Computation of physicochemical parameters, namely pH, in complex (bio)chemical systems: extension to gas-liquid systems

The first model has been proposed to compute, in complex liquid (bio)chemical systems, a number of physicochemical parameters, namely pH, concentration of one of any chemical species, partition between acid-base forms, global charge, or ionic strength, assuming the physicochemical equilibrium state. The extension of the present model, described here, permits moreover the computation of gas-liquid distributions, specific gas volumes, or total pressures. The model solely requires the knowledge of existing thermodynamic constants and of the concentration of every chemical species other than the species under examination. The model elicits a unique equilibrium state. Computed values agreed with experimental measurements, thereby validating the model. Digital computer programs were prepared to use the proposed algorithms.     

Thermodynamics of the reactions of carbamoyl phosphate

Two measurements of equilibrium constants by Marshall and Cohen make it possible to calculate standard Gibbs energies of formation of the species of carbamate and carbamoyl phosphate. Carbamate formation from carbon dioxide and ammonia does not require an enzyme, and the equilibrium concentrations of carbamate in ammonium bicarbonate are calculated. Knowing the values of standard Gibbs energies of formation of species of carbamate and carbamoyl phosphate make it possible to calculate the dependencies of the standard transformed Gibbs energies of formation of these reactants on pH and ionic strength and to calculate apparent equilibrium constants for several enzyme-catalyzed reactions and several chemical reactions. These calculations are sufficiently complicated that computer programs in Mathematica are used to make tables and plots. The dependences of apparent equilibrium constants on pH are consequences of the production or consumption of hydrogen ions, which are shown in plots. As usual the increase in the number of enzyme-catalyzed reactions for which apparent equilibrium constants can be calculated is larger than the number of reactions required to obtain the thermodynamic properties of the species involved.     

Standard transformed Gibbs energies of coenzyme A derivatives as functions of pH and ionic strength

The best way to store data on apparent equilibrium constants for enzyme-catalyzed reactions is to calculate the standard Gibbs energies of formation of the species involved at 298.15 K and zero ionic strength so that equilibrium constants can be calculated at the desired pH and ionic strength. These calculations are described for CoA, acetyl-CoA, oxalyl-CoA, succinyl-CoA, methylmalonyl-CoA, malyl-CoA and CoA-glutathione. The species properties are then used to calculate standard transformed Gibbs energies of formation for these reactants as functions of pH at ionic strength 0.25 M. The species data also make it possible to calculate apparent equilibrium constants of 23 enzyme-catalyzed reactions as a function of pH, including some that cannot be determined directly because they are so large.     

Binding and hydrolysis of ATP by cardiac myosin subfragment 1: effect of solution parameters on transient kinetics

Transient kinetic data of ATP binding and cleavage by cardiac myosin subfragment 1 (S1) were obtained by fluorescence stopped flow and analyzed by using computer modeling based on a consecutive, reversible two-step mechanism: (formula: see text) where M1 and M12 denote myosin species with enhanced fluorescence and K'O = K0/(K0[ATP] + 1). The kinetic constants K0, k12, k23, and k32 and the fractional contributions of M1 and M12 to the total fluorescence are analyzed over a range of systematically varied solution parameters. The initial ATP binding equilibrium (K0), which decreases with increasing pH, is facilitated by a positively charged protein residue with a pK of 7.1. An active-site charge of +1.5 is determined from the ionic strength dependence. The rate constants k12, k23, and k32 also exhibit pK's near neutrality but increase with increasing pH. The majority of the large (-54 kJ/mol) negative free energy of ATP binding occurs upon S1 isomerization, k12, and a large increase in entropy (183 J/kmol at 15 degrees C) is associated with the cleavage step. The equilibrium constant for the cleavage step, K2, is determined as 3.5 at pH 7.0, 15 degrees C, and 200 mM ionic strength. There are no significant changes in fractional contributions to total fluorescence enhancement due to solvent-dependent conformational changes of S1 in these data. When values for the combined rate constants are calculated and compared with those determined by graphical analysis, it is observed that graphical analysis overestimates the binding rate constant (K0k12) by 25% and the hydrolysis rate constant (k23 + k32) by as much as 30%.(ABSTRACT TRUNCATED AT 250 WORDS)     

Standard thermodynamic formation properties for the adenosine 5'-triphosphate series.

The criterion for chemical equilibrium at specified temperature, pressure, pH, concentration of free magnesium ion, and ionic strength is the transformed Gibbs energy, which can be calculated from the Gibbs energy. The apparent equilibrium constant (written in terms of the total concentrations of reactants like adenosine 5'-triphosphate, rather than in terms of species) yields the standard transformed Gibbs energy of reaction, and the effect of temperature on the apparent equilibrium constant at specified pressure, pH, concentration of free magnesium ion, and ionic strength yields the standard transformed enthalpy of reaction. From the apparent equilibrium constants and standard transformed enthalpies of reaction that have been measured in the adenosine 5'-triphosphate series and the dissociation constants of the weak acids and magnesium complexes involved, it is possible to calculate standard Gibbs energies of formation and standard enthalpies of formation of the species involved at zero ionic strength. This requires the convention that the standard Gibbs energy of formation and standard enthalpy of formation for adenosine in dilute aqueous solutions be set equal to zero. On the basis of this convention, standard transformed Gibbs energies of formation and standard transformed enthalpies of formation of adenosine 5'-trisphosphate, adenosine 5'-diphosphate, adenosine 5'-monophosphate, and adenosine at 298.15 K, 1 bar, pH = 7, a concentration of free magnesium ions of 10(-3) M, and an ionic strength of 0.25 M have been calculated.     

Cytochrome C interaction with cardiolipin/phosphatidylcholine model membranes: effect of cardiolipin protonation

Resonance energy transfer between anthrylvinyl-labeled phosphatidylcholine as a donor and heme moiety of cytochrome c (cyt c) as an acceptor has been employed to explore the protein binding to model membranes, composed of phosphatidylcholine and cardiolipin (CL). The existence of two types of protein-lipid complexes has been hypothesized where either deprotonated or partially protonated CL molecules are responsible for cyt c attachment to bilayer surface. To quantitatively describe cyt c membrane binding, the adsorption model based on scaled particle and double layer theories has been employed, with potential-dependent association constants being treated as a function of acidic phospholipid mole fraction, degree of CL protonation, ionic strength, and surface coverage. Multiple arrays of resonance energy transfer data obtained under conditions of varying pH, ionic strength, CL content, and protein/lipid molar ratio have been analyzed in terms of the model of energy transfer in two-dimensional systems combined with the adsorption model allowing for area exclusion and electrostatic effects. The set of recovered model parameters included effective protein charge, intrinsic association constants, and heme distance from the bilayer midplane for both types of protein-lipid complexes. Upon increasing CL mole fraction from 10 to 20 mol % (the value close to that characteristic of the inner mitochondrial membrane), the binding equilibrium dramatically shifted toward cyt c association with partially protonated CL species. The estimates of heme distance from bilayer center suggest shallow bilayer location of cyt c at physiological pH, whereas at pH below 6.0, the protein tends to insert into membrane core.     

Relations between biochemical thermodynamics and biochemical kinetics

The parameters in steady-state or rapid-equilibrium rate equations for enzyme-catalyzed reactions depend on the temperature, pH, and ionic strength, and may depend on the concentrations of specific species in the buffer. When the complete rate equation (i.e. the equation with parameters for the reverse reaction as well as the forward reaction) is determined, there are one or more Haldane relations between some of the kinetic parameters and the apparent equilibrium constant for the reaction that is catalyzed. When the apparent equilibrium constant can be calculated from the kinetic parameters, the equilibrium composition can be calculated. This is remarkable because the kinetic parameters all depend on the properties of the enzymatic site, but the apparent equilibrium constant and the equilibrium composition do not. The effects of ionic strength and pH on the unoccupied enzymatic site and the occupied enzymatic site have to cancel in the Haldane relation or in the calculation of the apparent equilibrium constant using the rate constants for the steps in the mechanism. Several simple enzymatic mechanisms and their complete rate equations are discussed.     

Interactions of lysozyme in concentrated electrolyte solutions from dynamic light-scattering measurements

The diffusion of hen egg-white lysozyme has been studied by dynamic light scattering in aqueous solutions of ammonium sulfate as a function of protein concentration to 30 g/liter. Experiments were conducted under the following conditions: pH 4-7 and ionic strength 0.05-5.0 M. Diffusivity data for ionic strengths up to 0.5 M were interpreted in the context of a two-body interaction model for monomers. From this analysis, two potential-of-mean-force parameters, the effective monomer charge, and the Hamaker constant were obtained. At higher ionic strength, the data were analyzed using a model that describes the diffusion coefficient of a polydisperse system of interacting protein aggregates in terms of an isodesmic, indefinite aggregation equilibrium constant. Data analysis incorporated multicomponent virial and hydrodynamic effects. The resulting equilibrium constants indicate that lysozyme does not aggregate significantly as ionic strength increases, even at salt concentrations near the point of salting-out precipitation.     

Golgi β-glucuronidase of androgen-stimulated mouse kidney

The equilibrium constant of the phosphoglyceromutase reaction was determined over a range of pH (5.4-7.9), in solutions of different ionic strength (0.06-0.3) and in the presence of Mg(2+), at 30 degrees C and at 20 degrees C. The values obtained (8.65-11.65) differ substantially from previously published values. The third acid dissociation constants were redetermined for 2- and 3-phosphoglycerate, and in contrast with previous reports the pK values (7.03 and 6.97 respectively at zero ionic strength) were closely similar. The Mg(2+)-binding constants were measured spectrophotometrically and the values, 286mm(-1) and 255mm(-1) for 2- and 3-phosphoglycerate at pH7 and ionic strength 0.02, were also very similar. From the relative lack of effect of temperature, pH and ionic strength it is concluded that the equilibrium constant differs from unity largely because of entropic factors. At low ionic strength, in the neutral region, the pH-dependence can be attributed to the small difference in the acid dissociation constants, but the difference in dissociation constants does not explain the pH-dependence in the acid region or at high ionic strength. Within physiological ranges of pH, Mg(2+) concentration and ionic strength there will be little variation in equilibrium constant.     

Effects of pH and ionic strength on the binding of egg white riboflavin binding protein with flavins

The effects of pH and ionic strength on the equilibrium constants and rate constants (binding and dissociation rate constants) between riboflavin binding protein (RBP) and flavins (riboflavin, 3-carboxymethylriboflavin [CMRF], and FMN) were studied by fluorometry. The equilibrium constant and the binding rate constant between RBP and riboflavin were pH-independent between pH 6 and 9, and both constants were also independent of the ionic strength, while the constants between RBP and CMRF or FMN were dependent on both pH and ionic strength. The dissociation rate constants between RBP and the flavins used here were not so dependent on pH and ionic strength in the pH region 6 to 9, and the patterns of pH profiles as a whole were similar to each other, although the constants for FMN were about 30-60 times larger than those for CMRF or riboflavin. RBP had lower affinity for FMN than for riboflavin in the neutral pH region, which is based on the small binding rate constant and the large dissociation rate constant for FMN. The former is due to an electrostatic repulsion force between negative net charges of RBP and the phosphate group of FMN, and the latter is due to steric interference by the phosphate group of FMN.     

Effect of dielectric constant on protonation equilibria of 2, 3-dihydroxybenzoic acid and malonic acid in 1, 2-propanediol-water mixtures

Abstract

The protonation constants of 2,3-diydroxybenzoic acid (2, 3-DHBA) and malonic acid (MA) at 303.0 ± 0.1 K and 0.16 mol L^-1 ionic strength in various concentrations (0–60% v/v) of 1,2-propanediol–water-mixtures were determined by pH-metric method. The protonation constants were calculated with MINIQUAD75 computer program. Selection of the best fit chemical models of the acid–base equilibria was based on statistical parameters. The log K values were found to increase with the increase in percentage of 1,2-propanediol and vary linearly with the reciprocal of the dielectric constant of the medium. This has been attributed to the dominance of electrostatic forces. Distributions of species and effect of influential parameters on the protonation constants are also presented.     

Kinetic studies on the conformational isomerization reaction of the four diastereomers of beta,gamma-bidentate CrATP

The rates of the conformational isomerization reaction of the diastereomers of beta,gamma-bidentate CrATP were studied as a function of pH, buffer concentration, ionic strength, and temperature. The progress of the reaction was monitored by quenching the reaction at various times, and then isolating the individual diastereomers and quantitating the percent of each. This was accomplished using the reverse-phase high-performance liquid chromatography separation technique developed in this laboratory [K. J. Gruys, and S. M. Schuster, Anal. Biochem. 125, 66-73 (1982)]. The rate constants for this isomerization were then determined by obtaining the best computer fit of the data to a reversible binary mechanism (i.e., A in equilibrium B) using interative descent methods. The reaction rate was shown to be dependent on pH, temperature, and ionic strength, but independent of buffer concentration. Keq. constants were independent of all variables except ionic strength. The results from this study are interpreted in terms of a reaction mechanism involving a preequilibrium ionization of the diastereomers followed by a rate-limiting interconversion process.     

Free energy relationships for thiol-disulfide interchange reactions between charged molecules in 50% methanol

Acid dissociation equilibrium constants and rate constants for disulfide interchange reactions have been measured in 50% methanol at low ionic strength for peptides containing cysteines with local ionic neighboring groups. These physical constants may be correlated by separation of free energy contributions into solvent-independent and solvent-dependent factors. The former represent inductive effects which may be evaluated by extrapolation of pKa values to the limit of infinite ionic strength. These solvent-independent contributions give Br onsted coefficients consistent with previously reported values for disulfides with neutral constituents. The solvent-dependent contributions represent thru-solvent electrostatic effects and are consistent with the form of the Bjerrum relationship correlating molecular charges, intergroup distances, and the dielectric constant of the solvent. These results provide a quantitative framework for developing strategies for employing coulombic interactions to direct disulfide pairing in synthetic polypeptides.     

Dielectric Relaxation of Molecules with Fluctuating Dipole Moment

When a dissolved macromolecule is in chemical equilibrium with a free ionic species, the charge configuration, and hence the dipole vector, of the macromolecule is fluctuating. Expressions for the static dielectric constant and the relaxation spectrum of such a mixture are here derived in terms of the components of the mean moment and the root mean square fluctuation moment, the molecular relaxation time constants, and the chemical rate constants of the ionic binding reaction. Contrary to a previous treatment of this problem by Kirkwood and Shumaker (1), it is shown that fluctuations introduce no independent components into the relaxation spectrum.     

Studies on the binding of FMN by apoflavodoxin from Peptostreptococcus elsdenii, pH and NaCl concentration dependence.

1. The pH and ionic strength dependence of the interaction of FMN with apoflavodoxin has been studied by fluorometry in the pH region 2-5, at 22 degrees C. 2. The rate constant of dissociation and the dissociation constant were experimentally determined; the rate constants of association were claculated at a given pH value. These constants depend on the ionic strength. The plots of these constants against the square root of the ionic strength are straight. 3. Our data have been interpreted in terms of the Br?nsted theory, which relates chemical reaction rates to ionic strength. The data indicate that the apoenzyme reaches its maximum net positive charge at pH 2.0-2.6. The calculated net charge in this pH region is between 11 and 12 and is in agreement with the theoretical value of 12 as deduced from the primary structure of the protein. The isoelectric point of the holoenzyme is about 4. 4. The rate constant of association extrapolated to zero ionic strength is 3.2-10(5)M-1-s-1 and is pH-independent. 5. The rate constant of dissociation and the dissociation constant extrapolated to zero ionic strength depend on the pH. The results are explained by assuming that there are two protein ionizations with a pK value of 3.4; these ionizing groups are possibly close to the FMN binding site.     

Thermodynamic properties of enzyme-catalyzed reactions involving cytosine, uracil, thymine, and their nucleosides and nucleotides

The standard Gibbs energies of formation of species in the cytidine triphosphate series, uridine triphosphate series, and thymidine triphosphate series have been calculated on the basis of the convention that Delta(f)G=0 for the neutral form of cytidine in aqueous solution at 298.15 K at zero ionic strength. This makes it possible to calculate apparent equilibrium constants for a number of reactions for which apparent equilibrium constants have not been measured or cannot be measured because they are too large. This paper adds fifteen reactants to the database BasicBiochemData3 at MathSource that includes 199 reactants. The standard transformed Gibbs energies of formation of these fifteen reactants are used to calculate apparent equilibrium constants at 298.15 K, ionic strength 0.25 M, and pHs 5, 6, 7, 8, and 9 for thirty two reactions. The pKs, standard Gibbs energies of hydrolysis, and standard Gibbs energies of deamination are given for these fifteen reactants.     

Thermodynamic properties of nucleotide reductase reactions

Recent thermodynamic measurements have made it possible to calculate the apparent equilibrium constants of the ribonucleoside diphosphate reductase reaction and the ribonucleoside triphosphate reductase reaction with various reducing agents. Third law heat capacity measurements on crystals of d-ribose and other calorimetric measurements make it possible to calculate Delta(f)G degrees for D-ribose and two species of D-ribose 5-phosphate. The experimental value of the apparent equilibrium constant K' for the deoxyribose-phosphate aldolase reaction makes it possible to calculate the standard Gibbs energies of formation Delta(f)G degrees for two protonation states of 2'-deoxy-D-ribose 5-phosphate. This shows that Delta(f)G degrees (2'-deoxy-D-ribose 5-phosphate(2)(-)) - Delta(f)G degrees (D-ribose 5-phosphate(2)(-)) = 147.86 kJ mol(-1) at 298.15 K and zero ionic strength in dilute aqueous solutions. This difference between reduced and oxidized forms is expected to apply to D-ribose, D-ribose 1-phosphate, ribonucleosides, and ribonucleotides in general. This expectation is supported by two other enzyme-catalyzed reactions for which apparent equilibrium constants have been determined. The availability of Delta(f)G degrees values for the species of 2'-deoxy-D-ribose and its derivatives makes it possible to calculate standard transformed Gibbs energies of formation of these reactants, apparent equilibrium constants for their reactions, changes in the binding of hydrogen ions in these reactions, and standard apparent reduction potentials of the half reactions involved as a function of pH and ionic strength at 298.15 K. The apparent equilibrium constant for ADP + thioredoxin(red) = 2'-deoxyADP + H(2)O + thioredoxin(ox) is 1.4 x 10(11) at 298.15 K, pH 7, and 0.25 M ionic strength.     

Formation of binary complexes of Pb(II), Cd(II) and Hg(II) with maleic acid in CTAB-water mixtures

Abstract

Complexation of toxic metal ions with maleic acid in (0.0–2.5% w/v) cetyltrimethylammonium bromide (CTAB)–water mixtures has been studied pH-metrically at ambient conditions and an ionic strength of 0.16 mol L^-1. The existence of different binary species was established from modelling studies using the computer program MINIQUAD75. The best-fit chemical models were selected based on statistical parameters such as the crystallographic R factor and sum of the squares of residuals in mass-balance equations. The models for binary complex systems contain the chemical species ML₂, ML₂H and ML₃ for Pb(II), Cd(II) and Hg(II) in CTAB–water mixtures. The trend in the variation of stability constants with change in the mole fraction of the medium was explained based on electrostatic and non-electrostatic forces. Distribution of the species with pH at different compositions of CTAB–water mixtures was also presented.     

Thermodynamic properties of enzyme-catalyzed reactions involving guanine, xanthine, and their nucleosides and nucleotides

The standard Gibbs energies of formation of species in the guanosine triphosphate and the xanthosine triphosphate series have been calculated on the basis of the convention that the standard Gibbs energy of formation for the neutral form of guanosine is equal to zero in aqueous solution at 298.15 K and zero ionic strength. This makes it possible to calculate apparent equilibrium constants for a number of enzyme-catalyzed reactions for which apparent equilibrium constants have not been measured or cannot be measured directly because they are too large. The eventual elimination of this convention is discussed. This adds ten reactants to the database BasicBiochemData3 that has 199 reactants. The standard transformed Gibbs energies of formation of these ten reactants are used to calculate apparent equilibrium constants at 298.15 K, 0.25 M ionic strength, and pHs 5, 6, 7, 8, and 9. The pKs, standard Gibbs energies of hydrolysis, and standard Gibbs energies of deamination are given for the reactants in the ATP, IMP, GTP, and XTP series.