Analysis of various indefinite self-associations of the AK type

Although we and others have developed equations to analyze for some indefinite self-associations that might be encountered, it is felt in some cases that these models, known as the sequential, equal equilibrium constant (SEK) models, might overestimate the size of aggregates encountered at higher solute concentrations. Thus, Garland and Christian proposed two attenuated equilibrium constant (AK) models that might overcome this problem. Their methods were restricted to ideal solutions and to osmometric procedures. We have removed these restrictions, and we have developed equations for analyzing four AK models that might be encountered. Various tests to aid in distinguishing these models are presented. These procedures have been tested with two simulated examples of a Type III AK indefinite self-association.     

Determination of the parameters of self-association by direct fitting of the omega function

Nonlinear regression is used to fit the omega function vs. protein concentration curves (first described by B.K. Milthorpe, P.D. Jeffrey and L.W. Nichol, Biophys. Chem. 3 (1975) 169) obtained from sedimentation equilibrium experiments on self-associating macromolecules. Nonlinear regression allows the direct fit of these curves with discrete or indefinite self-association reaction models in order to obtain values for the equilibrium constants and second virial coefficient. The method is independent of the choice of reference concentration and avoids the original method of extrapolating an omega function curve to zero concentration and then using the extrapolated value to construct a monomer activity curve used for analysis. This extrapolation can become very difficult for mild to strong self-associations where incorrectly extrapolated values lead to systematic error in the monomer activity curves. The method is applied to results from a mild, indefinite self-association, exemplified by the self-association of human spectrin, and to computer-simulated data of weak, mild and strong, indefinite self-associations.     

The temperature-dependent self-association of beta-lactoglobulin C in glycine buffers

The self-association of β-lactoglobulin C at low pH (ca. 2.5) in glycine buffers has been studied at four temperatures, 10, 16, 20, and 25 °C, by low- and high-speed sedimentation equilibrium experiments. One buffer had an ionic strength of 0.1 and the other an ionic strength of 0.2. With either buffer the concentration dependence of the apparent weight average molecular weight, M_wa, was characteristic of a nonideal self-association. Like its genetic variants, β-lactoglobulin A and B, the self-association of β-lactoglobulin C increased with decreasing temperature; however, at the same temperature the association was always stronger in the buffer having the higher ionic strength. Several models were used to test the self-association, and a monomer-dimer self-association seemed to describe the self-association best with either buffer. Values of the association equilibrium constant, K₂, and the second virial coefficient, BM₁, are reported at each temperature for both series of experiments. Values of the thermodynamic functions, ΔG °, ΔH °, and ΔS °, are also reported for these experiments.     

Thermodynamical model of indefinite mixed association of two components and NMR data analysis for caffeine-AMP interaction

This paper describes the model used to estimate the parameters of caffeine-AMP interactions from corresponding 1H-NMR measurements and some methods of data analysis by which the applicability of the model has been checked. The model of mixed association is applicable to a mixture of any two substances A and C which exhibit indefinite aggregates in both self-association and mixed association. In aggregates, only nearest neighbour interaction is assumed. The model is described by three equilibrium constants: Kaa and Kcc (for self-association of A, or C, respectively), and Kac (for mixed association).     

Self-association of β-lactoglobulin A in acid solution. I. Translational diffusion coefficients

We report measurements of the diffusion coefficient of β-lactoglobulin A (βLG-A) at pH = 5.60 and 4.58 in 0.10 ionic strength acetate buffer by the techniques of analog photocurrent signal correlation and digital single-clipped photon correlation. At a concentration of 21 mg/ml and a pH of 4.58, the self-association of β-lactoglobulin can be represented by a simple dimer–octamer equilibrium model. We determined the translational diffusion coefficient of the dimer and that of the octamer using the scattering results of Kumosinski and Timasheff in a dimer–octamer mixture. Our analysis shows that the dimer βLG-A does not change its size if the pH is varied from 5.60 to 4.58 and both species remain constant in size for temperature changes from 3.5° to 25°C Hydrodynamically, the octamers behave like closed-packed spheres with an effective radius of about 45 Å according to the Stokes-Einstein relation.     

Gene 5 protein of bacteriophage fd: A dimer which interacts Co-operatively with DNA

Isolated gene 5 protein from bacteriophage fd-infected Escherichia coli has been shown by sedimentation equilibrium to exist primarily as a dimer under non-denaturing conditions. The dimer was stable under conditions of high ionic strength, extremes in pH, dilution to 0.075 mg/ml, and increased temperature. Gene 5 protein did not undergo the indefinite self-association observed with gene 32 protein.Three lines of evidence for co-operative binding of gene 5 protein to DNA were developed. First, the interaction between gene 5 protein and phage T4 DNA was examined using a nitrocellulose filter assay. Scatchard plots of the binding data indicated that the interaction was co-operative. Similar results were obtained with gene 32 protein. Second, the co-operative binding of both proteins to DNA was shown by the sensitivity of the protein-DNA interaction to increasing ionic strength at various ratios of protein to DNA. Finally, by using the cross-linking agent, dimethyl suberixmidate, oligomeric structures containing at least seven monomers were found when the DNA was less than saturated.The possibility that gene 5 protein dimers undergo indefinite self-association in the presence of oligonucleotides was examined by sedimentation equilibrium. With oligo[d(pT)₄], the protein dimer was complexed with this oligonucleotide but no self-association was observed. With oligo[d(pT)₈], gene 5 protein formed tetramers, but no significant indefinite association was noted. These results do not suggest a DNA-induced conformational change, which results in indefinite association. A model for the co-operative binding of gene 5 protein to DNA is presented.     

Osmometric analysis of quasi-indefinite mixed associations of the first kind

Mixed associations of the type A + B----AB, A + AB----A2B, ..., A + Ai-1 B----AiB, ... are readily analyzed by osmometric methods. The equilibrium molar concentration of A, mA, is obtained very simply from mA = meq-m0B; here meq = c/Meqn is the equilibrium molar concentration of all associating species and m0B denotes the stoichiometric or original molar concentration of B. The quantity mB can then be obtained from methods developed by Steiner. The value of the binding polynomial lambda is given by lambda = m0B/mB; lambda is a function of mA only. In principle, one can evaluate the equilibrium constants (kA,B,etc.) by fitting lambda to the appropriate polynomial in mA of degree n (n = 2, 3, ...). The binding polynomial lambda is analogous to polynomials encountered in the analysis of self-associations. By making some simple assumptions one can develop four analogs of two sequential, equal equilibrium constant (SEK) or two attenuated equilibrium constant (AK) models. With the aid of r (the number average degree of binding), g (the osmotic coefficient), lambda, as well as mA and mB, one can evaluate the equilibrium constant or constants. The methods developed here can be extended to the nonideal case.     

The self-association of ATP: thermodynamics and geometry.

The concentration and temperature dependence of the self-association of ademosin-5'-triphosphate (ATP) in aqueous solution was studied by means of ultraviolet absorption spectroscopy and circular dichroism (CD). Of several possible models, a model was indefinite linear self-association, in which each step has the same equilibrium constant, describes the data best. The two different methods lead within experimental error to the same thermodynamic parameters. At pH 8.7, IN 1 M Tris and 0.5 M 7gCl-2, we find deltaH-0 equals -5.1 kcal/mole and deltaS-0 equals -13.0 e.u. These values do not differ much from those found for the self-association of uncharged bases and nucleosides in aqueous solution. The CD spectrum that results from the self-association is conservative and quite similar in shape to that observed for some stacked dinucleotides: it is interpreted as a first approximation within the framework of the exciton model.     

Self-association of sodium cholate in isotonic saline solutions

The self-association of dialyzed solutions of sodium cholate in isotonic saline solutions has been studied by vapor pressure osmometry and sedimentation equilibrium. These studies were carried out at 25, 31 and 37 degrees C. In all experiments the self-association could be described as a two-equilibrium constant, indefinite self-association in which odd species beyond monomer were absent. The plots of M1/Mna or M1/Mwa vs. c were quite smooth with no sharp breaks; this suggested that there were no critical phenomena. The temperature dependence of the self-association was quite small. Our results are in accord with other studies on sodium cholate which indicate that the self-association involves several species, and that it is not a monomer-n-mer self-association.     

Studies on human serum high-density lipoproteins. Self-association of human serum apolipoprotein A-II in aqueous solutions.

Some of the solution properties of pure preparations of human serum high-density apolipoprotein A-II were studied by sedimentation equilibrium ultracentrifugation, conducted at different apoprotein concentrations and at several speeds. The concentration dependence of the apparent weight average molecular weight indicated that apolipoprotein A-II, when dissolved in 0.02 MEDTA (pH 8.6), undergoes self-association. Over a protein concentration range between 0.8 and 1.5 mg/ml, the self-association could best be described by a monomer-dimer-trimer step association, although indefinite self-association could not be ruled out. The equilibrium constants obtained were sufficient to describe the system over the concentration range investigated.     

Self-association processes involving anthracene labeled phosphatidylcholines in model membrane

When studying lipid-lipid or lipid-protein interaction in membranes, the correct interpretation of data obtained when using fluorescent phospholipid probes requires the best possible knowledge of probe behaviour in phospholipid membranes. Analysis of the translational dynamics and photochemical properties of the anthracene-labeled phosphatidylcholine (EAPC) shows that a self-association process occurs with this probe in the membrane at the ground state. This anthracene self-association is characterized and leads to a hypochromic effect which has been studied by means of ultraviolet absorption spectroscopy in unilamellar egg-yolk phosphatidylcholine (EggPC) vesicles. A model with indefinite linear self-association, in which each step has the same equilibrium constant, best describes the data. The equilibrium constant was found to be in the 300-500 M(-1) range and the complex lateral distribution pattern of EAPC in model membranes, which results from this self-association process, is characterized and seems to be mainly controlled by the amount of EAPC incorporated into the lipid bilayer.     

A thermodynamic model for the self-association of human spectrin

The self-association of human spectrin at 28.8 degrees C in 0.11 M salt (pH 7.5) has been studied by means of sedimentation equilibrium. Coincidence of omega function plots as a function of total spectrin concentration (0-2 g/L) indicated that equilibrium was achieved and that no significant concentration of solute was incapable of participating in the self-association reaction. On the basis of the root-mean-square deviation of the fits and the randomness of the residuals, the behavior can be described equally well, either by a cooperative isodesmic model, in which K12 approximately 2 x 10(6) M-1 and all other K approximately 10(6) M-1, or by an attenuated scheme in which K(i-1)i approximately (3.5 x 10(6)/i M-1. The returned values of the second virial coefficient, B, for both these models fall within the range calculated from the charge and Stokes radius of spectrin. A mechanism for spectrin self-association consistent with both schemes is proposed in which spectrin heterodimers undergo a reversible opening at the self-association interface. These open heterodimers then undergo indefinite self-association to form a series of open-chain oligomers in dynamic equilibrium with closed-loop oligomers.     

Indefinite noncooperative self-association of chicken deoxy hemoglobin D

The minor tetrameric hemoglobin (Hb), Hb D, of chicken red blood cells self-associates upon deoxygenation. This self-association enhances the cooperativity of oxygen binding. The maximal Hill coefficient is greater than 4 at high Hb concentrations. Previous measurements at low Hb concentrations were consistent with a monomer-to-dimer equilibrium and an association constant of ～1.3-1.6 × 10(4) M(-1). Here, the Hb tetramer is considered as the monomer. However, new results indicate that the association extends beyond the dimer. We show by combination of Hb oligomer modeling and sedimentation velocity analyses that the data can be well described by an indefinite noncooperative or isodesmic association model. In this model, the deoxy Hb D associates noncooperatively to give a linear oligomeric chain with an equilibrium association constant of 1.42 × 10(4) M(-1) at 20°C for each step. The data are also well described by a monomer-dimer-tetramer equilibrium model with monomer-to-dimer and dimer-to-tetramer association constants of 1.87 and 1.03 × 10(4) M(-1) at 20°C, respectively. A hybrid recombinant Hb D was prepared with recombinant α(D)-globin and native β-globin to give a Hb D tetramer (α(2)(D)β(2)). This rHb D undergoes decreased deoxygenation-dependent self-association compared with the native Hb D. Residue glutamate 138 has previously been proposed to influence intertetramer interactions. Our results with recombinant Hb D show that Glu138 plays no role in deoxy Hb D intertetramer interactions.     

Relations between divalent cation binding and ATPase activity in coupling factor from chloroplast.

Although 150 individual samples of milk from Italian water buffalo (Bubalus arnee) were examined by acid and alkaline gel electrophoresis, no polymorphism was observed for α-lactalbumin and β-lactoglobulin. After isolation and purification of these two proteins their amino acid compositions were determined and compared with those of the corresponding bovine proteins. The sequence alignments of 36 and 17 amino-acids from the N-terminal ends and 2 amino-acids from the C-terminal ends of buffalo α-lactalbumin and β-lactoglobulin, respectively, have been established. Our results indicate that buffalo α-lactalbumin differs from its cow B counterpart by a substitution Asn/Gly at position 17 and by another substitution, likely Glu/Gln or Asp/Asn, at an unknown position. Buffalo β-lactoglobulin is homologous to the bovine B variant. Three substitutions differentiate the two proteins: Ile/Leu and Val/Ile at positions 1 and 162 respectively; a further one, Gln/Ile, has not yet been located. According to these results the B variant of bovine β-lactoglobulin might be the wild type of the Bos genus.     

Reversible effects of medium dielectric constant on structural transformation of β-lactoglobulin and its retinol binding

The secondary structure transformation of β-lactoglobulin from a predominantly β-structure into a predominantly α-helical one, under the influence of solvent polarity changes is reversible. Independent of the alcohol used — methanol, ethanol, or 2-propanol — the midpoints of the observed structural transformation occur around dielectric constant ε ≈ 60. The structural change destroying the hydrophobic core formed by the β-barrel structure leads, at room temperature, to the dissociation of the retinol/β-lactoglobulin complex in the neighborhood of dielectric constant ε ≈ 50. However, when the dielectric constant of the medium is raised back to ε ≈ 70 by the decrease of the temperature, both the refolding of BLG into a β-structure and the reassociation of the retinol/β-lactoglobulin complex are observed. The esterification of β-lactoglobulin carboxyl groups has two effects: on the one hand it accelerates the β-strand → α-helix transition induced by alcohols. On the other hand, the esterification of β-lactoglobulin strengthens its interaction with retinol as it may be deduced from the smaller apparent dissociation constant of retinol/methylated β-lactoglobulin complex. The binding of retinol to modified or unmodified β-lactoglobulin has no influence (stabilizing or destabilizing) on the folding changes induced by alcohol. © 1993 John Wiley & Sons, Inc.     

Hidden assumptions in a maximum-entropy method stacking analyses

Two models have been used to describe indefinite self-association (stacking). In the more popular isodesmic model addition of molecules to the growing stack occurs with the same equilibrium constant, while in the attenuated model successive equilibrium constants decrease in value. In an attempt to choose between the two models application was made of the maximum-entropy method. This paper points out that the conclusions drawn from this method are not proven as the application assumed specific limiting values for experimental values of a molecule in the interior of a stack, and these values are not identical in the two models for the two systems considered.     

Antigenic Reactivities of Chemically Modified β-Lactoglobulins with Antiserum to Bovine β-Lactoglobulin

Analysis of the quantitative precipitation of bovine β-lactoglobulin (β-Lg) with rabbit antiserum to β-Lg indicated that there were at least four antigenic sites on β-Lg. To study the antigenic property of bovine β-Lg, we examined the antigenic reactivity of anti β-Lg serum with β-Lg specifically modified with chemical reagents by immunodiffusion analysis, a quantitative precipitin test, and an enzyme-linked immunosorbent assay.

Modification of arginine residues, tryptophan residues, or sulfhydryl groups had little effect on the antigenic reactivity. A significant decrease in the reactivity was observed when β-Lg was acetylated, succinylated, modified with diethylpyrocarbonate or coupled with glycine amide.

These results suggest that 1.1 of three arginine residues, two tryptophan residues, and one sulfhydryl group are out of the antigenic sites, but there is a possibility that the amino group, histidine residue and carboxyl group may play an important role in the antigenicity of bovine β-Lg.     

Characteristics and effects of specific peptides on heat-induced aggregation of β-lactoglobulin

A bovine β-lactoglobulin hydrolysate, obtained by the hydrolysis by the Glu specific enzyme Bacillus licheniformis protease (BLP), was fractionated at pH 7.0 into a soluble and an insoluble fraction and characterized by LC-MS. From the 26 peptides identified in the soluble fraction, five peptides (A[f97-112] = [f115-128], AB[f1-45], AB[f135-157], AB[f135-158], and AB[f138-162]) bound to β-lactoglobulin at room temperature. After heating of β-lactoglobulin in the presence of peptides, eight peptides were identified in the pellet formed, three of them belonging to the previously mentioned peptides. Principle component analysis revealed that the binding at room temperature (to β-lactoglobulin) was related to the total hydrophobicity and the total charge of the peptides. The binding to the unfolded protein could not be attributed to distinct properties of the peptides. The presence of the peptides caused a 50% decrease in denaturation enthalpy (from 148 ± 3 kJ/mol for the protein alone to 74 ± 2 kJ/mol in the presence of peptides), while no change in secondary structure or denaturation temperature was observed. At temperatures <85 °C, the addition of peptides resulted in a 30-40% increase of precipitated β-lactoglobulin. At pH < 6, no differences in the amount of aggregated β-lactoglobulin were observed, which indicates the lack of binding of peptides to β-lactoglobulin at those pH values as was also observed by SELDI-TOF-MS. Although only a few peptides were found to participate in aggregation, suggesting specificity, principal component analysis was unable to identify specific properties responsible for this.