Prediction of protein solubility from calculation of transfer free energy

Solubility plays a major role in protein purification, and has serious implications in many diseases. We studied the effects of pH and mutations on protein solubility by calculating the transfer free energy from the condensed phase to the solution phase. The condensed phase was modeled as an implicit solvent, with a dielectric constant lower than that of water. To account for the effects of pH, the protonation states of titratable side chains were sampled by running constant-pH molecular dynamics simulations. Conformations were then selected for calculations of the electrostatic solvation energy: once for the condensed phase, and once for the solution phase. The average transfer free energy from the condensed phase to the solution phase was found to predict reasonably well the variations in solubility of ribonuclease Sa and insulin with pH. This treatment of electrostatic contributions combined with a similar approach for nonelectrostatic contributions led to a quantitative rationalization of the effects of point mutations on the solubility of ribonuclease Sa. This study provides valuable insights into the physical basis of protein solubility.     

An approximation of loop free energy values of RNA H-pseudoknots.

A set of free energy values is suggested for RNA H-pseudoknot loops. The parameters are adjusted to be consistent with the theory of polymer thermodynamics and known data on pseudoknots. The values can be used for estimates of pseudoknot stabilities and computer predictions of RNA structures.     

The role of solvent polarity in the free energy of transfer of amino acid side chains from water to organic solvents

The transfer free energies of amino acid side chains from water to N-methylacetamide have been determined and compared with those obtained from other model systems. Although the process of transfer from water to N-methylacetamide represents transfer from a lower dielectric phase to a higher dielectric phase, the transfer free energies of most of the amino acid side chains are nearly the same as those obtained from the water to ethanol system. Among the apolar side chains studied, only the transfer free energies of methionine and the aromatic side chains are apparently influenced to some extent by the polarity of the organic solvent phase. The transfer free energies of the neutral polar side chains also exhibit significant dependence on solvent polarity. The van't Hoff plots for most of the apolar side chains exhibit nonlinear curves, indicating that the enthalpy of transfer from water to N-methylacetamide is temperature-dependent. It is suggested that to assess the contribution of the hydrophobic free energy to the stability of globular proteins, it is probably not necessary to account for variation in the internal environment of the protein.     

Information-theoretic significance of Gibbs energy supply to editing mechanisms.

If a branched multistep editing mechanism is implemented by an enzyme with a single site for the specific substrates, there is no reason to believe that the number of testing steps is fixed and cannot be controlled by some external factors. The paper considers the mechanisms of single- or multistep editing done in response to various factors, particularly to the value of displacement from the reaction equilibrium. To avoid a complicated analysis of a fully specified case, which would be likely to obscure the general significant features, the operating modes of those mechanisms are estimated using the method of minimizing associated information gains. It turns out that sufficiently far from equilibrium the variable mechanisms can essentially operate just as well as the fixed multistep mechanisms.     

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.     

Interactions of myoglobin with urea and some alkylureas. I. Solvation in urea and alkylurea solutions

The interactions of myoglobin with urea, methyl-, N,N'-dimethyl- and ethylurea in aqueous solutions were studied by density measurements. From the densities at constant chemical potential and constant molality, the partial specific volumes of myoglobin in these solutions as well as the extent of preferential binding of urea and alkylurea to myoglobin were determined. It has been found that water and not the denaturant is preferentially bound in urea solutions and alkylurea solutions up to 4 M so that the Gibbs free energy of myoglobin, i.e., its chemical potential in a denaturant solution, is larger than in water. This behavior of myoglobin is different from that of other globular proteins for which preferential binding of urea has been found. It appears that preferential hydration of myoglobin is due to its high content of ionic groups.     

Contribution of water to free energy of hydrolysis of pyrophosphate

The energy of hydrolysis of phosphate compounds varies depending on whether they are in solution or bound to the catalytic site of enzymes. With the purpose of simulating the conditions at the catalytic site, the observed equilibrium constant for pyrophosphate hydrolysis (Kobsd) was measured in aqueous mixtures of dimethyl sulfoxide, ethylene glycol, or polymers of ethylene glycol. The reaction was catalyzed by yeast inorganic pyrophosphatase at 30 degrees C. All the cosolvents used promoted a decrease of Kobsd. Polymers of ethylene glycol were more effective than dimethyl sulfoxide or ethylene glycol in decreasing Kobsd. The higher the molecular weight of the polymer, the lower the value of Kobsd. A decrease in Kobsd from 346 M (delta G degree obsd = -3.5 kcal mol-1) to 0.1 M (delta G degree obsd = 1.3 kcal mol-1) was observed after the addition of 50% (w/v) poly(ethylene glycol) 8000 to a solution containing 0.9 mM MgCl2 and 1 mM Pi at pH 8.0. The association constants of Pi and pyrophosphate for H+ and Mg2+ were measured in presence of different ethylene glycol concentrations in order to calculate the Keq for hydrolysis of different ionic species of pyrophosphate. A decrease in all the Keq was observed. The results are interpreted according to the concept that the energy of hydrolysis of phosphate compounds depends on the different solvation energies of reactants and products.     

A correction to the calculation of the Gibbs free energy of adsorption for biomolecules in ion-exchange systems

We wish to propose a correction to the methodology introduced by Gerstner et al. [J.A. Gerstner, J.A. Bell, S.M. Cramer, Biophys. Chem. 52 (1994) 97-106] for the calculation of Gibbs free energies of adsorption of biomolecules to ion-exchange systems. Our approach is based on the requirement that the mobile phase and stationary phase concentrations be expressed in exactly the same units and the equilibrium constant be strictly dimensionless. The Gibbs free energies of ion-exchange calculated based on this correction appear to be more negative than those originally calculated by Gertner et al.     

Misconceptions arising from a sign discrepancy in thermodynamic data for the Gibbs free energy profile of ribonuclease a

An apparent discrepancy in the data for the Gibbs free energy change as a function of temperature at different pHs, originally published by Brandts in 1965 and repeated by Brandts and Hunt in 1967 with an unexplained change in sign, has lead to close to 40 years of misguided thinking in examining the thermodynamics of protein unfolding, including the frequently promulgated idea of cold denaturation. We have carried out a detailed analysis based on the Planck-Benzinger approach, which is very powerful in clarifying the fundamental aspects of biochemical energetics.     

The calculated free energy effects of 5-methyl cytosine on the B to Z transition in DNA

We have examined the free energy effects of 5-methylation of cytosine on the B in equilibrium Z conformational equilibrium in DNA. Free energy differences were calculated using the free energy perturbation approach, which uses an easily derived equation from classical statistical mechanics to relate the free energy difference between two states to the ensemble average of the potential energy difference between the states. Calculations were carried both in explicit solvent and (for comparison) in vacuo. The free energy values obtained for the explicit solvent systems are total free energies, with contributions from all parts of the system (solvent + solute), and so are relevant to the B in equilibrium Z transitions observed under real (physiological) conditions. We calculate that in solution, methylation makes the B in equilibrium Z transition more favorable by about -0.4 kcal/mole base pair (bp) in free energy. This value compares well with approximate experimentally derived values of about -0.3 kcal/mole-bp. We also discuss a method for determining the free energy difference between conformational states poorly maintained by a potential energy model. Finally, the effects of methylation on the melting temperature of DNA are examined.     

The chemical potential in solutions and the free energy of reaction

The expression for the chemical potential of a species in a multi-component solution is usually derived by a thermodynamic argument based on ideal gas theory. A direct statistical mechanical derivation is given below, using the methods of the preceding paper. The analysis is formulated in such a way that there is no need to introduce the notion of standard states. It is made clear why certain species (water, H⁺ in buffered systems) may be ignored in calculating the affinity (negative free energy change) of a chemical reaction. The equilibrium constant is expressed in terms of generalized phase integrals or partition functions.     

Delayed fluorescence from Rhodopseudomonas sphaeroides reaction centers. Enthalpy and free energy changes accompanying electron transfer from P-870 to quinones

Delayed fluorescence from isolated reaction centers of Rhodopseudomonas sphaeroides was measured to study the energetics of electron transfer from the bacteriochlorophyll complex (P-870, or P) to the primary and secondary quinones (Q_A and Q_B). The analysis was based on the assumption that electron transfer between P and Q reaches equilibrium quickly after flash excitation, and stays in equilibrium during the lifetime of the P⁺Q⁻ radical pair. Delayed fluorescence of 1Q reaction centers (reaction centers that contain only Q_A) has a lifetime of about 0.1 s, which corresponds to the decay of P⁺Q⁻_A. 2Q reaction centers (which contain both Q_A and Q_B) have a much weaker delayed fluorescence, with a lifetime that corresponds to that of P⁺Q⁻_B (about 1 s). In the presence of o-phenanthroline, the delayed fluorescence of 2Q reaction centers becomes similar in intensity and decay kinetics to that of 1Q reaction centers. From comparisons of the intensities of the delayed fluorescence from P⁺Q⁻_A and P⁺Q⁻_B, the standard free energy difference between P⁺Q⁻_A and P⁺Q⁻_B is calculated to be 78 ± 8 meV. From a comparison of the intensity of the delayed fluorescence with that of prompt fluorescence, we calculate that P⁺Q⁻_A is 0.86 ± 0.02 eV below the excited singlet state of P in free energy, or about 0.52 eV above the ground state PQ_A. The temperature dependence of the delayed fluorescence indicates that P⁺Q⁻_A is about 0.75 eV below the excited singlet state in enthalpy, or about 0.63 eV above the ground state.     

Efficiency of free energy transfer and entropy production in photosynthetic systems

The diagram method for the calculation of entropy production and efficiency associated with very first steps of photosynthetic mechanism is developed. By using one simple model for the bacteriorhodopsin light activated proton pump action, it is shown that in the steady state of biological interest, both entropy production and efficiency of transfer of light energy are maximal for the same optimal values of kinetic constants.     

Determination of the interfacial water content in protein-protein complexes from free energy simulations

The question as to how many tightly or weakly bound water molecules are located in interfaces between protein-protein complex constituents is addressed from a phase equilibrium point of view by developing a theory in the canonical ensemble. A fast method based on free energy simulations is described for computing the number of water molecules in the interface regions. Results are given for 211 interfacial cavities of 26 antigen-antibody complexes for which experimentally determined structures are found in the Protein Data Bank. The accuracy of the method is assessed and the computational water content is compared with experimental data, revealing the amount of water molecules not resolved by experimental approaches.     

锰矿修复区植物生态系统自由能与化学势分析

基于热力学理论建立了生态系统Gibbs自由能方程,用以计算湘潭锰矿生态修复区植被系统的自由能(G)和物种化学势(μ)。生态修复区(及对照区)以泡桐(Paulownia fortunei)和栾树(Koelreuteria bipinnata)作为建群植物,总面积为4 hm~2,修复区泡桐和栾树的根际施用了含有自试验点废弃矿渣中筛选出的耐性菌株的有机菌肥,目的是为植物生长提供必要养分和降低根际土壤重金属毒性,对照区泡桐和栾树的根际施用了等量的化肥。泡桐和栾树种植后5 a期间,修复区与对照区均自然萌发生长了许多本土植物种类。试验结果表明,修复区植物种类数达到48,为对照区的3.7倍;修复区的总生物量、锰吸收量分别达到23324 kg/hm~2和4280 g/hm~2,为对照区对应值的20.6和2.6倍;修复区系统自由能G远远大于对照区的值,说明有机菌肥具有显著的改良污染土壤根际环境的效果。修复区和对照区植物种类之间的化学势μ均存在显著差异(P0.001),μ值差异范围分别为-3.79—6.76和-3.42—3.59,该一差异反映不同物种适应和修复锰污染环境的能力。G和μ值包含了生态系统生产力、生物多样性,植物种类生长势、重金属富集能力、生态学行为等综合信息,能反映生态系统与立地环境的关系和修复植物的生态学特性,可作为重金属污染区植被修复效果评价和修复植物筛选的重要指标。     

Factors affecting energy transfer from phycobilisomes to thylakoids in Anacystis nidulans.

Short illumination with white light of dark-maintained Anacystis nidulans prior to immersion in liquid nitrogen resulted in a marked change of fluorescence emission characteristics at 77 K. The fluorescence of Photosystem II-associated membrane bound pigments increases, while the emission due to phycobilins decreases. This effect seems to be due to a light-dependent alteration in the extent of contact between phycobilisomes and thylakoids, since the effect is reversible in the dark and is abolished by short glutaraldehyde fixation. The preillumination effect is not inhibited by DCMU. Emission spectra obtained with actively growing and CO2-starved cells indicate that the light-dependent increase in energy transfer from phycobilins to chlorophyll depends upon the physiological state of the cells.     

Reconstituted energy transfer from antenna pigment-protein to reaction centres isolated from Rhodopseudomonas sphaeroides.

Efficient energy transfer has been reconstituted between an antenna pigment-protein and reaction centres isolated from the photosynthetic membrane of Rhodopseudomonas sphaeroides. The reconstituted system has fluorescence induction kinetics and fluorescence yields similar to those obtained from antenna bacteriochlorophyll in chromatophores. The results indicated that closed reaction centres quench fluorescence from the antenna pigment-protein, although not as strongly as photochemically active reaction centres. The measurement of fluorescence yields from chromatophores of the reaction centreless mutant PM-8 and of the parent strain Ga confirmed these observations. The fluorescence yield from the reconstituted system was approximately the same whether the reaction centres had been closed by photo-oxidation of the bacteriochlorophyll electron donor or chemical reduction of the primary acceptor, indicating a similar lifetime for the excited singlet state in both states of the reaction centres.