Thermodynamics of globular proteins

The analysis of temperature-induced unfolding of proteins in aqueous solutions was performed. Based on the data of thermodynamic parameters of protein unfolding and using the method of semi-empirical calculations of hydration parameters at reference temperature 298 K, we obtained numerical values of enthalpy, free energy, and entropy which characterize the unfolding of proteins in the ‘gas phase’. It was shown that specific values of the energy of weak intramolecular bonds (?H^int), conformational free energy (?G^conf) and entropy (?S^conf) are the same for proteins with molecular weight 7–25 kDa. Using the energy value (?H^int) and the proposed approach for estimation of the conformational entropy of native protein (S^NC), numerical values of the absolute free energy (G^NC) were obtained.     

On the calculation of binding free energies using continuum methods: Application to MHC class I protein-peptide interactions

This paper describes a methodology to calculate the binding free energy (ΔG) of a protein-ligand complex using a continuum model of the solvent. A formal thermodynamic cycle is used to decompose the binding free energy into electrostatic and non-electrostatic contributions. In this cycle, the reactants are discharged in water, associated as purely nonpolar entities, and the final complex is then recharged. The total electrostatic free energies of the protein, the ligand, and the complex in water are calculated with the finite difference Poisson-Boltzmann (FDPB) method. The nonpolar (hydrophobic) binding free energy is calculated using a free energy-surface area relationship, with a single alkane/water surface tension coefficient (γ_aw). The loss in backbone and side-chain configurational entropy upon binding is estimated and added to the electrostatic and the nonpolar components of ΔG. The methodology is applied to the binding of the murine MHC class I protein H-2K^b with three distinct peptides, and to the human MHC class I protein HLA-A2 in complex with five different peptides. Despite significant differences in the amino acid sequences of the different peptides, the experimental binding free energy differences (ΔΔG_exp) are quite small (<0.3 and <2.7 kcal/mol for the H-2K^b and HLA-A2 complexes, respectively). For each protein, the calculations are successful in reproducing a fairly small range of values for ΔΔG_calc (<4.4 and <5.2 kcal/mol, respectively) although the relative peptide binding affinities of H-2K^b and HLA-A2 are not reproduced. For all protein-peptide complexes that were treated, it was found that electrostatic interactions oppose binding whereas nonpolar interactions drive complex formation. The two types of interactions appear to be correlated in that larger nonpolar contributions to binding are generally opposed by increased electrostatic contributions favoring dissociation. The factors that drive the binding of peptides to MHC proteins are discussed in light of our results.     

Urea interactions with protein groups: A volumetric study

We determined the partial molar volumes and adiabatic compressibilities of N‐acetyl amino acid amides, N‐acetyl amino acid methylamides, N‐acetyl amino acids, and short oligoglycines as a function of urea concentration. We analyze these data within the framework of a statistical thermodynamic formalism to determine the association constants for the reaction in which urea binds to the glycyl unit and each of the naturally occurring amino acid side chains replacing two waters of hydration. Our determined association constants, k, range from 0.04 to 0.39M. We derive a general equation that links k with changes in free energy, ΔG_tr, accompanying the transfer of functional groups from water to urea. In this equation, ΔG_tr is the sum of a change in the free energy of cavity formation, ΔΔG_C, and the differential free energy of solute–solvent interactions, ΔΔG_I, in urea and water. The observed range of affinity coefficients, k, corresponds to the values of ΔΔG_I ranging from highly favorable to slightly unfavorable. Taken together, our data support a direct interaction model in which urea denatures a protein by concerted action via favorable interactions with a wide range of protein groups. Our derived equation linking k to ΔG_tr suggests that ΔΔG_I and, hence, the net transfer free energy, ΔG_tr, are both strongly influenced by the concentration of a solute used in the experiment. We emphasize the need to exercise caution when two solutes differing in solubility are compared to determine the ΔG_tr contribution of a particular functional group. © 2010 Wiley Periodicals, Inc. Biopolymers 93: 866–879, 2010.     

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.     

Thermodynamics calculation of protein–ligand interactions by QM/MM polarizable charge parameters

The calculation of protein–ligand binding free energy (ΔG) is of great importance for virtual screening and drug design. Molecular dynamics (MD) simulation has been an attractive tool to investigate this scientific problem. However, the reliability of such approach is affected by many factors including electrostatic interaction calculation. Here, we present a practical protocol using quantum mechanics/molecular mechanics (QM/MM) calculations to generate polarizable QM protein charge (QMPC). The calculated QMPC of some atoms in binding pockets was obviously different from that calculated by AMBER ff03, which might significantly affect the calculated ΔG. To evaluate the effect, the MD simulations and MM/GBSA calculation with QMPC for 10 protein–ligand complexes, and the simulation results were then compared to those with the AMBER ff03 force field and experimental results. The correlation coefficient between the calculated ΔΔG using MM/GBSA under QMPC and the experimental data is .92, while that with AMBER ff03 force field is .47 for the complexes formed by streptavidin or its mutants and biotin. Moreover, the calculated ΔΔG with QMPC for the complexes formed by ERβ and five ligands is positively related to experimental result with correlation coefficient of .61, while that with AMBER ff03 charge is negatively related to experimental data with correlation coefficient of .42. The detailed analysis shows that the electrostatic polarization introduced by QMPC affects the electrostatic contribution to the binding affinity and thus, leads to better correlation with experimental data. Therefore, this approach should be useful to virtual screening and drug design.     

Zinc finger protein binding to DNA: an energy perspective using molecular dynamics simulation and free energy calculations on mutants of both zinc finger domains and their specific DNA bases

Energy calculations based on MM-GBSA were employed to study various zinc finger protein (ZF) motifs binding to DNA. Mutants of both the DNA bound to their specific amino acids were studied. Calculated energies gave evidence for a relationship between binding energy and affinity of ZF motifs to their sites on DNA. ΔG values were ?15.82(12), ?3.66(12), and ?12.14(11.6) kcal/mol for finger one, finger two, and finger three, respectively. The mutations in the DNA bases reduced the value of the negative energies of binding (maximum value for ΔΔG = 42Kcal/mol for F1 when GCG mutated to GGG, and ΔΔG = 22 kcal/mol for F2, the loss in total energy of binding originated in the loss in electrostatic energies upon mutation (r = .98). The mutations in key amino acids in the ZF motif in positions-1, 2, 3, and 6 showed reduced binding energies to DNA with correlation coefficients between total free energy and electrostatic was .99 and with Van der Waal was .93. Results agree with experimentally found selectivity which showed that Arginine in position-1 is specific to G, while Aspartic acid (D) in position 2 plays a complicated role in binding. There is a correlation between the MD calculated free energies of binding and those obtained experimentally for prepared ZF motifs bound to triplet bases in other reports (), our results may help in the design of ZF motifs based on the established recognition codes based on energies and contributing energies to the total energy.     

Structural effects of point mutations in proteins

A structural database of 11 families of chains differing by a single amino acid substitution has been built. Another structural dataset of 5 families with identical sequences has been used for comparison. The RMSD computed after a global superimposition of the mutated protein on each native one is smaller than the RMSD calculated among proteins of identical sequences. The effect of the perturbation is very local, and not necessarily the highest at the position of the mutation. A RMSD between mutated and native proteins is computed over a 3‐residue or a 7‐residue window at each position. To separate the effects of structural fluctuations due to point mutations from other sources, pair RMSD have been translated into P values which themselves are included in a score called P‐RANK. This score allows highlighting small backbone distortions by comparing these RMSD between mutated and native positions to the RMSD at the same positions in the absence of a mutation. It results from the P‐RANK that 38% of all mutations produce a significant effect on the displacement. When compared with a random distribution of RMSD at un‐mutated positions, we show that, even if the RMSD is greater when the mutation is in loops than in regular secondary structure, the relative effect is more important for regular secondary structures and for buried positions. We confirm the absence of correlation between RMSD and the predicted variation of free energy of folding but we found a small correlation between high RMSD and the error in the prediction of ΔΔG.     

A detailed representation of electrostatic energy in prediction of sequence and pH dependence of protein stability

A molecular mechanics model, previously validated in applications to structure prediction, is shown to reproduce experiment in predictions of protein ionization state, and in predictions of sequence and pH dependence of protein stability. Over a large dataset, 1876 values of ΔΔG of folding, the RMSD is 1.34 kcal/mol. Using an alternative measure of accuracy, either the sign of the calculated ΔΔG agrees with experiment or the absolute value of the deviation is less than 1.0 kcal/mol, 1660 of 1876 data points (88.5%) pass the condition. Relative to models used previously in computer‐aided protein design, the concept, we propose, most responsible for the performance of our model, and for the extensibility to non‐neutral values of pH, is the treatment of electrostatic energy. The electronic structure of the protein is modeled using distributed atomic multipoles. The structured liquid state of the solvent is modeled using a dielectric continuum. A modification to the energetics of the reaction field, induced by the protein in the dielectric continuum, attempts to account for preformed multipoles of solvent water molecules and ions. An adjustable weight (with optimal value.141) applied to the total vacuum energy accounts implicitly for electronic polarization. A threshold distance, beyond which pairwise atomic interactions are neglected, is not used. In searches through subspaces of sequences and conformations, efficiency remains acceptable for useful applications. Proteins 2014; 82:2497–2511. © 2014 Wiley Periodicals, Inc.     

Sequence Variation in the tRNA Genes of Human Mitochondrial DNA

Recent analyses have shown that nonsynonymous variation in human mitochondrial DNA (mtDNA) contains nonneutral variants, suggesting the presence of mildly deleterious mutations. Many of the disease-causing mutations in mtDNA occur in the genes encoding the tRNAs. Nucleotide sequence variation in these genes has not been studied in human populations, nor have the structural consequences of nucleotide substitutions in tRNA molecules been examined. We therefore determined the nucleotide sequences of the 22 tRNA genes in the mtDNA of 477 Finns and, also, obtained 435 European sequences from the MitoKor database. No differences in population polymorphism indices were found between the two data sets. We assessed selective constraints against various tRNA domains by comparing allele frequencies between these domains and the synonymous and nonsynonymous sites, respectively. All tRNA domains except the variable loop were more conserved than synonymous sites, and T stem and D stem were more conserved than the respective loops. We also analyzed the energetic consequences of the 96 polymorphisms recovered in the two data sets or in the Mitomap database. The minimum free energy (ΔG) was calculated using the free energy rules as implemented in mfold version 3.1. The ΔG’s were normally distributed among the 22 wild-type tRNA genes, whereas the 96 polymorphic tRNAs departed significantly from a normal distribution. The largest differences in ΔG between the wild-type and the polymorphic tRNAs in the Finnish population tended to be in the polymorphisms that were present at low frequencies. Allele frequency distributions and minimum free energy calculations both suggested that some polymorphisms in tRNA genes are nonneutral.Reviewing Editor: Dr. Rüdiger Cerff     

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.     

Determination of binding affinity upon mutation for type I dockerin–cohesin complexes from Clostridium thermocellum and Clostridium cellulolyticum using deep sequencing

The comprehensive sequence determinants of binding affinity for type I cohesin toward dockerin from Clostridium thermocellum and Clostridium cellulolyticum was evaluated using deep mutational scanning coupled to yeast surface display. We measured the relative binding affinity to dockerin for 2970 and 2778 single point mutants of C. thermocellum and C. cellulolyticum, respectively, representing over 96% of all possible single point mutants. The interface ΔΔG for each variant was reconstructed from sequencing counts and compared with the three independent experimental methods. This reconstruction results in a narrow dynamic range of ?0.8–0.5 kcal/mol. The computational software packages FoldX and Rosetta were used to predict mutations that disrupt binding by more than 0.4 kcal/mol. The area under the curve of receiver operator curves was 0.82 for FoldX and 0.77 for Rosetta, showing reasonable agreements between predictions and experimental results. Destabilizing mutations to core and rim positions were predicted with higher accuracy than support positions. This benchmark dataset may be useful for developing new computational prediction tools for the prediction of the mutational effect on binding affinities for protein–protein interactions. Experimental considerations to improve precision and range of the reconstruction method are discussed. Proteins 2016; 84:1914–1928. © 2016 Wiley Periodicals, Inc.     

Engineering a thermostable protein via optimization of charge-charge interactions on the protein surface

A simple theoretical model for increasing the protein stability by adequately redesigning the distribution of charged residues on the surface of the native protein was tested experimentally. Using the molecule of ubiquitin as a model system, we predicted possible amino acid substitutions on the surface of this protein which would lead to an increase in its stability. Experimental validation for this prediction was achieved by measuring the stabilities of single-site-substituted ubiquitin variants using urea-induced unfolding monitored by far-UV CD spectroscopy. We show that the generated variants of ubiquitin are indeed more stable than the wild-type protein, in qualitative agreement with the theoretical prediction. As a positive control, theoretical predictions for destabilizing amino acid substitutions on the surface of the ubiquitin molecule were considered as well. These predictions were also tested experimentally using correspondingly designed variants of ubiquitin. We found that these variants are less stable than the wild-type protein, again in agreement with the theoretical prediction. These observations provide guidelines for rational design of more stable proteins and suggest a possible mechanism of structural stability of proteins from thermophilic organisms.     

Role of conformational sampling in computing mutation-induced changes in protein structure and stability

The prediction of changes in protein stability and structure resulting from single amino acid substitutions is both a fundamental test of macromolecular modeling methodology and an important current problem as high throughput sequencing reveals sequence polymorphisms at an increasing rate. In principle, given the structure of a wild-type protein and a point mutation whose effects are to be predicted, an accurate method should recapitulate both the structural changes and the change in the folding-free energy. Here, we explore the performance of protocols which sample an increasing diversity of conformations. We find that surprisingly similar performances in predicting changes in stability are achieved using protocols that involve very different amounts of conformational sampling, provided that the resolution of the force field is matched to the resolution of the sampling method. Methods involving backbone sampling can in some cases closely recapitulate the structural changes accompanying mutations but not surprisingly tend to do more harm than good in cases where structural changes are negligible. Analysis of the outliers in the stability change calculations suggests areas needing particular improvement; these include the balance between desolvation and the formation of favorable buried polar interactions, and unfolded state modeling.     

An improved experimental system for determining small folding entropy changes resulting from proline to alanine substitutions

Changes in protein stability can be achieved by making substitutions that increase or decrease the available conformations of the unfolded protein without altering the conformational freedom of the folded protein. Matthews and coworkers (1987) proposed that proline to alanine (P --> A) substitution would achieve this type of entropic destabilization. By comparing the Ramachandran area associated with alanine and proline residues, Matthews et al. estimated the unfolding entropy change resulting from P --> A substitution to be 4.8 cal mol(-1) K(-1). Although such an entropy difference would produce a substantial free energy change, accurately resolving such free energy changes into entropic and enthalpic components has been difficult. Here, we attempt to quantify the unfolding entropy change produced by P --> A substitution by amplifying the effect through multiple substitutions, and by decreasing the uncertainty in determining the unfolding entropy. Variants of a repeat protein, the Drosophila Notch ankyrin domain, were constructed with a varying number of P --> A substitutions at structurally conserved positions. Unfolding entropy values of the variants were determined from free energy measurements taken over a common temperature range using chemical denaturation. Our findings confirm the prediction that increasing the number of proline residues present in similar local environments increases the unfolding entropy. The average value of this increase in unfolding entropy is 7.7 +/- 4.2 cal mol(-1) K(-1), which is within error of the value estimated by Matthews et al. (1987).     

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.     

Correlation of structure with transforming activity of the P21 proteins with substitutions of L-amino acids for Gly at position 13

The effects of amino acid substitutions for Gly 13 on the structure of the transforming region (Leu 6-Gly 15) of the P21 proteins have been explored using conformational energy calculations. It has been found that the substitution of Asp for Gly at this position results in a protein capable of transforming cells into malignant ones. Proteins that contain Ser at position 13 (but no other substitutions), however, transform cells with a greatly reduced activity. The transforming peptide with Asp 13 adopts a conformation that is different from the one for the peptide from the normal protein (with Gly 12 and Gly 13) and that may result in expression of a higher energy malignancy-producing form. The Ser-containing peptide adopts as its lowest energy conformation one that is identical to that of the peptide from the normal protein, thus explaining its lack of transforming activity. From analysis of the interactions preventing the Asp 13-containing peptide from adopting the normal conformation, it is predicted that substitutions of amino acids with branched side chains atC , such as Val, Ile, and Thr, should promote cell transformation. This prediction with Val has recently been confirmed in genetic experiments.     

Molecular Dynamics/Free Energy Perturbation Studies of the Thermostable V74I Mutant of Ribonuclease HI

Abstract

Recent site-directed mutagenesis and thermodynamic studies have shown that the V74I mutant of Escherichia coli ribonuclease HI (RNase HI) is more stable than the wild type protein [Ishikawa et al., Biochemistry 32, 6171 (1993)]. In order to clarify the stabilization mechanism of this mutant, we calculated the free energy change due to the mutation Val 74→Ile in both the native and denatured states by free energy perturbations based on molecular dynamics (MD) simulations. We carried out inclusive MD simulations for the protein in water; i.e., fully solvated, no artificial constraints applied, and all long-range Coulomb interactions included. We found that the free energy of the mutant increased slightly relative to the wild type, in the native state by 1.60 kcal/mol, and in the denatured state by 2.25 kcal/mol. The unfolding free energy increment of the mutant (0.66 ± 0.19 kcal/mol) was in good agreement with the experimental value (0.6 kcal/mol). The hysteresis error in the free energy calculations, i.e., forward and reverse perturbations, was only ±0.19 kcal/mol. These results show that the V74I mutant is stabilized relative to the wild type by the increased free energy of the denatured state and not by a decrease in the free energy of the native state as had been proposed earlier based on the mutant X-ray structure. It was found that the stabilization was caused by a loss of solvation energy in the mutant denatured state and not by improved packing interactions inside the native protein.     

Structural basis of urea-induced unfolding of Fasciola gigantica glutathione S-transferase

Glutathione S-transferases (GSTs) are enzymes that are involved in the detoxification of harmful electrophilic endogenous and exogenous compounds by conjugating with glutathione (GSH). The liver fluke GSTs have multifunctional roles in the host–parasite interaction, such as general detoxification and bile acid sequestration to synthase activity. The GSTs have been highlighted as vaccine candidates towards parasitic flukes. In this study, we have thoroughly examined the urea-induced unfolding of a mu-class Fasciola gigantica GST1 ( FgGST1) using spectroscopic techniques and molecular dynamic simulations. FgGST1 is a highly cooperative molecule, because during urea-induced equilibrium unfolding, a concurrent unfolding of the protein without stabilization of any folded intermediate was observed. The protein was stabilized with conformational free energy of about ~12.36 kcal/mol. The protein loses its activity with increasing urea concentration, as the GSH molecule is not able to bind to the protein. We also studied the fluorescence quenching of Trp residues and the obtained K _SV data that provided additional information on the unfolding of FgGST1. Molecular dynamic trajectories simulated in different urea concentrations and temperatures indicated that urea destabilizes FgGST1 structure by weakening hydrophobic interactions and the hydrogen bond network. We observed a precise correlation between the in vitro and in silico studies.