The entropic nature of protein thermal stabilization

We performed thermodynamic analysis of temperature-induced unfolding of mesophilic and thermophilic proteins. It was shown that the variability in protein thermostability associated with pH-dependent unfolding or linked to the substitution of amino acid residues on the protein surface is evidence of the governing role of the entropy factor. Numerical values of conformational components in enthalpy, entropy and free energy which characterize protein unfolding in the “gas phase” were obtained. Based on the calculated absolute values of entropy and free energy, a model of protein unfolding is proposed in which the driving force is the conformational entropy of native protein, as an energy of the heat motion (T·S^NC) increasing with temperature and acting as an factor devaluating the energy of intramolecular weak bonds in the transition state.     

Adsorption Optimization of Lead (II) Using Saccharum Bengalense as a Non-Conventional Low Cost Biosorbent: Isotherm and Thermodynamics Modeling

In the present study a novel biomass, derived from the pulp of Saccharum bengalense, was used as an adsorbent material for the removal of Pb (II) ions from aqueous solution. After 50 minutes contact time, almost 92% lead removal was possible at pH 6.0 under batch test conditions. The experimental data was analyzed using Langmuir, Freundlich, Timken and Dubinin-Radushkevich two parameters isotherm model, three parameters Redlich—Peterson, Sip and Toth models and four parameters Fritz Schlunder isotherm models. Langmuir, Redlich—Peterson and Fritz-Schlunder models were found to be the best fit models. Kinetic studies revealed that the sorption process was well explained with pseudo second-order kinetic model. Thermodynamic parameters including free energy change (ΔG°), enthalpy change (ΔH°) and entropy change (ΔS°) have been calculated and reveal the spontaneous, endothermic and feasible nature of the adsorption process. The thermodynamic parameters of activation (ΔG ^#, ΔH ^#and ΔS ^#) were calculated from the pseudo-second order rate constant by using the Eyring equation. Results showed that Pb (II) adsorption onto SB is an associated mechanism and the reorientation step is entropy controlled.     

Structural and functional studies on a variant of cystatin purified from brain of Capra hircus

Cystatins, known for their ubiquitous presence in mammalian system are thiol protease inhibitors serving important physiological functions. Here, we present a variant of cystatin isolated from brain of Capra hircus (goat) which is glycosylated but lacks disulphide bonds. Caprine brain cystatin (CBC) was isolated using alkaline treatment, ammonium sulphate fractionation (40–60%) and gel filtration chromatography on Sephacryl S-100HR column with an overall yield of 26.29% and 322-fold purification. The inhibitor gave a molecular mass of ~44 kDa as determined by SDS-PAGE and gel filtration behaviour. The Stokes radius and diffusion coefficient of CBC were 27.14 Å and 8.18 × 10^?7 cm² s^?1, respectively. Kinetic data revealed that CBC inhibited thiol proteases reversibly and competitively, with the highest inhibition towards papain (K_i = 4.10 nM) followed by ficin and bromelain. CBC possessed 34.7% α-helical content as observed by CD spectroscopy. UV, fluorescence, CD and FTIR spectroscopy revealed significant conformational change upon CBC-papain complex formation. Isothermal titration calorimetry (ITC) was used to measure the thermodynamic parameters – ΔH, ΔS, ΔG along with N (binding stoichiometry) for CBC-papain complex formation. Binding stoichiometry (N = .97 ± .07 sites) for the CBC-papain complex indicates that cystatin is surrounded by nearly one papain molecule. Negative ΔH (?5.78 kcal mol^?1) and positive ΔS (11.01 cal mol^?1 deg^?1) values suggest that the interaction between CBC and papain is enthalpically as well as entropically favoured process. The overall negative ΔG (?9.19 kcal mol^?1) value implies a spontaneous CBC-papain interaction.     

Temperature and pressure effects on C112S azurin: Volume,expansivity, and flexibility changes

The pressure‐induced unfolding of the mutant C112S azurin from Pseudomonas aeruginosa was monitored both under steady state and dynamic conditions. The unfolding profiles were obtained by recording the spectral shift of the fluorescence emission as well as by phosphorescence intensity measurements. We evaluated the difference in free energy, ΔG, as a function of pressure and temperature. The dependence of ΔG on temperature showed concave profile at all pressures studied. A positive heat capacity change of about 4.3 kJ mol^?1 deg^?1 fitted all the curves. The volume change of the reaction showed a moderate dependence on temperature when compared with other proteins previously studied. The kinetic activation parameters (ΔV*, ΔH*, ΔS*) were obtained from upward and downward pressure‐jump experiments and used to characterize the volumetric and energetic properties of the transition state between native and unfolded protein. Our findings suggest that the folding and unfolding reaction paths passed through different transition states. The change in the phosphorescence lifetime with pressure pointed out that pressure‐induced unfolding occurred within two steps: the first leading to an increased protein flexibility, presumably caused by water penetration into the protein. Major structural changes of the tryptophan environment occurred in a second step at higher pressures. Proteins 2014; 82:1787–1798. © 2014 Wiley Periodicals, Inc.     

Effects of ligand binding on the stability of aldo–keto reductases: Implications for stabilizer or destabilizer chaperones

Ligands such as enzyme inhibitors stabilize the native conformation of a protein upon binding to the native state, but some compounds destabilize the native conformation upon binding to the non‐native state. The former ligands are termed “stabilizer chaperones” and the latter ones “destabilizer chaperones.” Because the stabilization effects are essential for the medical chaperone (MC) hypothesis, here we have formulated a thermodynamic system consisting of a ligand and a protein in its native‐ and non‐native state. Using the differential scanning fluorimetry and the circular dichroism varying the urea concentration and temperature, we found that when the coenzyme NADP⁺ was absent, inhibitors such as isolithocholic acid stabilized the aldo–keto reductase AKR1A1 upon binding, which showed actually the three‐state folding, but destabilized AKR1B10. In contrast, in the presence of NADP⁺, they destabilized AKR1A1 and stabilized AKR1B10. To explain these phenomena, we decomposed the free energy of stabilization (ΔΔG) into its enthalpy (ΔΔH) and entropy (ΔΔS) components. Then we found that in a relatively unstable protein showing the three‐state folding, native conformation was stabilized by the negative ΔΔH in association with the negative ΔΔS, suggesting that the stabilizer chaperon decreases the conformational fluctuation of the target protein or increase its hydration. However, in other cases, ΔΔG was essentially determined by the delicate balance between ΔΔH and ΔΔS. The proposed thermodynamic formalism is applicable to the system including multiple ligands with allosteric interactions. These findings would promote the development of screening strategies for MCs to regulate the target conformations.     

Equilibrium folding and unfolding pathways for a model protein

The folding–unfolding process of reduced bovine pancreatic trypsin inhibitor was investigated with an idealized model employing approximate free energies. The protein is regarded to consist of only C^α and C^β atoms. The backbone dihedral angles are the only conformational variables and are permitted to take discrete values at every 10°. Intraresidue energies consist of two terms: an empirical part taken from the observed frequency distributions of (?,ψ) and an additional favorable energy assigned to the native conformation of each residue. Interresidue interactions are simplified by assuming that there is an attractive energy operative only between residue pairs in close contact in the native structure. A total of 230,000 molecular conformations, with no atomic overlaps, ranging from the native state to the denatured state, are randomly generated by changing the sampling bias. Each conformation is classified according to its conformational energy, F; a conformational entropy, S(F) is estimated for each value of F from the number of samples. The dependence of S(F) on energy reveals that the folding–unfolding transition for this idealized model is an “all-or-none” type; this is attributable to the specific long-range interactions. Interresidue contact probabilities, averaged over samples representing various stages of folding, serve to characterize folding intermediates. Most probable equilibrium pathways for the folding–unfolding transition are constructed by connecting conformationally similar intermediates. The specific details obtained for bovine pancreatic trypsin inhibitor are as follows: (1) Folding begins with the appearance of nativelike medium-range contacts at a β-turn and at the α-helix. (2) These grow to include the native pair of interacting β-strands. This state includes intact regular secondary conformations, as well as the interstrand sheet contacts, and corresponds to an activated state with the highest free energy on the pathway. (3) Additional native long-range contacts are completely formed either toward the amino terminus or toward the carboxyl terminus. (4) In a final step, the missing contacts appear. Although these folding pathways for this model are not consistent with experimental reports, it does indicate multiple folding pathways. The method is general and can be applied to any set of calculated conformational energies and furthermore permits investigation of gross folding features.     

Computation of entropy contribution to protein-ligand binding free energy

The entropy contribution ΔS to protein-ligand binding free energy is studied for nine protein-lipid complexes. The entropy effect from the loss of the translational/rotational degrees of freedom (ΔS _tr) is calculated using the ideal gas approach. The change in the vibrational entropy (ΔS _vib) is calculated using the effective quantum oscillator approach with frequencies derived from the coordinate covariance matrix, so the inharmonic effects are taken into account. The change in the entropy of solvation (ΔS _solv) is considered using the binomial cell model (developed by the authors) for the hydrophobic effect. The entropy contribution from loss of conformations that are available for the free ligand (ΔS _conf) is also estimated. It is revealed that the negative in view of binding term ΔS _tr is only partly compensated by increasing of ΔS _vib, so T(ΔS _tr + ΔS _vib + ΔS _conf) < 0 for all complexes under investigation, but taking into account ΔS _solv leads to significantly increased ΔS. For all complexes except biotin-streptavidin, the results are found to be in reasonable agreement with experimental data. Published in Russian in Biokhimiya, 2007, Vol. 72, No. 7, pp. 963–973.     

Study on the interaction between anti‐tuberculosis drug ethambutol and bovine serum albumin: multispectroscopic and cyclic voltammetric approaches

The binding of bovine serum albumin (BSA) to ethambutol (EMB) was investigated using spectroscopic methods, viz., fluorescence, Fourier transform infrared (FTIR), ultraviolet (UV)/vis absorption and cyclic voltammetry techniques. Spectroscopic analysis of the emission quenching at different temperatures revealed that the quenching mechanism of serum albumin by EMB is static, which was also confirmed by lifetime measurements. The number of binding sites, n, and binding constant, K, were obtained at various temperatures. The distance, r, between EMB and the protein was evaluated according to the Förster energy transfer theory. Based on displacement experiments using site probes, viz., warfarin, ibuprofen and digitoxin, the site of binding of EMB in BSA was proposed to be Sudlow's site I. The effect of EMB on the conformation of BSA was analyzed by using synchronous fluorescence spectra (SFS) and 3D fluorescence spectra. The results of fluorescence, UV/vis absorption and FTIR spectra showed that the conformation of BSA was changed in the presence of EMB. The thermodynamic parameters including enthalpy change (ΔH⁰), entropy change (ΔS⁰) and free energy change (ΔG⁰) for BSA–EMB were calculated according to the van't Hoff equation and are discussed.     

The random coil → β transition of copolymers of L-lysine and L-isoleucine: Potentiometric titration and circular dichroism studies

Copolymers of L -lysine and L -isoleucine [poly(L -Lys^f,L -Val^{1 ? f})] containing 4–15% isoleucine were investigated using potentiometric titration and circular dichroism (CD) spectroscopy. With increasing isoleucine content, β-sheet formation is favored over α-helix formation at high pH and room temperature. The fraction of β-sheet present, as a function of pH, calculated from titrations of poly(L -Lys^85.2,L -Ile^14.8), agreed well with data obtained from CD studies for the same copolymer. Thermodynamic parameters were determined from titrations using the method of Zimm and Rice; the partial free energy (ΔG°_{C → β}) at 25° for the coil-to-β-sheet transition for isoleucine was estimated to be ?515 cal/mol; from the temperature dependence of free energy, the partial entropy (ΔS°_cβ), and the partial free enthalpy (ΔH°_{c → β}) of the coil → β transition for isoleucine is estimated to be 2.6 e.u. and 260 cal/mol, respectively. The partial thermodynamic parameters obtained for lysine are in good agreement with literature values. It is concluded from these studies that isoleucine has a very high potential for a β-sheet formation.     

Binding of ibuprofen to human hemoglobin: elucidation of their molecular recognition by spectroscopy,calorimetry, and molecular modeling techniques

Ibuprofen, used for the treatment of acute and chronic pain, osteoarthritis, rheumatoid arthritis, and related conditions has ample affinity to globular proteins. Here we have explored this fundamental study pertaining to the interaction of ibuprofen with human hemoglobin (HHb), using multispectroscopic, calorimetric, and molecular modeling techniques to gain insights into molecular aspects of binding mechanism. Ibuprofen-induced graded decrease in absorption spectra indicates protein disruption along with sedimentation of HHb particle. Red shifting of absorption peak at 195 nm indicates alteration in the secondary structure of HHb upon interaction with ibuprofen. Flouremetric and isothermal titration calorimetric (ITC) studies suggested one binding site in HHb for ibuprofen at 298.15 K. However, with increase in temperature, ITC revealed increasing number of binding sites. The negative values of Gibbs energy change (ΔG⁰) and enthalpy change (ΔH⁰) along with positive value of entropy change (ΔS⁰) strongly suggest that it is entropy-driven spontaneous exothermic reaction. Moreover, hydrophobic interaction, hydrogen bonding, and π–π interaction play major role in this binding process as evidenced from ANS (8-anilino-1-napthalenesulphonic acid), sucrose binding, and molecular modeling studies. The interaction impacts on structural integrity and functional aspects of HHb as confirmed by CD spectroscopy, increased free iron release, increased rate of co-oxidation and decreased rate of esterase activity. These findings suggest us to conclude that ibuprofen upon interaction perturbs both structural and functional aspects of HHb.     

Application of isothermal titration calorimetry in bioinorganic chemistry

The thermodynamics of metals ions binding to proteins and other biological molecules can be measured with isothermal titration calorimetry (ITC), which quantifies the binding enthalpy (ΔH°) and generates a binding isotherm. A fit of the isotherm provides the binding constant (K), thereby allowing the free energy (ΔG°) and ultimately the entropy (ΔS°) of binding to be determined. The temperature dependence of ΔH° can then provide the change in heat capacity (ΔC _p°) upon binding. However, ITC measurements of metal binding can be compromised by undesired reactions (e.g., precipitation, hydrolysis, and redox), and generally involve competing equilibria with the buffer and protons, which contribute to the experimental values (K _ITC, ΔH _ITC). Guidelines and factors that need to be considered for ITC measurements involving metal ions are outlined. A general analysis of the experimental ITC values that accounts for the contributions of metal–buffer speciation and proton competition and provides condition-independent thermodynamic values (K, ΔH°) for metal binding is developed and validated.     

Interaction of iron nanoparticles with nervous system: an in vitro study

Nanoparticles (NPs) are one of the interesting and widely studying issues mainly because of their particular physico-chemical features and broad applications in the field of biomedical sciences, such as diagnosis and drug delivery. In this study, the interaction of iron nanoparticles (Fe–NPs) with Tau protein and PC12 cell, as potential nervous system models, was investigated with a range of techniques including dynamic light scattering, intrinsic fluorescence spectroscopy, circular dichroism, [(3-(4,5-dimethylthiazol-2-yl)-2,5-diphenyl-tetrazolium-bromid] assay, and acridine orange/ethidium bromide (AO/EB) dual staining method. An inverse correlation between Stern and Volmer constant (K_SV) and temperature indicated a probable static quenching mechanism occurred between Tau protein and Fe–NPs. The number of binding site (n = 0.86) showed that there is almost one binding site of Fe–NP per protein. The negative values of ?H (?53.21 kJ/mol) and T?S (?42.44 kJ/mol) revealed that Fe–NPs interacts with Tau protein with dominate role of hydrogen bonds and van der Waals interactions and this interaction was spontaneous (?G = ?10.77 kJ/mol). Also, Fe–NPs stabilized the random coil structure of Tau protein. Moreover, Fe–NPs reduced PC12 cells viability by fragmentation of DNA in an apoptotic manner. In conclusion, induced conformational changes of Tau protein and cytotoxicity of PC12 cells by Fe–NP were revealed to be in a concentration and time-dependent manner.     

Molecular interactions of thymol with bovine serum albumin: Spectroscopic and molecular docking studies

Thymol is the main monoterpene phenol present in the essential oils which is used in the food industry as flavoring and preservative agent. In this study, the interaction of thymol with the concentration range of 1 to 6 μM and bovine serum albumin (BSA) at fixed concentration of 1 μM was investigated by fluorescence, UV‐vis, and molecular docking methods under physiological‐like condition. Fluorescence experiments were performed at 5 different temperatures, and the results showed that the fluorescence quenching of BSA by thymol was because of a static quenching mechanism. The obtained binding parameters, K, were in the order of 10⁴ M^?1, and the binding number, n, was approximately equal to unity indicating that there is 1 binding site for thymol on BSA. Calculated thermodynamic parameters for enthalpy (ΔH), entropy (ΔS), and Gibb's free energy (ΔG) showed that the reaction was spontaneous and hydrophobic interactions were the main forces in the binding of thymol to BSA. The results of UV‐vis spectroscopy and Arrhenius' theory showed the complex formation in the interaction of thymol and BSA. Negligible conformational changes in BSA by thymol were observed in fluorescence experiments, and the same results were also obtained from UV‐vis studies. Results of molecular docking indicated that the subdomain IA of BSA was the binding site for thymol.     

Evaluation of DNA,BSA binding,and antimicrobial activity of new synthesized neodymium complex containing 29-dimethyl 110-phenanthroline

In order to evaluate biological potential of a novel synthesized complex [Nd(dmp)₂Cl₃.OH₂] where dmp is 29-dimethyl 110-phenanthroline, the DNA-binding, cleavage, BSA binding, and antimicrobial activity properties of the complex are investigated by multispectroscopic techniques study in physiological buffer (pH 7.2).The intrinsic binding constant (K_b) for interaction of Nd(III) complex and FS–DNA is calculated by UV–Vis (K_b = 2.7 ± 0.07 × 10⁵) and fluorescence spectroscopy (K_b = 1.13 ± 0.03 × 10⁵). The Stern–Volmer constant (K_SV), thermodynamic parameters including free energy change (ΔG°), enthalpy change (?H°), and entropy change (?S°), are calculated by fluorescent data and Vant’ Hoff equation. The experimental results show that the complex can bind to FS–DNA and the major binding mode is groove binding. Meanwhile, the interaction of Nd(III) complex with protein, bovine serum albumin (BSA), has also been studied by using absorption and emission spectroscopic tools. The experimental results show that the complex exhibits good binding propensity to BSA. The positive ΔH° and ?S° values indicate that the hydrophobic interaction is main force in the binding of the Nd(III) complex to BSA, and the complex can quench the intrinsic fluorescence of BSA remarkably through a static quenching process. Also, DNA cleavage was investigated by agarose gel electrophoresis that according to the results cleavage of DNA increased with increasing of concentration of the complex. Antimicrobial screening test gives good results in the presence of Nd(III) complex system.     

Spectroscopic studies of bovine serum albumin adsorbed onto magnetic–thermosensitive carbon microspheres

To investigate the influence of magnetic–thermosensitive carbon microspheres (MTCMSs) as a targeting drug carrier on serum albumins in vitro, in this study, bovine serum albumin (BSA) was chosen as a template protein to explore the interaction between serum proteins and MTCMSs. Fluorescence spectrophotometry, ultraviolet–visible absorbance (UV–vis) spectrophotometry and circular dichroism spectrometry were used to investigate the interaction between MTCMSs and BSA. Results indicate that BSA interacts with MTCMSs and the fluorescence intensity of BSA is quenched by 50% in a static quenching at 310 K when the concentration of MTCMSs reaches 30 mg/L. Thermodynamic parameters including free energy change (△G^θ), enthalpy change (△H^θ) and entropy change (△S^θ) were calculated. The results (△G^θ < 0, △H^θ < 0 and △S^θ > 0) suggest a spontaneous process and the formation of a hydrogen bond between MTCMSs and BSA. UV–vis measurements reveal that the micro‐environment of an amino acid residue is altered in the presence of MTCMSs. The α‐helix content of BSA decreases by 4% and the β‐sheet content increases by 3.2% with increasing concentrations of MTCMSs to 30 mg/L, illustrating a change in the skeletal structure of BSA. These results demonstrate that MTCMSs as a targeting drug carrier impact the structure of serum albumins. This work provides not only a theoretical basis of BSA adsorption onto MTCMSs, but also an understanding of safe drug carriers in biomedicine. Copyright © 2016 John Wiley & Sons, Ltd.     

Common mechanism of thermostability in small α- and β-proteins studied by molecular dynamics

Protein thermostability is important to evolution, diseases, and industrial applications. Proteins use diverse molecular strategies to achieve stability at high temperature, yet reducing the entropy of unfolding seems required. We investigated five small α-proteins and five β-proteins with known, distinct structures and thermostability (T_m) using multi-seed molecular dynamics simulations at 300, 350, and 400 K. The proteins displayed diverse changes in hydrogen bonding, solvent exposure, and secondary structure with no simple relationship to T_m. Our dynamics were in good agreement with experimental B-factors at 300 K and insensitive to force-field choice. Despite the very distinct structures, the native-state (300 + 350 K) free-energy landscapes (FELs) were significantly broader for the two most thermostable proteins and smallest for the three least stable proteins in both the α- and β-group and with both force fields studied independently (tailed t-test, 95% confidence level). Our results suggest that entropic ensembles stabilize proteins at high temperature due to reduced entropy of unfolding, viz., ΔG = ΔH − TΔS. Supporting this mechanism, the most thermostable proteins were also the least kinetically stable, consistent with broader FELs, typified by villin headpiece and confirmed by specific comparison to a mesophilic ortholog of Thermus thermophilus apo-pyrophosphate phosphohydrolase. We propose that molecular strategies of protein thermostabilization, although diverse, tend to converge toward highest possible entropy in the native state consistent with the functional requirements. We speculate that this tendency may explain why many proteins are not optimally structured and why molten-globule states resemble native proteins so much.     

Quantitative estimates of steric effects: Intramolecular strain energy effects on the activation energy for aquation of some trans-dichlorotetraaminecobalt(III) complexes

In an effort to quantitatively estimate steric contributions to the aquation rates of a series of structurally related cobalt(III) tetraamine complexes, strain energy minimization calculations have been performed on the reactant and some plausible transition state structures. Free energies of activation ΔG*_obs, are factored as: ΔG*_obs, = ΔG*_bb + ΔG*_strain + Δ_G*_CF + ΔG*_solvation + … where ΔG*_bb is the free energy change associated with bond breaking, ΔG*_solvation is the solvation free energy difference between the reactant and a proposed transition stare, ΔG*_CF is the difference in crystal field stabilization between the reactant and a proposed transition state, and ΔG*_strain is the strain energy difference between the reactant complex and a proposed transition state. The activation energy for the aquation of a hypothetical ‘strain free’ complex is defined as ΔG*_int and reflects the energy required for the bond breaking step with all other terms. For the cations trans-(RR,SS)-dichloro-1,8- diamino-3,6-diazaoctanecobalt(III)(trans [Co(2,2,2- tet)Cl₂]⁺), trans-(RR,SS)- or trans-(RS)-dichloro-1.9- diamino-3,7-diazanonanecobalt(III)(trans [Co(2,3,2- tet)Cl₂]⁺ and trans-(RS)-dichloro-1,10-diamino-4,7- diazadecanecobalt(III)(trans[Co(3,2,3-tet)Cl₂]⁺) ΔG*_int is found to be a constant 123 kJ/mol. For the trans-dichlorocobalt(III) complexes with the ligands 1,4,7,10-tetraazacyclotridecane([13]-ane-N₄), 1,4,8, 11-tetraazacyclotetradecane([14]-ane-N₄), 1,4,8,12- tetraazacyclopentadecane([15]-ane-N₄) and 1,5,9,13- tetraazacyclohexadecane([16]-ane-N₄), ΔG*_int lies in the range 133–139 kJ/mol.     

Kinetics and thermodynamics of catalysis and thermal inactivation of a novel α-amylase (Tp-AmyS) from Thermotoga petrophila

Abstract

This research is focussed on kinetic, thermodynamic and thermal inactivation of a novel thermostable recombinant α-amylase (Tp-AmyS) from Thermotoga petrophila. The amylase gene was cloned in pHIS-parallel1 expression vector and overexpressed in Escherichia coli. The steady-state kinetic parameters (V_max, K_m, k_cat and k_cat/K_m) for the hydrolysis of amylose (1.39?mg/min, 0.57?mg, 148.6?s^?1, 260.7), amylopectin (2.3?mg/min, 1.09?mg, 247.1?s^?1, 226.7), soluble starch (2.67?mg/min, 2.98?mg, 284.2?s^?1, 95.4) and raw starch (2.1?mg/min, 3.6?mg, 224.7?s^?1, 61.9) were determined. The activation energy (E_a), free energy (ΔG), enthalpy (ΔH) and entropy of activation (ΔS) at 98?°C were 42.9?kJ mol^?1, 74?kJ mol^?1, 39.9?kJ mol^?1 and ?92.3 J mol^?1 K^?1, respectively, for soluble starch hydrolysis. While ΔG of substrate binding (ΔG_E-S) and ΔG of transition state binding (ΔG_E-T) were 3.38 and ?14.1?kJ mol^?1, respectively. Whereas, EaD, Gibbs free energy (ΔG*), increase in the enthalpy (ΔH*) and activation entropy (ΔS*) for activation of the unfolding of transition state were 108, 107, 105?kJ mol^?1 and ?4.1 J mol^?1 K^?1. The thermodynamics of irreversible thermal inactivation of Tp-AmyS revealed that at high temperature the process involves the aggregation of the protein.     

Influence of precipitating agents on thermodynamic parameters of protein crystallization solutions

X‐ray crystallography is the most powerful method for determining three‐dimensional structures of proteins to (near‐)atomic resolution, but protein crystallization is a poorly explained and often intractable phenomenon. Differential Scanning Calorimetry was used to measure the thermodynamic parameters (ΔG, ΔH, ΔS) of temperature‐driven unfolding of two globular proteins, lysozyme, and ribonuclease A, in various salt solutions. The mixtures were categorized into those that were conducive to crystallization of the protein and those that were not. It was found that even fairly low salt concentrations had very large effects on thermodynamic parameters. High concentrations of salts conducive to crystallization stabilized the native folded forms of proteins, whereas high concentrations of salts that did not crystallize them tended to destabilize them. Considering the ΔH and TΔS contributions to the ΔG of unfolding separately, high concentrations of crystallizing salts were found to enthalpically stabilize and entropically destabilize the protein, and vice‐versa for the noncrystallizing salts. These observations suggest an explanation, in terms of protein stability and entropy of hydration, of why some salts are good crystallization agents for a given protein and others are not. This in turn provides theoretical insight into the process of protein crystallization, suggesting ways of predicting and controlling it. © 2016 Wiley Periodicals, Inc. Biopolymers 105: 642–652, 2016.     

Microsecond simulations of the folding/unfolding thermodynamics of the Trp‐cage miniprotein

We study the unbiased folding/unfolding thermodynamics of the Trp‐cage miniprotein using detailed molecular dynamics simulations of an all‐atom model of the protein in explicit solvent using the Amberff99SB force field. Replica‐exchange molecular dynamics simulations are used to sample the protein ensembles over a broad range of temperatures covering the folded and unfolded states at two densities. The obtained ensembles are shown to reach equilibrium in the 1 μs/replica timescale. The total simulation time used in the calculations exceeds 100 μs. Ensemble averages of the fraction folded, pressure, and energy differences between the folded and unfolded states as a function of temperature are used to model the free energy of the folding transition, ΔG(P, T), over the whole region of temperatures and pressures sampled in the simulations. The ΔG(P, T) diagram describes an ellipse over the range of temperatures and pressures sampled, predicting that the system can undergo pressure‐induced unfolding and cold denaturation at low temperatures and high pressures, and unfolding at low pressures and high temperatures. The calculated free energy function exhibits remarkably good agreement with the experimental folding transition temperature (T_f = 321 K), free energy, and specific heat changes. However, changes in enthalpy and entropy are significantly different than the experimental values. We speculate that these differences may be due to the simplicity of the semiempirical force field used in the simulations and that more elaborate force fields may be required to describe appropriately the thermodynamics of proteins. Proteins 2010. © 2010 Wiley‐Liss, Inc.