimensional structure of the native state using network rigidity

Given the three-dimensional structure of a protein, its thermodynamic properties are calculated using a recently introduced distance constraint model (DCM) within a mean-field treatment. The DCM is constructed from a free energy decomposition that partitions microscopic interactions into a variety of constraint types, i.e., covalent bonds, salt-bridges, hydrogen-bonds, and torsional-forces, each associated with an enthalpy and entropy contribution. A Gibbs ensemble of accessible microstates is defined by a set of topologically distinct mechanical frameworks generated by perturbing away from the native constraint topology. The total enthalpy of a given framework is calculated as a linear sum of enthalpy components over all constraints present. Total entropy is generally a nonadditive property of free energy decompositions. Here, we calculate total entropy as a linear sum of entropy components over a set of independent constraints determined by a graph algorithm that builds up a mechanical framework one constraint at a time, placing constraints with lower entropy before those with greater entropy. This procedure provides a natural mechanism for enthalpy-entropy compensation. A minimal DCM with five phenomenological parameters is found to capture the essential physics relating thermodynamic response to network rigidity. Moreover, two parameters are fixed by simultaneously fitting to heat capacity curves for histidine binding protein and ubiquitin at five different pH conditions. The three free parameter DCM provides a quantitative characterization of conformational flexibility consistent with thermodynamic stability. It is found that native hydrogen bond topology provides a key signature in governing molecular cooperativity and the folding-unfolding transition.     

A study on the enthalpy-entropy compensation in protein unfolding

A large number of thermodynamic data including the free energy, enthalpy, entropy, and heat capacity changes were collected for the denaturation of various proteins. Regression indicated that remarkable enthalpy-entropy compensation occurred in protein unfolding, which meant that the change in enthalpy was almost compensated by a corresponding change in entropy resulting in a smaller net free energy change. This behavior was proposed to result from the water molecule reorganization, which contributed significantly to the enthalpy and entropy changes but little to the free energy change in protein unfolding. It turned out that the enthalpy-entropy compensation could provide novel insights into the problem of enthalpy and entropy convergence in protein unfolding.     

Is a constant low-entropy process at the root of glycolytic oscillations?

We measured temporal oscillations in thermodynamic variables such as temperature, heat flux, and cellular volume in suspensions of non-dividing yeast cells which exhibit temporal glycolytic oscillations. Oscillations in these variables have the same frequency as oscillations in the activity of intracellular metabolites, suggesting strong coupling between them. These results can be interpreted in light of a recently proposed theoretical formalism in which isentropic thermodynamic systems can display coupled oscillations in all extensive and intensive variables, reminiscent of adiabatic waves. This interpretation suggests that oscillations may be a consequence of the requirement of living cells for a constant low-entropy state while simultaneously performing biochemical transformations, i.e., remaining metabolically active. This hypothesis, which is in line with the view of the cellular interior as a highly structured and near equilibrium system where energy inputs can be low and sustain regular oscillatory regimes, calls into question the notion that metabolic processes are essentially dissipative.     

Active transport: Definitions and criteria

The thermodynamic definition of active transport is restated in terms of the rate of entropy production. A substance is said to be transported actively when the product of its flux by the force acting upon it across the membrane is negative. A general expression for the rate of entropy production in a complex membrane is which chemical reactions may occur is given, and this expression is developed for a somewhat simplified case. The resulting relation is used as a basis for defining and establishing experimental criteria for types of active transport. Two basic types are distinguished and are designatedcoupled transport andforced transport, respectively. Only the latter type is dependent upon energyielding chemical reactions.     

Identification of Clausine E as an inhibitor of fat mass and obesity‐associated protein (FTO) demethylase activity

The alkaloids containing a carbazole nucleus are an established class of natural products with wide range of biological activities. A combination of thermodynamic and enzymatic activity studies provides an insight into the recognition of Clausine E by the fat mass and obesity‐associated protein (FTO). The binding of Clausine E to FTO was driven by positive entropy and negative enthalpy changes. Results also indicated that the hydroxyl group was crucial for the binding of small molecules with FTO. The structural and thermodynamic information provides the basis for the design of more effective inhibitors for FTO demethylase activity.     

Adsorption thermodynamics to clean up wastewater; critical review

The current review paper deals with critical evaluation of the thermodynamic parameters of adsorption equilibrium uptakes of heavy metals, dyes and other organic pollutants from the wastewater using low-cost adsorbents, activated carbon derived from agricultural waste, industrial wastes and other important adsorbent materials. Present review paper focus the spontaneity of adsorption processes when the thermodynamic parameters were assessed with the compensation effects of standard enthalpy change (ΔH^o) and standard entropy change (ΔS^o) with temperature. This paper also investigates the spontaneity of adsorption on the basis of thermodynamic criteria of spontaneity and the temperature range to predict feasibility of the adsorption processes.     

Thermodynamics of stoichiometric biochemical networks in living systems far from equilibrium

The principles of thermodynamics apply to both equilibrium and nonequilibrium biochemical systems. The mathematical machinery of the classic thermodynamics, however, mainly applies to systems in equilibrium. We introduce a thermodynamic formalism for the study of metabolic biochemical reaction (open, nonlinear) networks in both time-dependent and time-independent nonequilibrium states. Classical concepts in equilibrium thermodynamics-enthalpy, entropy, and Gibbs free energy of biochemical reaction systems-are generalized to nonequilibrium settings. Chemical motive force, heat dissipation rate, and entropy production (creation) rate, key concepts in nonequilibrium systems, are introduced. Dynamic equations for the thermodynamic quantities are presented in terms of the key observables of a biochemical network: stoichiometric matrix Q, reaction fluxes J, and chemical potentials of species mu without evoking empirical rate laws. Energy conservation and the Second Law are established for steady-state and dynamic biochemical networks. The theory provides the physiochemical basis for analyzing large-scale metabolic networks in living organisms.     

Solvation and the hidden thermodynamics of a zinc finger probed by nonstandard repair of a protein crevice

The classical Zn finger contains a phenylalanine at the crux of its three architectural elements: a beta-hairpin, an alpha-helix, and a Zn(2+)-binding site. Surprisingly, phenylalanine is not required for high-affinity Zn2+ binding, but instead contributes to the specification of a precise DNA-binding surface. Substitution of phenylalanine by leucine leads to a floppy but native-like structure whose Zn affinity is maintained by marked entropy-enthalpy compensation (DeltaDeltaH -8.3 kcal/mol and -TDeltaDeltaS 7.7 kcal/mol). Phenylalanine and leucine differ in shape, size, and aromaticity. To distinguish which features correlate with dynamic stability, we have investigated a nonstandard finger containing cyclohexanylalanine at this site. The structure of the nonstandard finger is similar to that of the native domain. The cyclohexanyl ring assumes a chair conformation, and conformational fluctuations characteristic of the leucine variant are damped. Although the nonstandard finger exhibits a lower affinity for Zn2+ than does the native domain (DeltaDeltaG -1.2 kcal/mol), leucine-associated perturbations in enthalpy and entropy are almost completely attenuated (DeltaDeltaH -0.7 kcal/mol and -TDeltaDeltaS -0.5 kcal/mol). Strikingly, global changes in entropy (as inferred from calorimetry) are in each case opposite in sign from changes in configurational entropy (as inferred from NMR). This seeming paradox suggests that enthalpy-entropy compensation is dominated by solvent reorganization rather than nominal molecular properties. Together, these results demonstrate that dynamic and thermodynamic perturbations correlate with formation or repair of a solvated packing defect rather than type of physical interaction (aromatic or aliphatic) within the core.     

Equilibrium binding studies of a tryptophan-shifted mutant of phosphofructokinase from Bacillus stearothermophilus

A tryptophan-shifted mutant of phosphofructokinase (PFK) from Bacillus stearothermophilus has been constructed. This mutant, which is functionally similar to wild-type, provides the opportunity to examine the allosteric properties of PFK under equilibrium conditions. The unique fluorescence properties of the tryptophan-shifted mutant enzyme, W179F/F230W, have been utilized to deduce the thermodynamics of ligand binding and the allosteric perturbations in the absence of catalytic turnover. Specifically, phospho(enol)pyruvate (PEP) and MgADP binding to the mutant PFK can be directly observed using tryptophan fluorescence, and dissociation constants for these ligands have been measured to be equal to 2.71 +/- 0.04 and 90.4 +/- 3.5 microM, respectively. In addition, the homotropic couplings for the allosteric ligands have been assessed for the first time. PEP binds cooperatively with a Hill number of 2.9 +/- 0.3, while MgADP binding is not cooperative. The equilibrium couplings between these ligands and the substrate fructose 6-phosphate (Fru-6-P) have also been determined and follow the same trends with temperature observed under steady-state kinetic assay conditions using wild-type PFK, indicating that the presence of bound MgATP has little influence on the allosteric interactions. Like wild-type PFK, the coupling free energies for the mutant result from largely compensating enthalpy and entropy components at 25 degrees C. Furthermore, the sign of each coupling free energy, which signifies the nature of the allosteric effect, is opposite that of the enthalpy contribution and is therefore due to the larger absolute value of the associated entropy change. This characteristic stands in direct contrast to the thermodynamic basis of the allosteric response in the homologous PFK from E. coli in which the sign of the coupling free energy is established by the sign of the coupling enthalpy.