Thermodynamics of protein folding using a modified Wako-Sait?-Mu?oz-Eaton model

Herein, we propose a modified version of the Wako-Saitô-Muñoz-Eaton (WSME) model. The proposed model introduces an empirical temperature parameter for the hypothetical structural units (i.e., foldons) in proteins to include site-dependent thermodynamic behavior. The thermodynamics for both our proposed model and the original WSME model were investigated. For a system with beta-hairpin topology, a mathematical treatment (contact-pair treatment) to facilitate the calculation of its partition function was developed. The results show that the proposed model provides better insight into the site-dependent thermodynamic behavior of the system, compared with the original WSME model. From this site-dependent point of view, the relationship between probe-dependent experimental results and model’s thermodynamic predictions can be explained. The model allows for suggesting a general principle to identify foldon behavior. We also find that the backbone hydrogen bonds may play a role of structural constraints in modulating the cooperative system. Thus, our study may contribute to the understanding of the fundamental principles for the thermodynamics of protein folding.     

Hexavalent chromium removal from aqueous solutions by a novel powder prepared from Colocasia esculenta leaves

In this study, batch removal of hexavalent chromium from aqueous solutions by powdered Colocasia esculenta leaves was investigated. Batch experiments were conducted to study the effects of adsorption of Cr(VI) at different pH values, initial concentrations, agitation speeds, temperatures, and contact times. The biosorbent was characterized by scanning electron microscopy, energy-dispersive X-ray spectroscopy, and Fourier transform infrared spectrometer analysis. The biosorptive capacity of the adsorbent was dependent on the pH of the chromium solution in which maximum removal was observed at pH 2. The adsorption equilibrium data were evaluated for various adsorption isotherm models, kinetic models, and thermodynamics. The equilibrium data fitted well with Freundlich and Halsey models. The adsorption capacity calculated was 47.62 mg/g at pH 2. The adsorption kinetic data were best described by pseudo-second-order kinetic model. Thus, Colocasia esculenta leaves can be considered as one of the efficient and cheap biosorbents for hexavalent chromium removal from aqueous solutions.     

Interfacial thermodynamics of protein adsorption, ion co-adsorption and ion binding in solution. I. Phenomenological linkage relations for ion exchange in lysozyme chromatography and titration in solution

In this paper we discuss the thermodynamics of ion binding in solution, protein adsorption and ion co-adsorption. The emphasis is on charge regulation effects. To this end, we introduce phenomenological linkage relations from which the ion binding can be calculated from the electrolyte dependency of proton titration curves and the co-adsorption from the electrolyte dependency of protein adsorption isotherms. The linkage relations are derived from classical interfacial thermodynamics, and thus offer an alternative approach as compared to the mass balance equations which are currently used in biotechnology, and Record et al.'s 1978 analysis of Wyman's Binding Polynomial for protein interactions. The co-adsorption theory is an extension of our previous analysis of ion binding in solution, which we include here for comparison of the ion co-adsorption with the ion binding in solution. The theory is applied to the chromatography of lysozyme on the strong cation exchanger ‘mono S’ and to the proton titration of lysozyme in solution. In the accompanying Part 2 of this paper the results are interpreted with a simple model.     

Thermodynamics of T-cell receptor-peptide/MHC interactions: progress and opportunities

alphabeta T-cell receptors (TCRs) recognize peptide antigens presented by class I or class II major histocompatibility complex molecules (pMHC). Here we review the use of thermodynamic measurements in the study of TCR-pMHC interactions, with attention to the diversity in binding thermodynamics and how this is related to the variation in TCR-pMHC interfaces. We show that there is no enthalpic or entropic signature for TCR binding; rather, enthalpy and entropy changes vary in a compensatory manner that reflects a narrow free energy window for the interactions that have been characterized. Binding enthalpy and entropy changes do not correlate with structural features such as buried surface area or the number of hydrogen bonds within TCR-pMHC interfaces, possibly reflecting the myriad of contributors to binding thermodynamics, but likely also reflecting a reliance on van't Hoff over calorimetric measurements and the unaccounted influence of equilibria linked to binding. TCR-pMHC binding heat capacity changes likewise vary considerably. In some cases, the heat capacity changes are consistent with conformational differences between bound and free receptors, but there is little data indicating these conformational differences represent the need to organize disordered CDR loops. In this regard, we discuss how thermodynamics may provide additional insight into conformational changes occurring upon TCR binding. Finally, we highlight opportunities for the further use of thermodynamic measurements in the study of TCR-pMHC interactions, not only for understanding TCR binding in general, but also for understanding specifics of individual interactions and the engineering of TCRs with desired molecular recognition properties.     

Thermodynamic penalty arising from burial of a ligand polar group within a hydrophobic pocket of a protein receptor

Here, we examine the thermodynamic penalty arising from burial of a polar group in a hydrophobic pocket that forms part of the binding-site of the major urinary protein (MUP-I). X-ray crystal structures of the complexes of octanol, nonanol and 1,8 octan-diol indicate that these ligands bind with similar orientations in the binding pocket. Each complex is characterised by a bridging water molecule between the hydroxyl group of Tyr120 and the hydroxyl group of each ligand. The additional hydroxyl group of 1,8 octan-diol is thereby forced to reside in a hydrophobic pocket, and isothermal titration calorimetry experiments indicate that this is accompanied by a standard free energy penalty of +21 kJ/mol with respect to octanol and +18 kJ/mol with respect to nonanol. Consideration of the solvation thermodynamics of each ligand enables the "intrinsic" (solute-solute) interaction energy to be determined, which indicates a favourable enthalpic component and an entropic component that is small or zero. These data indicate that the thermodynamic penalty to binding derived from the unfavourable desolvation of 1,8 octan-diol is partially offset by a favourable intrinsic contribution. Quantum chemical calculations suggest that this latter contribution derives from favourable solute-solute dispersion interactions.     

Baseline length and automated fitting of denaturation data.

To understand relationships between protein sequence and stability, we often compare data from proteins that differ by the substitution of one amino acid. Frequently, an amino acid change causes the cooperative denaturation transitions to shift to lower temperatures, diminishing the signal from the native state. Here we show that apparent stability changes, i.e., the free energy of denaturation, deltaGD, can also be caused by a deficiency of points in the low temperature end of the transition. In addition, we suggest a method for overcoming this problem.     

Studies on Pidotimod Enantiomers With Chiralpak‐IA: Crystal Structure,Thermodynamic Parameters and Molecular Docking

Pidotimod, a synthetic dipeptide, has two chiral centers with biological and immunological activity. Its enantiomers were characterized by x‐ray crystallographic analysis. A chiral stationary phase (CSP) Chiralpak‐IA based on amylose derivatized with tris‐(3, 5‐dimethylphenyl carbamate) was used to separate pidotimod enantiomers. The mobile phase was prepared in a ratio of 35:65:0.2 of methyl‐tert‐butyl‐ether and acetonitrile trifluoroaceticacid. In addition, thermodynamics and molecular docking methods were used to explain the enantioseparation mechanism by Chiralpak‐IA. Thermodynamic studies were carried out from 10 to 45 °C. In general, both retention and enantioselectivity decreased as the temperature increased. Thermodynamic parameters indicate that the interaction force between the pidotimod enantiomer (4S, 2'R) and IA CSP is stronger and their complex model is more stable. According to GOLD molecular docking simulation, Van der Waals force is the leading cause of pidotimod enantiomers separation by IA CSP. Chirality 27:802–808, 2015. © 2015 Wiley Periodicals, Inc.     

Thermodynamic analysis of product formation in mesophilic acidogenesis of lactose

Thermodynamic analysis on the acidogenesis of lactose was performed to evaluate the different acidogenic patterns and mechanisms by using Gibbs free energy calculation. Batch acidogenesis of lactose was investigated by using an enriched culture at 37 degrees C, pH 5.5 and varied substrate levels. In addition to usual acidogenic products, i-butyrate, valerate, i-valerate, caproate, and propanol were also produced at a significant level. Thermodynamic analysis shows that valerate might be formed through the reaction requiring hydrogen as electron donor and consuming of propionate and carbon dioxide. Caproate was most likely produced directly from butyrate, hydrogen, and carbon dioxide. The minimum amount of Gibbs free energies needed to sustain isomerization of butyrate and valerate were approximately 5.7-5.8 and 4.5-4.6 kJ/mol, respectively. Propanol was produced from acetate, hydrogen, and carbon dioxide with a minimum amount of Gibbs free energy of 41.8-42.0 kJ/mol. Formation of butanol was controlled more by substrate level or population dynamics than by thermodynamics.     

On the relationship between dissipation and the rate of spontaneous entropy production from linear irreversible thermodynamics

When systems are far from equilibrium, the temperature, the entropy and the thermodynamic entropy production are not defined and the Gibbs entropy does not provide useful information about the physical properties of a system. Furthermore, far from equilibrium, or if the dissipative field changes in time, the spontaneous entropy production of linear irreversible thermodynamics becomes irrelevant. In 2000 we introduced a definition for the dissipation function and showed that for systems of arbitrary size, arbitrarily near or far from equilibrium, the time integral of the ensemble average of this quantity can never decrease. In the low-field limit, its ensemble average becomes equal to the spontaneous entropy production of linear irreversible thermodynamics. We discuss how these quantities are related and why one should use dissipation rather than entropy or entropy production for non-equilibrium systems.     

Thermodynamic characterization of an artificially designed amphiphilic alpha-helical peptide containing periodic prolines: observations of high thermal stability and cold denaturation.

To investigate the structural stability of proteins, we analyzed the thermodynamics of an artificially designed 30-residue peptide. The designed peptide, NH2-EELLPLAEALAPLLEALLPLAEALAPLLKK-COOH (PERI COIL-1), with prolines at i + 7 positions, forms a pentameric alpha-helical structure in aqueous solution. The thermal denaturation curves of the CD at 222 nm (pH 7.5) show an unusual cold denaturation occurring well above 0 degrees C and no thermal denaturation is observable under 90 degrees C. This conformational change is reversible and depends on peptide concentration. A 2-state model between the monomeric denatured state (5D) and the pentameric helical state (H5) was sufficient to analyze 5 thermal denaturation curves of PERI COIL-1 with concentrations between 23 and 286 microM. The analysis was carried out by a nonlinear least-squares method using 3 fitting parameters: the midpoint temperature, Tm, the enthalpy change, delta H(Tm), and the heat capacity change, delta Cp. The association number (n = 5) was determined by sedimentation equilibrium and was not used as a fitting parameter. The heat capacity change suggests that the hydrophobic residues are buried in the helical state and exposed in the denatured one, as it occurs normally for natural globular proteins. On the other hand, the enthalpy and the entropy changes have values close to those found for coiled-coils and are quite distinct from typical values reported for natural globular proteins. In particular, the enthalpy change extrapolated at 110 degrees C is about 3 kJ/mol per amino acid residue, i.e., half of the value found for globular proteins.(ABSTRACT TRUNCATED AT 250 WORDS)     

Thermodynamics and bioenergetics

Bioenergetics is concerned with the energy conservation and conversion processes in a living cell, particularly in the inner membrane of the mitochondrion. This review summarizes the role of thermodynamics in understanding the coupling between the chemical reactions and the transport of substances in bioenergetics. Thermodynamics has the advantages of identifying possible pathways, providing a measure of the efficiency of energy conversion, and of the coupling between various processes without requiring a detailed knowledge of the underlying mechanisms. In the last five decades, various new approaches in thermodynamics, non-equilibrium thermodynamics and network thermodynamics have been developed to understand the transport and rate processes in physical and biological systems. For systems not far from equilibrium the theory of linear non-equilibrium thermodynamics is used, while extended non-equilibrium thermodynamics is used for systems far away from equilibrium. All these approaches are based on the irreversible character of flows and forces of an open system. Here, linear non-equilibrium thermodynamics is mostly discussed as it is the most advanced. We also review attempts to incorporate the mechanisms of a process into some formulations of non-equilibrium thermodynamics. The formulation of linear non-equilibrium thermodynamics for facilitated transport and active transport, which represent the key processes of coupled phenomena of transport and chemical reactions, is also presented. The purpose of this review is to present an overview of the application of non-equilibrium thermodynamics to bioenergetics, and introduce the basic methods and equations that are used. However, the reader will have to consult the literature reference to see the details of the specific applications.     

Denatured-state energy landscapes of a protein structural database reveal the energetic determinants of a framework model for folding

Position-specific denatured-state thermodynamics were determined for a database of human proteins by use of an ensemble-based model of protein structure. The results of modeling denatured protein in this manner reveal important sequence-dependent thermodynamic properties in the denatured ensembles as well as fundamental differences between the denatured and native ensembles in overall thermodynamic character. The generality and robustness of these results were validated by performing fold-recognition experiments, whereby sequences were matched with their respective folds based on amino acid propensities for the different energetic environments in the protein, as determined through cluster analysis. Correlation analysis between structure and energetic information revealed that sequence segments destined for β-sheet in the final native fold are energetically more predisposed to a broader repertoire of states than are sequence segments destined for α-helix. These results suggest that within the subensemble of mostly unstructured states, the energy landscapes are dominated by states in which parts of helices adopt structure, whereas structure formation for sequences destined for β-strand is far less probable. These results support a framework model of folding, which suggests that, in general, the denatured state has evolutionarily evolved to avoid low-energy conformations in sequences that ultimately adopt β-strand. Instead, the denatured state evolved so that sequence segments that ultimately adopt α-helix and coil will have a high intrinsic structure formation capability, thus serving as potential nucleation sites.     

The mechanochemistry of cytoskeletal force generation

In this communication, we propose a model to study the non-equilibrium process by which actin stress fibers develop force in contractile cells. The emphasis here is on the non-equilibrium thermodynamics, which is necessary to address the mechanics as well as the chemistry of dynamic cell contractility. In this setting, we are able to develop a framework that relates (a) the dynamics of force generation within the cell and (b) the cell’s response to external stimuli to the chemical processes occurring within the cell, as well as to the mechanics of linkage between the stress fibers, focal adhesions and extracellular matrix.     

Thermodynamics of ligand binding to histone deacetylase like amidohydrolase from Bordetella/Alcaligenes

Thermodynamic studies on ligand–protein binding have become increasingly important in the process of drug design. In combination with structural data and molecular dynamics simulations, thermodynamic studies provide relevant information about the mode of interaction between compounds and their target proteins and therefore build a sound basis for further drug optimization. Using the example of histone deacetylases (HDACs), particularly the histone deacetylase like amidohydrolase (HDAH) from Bordetella/Alcaligenes, a novel sensitive competitive fluorescence resonance energy transfer‐based binding assay was developed and the thermodynamics of interaction of both fluorescent ligands and inhibitors to histone deacetylase like amidohydrolase were investigated. The assay consumes only small amounts of valuable target proteins and is suitable for fast kinetic and mechanistic studies as well as high throughput screening applications. Binding affinity increased with increasing length of aliphatic spacers (n = 4–7) between the hydroxamate moiety and the dansyl head group of ligand probes. Van't Hoff plots revealed an optimum in enthalpy contribution to the free energy of binding for the dansyl‐ligand with hexyl spacer. The selectivity in the series of dansyl‐ligands against human class I HDAC1 but not class II HDACs 4 and 6 increased with the ratio of ΔH⁰/ΔG⁰. The data clearly emphasize the importance of thermodynamic signatures as useful general guidance for the optimization of ligands or rational drug design. Copyright © 2014 John Wiley & Sons, Ltd.     

From the test tube to the cell: exploring the folding and aggregation of a beta-clam protein

A crucial challenge in present biomedical research is the elucidation of how fundamental processes like protein folding and aggregation occur in the complex environment of the cell. Many new physico-chemical factors like crowding and confinement must be considered, and immense technical hurdles must be overcome in order to explore these processes in vivo. Understanding protein misfolding and aggregation diseases and developing therapeutic strategies to these diseases demand that we gain mechanistic insight into behaviors and misbehaviors of proteins as they fold in vivo. We have developed a fluorescence approach using FlAsH labeling to study the thermodynamics of folding of a model beta-rich protein, cellular retinoic acid binding protein (CRABP) in Escherichia coli cells. The labeling approach has also enabled us to follow aggregation of a modified version of CRABP and chimeras between CRABP and huntingtin exon 1 with its glutamine repeat tract. In this article, we review our recent results using FlAsH labeling to study in-vivo folding and present new observations that hint at fundamental differences between the thermodynamics and kinetics of protein folding in vivo and in vitro.     

Near Ambient Condition Hydrogen Storage in a Synergized Tricomponent Hydride System

Reversible hydrogen storage over hydrides of light elements (HLEs) under ambient condition has been pursued actively for nearly two decades. However, because of unfavorable thermodynamics and/or severe kinetic barrier of HLEs, limited progress has been made. Here, it is demonstrated that the interaction of LiBH₄ with Mg(NH₂)₂ and LiH, three of the most investigated HLEs, can lead to a fully reversible dehydrogenation/rehydrogenation cycle at temperatures below 373 K. More importantly, with the desorption enthalpy of 24 kJ (mol H₂)^?1 the dehydrogenation process at 1.0 bar H₂ is theoretically possible to be as low as 266 K. Characterization of this combination of HLEs shows that LiBH₄ serves as a reagent complexing with intermediates and products of the dehydrogenation of Mg(NH₂)₂‐LiH, and significantly alters the overall thermodynamic and kinetic properties of the system.     

Relating a calcium indicator signal to the unperturbed calcium concentration time-course

Carbohydrate restriction as a strategy for control of obesity is based on two effects: a behavioral effect, spontaneous reduction in caloric intake and a metabolic effect, an apparent reduction in energy efficiency, greater weight loss per calorie consumed. Variable energy efficiency is established in many contexts (hormonal imbalance, weight regain and knock-out experiments in animal models), but in the area of the effect of macronutrient composition on weight loss, controversy remains. Resistance to the idea comes from a perception that variable weight loss on isocaloric diets would somehow violate the laws of thermodynamics, that is, only caloric intake is important ("a calorie is a calorie"). Previous explanations of how the phenomenon occurs, based on equilibrium thermodynamics, emphasized the inefficiencies introduced by substrate cycling and requirements for increased gluconeogenesis. Living systems, however, are maintained far from equilibrium, and metabolism is controlled by the regulation of the rates of enzymatic reactions. The principles of nonequilibrium thermodynamics which emphasize kinetic fluxes as well as thermodynamic forces should therefore also be considered. Here we review the principles of nonequilibrium thermodynamics and provide an approach to the problem of maintenance and change in body mass by recasting the problem of TAG accumulation and breakdown in the adipocyte in the language of nonequilibrium thermodynamics. We describe adipocyte physiology in terms of cycling between an efficient storage mode and a dissipative mode. Experimentally, this is measured in the rate of fatty acid flux and fatty acid oxidation. Hormonal levels controlled by changes in dietary carbohydrate regulate the relative contributions of the efficient and dissipative parts of the cycle. While no experiment exists that measures all relevant variables, the model is supported by evidence in the literature that 1) dietary carbohydrate, via its effect on hormone levels controls fatty acid flux and oxidation, 2) the rate of lipolysis is a primary target of insulin, postprandial, and 3) chronic carbohydrate-restricted diets reduce the levels of plasma TAG in response to a single meal. In summary, we propose that, in isocaloric diets of different macronutrient composition, there is variable flux of stored TAG controlled by the kinetic effects of insulin and other hormones. Because the fatty acid-TAG cycle never comes to equilibrium, net gain or loss is possible. The greater weight loss on carbohydrate restricted diets, popularly referred to as metabolic advantage can thus be understood in terms of the principles of nonequilibrium thermodynamics and is a consequence of the dynamic nature of bioenergetics where it is important to consider kinetic as well as thermodynamic variables.     

Models of growth, self-reproduction and autoregulation based on consideration of reaction vessels with distensible, semipermeable walls]

We constructed non-equilibrium thermodynamics of the open physical-chemical irreversible processes in reactors with the strain semipermeable walls. This thermodynamics does not use the reciprocal relations of Onsager, so it may be applied when the stability stationary state is far from equilibrium. One of a general consequences of this thermodynamics is the statement: coordinated growth and self-reproduction are possible near the absolute equilibrium of the dissolvent and near the absolute stability stationary state of all chemicals with the absolute conservation of the differential equations of chemical kinetics. The supposition of ideal mixing is unnecessary; this condition is fulfilled automatically with diffusion. Growth and self-reproduction are not connected with positive eigenvalue of the differential equation of chemical kinetics. It is possible to construct a model of autoregulation and differentiation with this thermodynamics. The uniquness of such autoregulation follows from the mathematical theory [1]. The mathematical foundation of this thermodynamics is given in [1].     

Triadic conceptual structure of the maximum entropy approach to evolution

Many problems in evolutionary theory are cast in dyadic terms, such as the polar oppositions of organism and environment. We argue that a triadic conceptual structure offers an alternative perspective under which the information generating role of evolution as a physical process can be analyzed, and propose a new diagrammatic approach. Peirce's natural philosophy was deeply influenced by his reception of both Darwin's theory and thermodynamics. Thus, we elaborate on a new synthesis which puts together his theory of signs and modern Maximum Entropy approaches to evolution in a process discourse. Following recent contributions to the naturalization of Peircean semiosis, pointing towards ‘physiosemiosis’ or ‘pansemiosis’, we show that triadic structures involve the conjunction of three different kinds of causality, efficient, formal and final. In this, we accommodate the state-centered thermodynamic framework to a process approach. We apply this on Ulanowicz's analysis of autocatalytic cycles as primordial patterns of life. This paves the way for a semiotic view of thermodynamics which is built on the idea that Peircean interpretants are systems of physical inference devices evolving under natural selection. In this view, the principles of Maximum Entropy, Maximum Power, and Maximum Entropy Production work together to drive the emergence of information carrying structures, which at the same time maximize information capacity as well as the gradients of energy flows, such that ultimately, contrary to Schrödinger's seminal contribution, the evolutionary process is seen to be a physical expression of the Second Law.