Chemical synthesis of [32P]pyrophosphate with high specific activity

Graphical methods have traditionally been the principal means for estimation of parameters (e.g., affinity constants, cooperativity parameters, and concentrations of receptor sites) in enzymology and ligand-binding problems. The present report provides a review of these methods as well as new results, as applied to three coordinate systems popularly used in ligand-binding studies: $\text{B}\text{F}$ vs [Bound]. $\text{B}\text{F}$ vs [Free], and $\text{B}\text{F}$ vs [Total]. We consider two extremely general models, the statistical mechanical model and the Adair model for equilibrium ligand binding. We also consider a very specialized case of receptor interaction wherein the equilibrium constannt of dissociation is linearly related to receptor occupancy. We collect previously described equations and derive new ones, to enable the user to estimate the parameters of the models in terms of relatively easily measurable graphical characteristics. We have evaluated the performance of these methods in representative cases using Monte Carlo studies. The results indicate the kind of precision and accuracy which can be obtained with typical experimental designs. Depending upon the magnitude of experimental error, the graphical methods can provide dependable values for the binding parameters. However, in general, the results obtained by the graphical methods should be regarded as reasonable initial estimates for further refinement by weighted nonlinear least-squares curve fitting.     

Sedimentation coefficients of self-associating species: I. Basic theory

Under the same solution conditions, the apparent weight average sedimentation coefficient, s_wa, and some quantities obtained from it can be combined with the equilibrium constant or constants, K_i, and the monomer concentration, c_I, obtained from sedimentation equilibrium, light scattering or osmotic pressure experiments on the same self-associating solute, so that the individual sedimentation coefficients, s_i, of the self-associating species, and also the hydrodynamic concentration dependence parameter,g or $\text{g}$, can be evaluated. Using two different models for the hydrodynamic concentration parameter, four different methods are presented for the evaluation of the s_i's. Methods for evaluating g or $\text{g}$, once the s_i's are known, are presented. A method for obtaining the number average sedimentation coefficient, s_N, and its application to self-associations is presented. Methods are shown for the evaluation of Z average properties, x_zc, as well as number average properties,x_Nc, of a self-associating solute from its weight average properties, x_wc.     

The theoretical analysis of kinetic behaviour of "hysteretic" allosteric enzymes. IV. Kinetics of dissociation-association processes of allosteric enzymes.

The kinetics of equilibration of dissociating enzyme system

$\text{2}\text{p}\text{?}\text{k ? 0}\text{k + 0}\text{P}$

(P is enzyme oligomer which is able to dissociate reversibly forming two identical halves p) is analysed after changes in storage conditions or after addition of allosteric ligands. The expressions for changes in the proportions of p and P forms with time and the expressions for dependence of initial rate of dissociation-association processes and half-life time on enzyme concentration or allosteric ligand concentration are deduced. It is shown that the dependences of intial rate of dissociation-association processes on allosteric ligand concentration has co-operative character at definite values of kinetic parameters. The graphic methods of determination of the first-order rate constant for dissociation (k_?0) and the second-order rate constant for association (k₊₀) are developed. The experimental kinetic data of dissociation of L-threonine dehydratase, glycogen phosphorylase a and aspartic-β-semialdehyde dehydrogenase are used for illustration of applicability of deduced expression.     

Transient state isoelectric focusing: effects of zone load and carrier ampholyte concentration on the kinetics of defocusing and refocusing in sucrose density gradients

The kinetics of focusing, defocusing, and refocusing of l-histidyl-l-tyrosine in a sucrose density gradient have been studied utilizing a special apparatus for repetitive scanning of the isoelectric focusing column, employing uv absorption optics and a digital data acquisition system. Starting from a uniform or triangular concentration profile, the band is “focused” and a nearly linear pH gradient is formed during initial focusing. The electrical field is then abolished and free diffusion occurs. The electrical field is then reapplied (“refocusing”) and the band is allowed to sharpen, presumably reapproaching a steady state. The band width was measured quantitatively as the second moment about the mean (square of the standard deviation, σ²). In theory, measurements of σ² versus time permit the estimation of the apparent diffusion coefficient (D) and the isoelectric focusing parameter (pE). If the electrical field strength E and the pH gradient, $\text{d(}\text{pH}\text{)}\text{dx}$, were also measured, then one could calculate the slope of the pH mobility curve of the protein $\text{dM}\text{d(}\text{pH}\text{)}$ evaluated at the isoelectric point. D can be measured during the defocusing stage, and $\text{pE,}\text{D}\text{pE}\text{,}\text{or}\text{D}$ can be measured during focusing or refocusing. Several limitations and difficulties in the verification of this theory have been encountered: First, the apparent diffusion coefficient depends on zone load in approximately a linear fashion. Accordingly, it is necessary to measure D at several zone loads, and then extrapolate to zero load by linear regression techniques. Second, the ampholyte concentration has a marked effect on both D and pE. Here we have no a priori reason to extrapolate to zero ampholyte concentration. Also, at present we have no satisfactory method for measurement of E. These preliminary studies should be helpful in indicating further directions for experimental refinement and for generalization of theory.     

The composition-dependence of the extent of reaction between a multivalent acceptor and a bivalent ligand: Implications of self-interaction of the ligand in precipitin effects

Theory is presented relating to the reversible interaction of an f-valent acceptor, A, with a bivalent ligand, B, which leads to the formation of a series of complexes comprising networks of alternating A and B molecules. An explicit expression is derived for the overall extent of reaction in terms of the total molar concentrations of reactants $\text{(}\text{m}{}_{\mathrm{A}}$ and $\text{m}{}_{\mathrm{B}}\text{)}$, the valency of the acceptor and the site-binding constant, k, governing the equilibria. It is shown by differentiation of this expression holding $\text{m}{}_{\mathrm{A}}$ (or $\text{m}{}_{\mathrm{B}}$) fixed that relations are available for the independent evaluation of f and k from a combination of precipitin and radioimmunoassay experiments. Moreover, it is established that dilution with solvent ($\text{m}{}_{\mathrm{A}}\text{/}\text{m}{}_{\mathrm{B}}$ fixed) cannot lead to the appearance of a precipitate with this type of crosslinking system. The latter observation forms the background for the development of theory pertaining to the joint operation of ligand dimerization, 2B?B₂, and crosslinking of the multivalent acceptor with bivalent B₂. The theoretical examination of this system is developed in terms of site-probability functions and involves the delineation of unique solutions for the extent of crosslinking reaction aided by the definition of the extent of binding in defined limits. It is shown with the use of numerical examples that the system involving self-associating ligand may result in the appearance of a precipitate on dilution with solvent and the conditions for the operation of this phenomenon are elucidated. It is noted that other types of ligand self-interaction may lead to similar effects in crosslinking systems, and the general principles emerging from this study are discussed in terms of systems in which antibody ligands are known to be involved in association reactions or are suspected to be so involved on the basis of precipitation effects observed on dilution with solvent.     

Ultracentrifugation studies on early stage polymerization of tobacco mosaic virus protein

The effects of absolute temperature (T), ionic strength (μ), and pH on the polymerization of tobacco mosaic virus protein from the 4 S form (A) to the 20 S form (D) were investigated by the method of sedimentation velocity. The loading concentration in grams per liter (C) was determined at which a just-detectable concentration (β) of 20 S material appeared. It was demonstrated experimentally that under the conditions employed herein, an equilibrium concentration of 20 S material was achieved in 3 h at the temperature of the experiment and that 20 S material dissociated again in 4 h or less to 4 S material either upon lowering the temperature or upon dilution. Thus, the use of thermodynamic equations for equilibrium processes was shown to be valid. The equation used to interpret the results, log ($\text{C?β) =}\text{constant}\text{+ (}\text{ΔH}{}^1\text{2.3RT}$) + ($\text{Δ}\text{W}{}^1{}_{\mathrm{<mtext>el</mtext>}}\text{2.3RT}$) ? K′_sμ + ζpH, was derived from three separate models of the process, the only difference being in the anatomy of the constant; thus, the method of analysis is essentially independent of the model. $\text{ΔH}{}^1$ and ΔW¹_el are the enthalpy and the change in electrical work per mole of A protein (the trimer of the polypeptide chain), K^′_s is the salting-out constant on the ionic strength basis, ζ is the number of moles of hydrogen ion bound per mole of A protein in the polymerization, and R is the gas constant. The three models leading to this equation are: a simple 11th-order equilibrium between A₁ (the trimer of the polypeptide chain) and D, either the double disk or the double spiral of approximately the same molecular weight, designated model A; a second model, designated B, in which A₁ was assumed to be in equilibrium with D at the same time that it is in equilibrium with A₂, A₃, etc., dimers and trimers, etc., of A₁ in an isodesmic system; and a phase-separation model, designated model C, in which A protein is treated as a soluble material in equilibrium with D, considered as an insoluble phase. From electrical work theory, $\text{Δ}\text{W}{}_{\mathrm{el}}{}^1\text{/T}$ was shown to be essentially independent of T; therefore, in experiments at constant μ and constant pH the equation of log (C ? β) versus 1/T is linear with a slope of $\text{ΔH}{}^1\text{/2.3R}$. The results fit such an equation over nearly a 20 °C-temperature range with a single value of $\text{Δ}\text{H}{}^1$ of +32 kcal/mol A₁. Results obtained when T and pH were held constant but μ was varied did not fit a straight line, which shows that more than simple salting-out is involved. When the effect of ionic strength on the electrical work contribution was considered in addition to salting-out, the data were interpreted to indicate a value of $\text{Δ}\text{W}{}^1{}_{\mathrm{el}}$ of 1.22 kcal/mol A₁ at pH 6.7 and a value of 4.93 for K_s^′. When μ and T were held constant but pH was varied, and when allowance was made for the effect of pH changes on the electrical work contribution, a value of 1.1 was found for ζ. This means that something like 1.1 mol of hydrogen ion must be bound per mole of A₁ protein in the formation of D. When this is added to the small amount of hydrogen ion bound per A₁ before polymerization, at the pH values used, it turned out that for D to be formed, 1.5 H⁺ ions must be bound per A₁ or 0.5 per protein polypeptide chain. This amounts to 1 H⁺ ion per polypeptide chain for half of the protein units, presumably those in one but not the other layer of the double disk or turn of the double spiral. When polymerization goes beyond the D stage, as shown by previously published data, additional H⁺ ions are bound. Simultaneous osmotic pressure studies and sedimentation studies were carried out, in both cases as a function of loading concentration C. These results were in complete disagreement with models A and C but agreed reasonably well with model B. The sedimentation studies permitted evaluation of the constant, β, to be 0.33 g/liter.     

A novel radioiodinated high affinity ligand for the D2-dopamine receptor: Characterization of its binding in bovine anterior pituitary membranes

A novel high affinity dopaminergic ligand, N-(p-aminophenethyl)spiroperidol, has been synthesized and radioiodinated to a specific radioactivity of 2175 $\text{Ci}\text{mmol}$. Binding of this ligand to bovine anterior pituitary membranes is: (i) rapid (40–60 min to equilibrium at 25°C) and reversible t_{$\text{1}\text{2}$} = 1 h at 25°C); (ii) saturable and of high affinity (K_D ~ 20 pM) and (iii) displays a typical D₂-dopaminergic specificity. The ligand, which identifies the same number of receptor sites as other tritiated antagonist ligands, can be used in different tissues and preparations to delineate the characteristics of the D₂ receptor. Thus, this high affinity, high specific radioactivity ligand (N-(p-amino-m-[¹²⁵I]iodophenethyl)spiroperidol) represents a tool which until now had not been available for the characterization of the D₂-dopamine receptor.     

Binding equations for interacting systems comprising multivalent acceptor and bivalent ligand: application to antigen-antibody systems

Consideration is given to the reversible interaction of a bivalent ligand, B, with a multivalent acceptor, A (possessing f reactive sites) which leads to the formation of a series of complexes, A_iB_j, comprising networks of alternating acceptor and ligand molecules. A binding equation is derived on the basis of a site association constant, k, defined in terms of reacted site probability functions. This equation, which relates the binding function, r (the moles of ligand bound per mole of acceptor) to the concentration of unbound ligand, m_b, is used to show that plots of r vs. 2km_B constructed with fixed but different values of $\text{k}\text{m}{}_{\mathrm{A}}$ intersect at the point ($\text{m}{}_{\mathrm{B}}\text{=}\text{1}\text{2k}\text{, r =}\text{f}\text{2}$) where the extent of reaction and the concentrations of those complexes for which $\text{j}\text{i}\text{=}\text{f}\text{2}$ attain maximal values. Corresponding Scatchard plots are shown by numerical example to be non-linear, their second derivative being positive for all r. It follows that such deviations from linearity cannot be taken alone as evidence for site heterogeneity in cross-linking systems. The binding equation obtained directly is shown to be identical with that obtained with f = 2 by summation procedures involving the general expression for concentrations of complexes, m_AiBj, formulated in terms of appropriate statistical factors. In this way, previous findings on precipitation and gel formation in cross-linking systems are correlated with the present development of binding theory.     

Energy dependent changes in the cytochromes of the mitochondrial respiratory chain

In intact mitochondria a stoichiometric coupling exists between cytochrome a₃ and the hydrolysis of adenosine triphosphate (ATP). In each case the modification of one cytochrome a₃ (measured as a spectral change) is coupled to the hydrolysis of one ATP molecule. When both cytochromes a₃ and a are reduced the measured equilibrium constant is 0.06 m^?1 but this constant is 10³ M^?1 when both cytochromes are oxidized. When the sixth ligand for cytochrome a₃ is an externally added ligand (HCN, H₂S, CO, NO) the equilibrium constant is different for each ligand, suggesting that the ATP induced modification is of the fifth ligand but that it is energetically dependent on the chemical nature of the sixth ligand. The measured half-reduction potentials for cytochromes a₃ and b_T are dependent on the concentrations of added ATP, adenosine diphosphate (ADP), and orthophosphate. The relationship is consistent with a ligand exchange mechanism in which the ligand on the cytochrome is dependent on the phosphate potential ($\text{ATP}\text{ADP}$ × P_i). The equilibrium constants obtained by the ligand exchange treatment of the E_m values for cytochrome a₃ are consistent with those obtained by direct measurement of the equilibrium constants for the spectrally measured changes.     

The effect of sodium dodecyl sulfate on the structure and function of a protein proteinase inhibitor, Streptomyces subtilisin inhibitor.

Streptomyces subtilisin inhibitor (SSI) has been shown to exist as a dimer of molecular weight of 23,000 in 25 mm phosphate buffer, at pH 7.0 (the ionic strength 0.1 m with NaCl), 25.0 °C in the concentration range of 0.01–10 mg/ml. In the present paper, the effects of an anionic detergent, sodium dodecyl sulfate (SDS), on the structure and function of SSI has been examined, [a]The molecular weight of SSI was measured in the SDS solution with the sedimentation equilibrium method of the multicomponent-polydisperse system under the conditions described above, and thereby it has been shown that SSI dissociates into monomers with SDS of 0.03–0.12% ($\text{w}\text{v}$) when the concentration of SSI is 1.00 mg/ml (87.0 μm as monomer), [b]As SSI dissociates into monomers, there were observed blue-shift troughs at 293 nm and 300 nm due to a tryptophyl residue and a red-shift of phenylalanyl residues in the absorption difference spectrum induced by the binding of SSI and SDS. [c] The inhibitory activity of SSI against subtilisin BPN′-catalyzed hydrolysis of p-nitrophenyl acetate was measured under the conditions that SSI is in monomer in the SDS solution. Unexpectedly half of the inhibitory activity of SSI against subtilisin BPN′ is lost in the SDS solution.     

Kinetics of isotope exchange at equilibrium for a one substrate-one product enzyme mechanism

It is shown that the general solution of Morales, Horovitz &; Botts (1962) describing isotope exchange kinetics at equilibrium for the one substrateone product enzyme mechanism:

$\text{E+S?X?E+P}$

reduces to the steady-state solution normally applied to experimental data, under usual experimental conditions.The analysis provides a firmer theoretical basis for the equations generally used in analysing kinetic data from isotope exchange experiments.     

Kinetic mechanism of chlorpromazine inhibition of erythrocyte 3-O-methylglucose transport

The kinetic mechanism of chlorpromazine inhibition of erythrocyte hexose transport was investigated using the non-metabolizable glucose analog $\text{3-O-}\text{methylglucose}$. It was found that chlorpromazine added to the external medium is a non-competitive inhibitor of both equilibrium exchange and net $\text{3-O-}\text{methylglucose}$ transport at pH 7.8, 15°C. The $\text{K}{}_{\mathrm{<mtext>i</mtext>}}$ for equilibrium exchange is $\text{76 ± 21 μM}$. When net efflux and equilibrium exchange were measured on the same population of cells the equilibrium exchange was 2.5-times the maximum net efflux. The percent reduction of $\text{3-O-}\text{methylglucose}$ flux by chlorpromazine is dependent upon chlorpromazine concentration and not $\text{3-O-}\text{methylglucose}$ concentration as expected for a non-competitive inhibitor. Equilibrium exchange and net efflux show the same extent of inhibition at each concentration of chlorpromazine evaluated. These results suggest that exchange and net efflux of $\text{3-O-}\text{methylglucose}$ in the human erythrocyte may share a common transport system.     

Energy transfer by chlorophyll a in detergent micelles

The process of energy transfer was studied in the chlorophyll a-containing detergent micelle, serving as a possible model of the photosynthetic unit. Chlorophyll a was added to aqueous solutions of the detergent Triton X-100 and incorporated into the micelles. The energy transfer process was studied by investigating the concentration depolarization of fluorescence of chlorophyll a. On the basis of the experimental depolarization curves as well as the value of the Förster parameter $\text{R}{}_0\text{= 56}\text{A}\text{?}$ calculated from the overlap of absorption and fluorescence spectra it was concluded that energy transfer between chlorophyll a molecules in this model follows the Förstertype mechanism of inductive resonance. Furthermore it was found that the local concentration of chlorophyll a in the micelles is higher by 1–3 orders of magnitude than its overall concentration in the solution and by choosing the appropriate ratio between the concentration of chlorophyll a and the detergent it is possible to reach the in vivo chlorophyll concentration of 0.1 M within the micelles. Thus the chlorophyll-detergent micelle model may be applied as a model of the separate package-type photosynthetic unit.     

Studies on lectins: XXXIX. S-glycosyl polyacrylamide gels for affinity chromatography of lectins

Hydrophilic water-insoluble gels suitable for affinity chromatography of lectins have been prepared by copolymerization of acrylamide, N,N′-methylene bisacrylamide and alkenyl 1-thioglycosides. Water-soluble copolymers of analogous type have been obtained by omitting the cross-linking agent, N,N′-methylene bisacrylamide.In affinity chromatography of the Ricinus communis lectin it could be shown that the capacity for the lectin of the water insoluble copolymers was more than four times higher in copolymers having the $\text{S-β-}\text{D}\text{-}\text{galactosyl}$ ligand attached through a methylene bridge than in derivatives with a nonamethylene spacer.None of the insoluble $\text{S-β-}\text{D}\text{-}\text{glycosyl}$ copolymers prepared could be shown usable as affinity adsorbent for glycosidases though the corresponding soluble copolymers inhibited the activity of the enzymes.     

Non-equilibrium thermodynamics of marginal- and conditional-open chemical systems

Every open chemical system treated in this paper is restricted to the case involving a sequence of monomolecular reactions. Various kinds of probability distribution governing it are introduced according to the situations in which it is placed. The chemical system subject to marginal distribution is given the term marginal-open system MO. The open chemical system ō discussed by Nicolis and Babloyantz can be regarded as the limiting system of MO. For an open chemical system, itself in contact with an external reservoir of finite volume, the probability distribution conditioned on the marginal distribution for the external reservoir in an arbitrarily fixed state is more appropriate. Such an open chemical system is called a conditional-open system CO. However, in the case of the external reservoir of infinite volume, although it is not certainly trivial, another conditional probability distribution has to be proposed; it is derived on the hypothesis that the probability distribution for an arbitrary total number of molecules in the open chemical system is known. The open chemical system so specified is called conditional-open system $\text{C}\text{O}\text{?}$. It is shown that for each system $\text{MO, CO}\text{and}\text{C}\text{O}\text{?}$ the change of entropy starting from the steady state provides a Liapunov function under some conditions and that the steady state is asymptotically stable. The relation of the entropy change to non-equilibrium fluctuations of chemical components in each system is discussed in comparison with that in the corresponding open chemical system ō, for which the steady state surely exists and is always stable. It is shown that the concept of $\text{C}\text{O}\text{?}$ is useful for investigating the phenomenon of steady-state coupling.     

A simple, rapid, and precise method for calculating the steroid hormone-receptor complex concentration in the presence of saturating levels of hormone by using "differential dissociation" techniques.

The steroid hormone-receptor complex concentrations measured by “differential dissociation” techniques have to be corrected to obtain the true concentrations of receptor binding sites (B_s). For the calculation of B_s, the parameters kn (product of the equilibrium association constant and the concentration of binding sites of the “nonspecific” component) and f (fraction of the nonspecific binding measured in the experimental estimates of bound ligand by a given technique), previously proposed by Blondeau and Robel (J. P. Blondeau and P. Robel, 1975, Eur. J. Biochem.55, 375–384) are important. A new parameter of interest, ? [$\text{?}\text{=}\text{knf}\text{(kn + 1)}$], is discussed. The measurement of this parameter ? for three “differential dissociation” techniques allows the comparison of their efficiency and their reliability under various conditions for hormone receptor measurement in cytosol. Charcoal and hydroxylapatite methods are more efficient than the Sephadex G-25 filtration method. It is demonstrated that the “isotopic dilution” correction generally used for the estimation of the background of a given technique may be incorrect whatever the method of correction. A new method, the “double concentration measurement,” is developed. This method is simple, rapid, and precise. It requires two receptor binding measurements at two different saturating concentrations of ligand. This method allows the measurement of the estradiol receptor binding activity from calf uterine cytosol, with an error of less than 5% in samples containing the receptor either free or previously complexed with radioactive hormone, even in the presence of very high concentrations (≤0.5 μm) of radioactive steroid.     

The mechanism of anion inhibition of pork heart aspartate aminotransferase

The mechanism of anion inhibition of the reaction of the pork heart extramitochondrial aspartate aminotransferase (EC 2.6.1.1) with erythro-β-hydroxy-l-aspartate was investigated. This reaction produces a mixture of complexes, one of which is characterized by an absorption maximum at 492 nm. Spectrophotometric analysis of equilibrium mixtures of aspartate aminotransferase and erythro-β-hydroxy-l-aspartate, in different buffers, indicated that acetate, chloride, and cacodylate were competitive inhibitors of hydroxyaspartate binding. Pyrophosphate, however, was not a competitive inhibitor. Between pH 4.5 and 9.0 the affinity of the enzyme for the monovalent anions decreased as the pH increased. The data indicated that the anion binding group had a pK_a in the range from pH 6 to 7, depending upon the anion studied. From pH 4.5 to 9.0, the substrate dissociation constant and the distribution of enzyme-substrate complexes were both unaffected by pH. By stopped-flow spectrophotometry, an initial rapid relaxation ($\text{t}\text{1}\text{2}\text{= 2–8}\text{ms}$) was associated with an increase in absorbance at 492 nm, and this rate depended upon both substrate and buffer concentrations. A slower relaxation ($\text{t}\text{1}\text{2}\text{= 180}\text{ms}$) was associated with a decrease in the absorbance at 492 nm to approximately 70% of the value attained in the first rapid reaction. The rate of this slower reaction was largely independent of substrate and buffer concentrations. Kinetic analysis of the rates of the first relaxation in several different concentrations of Tris-acetate buffer of pH 8 showed that the rate of association decreased with increasing acetate concentration whereas the reaction rate for dissociation was unaffected. Thus, acetate appears to exert its inhibitory effect by preventing the formation of the enzyme-substrate complex rather than by displacing the substrate from the enzyme.     

The study of multiple polymerization equilibria by glass bead exclusion chromatography with allowance for thermodynamic non-ideality effects

Two related aspects are explored of the frontal exclusion chromatography of proteins employing controlled-pore glass beads as the stationary phase. First, it is shown theoretically that, despite the absence of osmotic shrinkage effects previously encountered with Sephadex matrices, the experimentally measurable partition coefficient of a single non-associating solute will be dependent on its concentration due to the differing ratios of activity coefficients in mobile and stationary phases at different total concentrations. The effect is demonstrated with results obtained using ovalbumin in phosphate buffer of pH 7.4, and is Shown to be consistent (up to a solute concentration of 5 $\text{g}\text{litre}$) with theoretical prediction formulated in terms of a single virial coefficient. Secondly, it is shown for self-associating systems that it is possible to determine the monomer concentration as a function of total concentration, provided the stationary phase is selected to ensure exclusion of all oligomeric species except monomer: the relation derived for this purpose accounts for the concentrationdependence of the partition coefficient of monomer, again as a first approximation involving one virial coefficient. Such information on the monomer concentration permits elucidation of the polymerization characteristics of the system in terms of the types of species present and the relevant equilibrium constants. The feasibility of the method, its likely sources of error and the relative contribution of the non-ideality effect are investigated using bovine glutamate dehydrogenase (up to a total concentration of 5.4 $\text{g}\text{litre}$) in phosphate buffer of pH 6.9. This system was selected since comparison was possible with results obtained by other methods, which have established the enzyme polymerization pattern as an isodesmic indefinite self-association. The isodesmic equilibrium constant of 1.5 ± 0.3 $\text{litre}\text{g}$ found in this work is in reasonable agreement with previous findings.     

Kinetic parameters for the binding of p-nitrophenyl alpha-d-mannopyranoside to concanavalin A.

Binding of the chromogenic ligand p-nitrophenyl α-d-mannopyranoside to concanavalin A was studied in a stopped-flow spectrometer. Formation of the protein-ligand complex could be represented as a simple one-step process. No kinetic evidence could be obtained for a ligand-induced change in the conformation of concanavalin A, although the existence of such a conformational change was not excluded. The entire change in absorbance produced on ligand binding occurred in the monophasic process monitored in the stopped-flow spectrometer. The value of the apparent second-order rate constant (k_a) for complex formation (k_a = 54,000 s^?1m^? at 25 °C, pH 5.0, Γ/2 0.5) was independent of the protein concentration when the protein was in the range of 233–831 μm in combining sites and in excess of the ligand. The apparent first-order rate constant (k_?a) for dissociation of the complex was obtained from the rate constant for the decomposition of the complex upon the addition of excess methyl α-d-mannopyranoside (k_?a = 6.2 s^?1 at 25 °C, pH 5.0, Γ/2 0.5). The ratio $\text{k}{}_{\mathrm{<mtext>a</mtext>}}{}_{\mathrm{<mtext>?</mtext><mtext>a</mtext>}}$ (0.9 × 10₄m^?1) was in reasonable agreement with value of 1.1 ± 0.1 × 10⁴m^?1 determined for the equilibrium constant for complex formation by ultraviolet difference spectrometry. Plots of ln($\text{k}{}_{\mathrm{<mtext>a</mtext>}}\text{T}$) and ln($\text{k}{}_{\mathrm{<mtext>a</mtext>}}\text{T}$) vs $\text{1}\text{T}$ were linear (T is temperature) and were used to evaluate activation parameters. The enthalpies of activation for formation and dissociation of the complex are 9.5 ± 0.3 and 16.8 ± 0.2 kcal/mol, respectively. The unitary entropies of activation for formation and dissociation of the complex are 2.8 ± 1.1 and 1.3 ± 0.7 entropy units, respectively. These entropy changes are much less than those usually associated with substantial changes in the conformation of proteins.