Evidence for a high proton translocation stoichiometry of the H+-ATPase complex in well coupled proteoliposomes reconstituted from a thermophilic cyanobacterium

Evidence is presented for a high proton translocation stoichiometry (H+/ATP) of approx. 9 in ATPase proteoliposomes with extremely low permeability for ions, reconstituted from a thermophilic cyanobacterium. A proportional relation between the phosphate potential (ΔG_fp) and the proton-motive force (Δp) was observed in thermodynamic equilibrium. A bulk-to-bulk Δp was imposed by valinomycin-induced K⁻ diffusion potentials of different size while the initial ΔG_fp was varied. In all cases equilibrium was reached in about 1.5 h. A high H⁻/ATP ratio was also deduced from the relation between the initial rates of ATP synthesis or hydrolysis at varying ΔG_fp and Δp. The implications of these results for the mechanism of energy transduction in energy-conserving membranes are discussed.     

Enzymatic synthesis of β-lactam antibiotics: A thermodynamic background

The equilibrium constants and the respective standard Gibbs energy changes for hydrolysis of some β-lactam antibiotics have been determined. Native and immobilized penicillin amidase (EC 3.5.1.11) from Escherichia coli has been used as a catalyst. The values of standard Gibbs energy changes corresponding to the pH-independent product of equilibrium concentrations (ΔG⁰_c = ? RT ln K_c) have been calculated. The differences in the structure of the antibiotics nucleus hardly ever affect the value of the pH-independent component of the standard Gibbs energy change (ΔG⁰_c) and value of apparent standard Gibbs energy change at a fixed pH (ΔG^0′_c). At the same time, the value of ΔG⁰_c is more sensitive to the structure of the acyl moiety of the antibiotic; when ampicillin is used instead of benzylpenicillin, ΔG⁰_c increases by ～6.3 kJ mol^?1 (1.5 kcal mol^?1). pH-dependences of the apparent standard Gibbs energy changes for hydrolysis of β-lactam antibiotics have been calculated. The pH-dependences of ΔG^0′_c for hydrolysis of all β-lactam antibiotics have a similar pattern. The thermodynamic pH optimum of the synthesis of these compounds is in the acid pH range (pH < 5.0). The breakage of the β-lactam ring leads to a sharp decrease in the ΔG^0′_c value and a change in the pattern of the pH-dependence. For example, at pH 5.0 ΔG^0′_c decreases from 14.4 kJ mol^?1 for benzylpenicillin to ?1.45 kJ mol^?1 for benzylpenicilloic acid. The reason for these changes is mainly a considerable increase in the pK of the amino group of the nucleus of the antibiotic and, as a consequence, a decrease in the component of standard Gibbs energy change, corresponding to the ionization of the system. The thermodynamic potentials of the enzymatic synthesis of semisynthetic penicillins and cephalosporins on the basis of both free acids and their derivatives (N-acylated amino acids, esters) are discussed. It is shown that with esters of the acids, a high yield of the antibiotic can, in principle, be achieved at higher pH values.     

Binding of 1-substituted carbazolyl-3,4-dihydro-β-carbolines with DNA: Molecular dynamics simulation and MM-GBSA analysis

Molecular Mechanics-Generalized Born-Solvent Accessibility free energy calculations were used to analyse DNA binding affinity of 1-substituted carbazolyl-3,4-dihydro-β-carboline molecules. In this study, DNA structure with sequence of d(CGATCG)2 was used for simulations. 15 ns molecular dynamics simulations of the studied complexes were performed. The calculated free energy was compared with experimental antitumor activity (IC₅₀). The predicted free energies decreased with the increase of IC₅₀ values. It was shown that molecules 1–6 bind to DNA via intercalation mode, while molecules 7–9 bind through groove binding mode. Also, it was found that the vdW energy term (ΔE_vdW) and the non-polar desolvation energy (ΔG_SA) are the favorable terms for binding energy, whereas net electrostatic energies (ΔE_ele + ΔG_GB) and conformational entropy energy (TΔS) are unfavorable ones.     

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.     

A hill-type muscle model expansion accounting for effects of varying transverse muscle load

Recent studies demonstrated that uniaxial transverse loading (F_G) of a rat gastrocnemius medialis muscle resulted in a considerable reduction of maximum isometric muscle force (ΔF_im). A hill-type muscle model assuming an identical gearing G between both ΔF_im and F_G as well as lifting height of the load (Δh) and longitudinal muscle shortening (Δl_CC) reproduced experimental data for a single load.Here we tested if this model is able to reproduce experimental changes in ΔF_im and Δh for increasing transverse loads (0.64 N, 1.13 N, 1.62 N, 2.11 N, 2.60 N). Three different gearing ratios were tested: (I) constant G_c representing the idea of a muscle specific gearing parameter (e.g. predefined by the muscle geometry), (II) G_exp determined in experiments with varying transverse load, and (III) G_f that reproduced experimental ΔF_im for each transverse load.Simulations using G_c overestimated ΔF_im (up to 59%) and Δh (up to 136%) for increasing load. Although the model assumption (equal G for forces and length changes) held for the three lower loads using G_exp and G_f, simulations resulted in underestimation of ΔF_im by 38% and overestimation of Δh by 58% for the largest load, respectively. To simultaneously reproduce experimental ΔF_im and Δh for the two larger loads, it was necessary to reduce F_im by 1.9% and 4.6%, respectively. The model seems applicable to account for effects of muscle deformation within a range of transverse loading when using a linear load-dependent function for G.     

Determination of Gibbs free energy of transfer for some univalent ions from water to methanol,acetonitrile, dimethylsulfoxide,pyridine, tetrahydrothiophene and liquid ammonia; standard electrode potentials of some couples in these solvents

The free energy of transfer, ΔG°_tr, for 21 univalent ions are determined from water to methanol, acetonitrile, dimethylsulfoxide (DMSO), pyridine, tetrahydrothiophene and liquid ammonia. These solvents show a wide range of donor properties, whereby water and methanol are regarded as hard donors, dimethylsulfoxide and acetonitrile are on the borderline between hard and soft, and the remaining solvents are regarded as typical soft donors. The ΔG°_tr values of ionic compounds are calculated from solubility product measurements of 1:1 salts. The extrathermodynamic tetraphenylarsonium tetraphenylborate (TATB) assumption has been applied in order to calculate the contributions from the single ions. The TATB assumption implies that the two large ions Ph₄As⁺ and BPh₄⁻ are equally solvated, thus ΔG°_tr(AsPh₄⁺)=ΔG°_tr(BPh₄⁻), for all solvent pairs. Standard electrode potentials in non-aqueous solvents can be calculated from the standard electrode potentials in water and the ΔG°_tr values. The standard electrode potentials calculated from the solubility product measurements, and the potentiometrically determined ones were found to be in excellent agreement. The extrathermodynamic assumption has thereby been experimentally shown to be close to the truth.     

An analysis of the influence of age and school-attendance status on the spread of variola minor.

Definitions are proposed for the independent and joint contributions that the chemical groups A and B make to the free energy of association of the ligand A?B with a receptor. The definitions are independent of the choice of the standard state and are consistent with the basic thermodynamic cycle relating the association of the ligands A?B, A?Y and X?B to the receptor Rappaport 1976. The basic idea is the use of the excess free energy of association of the ligand A?Y over the free energy of association of the reference ligand X?Y as the measure of the “independent” contribution of the group A to the binding. This definition allows the free energy of association of the ligand A?B to be written as the sum of the independent contributions of the groups A and B, their joint contribution, and an invariant free energy of association of the reference ligand with any receptor. With the appropriate definition of the receptor-reference ligand complex, water can be chosen as the reference ligand. Using ΔG(A?OH)?AG(HOH), ΔG(H?B?H)?ΔG(HOH) and ΔG(HO?C)?ΔG(HOH) as the definitions of the “independent” contributions of the chemical groups A, B and C to the binding of the ligand A?B?C, the joint contribution of the groups A and C to the binding is ΔG(A?B?C) ? ΔG(A?B?H) ? ΔG(H-B-C) + ΔG(H?B?H).     

Hexavalent chromium removal from aqueous solution by adsorption on treated sawdust

The studies on adsorption of hexavalent chromium were conducted by varying various parameters such as contact time, pH, amount of adsorbent, concentration of adsorbate and temperature. The kinetics of adsorption of Cr(VI) ion followed pseudo second order. Langmuir adsorption isotherm was employed in order to evaluate the optimum adsorption capacity of the adsorbent. The adsorption capacity was found to be pH dependant. Sawdust was found to be very effective and reached equilibrium in 3 h (adsorbate concentration 30 mg l⁻¹). The rate constant has been calculated at 303, 308, 313 and 318 K and the activation energy (E_a) was calculated using the Arrhenius equation. Thermodynamic parameters such as standard Gibbs energy (ΔG°) and heat of adsorption (ΔH_r) were calculated. The ΔG° and ΔH_r values for Cr(VI) adsorption on the sawdust showed the process to be exothermic in nature. The percentage of adsorption increased with decrease in pH and showed maximum removal of Cr(VI) in the pH range 4.5–6.5 for an initial concentration of 5 mg l⁻¹.     

IGERS: Inferring Gibbs Energy Changes of Biochemical Reactions from Reaction Similarities

Mathematical analysis and modeling of biochemical reaction networks requires knowledge of the permitted directionality of reactions and membrane transport processes. This information can be gathered from the standard Gibbs energy changes (ΔG⁰) of reactions and the concentration ranges of their reactants. Currently, experimental ΔG⁰ values are not available for the vast majority of cellular biochemical processes. We propose what we believe to be a novel computational method to infer the unknown ΔG⁰ value of a reaction from the known ΔG⁰ value of the chemically most similar reaction. The chemical similarity of two arbitrary reactions is measured by the relative number (T) of co-occurring changes in the chemical attributes of their reactants. Testing our method across a validated reference set of 173 biochemical reactions with experimentally determined ΔG⁰ values, we found that a minimum reaction similarity of T = 0.6 is required to infer ΔG⁰ values with an error of <10 kJ/mol. Applying this criterion, our method allows us to assign ΔG⁰ values to 458 additional reactions of the BioPath database. We believe our approach permits us to minimize the number of ΔG⁰ measurements required for a full coverage of a given reaction network with reliable ΔG⁰ values.     

Contribution of hydrophobic interactions to protein stability

Our goal was to gain a better understanding of the contribution of hydrophobic interactions to protein stability. We measured the change in conformational stability, Δ(ΔG), for hydrophobic mutants of four proteins: villin headpiece subdomain (VHP) with 36 residues, a surface protein from Borrelia burgdorferi (VlsE) with 341 residues, and two proteins previously studied in our laboratory, ribonucleases Sa and T1. We compared our results with those of previous studies and reached the following conclusions: (1) Hydrophobic interactions contribute less to the stability of a small protein, VHP (0.6 ± 0.3 kcal/mol per -CH₂- group), than to the stability of a large protein, VlsE (1.6 ± 0.3 kcal/mol per -CH₂- group). (2) Hydrophobic interactions make the major contribution to the stability of VHP (40 kcal/mol) and the major contributors are (in kilocalories per mole) Phe18 (3.9), Met13 (3.1), Phe7 (2.9), Phe11 (2.7), and Leu21 (2.7). (3) Based on the Δ(ΔG) values for 148 hydrophobic mutants in 13 proteins, burying a -CH₂- group on folding contributes, on average, 1.1 ± 0.5 kcal/mol to protein stability. (4) The experimental Δ(ΔG) values for aliphatic side chains (Ala, Val, Ile, and Leu) are in good agreement with their ΔG_tr values from water to cyclohexane. (5) For 22 proteins with 36 to 534 residues, hydrophobic interactions contribute 60 ± 4% and hydrogen bonds contribute 40 ± 4% to protein stability. (6) Conformational entropy contributes about 2.4 kcal/mol per residue to protein instability. The globular conformation of proteins is stabilized predominantly by hydrophobic interactions.     

Isothermal titration calorimetry for drug design: Precision of the enthalpy and binding constant measurements and comparison of the instruments

Isothermal titration calorimetry (ITC) is one of the most robust label- and immobilization-free techniques used to measure protein – small molecule interactions in drug design for the simultaneous determination of the binding affinity (ΔG) and the enthalpy (ΔH), both of which are important parameters for structure-thermodynamics correlations. It is important to evaluate the precision of the method and of various ITC instrument models by performing a single well-characterized reaction. The binding between carbonic anhydrase II and acetazolamide was measured by four ITC instruments – PEAQ-ITC, iTC200, VP-ITC, and MCS-ITC and the standard deviation of ΔG and ΔH was determined. Furthermore, the limit of an approach to reduce the protein concentration was studied for a high-affinity reaction (K_d = 0.3 nM), too tight to be measured by direct (non-displacement) ITC. Chemical validation of the enthalpy measurements is discussed.     

A new method for predicting binding free energy between receptor and ligand

A practical method to estimate binding free energy, ΔG_bind, of a given ligand structure to the target receptor has been developed. The method assumes that ΔG_bind is given by the summation of intermolecular interaction energy, ΔG_inter, and partial desolvation energy, ΔG_desolv. ΔG_desolv is calculated from the buried surface area in the complex between the ligand and receptor, based on solvation energy, ΔG_solv, formulated by an equation which can be calibrated with observed values. Then, the method was applied to arabinose-binding protein (ABP) and dihydrofolate reductase (DHFR), after recalibrating the weights for ΔG_inter and each term of ΔG_desolv using observed ΔG_bind data for 29 known ligands to avidin (AV). The usefulness of our method was confirmed by the fact that correlation coefficients between the calculated and observed ΔG_bind's in AV, ABP and DHFR were 0.92, 0.77, and 0.88, whereas the corresponding values obtained by simple force field calculation were 0.79, 0.30, and 0.79, respectively. Further investigations to improve the method and validate the parameters are in progress. Proteins 33:62–73, 1998. © 1998 Wiley-Liss, Inc.     

Effect of Interdomain Linker Length on an Antagonistic Folding-Unfolding Equilibrium between Two Protein Domains

Fusion of one protein domain with another is a common event in both evolution and protein engineering experiments. When insertion is at an internal site (e.g., a surface loop or turn), as opposed to one of the termini, conformational strain can be introduced into both domains. Strain is manifested by an antagonistic folding-unfolding equilibrium between the two domains, which we previously showed can be parameterized by a coupling free-energy term (ΔG_X). The extent of strain is predicted to depend primarily on the ratio of the N-to-C distance of the guest protein to the distance between ends of the surface loop in the host protein. Here, we test that hypothesis by inserting ubiquitin (Ub) into the bacterial ribonuclease barnase (Bn), using peptide linkers from zero to 10 amino acids each. ΔG_X values are determined by measuring the extent to which Co²⁺ binding to an engineered site on the Ub domain destabilizes the Bn domain. All-atom, unforced Langevin dynamics simulations are employed to gain structural insight into the mechanism of mechanically induced unfolding. Experimental and computational results find that the two domains are structurally and energetically uncoupled when linkers are long and that ΔG_X increases with decreasing linker length. When the linkers are fewer than two amino acids, strain is so great that one domain unfolds the other. However, the protein is able to refold as dimers and higher-order oligomers. The likely mechanism is a three-dimensional domain swap of the Bn domain, which relieves conformational strain. The simulations suggest that an effective route to mechanical unfolding begins with disruption of the hydrophobic core of Bn near the Ub insertion site.     

Structural investigation into the inhibitory mechanisms of indomethacin and its analogues towards human glyoxalase I

In the present work, a combined study of kinetic analysis, molecular docking, and molecular dynamics simulations on indomethacin and its analogues is performed to better understand their inhibitory mechanisms towards human glyoxalase I (GLOI). A remarkable correlation (R² = 0.974) was observed for six inhibitors including indomethacin between their experimental inhibitory affinities and predicted binding free energy parameter (ΔG_bind,pred). This suggests that ΔG_bind,pred of a GLOI/inhibitor complex can be efficiently used to interpolate the experimental inhibitory affinity of a ligand of similar nature in the GLOI enzyme system. Energetic analyses revealed that electrostatic contribution plays an important role in their inhibitory mechanisms, which reflects the significant contribution of the coordination bond between zinc and ligands. The present work highlights that indomethacin is a promising lead as GLOI inhibitors for further development since it may bind all subsites in the active site pocket of GLOI and stabilize the flexible loop (152-159).     

Studies of lysozyme binding to histamine as a ligand for hydrophobic charge induction chromatography

Histamine was immobilized on Sepharose CL‐6B (Sepharose) for use as a ligand of hydrophobic charge induction chromatography (HCIC) of proteins. Lysozyme adsorption onto Histamine‐Sepharose (HA‐S) was studied by adsorption equilibrium and calorimetry to uncover the thermodynamic mechanism of the protein binding. In both the experiments, the influence of salt (ammonium sulfate and sodium sulfate) was examined. Adsorption isotherms showed that HA‐S exhibited a high salt tolerance in lysozyme adsorption. This property was well explained by the combined contributions of hydrophobic interaction and aromatic stacking. The isotherms were well fitted to the Langmuir equation, and the equilibrium parameters for lysozyme adsorption were obtained. In addition, thermodynamic parameters (ΔH_ads, ΔS_ads, and ΔG_ads) for the adsorption were obtained by isothermal titration calorimetry by titrating lysozyme solutions into the adsorbent suspension. Furthermore, free histamine was titrated into lysozyme solution in the same salt‐buffers. Compared with the binding of lysozyme to free histamine, lysozyme adsorption onto HA‐S was characterized by a less favorable ΔG_ads and an unfavorable ΔS_ads because histamine was covalently attached to Sepharose via a three‐carbon‐chain spacer. Consequently, the immobilized histamine could only associate with the residues on the protein surface rather than those in the hydrophobic pocket, causing a less favorable orientation between histamine and lysozyme. Further comparison of thermodynamic parameters indicated that the unfavorable ΔS_ads was offset by a favorable ΔH_ads, thus exhibiting typical enthalpy‐entropy compensation. Moreover, thermodynamic analyses indicated the importance of the dehydration of lysozyme molecule and HA‐S during the adsorption and a substantial conformational change of the protein during adsorption. The results have provided clear insights into the adsorption mechanisms of lysozyme onto the new HCIC material. © 2009 American Institute of Chemical Engineers Biotechnol. Prog., 2010     

Group contribution method for thermodynamic analysis of complex metabolic networks

A new, to our knowledge, group contribution method based on the group contribution method of Mavrovouniotis is introduced for estimating the standard Gibbs free energy of formation (Δ_fG′°) and reaction (Δ_rG′°) in biochemical systems. Gibbs free energy contribution values were estimated for 74 distinct molecular substructures and 11 interaction factors using multiple linear regression against a training set of 645 reactions and 224 compounds. The standard error for the fitted values was 1.90 kcal/mol. Cross-validation analysis was utilized to determine the accuracy of the methodology in estimating Δ_rG′° and Δ_fG′° for reactions and compounds not included in the training set, and based on the results of the cross-validation, the standard error involved in these estimations is 2.22 kcal/mol. This group contribution method is demonstrated to be capable of estimating Δ_rG′° and Δ_fG′° for the majority of the biochemical compounds and reactions found in the iJR904 and iAF1260 genome-scale metabolic models of Escherichia coli and in the Kyoto Encyclopedia of Genes and Genomes and University of Minnesota Biocatalysis and Biodegradation Database. A web-based implementation of this new group contribution method is available free at http://sparta.chem-eng.northwestern.edu/cgi-bin/GCM/WebGCM.cgi.     

Energy thresholds for ATP synthesis in chloroplasts

We have investigated the ATP synthesis associated with acid-base transitions in chloroplast lamellae under conditions which allow simultaneous control of the thermodynamic variables, ΔpH, membrane potential and ΔG_ATP. These variables have been directly imposed rather than simply inferred. Since the initiation of labeled P_i incorporation seems to measure accurately the initiation of net ATP synthesis, the following conclusions can be drawn: (1) The proton-motive force which is just sufficient for ATP synthesis provides almost exactly the required energy for ΔG_ATP if the efflux of three H⁺ is required for each ATP molecule formed. (2) The membrane potential and the ΔpH contribute to the proton-motive force in a precisely additive way. Thus, the threshold can be reached or exceeded by a ΔpH in the absence of a membrane potential, by a membrane potential in the absence of a ΔpH, or by any combination of membrane potential and ΔpH. With a large enough membrane potential, ATP synthesis occurs even against a small inverse ΔpH. In each instance the combined ΔpH and membrane potential necessary for initiation of ATP synthesis represent the same threshold proton-motive force.     

Instantaneous Normal Modes as an Unforced Reaction Coordinate for Protein Conformational Transitions

We present a novel sampling approach to explore large protein conformational transitions by determining unique substates from instantaneous normal modes calculated from an elastic network model, and applied to a progression of atomistic molecular dynamics snapshots. This unbiased sampling scheme allows us to direct the path sampling between the conformational end states over simulation timescales that are greatly reduced relative to the known experimental timescales. We use adenylate kinase as a test system to show that instantaneous normal modes can be used to identify substates that drive the structural fluctuations of adenylate kinase from its closed to open conformations, in which we observe 16 complete transitions in 4 μs of simulation time, reducing the timescale over conventional simulation timescales by two orders of magnitude. Analysis shows that the unbiased determination of substates is consistent with known pathways determined experimentally.     

Thermodynamic parameters of stabilization of the Yersinia pestis Caf113-149 subunit in compact form

Several experimental methods (circular dichroism, viscosity, intrinsic fluorescence, and fluorescence labeling) were used to study the conformational folding/unfolding transitions in a compact monomeric form of the Caf1_13-149 subunit under the action of guanidine hydrochloride in the temperature range 5–45°C. It has been shown that transitions always occur between two major states (unfolded and compact). This has made it possible to determine all the main thermodynamic functions that characterize the compact state of the Caf1_13-149 subunit: stability temperature T _m, free energy of stabilization ΔG _st, enthalpy ΔH _tr, and heat capacity jump ΔC in collapse of the structure. These data have been confirmed by an independent experiment on melting of fluorescently labeled protein.     

Systematic investigation of interactions between papain and MPA-capped CdTe quantum dots

Fluorescent quantum dots (QDs) have been widely applied in biological and biomedical areas, but relatively little is known about the interaction of QDs with some natural enzymes. Herein, the interactions between 3-mercaptopropionic acid-capped CdTe QDs (MPA-QDs) and papain were systematically investigated by UV–Vis absorption spectra, fluorescence spectra and circular dichroism (CD) spectra under the physiological conditions. The fluorescence spectra results indicated that MPA-QDs quenched the fluorescence intensity of papain. The modified Stern–Volmer quenching constant K _a at different temperatures and the corresponding thermodynamic parameters ΔH, ΔG and ΔS were also calculated. The binding of MPA-QDs and papain is a result of the formation of QDs-papain complex and the electrostatic interactions play a major role in stabilizing the complex. The CD technique was further used to analyze the conformational changes of papain induced by MPA-QDs and the results indicated that the biological activity of papain was affected by MPA-QDs dramatically.