Absence of positive co-operativity in the binding of 2,3,7,8-tetrachlorodibenzo-p-dioxin to its cytosolic receptor protein.

The role of positive co-operativity in stabilizing the binding of 2,3,7,8-tetrachlorodibenzo-p-dioxin (TCDD) to the rat hepatic cytosolic TCDD receptor protein (Ah receptor) was investigated. The binding mechanism of TCDD was determined by kinetic means through equilibrium and saturation binding studies, and Scatchard and Hill plot analysis. In all studies, the slope of the Hill plot was close to 1.0, indicating the absence of positive co-operativity. Interpretation of the Scatchard plot was however complicated by the fact that both linear and nonlinear plots were experimentally obtained. The nonlinearity was shown to be an experimental artifact and a consequence not of co-operativity, but of high levels of nonspecific binding. The high level of nonspecific binding could be attributed to: (1) lipophilicity of the TCDD ligand, and (2) inefficient competition of receptor-bound [3H]TCDD. When nonspecific binding was minimized, the Scatchard slope was linear and in agreement with the Hill coefficient, thus indicating the lack of positive co-operativity in the binding of TCDD to the Ah receptor.     

A new measure of cooperativity in protein-ligand binding

An allosteric binding system consisting of a single ligand and a nondissociating macromolecule having multiple binding sites can be represented by a binding polynomial. Various properties of the binding process can be obtained by analyzing the coefficients of the binding polynomial and such functions as the binding curve and the Hill plot. The Hill plot has an asymptote of unit slope at each end and the departure of the slope from unity at any point can be used to measure the effective interaction free energy at that point. Of particular interest in detecting and measuring cooperativity are extrema of the Hill slope and its value at the half-saturation point. If the binding polynomial is symmetric, then there is an extremum of the Hill slope at the half-saturation point. This value, the Hill coefficient, is a convenient measure of cooperativity. The purpose of this paper is to express the Hill coefficient for symmetric binding polynomials in terms of the roots of the polynomial and to give an interpretation of cooperativity in terms of the geometric pattern of the roots in the complex plane. This interpretation is then applied to the binding polynomials for the MWC (Monod-Wyman-Changeux) and KNF (Koshland-Nemethy-Filmer) models.     

Interaction of chlorpromazine with hemoglobin

Binding of chlorpromazine (CPZ), a widely used antidepressant tranquilizer, with hemoglobin has been studied by equilibrium dialysis method. r/Cf versus r plot was typically concave downwards revealing the positive cooperative nature of binding. Binding parameters, namely the affinity constant (K) and the degree of cooperativity (nH) were determined from the Hill plot. Oxygen was found to be released gradually from hemoglobin with gradual addition of CPZ, the extent of oxygen release depending on the stoichiometric ratio of CPZ: hemoglobin (D/P).     

ATP sulfurylase from Penicillium chrysogenum. Molecular basis of the sigmoidal velocity curves induced by sulfhydryl group modification

ATP sulfurylase from Penicillium chrysogenum is a noncooperative homooligomer containing three free sulfhydryl groups per subunit. Under nondenaturing conditions, one SH group per subunit was modified by 5,5'-dithiobis-(2-nitrobenzoate), or N-ethylmaleimide. Modification had only a small effect on kcat, but markedly increased the [S]0.5 values for the substrates, MgATP and SO4(2-). MgATP and adenosine-5'-phosphosulfate protected against modification. The SH-modified enzyme displayed sigmoidal velocity curves for both substrates with Hill coefficients (nH) of 2. Fluorosulfonate (FSO3-) and other dead-end inhibitors competitive with SO4(2-) activated the SH-modified enzyme at low SO4(2-) concentration. In order to determine whether the sigmoidicity resulted from true cooperative binding (as opposed to a kinetically based mechanism), the shapes of the binding curves were established from the degree of protection provided by a ligand against phenylglyoxal-dependent irreversible inactivation under noncatalytic conditions. Under standard conditions (0.05 M Na-N-(2-hydroxyethyl)piperazine-N'-3-propanesulfonic acid buffer, pH 8, 30 degrees C, and 3mM phenylglyoxal) the native enzyme was inactivated with a k of 2.67 +/- 0.25 X 10-3 s-1, whereas k for the SH-modified enzyme was 5.44 +/- 0.27 X 10-3 s-1. The increased sensitivity of the modified enzyme resulted from increased reactivity of ligand-protectable groups. Both the native and the SH-modified enzyme displayed hyperbolic plots of delta k (i.e. protection) versus [MgATP], or [FSO3-], or [S2O3(2-]) in the absence of coligand (nH = 0.98 +/- 0.06). The plots of delta k versus [ligand] for the native enzyme were also hyperbolic in the presence of a fixed concentration of coligand. However, in the presence of a fixed [FSO3-] or [S2O3(2-]), the delta k versus [MgATP] plot for the SH-modified enzyme was sigmoidal, as was the plot of delta k versus [FSO3-] or [S2O3(2-]) in the presence of a fixed [MgATP]. The nH values were 1.92 +/- 0.09. The results indicate that substrates (or analogs) bind hyperbolically to unoccupied SH-modified subunits, but in a subunit-cooperative fashion to form a ternary complex.     

An analytic solution to the Monod-Wyman-Changeux model and all parameters in this model.

Starting from the Monod-Wyman-Changeux (MWC) model (Monod, J., J. Wyman, and J. P. Changeux. 1965. J. Mol. Biol. 12:88-118), we obtain an analytical expression for the slope of the Hill plot at any ligand concentration. Furthermore, we derive an equation satisfied by the ligand concentration at the position of maximum slope. From these results, we derive a set of formulas which allow determination of the parameters of the MWC model (kR, C, and L) from the value of the Hill coefficient, nH, the ligand concentration at the position of maximum slope [( A]0), and the value of nu/(n-nu) at this point. We then outline procedures for utilizing these equations to provide a "best fit" of the MWC model to the experimental data, and to obtain a refined set of the parameters. Finally, we demonstrate the applicability of the technique by analysis of oxygen binding data for Octopus hemocyanin.     

Hill coefficient for estimating the magnitude of cooperativity in gating transitions of voltage-dependent ion channels

A frequently used measure for the extent of cooperativity in ligand binding by an allosteric protein is the Hill coefficient, obtained by fitting data of initial reaction velocity (or fractional binding saturation) as a function of substrate concentration to the Hill equation. Here, it is demonstrated that the simple two-state Boltzmann equation that is widely used to fit voltage-activation data of voltage-dependent ion channels is analogous to the Hill equation. A general empiric definition for a Hill coefficient (n(H)) for channel gating transitions that is analogous to the logarithmic potential sensitivity function of Almers is derived. This definition provides a novel framework for interpreting the meaning of the Hill coefficient. In considering three particular and simple gating schemes for a voltage-activated cation channel, the relation of the Hill coefficient to the magnitude and nature of cooperative interactions along the reaction coordinate of channel gating is demonstrated. A possible functional explanation for the low value of the Hill coefficient for gating transitions of the Shaker voltage-activated K(+) channel is suggested. The analogy between the Hill coefficients for ligand binding and for channel gating transitions further points to a unified conceptual framework in analyzing enzymes and channels behavior.     

Interrelationships among quinidine, amiloride, and lithium as inhibitors of the renal Na+-H+ exchanger

We examined the effects of quinidine, amiloride and Li+ on the kinetics of Na+-H+ exchange in microvillus membrane vesicles isolated from the rabbit renal cortex. Quinidine reversibly inhibited the initial rate of Na+-H+ exchange (I50 200 microM). The plot of 1/V versus [quinidine] was curvilinear, with Hill coefficient greater than 1.0, indicating that the drug interacts at two or more inhibitory sites or at a single site on at least two different conformations of the transporter. Quinidine decreased the Vmax for Na+-H+ exchange and increased the Km for Na+, indicating a mixed-type mechanism of inhibition. In contrast, plots of 1/V versus [amiloride] and 1/V versus [Li+] were linear, indicating single inhibitory sites; amiloride and Li+ each increased the Km for Na+ with no effect on Vmax, indicating a competitive mechanism of inhibition. Addition of Li+ increased the intercept with no change in slope of the 1/V versus [amiloride] plot, indicating that Li+ and amiloride are mutually exclusive inhibitors of Na+-H+ exchange. Addition of quinidine increased the slopes of the plots of 1/V versus [amiloride] and 1/V versus [Li+], indicating that the binding of quinidine is not mutually exclusive with the binding of amiloride and Li+. Results from this and previous studies are consistent with the concept that the inhibitor amiloride and the transportable substrates Na+, H+, Li+, and NH+4 all mutually compete for binding to a single site, the external transport site of the renal Na+-H+ exchanger. However, our findings indicate that quinidine interacts with the Na+-H+ exchanger on at least one additional site that is not shared by Na+, Li+, or amiloride.     

On the Hill plot of NMR data for titration of protein residues

The Hill plots of NMR titration data for protein residues disclose more clearly than the usual titration curves the presence of multiple weak perturbations originating from other titratable groups, and should be used whenever the conventional curve fitting is poor. For a quantitative interpretation, we derive here expressions for the Hill equation and the Hill coefficient when the titration of the observed group is perturbed by more than one titratable group. When the generalized Hill equation is fitted to the data, values of the interaction parameters between the observed group and the others are extracted provided that there are no mutual interactions between the latter groups. The method is applied to the titration data of two histidyl residues of l-arginine phosphotransferase (E.C. 2.7.3.3.) in the transition state analogue complex (enzyme-Mg²⁺-ADP-NOsk3/–l-Arg). From the Hill plots, interactions with three titratable groups are disclosed for both residues, and the fitting with the Hill equation reveals that they experience perturbations from the same three groups. Microscopic pK values are obtained for all the involved groups, indicating large changes (up to 3 pH units) upon protonation of the interacting groups. As compared to the conventional fitting procedure, the use and fitting of Hill plots yields from NMR data more information on the neighbourhood of enzyme residues and on the changes intervening therein through the steps involved in the catalysis.     

Effect of digitonin on the activity of Na,K-ATPase from bovine brain

The kinetic properties of intact and digitonin-treated Na,K-ATPase from bovine brain were studied. The temperature dependence curve for the rate of ATP hydrolysis under optimal conditions (upsilon 0) in the Arrhenius plots shows a break at 19-20 degrees. The temperature dependence curves for Km' and Km" have breaks at the same temperatures, while the Arrhenius plot for V is linear. The value of the Hill coefficient (nH) for ATP at 37 degrees is variable depending on ATP concentration, i. e. it is less than 1 at ATP concentrations below 50 mkM and is increased up to 3.2 at higher concentrations of the substrate. At high ATP concentrations the value of nH depends on temperature, falling down to 2.1 at 23 degrees and then down to 1 within the temperature range of 21-19 degrees. A further decrease in temperature does not significantly affect the nH value. Digitonin irreversibly inhibits Na, K-ATPase. ATP hydrolysis is more sensitive to the effect of the detergent than is nNPP hydrolysis, i. e. after complete inhibition of the ATPase about 40% of the phosphatase activity are retained. Treatment of Na,K-ATPase by digitonin results in elimination of the breaks in the Arrhenius plots for upsilon 0, Km' and Km", whereas the temperature dependence plot of V remains linear. Simultaneously digitonin eliminates the positive cooperativity of the enzyme for ATP. It is assumed that Na, K-ATPase from bovine brain is an oligomer of the (alpha beta) 4 type. Digitonin changes the type of interaction between the protomers within the oligomeric complex by changing the lipid environment of the enzyme or the type of protein -- lipid interactions.     

Biochemical characterization of positive cooperativity in the binding of 1 alpha, 25-dihydroxyvitamin D3 to its chick intestinal chromatin receptor

We have characterized a positive cooperativity mechanism in the binding of 1,25-dihydroxyvitamin D3 (1,25-(OH)2D3) to its chick duodenum chromatin receptor. The Hill plot which can take account of the possibility of cooperativity resulted in a much better fitting of the experimental data than the Scatchard model (r = +0.998 versus r = -0.94). Concentrating the chromatin receptor preparation from 10 to 40% resulted in an increase of the Hill coefficient (nH) from 1.09 +/- 0.08 to 1.46 +/- 0.08 (S.D.). Increasing the temperature of incubation from 1 degree C to 40 degrees C resulted in a decrease of nH from 1.46 +/- 0.08 to 1.10 +/- 0.02 (S.D.). The calculation of the thermodynamics of the interaction of 1,25-(OH)2D3 with the second binding site of the receptor (from a Van't Hoff plot) showed that this process occurred spontaneously (delta G0 = -11.6 kcal X mol-1 at 1 degree C), was entropy-driven (delta S0 = +26 cal degree-1 mol-1), and was energy-requiring (delta H0 = -4.37 kcal X mol-1). The temperature controlled reversibility of the cooperativity demonstrates that this phenomenon is not an artifact. Finally, in a study of the rate of dissociation of [3H]1,25-(OH)2D3 from the duodenal receptor preparation, we have found two slopes (k-1 = 32 X 10(-3) min-1; k-2 = 3.2 X 10(-3) min-1); this suggests the existence of two species of receptor. These receptor species could result possibly from either a monomer-dimer system or from a conformational change of a monomer via site-site interactions. In conclusion, the positive cooperativity in the binding of 1,25-(OH)2D3 to the two binding sites of its intestinal receptor is an entropy-driven process and requires energy, is reversible with temperature, and has been shown to take place in concentrated chromatin aggregates.     

Cooperativity: over the Hill

Cooperativity, the ability of ligand binding at one site on a macromolecule to influence ligand binding at a different site on the same macromolecule, is a fascinating biological property that is often poorly explained in textbooks. The Hill coefficient is commonly used in biophysical studies of cooperative systems although it is not a quantitative measure of cooperativity. The free energy of interaction between binding sites (ΔΔG) is a more stringent definition of cooperativity and provides a direct quantitative measure of how the binding of ligand at one site affects the ligand affinity of another site.     

Cooperative binding of calcium to glycerinated skeletal muscle fibers

The binding of ⁴⁵Ca²⁺ to glycerinated rabbit psoas fibers was measured by means of a double isotope technique. With 5 mM Mg²⁺ (no ATP) binding was half-maximal at 1.4 · 10^?6M Ca²⁺ and the maximal amount bound was 1.6 μmol/g protein. At < 50% saturation, the Scatchard plot had a positive slope and the Hill coefficient was 2.2. At greater than 50% saturation, the Scatchard plot was linear with a negative slope (K′ = 0.8 · 10⁶ M^?1) and the Hill coefficient was 1.0. In the absence of Mg²⁺, binding was half-maximal at 3 · 10^?7 M Ca²⁺ and the maximal amount bound was 2.9 μmol/g protein. The Scatchard plot indicated two classes of sites with K′ values of about 2 · 10⁷ and 2 · 10⁶ M^?1. The Hill coefficient in the mid-saturation range was approx. 0.6. The data indicate that in the presence of Mg²⁺ binding to about half of the total Ca²⁺ binding sites is suppressed and there is a strong positive cooperativity involving half of the remaining sites.     

Acetylcholinesterase. I. Kinetic aspects of interaction with reversible effectors]

Interaction of an effector M with acetylcholinesterase (EC 3.1.1.7) according to the model of Krupka and Laidler was analysed. Some usual functions of [M] : 1/VM, [(VO/VM)-1]/[M] (where VO and VM are the steady state rates in the absence and in the presence of modifiers, respectively), vertical intercept 1/VM, slope KM/VM and absolute value of reciprocal horizontal intercept KM of Lineweaver-Burk plots are investigated and corresponding plots described. It is particularly shown that if Dixon plots are curves concave downwards, plots of [VO/VM)-1]/[M] and 1/VM against [M] are hyperbolas concave upwards and downwards respectively. If Dixon plots are curves concave upwards, plots of [(VO/VM)-1]/[M] and 1/VM versus [M] are hyperbolas concave downwards and upwards respectively. Moreover plots of KM/VM against [M] are linear. However, this model does not explain some observations, under conditions of high ionic strength (gamma/2 greater than or equal to 0,1), where Dixon plots are curves concave upwards, plots of [VO/VM)-1]/[M] versus [M] strainght lines, the plot of 1/VM against [M] is a straight line or a curve concave upwards of positives slopes and the plot of KM/VM versus [M] a curve of positive slope concave upwards. These experimental data might be interpreted by an extension of the preceding model to a mechanism with two enzymatic binding sites under kinetic conditions that are determined.     

Comparison of steady-state kinetics of thiophosphorylated versus unphosphorylated smooth muscle myosin

(i) The steady-state kinetic data obtained with purified gizzard and uterus smooth muscle myosins indicated the presence of a plateau region on the substrate-saturation curves. Hill plots of these data provided evidence for mixed positive and negative cooperative interactions. In contrast, when gizzard myosin was prepared according to the method of A. Sobieszek and R.D. Bremel (1975, Eur. J. Biochem.55, 49–60), the saturation curve in the presence of CaATP was hyperbolic and no cooperativity of the binding site(s) was discerned. However, in the presence of MgATP although the curve appeared hyperbolic the Hill plot of the data was biphasic with negative cooperativity at low MgATP concentration, (ii) When thiophosphorylated gizzard myosin was used for kinetic analysis, the plateau region in the presence of MnATP was eliminated from the saturation curve and this curve became hyperbolic. However, in the presence of MgATP, although the plateau was almost eliminated, the saturation curve was still biphasic with either no or greatly reduced negative cooperativity of binding sites at low MgATP concentrations but positive cooperativity of binding at high MgATP concentrations. In addition, the thiophosphorylation of myosin also increased the K_m and V of MgATP and MnATP, thus indicating weaker affinity for these substrates with thiophosphorylated myosin. (iii) Gizzard myosin also hydrolyzed other nucleotides (the order of rates being CTP = ITP > ATP = UTP > GTP), therefore saturation kinetics using different nucleotides as substrates was also carried out. The saturation curves with each nucleotide were different i.e., hyperbolic with CTP, sigmoid with GTP, hyperbolic with biphasic Hill plot with ITP, and possessing plateau with UTP. In addition, it was observed that the kinetic pattern with each nucleotide was very sensitive to temperature and pH.     

Kinetic co-operativity of monomeric mnemonical enzymes. The significance of the kinetic Hill coefficient

The expression of the kinetic Hill coefficient for a two-substrate, two-product mnemonical enzyme has been derived. Its relation with the gamma coefficient, that is the slope of the reciprocal plots for 1/[A]----O, has been established. The variation of this Hill coefficient, as a function of the second substrate and product concentrations, has been studied theoretically. Whereas the gamma coefficient does not vary as a function of the substrate and first product concentrations, the kinetic Hill coefficient does. If the enzyme is positively co-operative, the Hill coefficient increases upon increasing the second substrate concentration and decreases if the first product concentration is increased. The converse is expected to occur if the enzyme displays a negative co-operativity. The last product may either reverse a positive co-operativity into a negative one or, alternatively, strengthen an already negative co-operativity. The co-operativity generated by the mnemonical model has been compared to the kinetic behaviour of a random model. These two models have been shown to be discriminated on the basis of the departure they show with respect to the Michaelis-Menten behaviour. These theoretical considerations have been applied to previously published data, obtained with wheat germ hexokinase LI. This monomeric enzyme has a negative co-operativity with respect to the preferred substrate, glucose. The Hill coefficient decreases with MgATP concentration, increases with MgADP concentration and decreases with glucose-6-phosphate concentration. This is exactly what is to be expected on the basis of the above theory of kinetic co-operativity.     

Rigorous determination of the Hill coefficient of non-Michaelian substrate-inhibited enzymes

The Hill coefficient (n), the max. velocity (VM) and the dissociation constants of the competent enzyme-substrate complex (Ks) and of the inhibitory bindings of substrate to both pure enzyme (Kse) and to ES (Kses) can be determined using a particular property of the representative equation. Choosing successive pairs of substrate concns (Si, Sj) in such a way as Si.Sj = 1, and plotting Sj-1 versus Si-1 gives a family of straight lines whose slopes are: b = Ks.kses, i.e.b = Sm2n, independent of Si, Sj. Then: n = Lnb/2 LnSm, where Sm corresponds to vm, maximum value of v on the curve. All of the other parameters can be calculated from the value of n.     

Protein-ligand binding with a missing species

Considerable experimental evidence has been produced recently that shows that in the binding of oxygen or carbon monoxide to certain tetrameric hemoglobins, the triply-ligated species is virtually non-existent. The binding polynomial representing this phenomenon for the general case is P(x) = 1 + beta 1x + ... + beta n-1xn-1 + beta nxn, where beta n-1 is nearly zero. The zeros, factorization and associated Hill plots of such binding polynomials with beta n-1 = 0 are investigated for the general case, and are analyzed in detail for n = 3 and n = 4. These results are then compared with the results obtained from experimental data on a number of tetrameric hemoglobins for which beta 3 is small. One concludes that, apart from the slope of the high-saturation asymptote of the Hill plot, a small perturbation of beta 3 from zero produces small changes in other properties associated with the binding process, such as fractional saturation, maximum Hill slope, and zeros and factorization of the binding polynomial.     

The ryanodine receptor-Ca2+ release channel complex of skeletal muscle sarcoplasmic reticulum. Evidence for a cooperatively coupled, negatively charged homotetramer

The subunit structure of the rabbit skeletal muscle ryanodine receptor-Ca2+ release channel complex was examined following solubilization of heavy sarcoplasmic reticulum membranes in two zwitterionic detergents, 3-[(3-cholamidopropyl)dimethylammonio]-1-propanesulfonic acid (Chaps) and Zwittergent 3-14. High and low affinity [3H]ryanodine binding was retained upon solubilization of the complex in Chaps but was lost in Zwittergent 3-14. The purified complex migrated as a single peak with an apparent sedimentation coefficient of approximately 30 and approximately 9 S upon density gradient centrifugation and with isoelectric points of 3.7 and 3.9 upon two-dimensional gel electrophoresis in Chaps and Zwittergent 3-14, respectively. Electron microscopy of negatively stained samples indicated that the distinct four-leaf clover structure of the ryanodine receptor observed in Chaps disappeared following Zwittergent treatment of the 30 S complex and instead showed smaller, round particles. Ferguson plot analysis following sodium dodecyl sulfate-polyacrylamide gel electrophoresis of partial and fully cross-linked and incompletely denatured complexes suggested a stoichiometry of four Mr approximately 400,000 peptides/30 S ryanodine receptor oligomer. [3H]Ryanodine binding to the membrane-bound receptor in 50 microM--1 mM free Ca2+ revealed the presence of both high affinity (KD = 8 nM, Hill coefficient (nH) = 0.9) and low affinity (nH approximately 0.45) sites with a ratio of 1:3. Reduction in free Ca2+ to less than or equal to 0.1 microM or trypsin digestion of the membranes resulted in loss of high affinity but not low affinity ryanodine binding (Hill KD = 5,000 nM, nH = 0.9). Addition of 20 mM caffeine to the nanomolar Ca2+ medium decreased the Hill KD to 1,000 nM without changing the Hill coefficient. Occupation of the low affinity sites altered the rate of [3H]ryanodine dissociation from the high affinity sites. Single channel recordings of the purified ryanodine receptor channel incorporated into planar lipid bilayers also indicated the existence of high and low affinity sites for ryanodine, occupation of which resulted in formation of a subconducting and completely closed state of the channel, respectively. These results are compatible with a subunit structural model of the 30 S ryanodine receptor-Ca2+ release channel complex which comprises a homotetramer of negatively charged and allosterically coupled polypeptides of Mr approximately 400,000.     

Inhibition of the methylcoenzyme M methylreductase system by NAD+ and NADP+ in cell-extracts of Methanosarcina barkeri

In cell extracts of Methanosarcina barkeri, the methylcoenzyme M methylreductase system with H2 as the electron donor was inhibited by NAD+ and NADP+, but NADH and NADPH had no effect on enzyme activity. NAD+ (4 and 8 mM) shifted the saturation curve for methylcoenzyme M from hyperbolic (Hill coefficient [nH] = 1.0; concentration of substrate giving half maximal velocity [Km] = 0.21 mM) to sigmoidal (nH = 1.5 and 2.0), increased Km (Km = 0.25 and 0.34 mM), and slightly decreased Vmax. Similarly NADP+ at 4m and 8 mM increased nH to 1.6 and 1.85 respectively, but the Km values (0.3 and 0.56 mM) indicated that NADP+ was a more efficient inhibitor than NAD+.     

A computer program for the implicit regression of the Hill equation]

A computer program for implicit regression of the Hill equation. The fundamentals for the regression of implicit functions following the Gauss method are dealt with. Basing on these fundamentals a program for the regression of the Hill equation is described. The binding constant, the Hill coefficient and end extinction can be estimated. The mean errors of parameters were calculated in the linear model. The program was written in ALGOL 60 for the computer Robotron 300. The program is available on request.