Derivation of the Crick–Wyman Equation for Allosteric Proteins Defining the Difference between the Number of Binding Sites and the Hill Coefficient

When ATP, the normal phosphate donor for hexokinase D (‘glucokinase’), is replaced by ITP, the positive co-operativity with respect to glucose disappears. This may be rationalized in relation to kinetic models for hexokinase D co-operativity, which assume that with the normal substrates the chemical reaction and subsequent release of products occur so rapidly that binding of substrates cannot approach equilibrium and is therefore not constrained by the thermodynamic requirement that the Hill coefficient for substrate binding cannot exceed the number of binding sites. ITP is a much poorer substrate than ATP, however: its Km value at high glucose concentrations is 24 times the value for ATP, whereas the value of the limiting rate V is decreased about 8-fold. Consequently it is no longer possible for the ternary complex to be converted into products rapidly enough to generate kinetic co-operativity. The negative co-operativity with respect to glucose observed in 2H2O with ATP as phosphate donor also disappears when ITP is used instead of ATP.

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Allosteric effects of Mg2+ on the gating of Ca2+-activated K+ channels from mammalian skeletal muscle

Journal of Experimental Biology ◽

10.1242/jeb.124.1.5 ◽

1986 ◽

Vol 124 (1) ◽

pp. 5-13

Author(s):

J. Golowasch ◽

A. Kirkwood ◽

C. Miller

Keyword(s):

Binding Sites ◽

Hill Coefficient ◽

K Channel ◽

Activation Process ◽

Mammalian Skeletal Muscle ◽

Activation Curve ◽

K Channels ◽

The Hill ◽

Cytoplasmic Side ◽

High Conductance

Ca2+-activated K+ channels from rat muscle transverse tubule membranes were inserted into planar phospholipid bilayers, and the activation of these channels by Ca2+ was studied. On the cytoplasmic side of the channel, calcium ions (in the range 10–100 mumol l-1) increase the opening probability of the channel in a graded way. This ‘activation curve’ is sigmoid, with an average Hill coefficient of about 2. Magnesium ions, in the range 1–10 mmol l-1, increase the apparent affinity of the channel for Ca2+ and greatly enhance the sigmoidicity of the Ca2+ activation curve. In the presence of 10 mmol l-1 Mg2+, the Hill coefficient for Ca2+ activation is about 4.5. This effect depends upon Mg2+ concentration but not upon applied voltage. Mg2+ is effective only when added to the cytoplasmic side of the channel. The results argue that this high-conductance, Ca2+-activated K+ channel contains at least six Ca2+-binding sites involved in the activation process.

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The interaction of sialidase-treated hCG with ovarian cellular membranes

Acta Endocrinologica ◽

10.1530/acta.0.0970270 ◽

1981 ◽

Vol 97 (2) ◽

pp. 270-280 ◽

Cited By ~ 1

Author(s):

E. C. Brand ◽

J. Odink ◽

G. Klok ◽

E. V. van Hall

Keyword(s):

Binding Sites ◽

Association Constant ◽

Apparent Difference ◽

Receptor Complexes ◽

Number Of Binding Sites ◽

Biological Potency ◽

The Difference ◽

The Stability ◽

Dissociation Curves ◽

Hcg Receptor

Abstract. The potency of human chorionic gonadotrophin (hCG) in competition for binding to a gonadal membrane fraction is remarkably enhanced by sialidase treatment. The present study was undertaken to investigate the specificity and characteristics of the binding of sialidase-treated hCG (asialo-hCG) in a particulate hCG-binding system from luteinized rat ovaries. The competitive potency of asialo-hCG relative to hCG was 2.5, irrespective of whether [125I]hCG or [125I]asialo-hCG was used for tracer. This was due to a 2.1 times higher equilibrium association constant for asialo-hCG, whereas the estimated number of binding sites did not differ. There was no apparent difference in the stability of hCG and asialo-hCG, or in the stability of the respective hormone-receptor complexes. The effect of variation of the incubation conditions on the binding of both tracers was similar. In accordance with the difference in the equilibrium association constant, the association velocity of asialo-hCG was more than double that of hCG. With all of the tracers used the dissociation curves were biphasic, the size of the initial fast-dissociating fraction being inversely related to the pre-incubation time. Under identical conditions, the fast-dissociating fraction was smaller for the [125I]asialo-hCG complex than for the [125I]hCG complex. The dissociation velocities of these fractions appeared to be similar. The results indicate that asialo-hCG binds to the hCG receptor in a way similar to the binding of the unmodified hormone, but with a higher affinity. The smaller size of the fast-dissociation form of the asialo-hCG-receptor complex may be related to the lower biological potency of the hormone derivative.

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A comparative study of the activation of the cholinergic receptor by various agonists

Proceedings of the Royal Society of London Series B Biological Sciences ◽

10.1098/rspb.1983.0037 ◽

1983 ◽

Vol 218 (1211) ◽

pp. 241-251 ◽

Cited By ~ 2

Keyword(s):

Dose Response ◽

Binding Sites ◽

Nicotinic Receptor ◽

Response Curve ◽

Cholinergic Receptor ◽

Hill Coefficient ◽

Frog Neuromuscular Junction ◽

Cholinergic Agonists ◽

The Mean ◽

The Hill

At the frog neuromuscular junction, a dose-response curve for the activation of the nicotinic receptor by carbachol has been determined under conditions where desensitization could be estimated and corrected for. The value of the Hill coefficient was 2 and that of the dissociation constant for carbachol was 400 μm, the two binding sites of the receptor being assumed identical. The properties of six cholinergic agonists were then compared. The potencies and mean open times of these agonists are ranked in the same order, but the range of the potencies is much larger (1–200) than that of the mean open times (1-4). The differences in the properties of the different agonists could simply be due to differences in the rate of dissociation of the agonist, if it is assumed that one apparent opening of the channel is in fact a burst of several oscillations between the open and closed conformations, such that a burst is interrupted by the dissociation of one agonist molecule.

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Kinetic Characterisation of Phosphofructokinase Purified from Setaria cervi: A Bovine Filarial Parasite

Enzyme Research ◽

10.4061/2011/939472 ◽

2011 ◽

Vol 2011 ◽

pp. 1-10 ◽

Cited By ~ 7

Author(s):

Bechan Sharma

Keyword(s):

Adult Female ◽

Binding Sites ◽

Inhibitory Concentration ◽

Product Inhibition ◽

Hill Coefficient ◽

Enzyme Protein ◽

Setaria Cervi ◽

The Hill ◽

Inhibition Studies ◽

Cooperative Kinetics

Phosphofructokinase (PFK), a regulatory enzyme in glycolytic pathway, has been purified to electrophoretic homogeneity from adult female Setaria cervi and partially characterized. For this enzyme, the Lineweaver-Burk's double reciprocal plots of initial rates and D-fructose-6-phosphate (F-6-P) or Mg-ATP concentrations for varying values of cosubstrate concentration gave intersecting lines indicating that Km values for F-6-P (1.05 mM) and ATP (3 μM) were independent of each other. S. cervi PFK, when assayed at inhibitory concentration of ATP (>0.1 mM), exhibited sigmoidal behavior towards binding with F-6-P with a Hill coefficient (n) value equal to 1.8 and 1.7 at 1.0 and 0.33 mM ATP, respectively. D-fructose-1,6-diphosphate (FDP) competitively inhibited the filarial enzyme: Ki and Hill coefficient values being 0.18 μM and 2.0, respectively. Phosphoenolpyruvate (PEP) also inhibited the enzyme competitively with the Ki value equal to 0.8 mM. The Hill coefficient values (>1.5) for F-6-P (at inhibitory concentration of ATP) and FDP suggested its positive cooperative kinetics towards F-6-P and FDP, showing presence of more than one binding sites for these molecules in enzyme protein and allosteric nature of the filarial enzyme. The product inhibition studies gave us the only compatible mechanism of random addition process with a probable orientation of substrates and products on the enzyme surface.

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Inhibitory Effects of Synthetic Lanthanum-Crown Ether at the Reducing Side of Photosystem II

Zeitschrift für Naturforschung C ◽

10.1515/znc-1998-1-210 ◽

1998 ◽

Vol 53 (1-2) ◽

pp. 49-54

Author(s):

Surendra Chandra Sabat ◽

Subash Padhye ◽

Prasanna Mohanty

Keyword(s):

Electron Flow ◽

Hill Coefficient ◽

Inhibitory Effects ◽

Ps Ii ◽

Binding Domains ◽

Acceptor Side ◽

Plot Analysis ◽

Number Of Binding Sites ◽

Straight Lines ◽

The Hill

Abstract Inhibitory effects of lanthanum-crown [La-(Pic)3 (15-crown-6) 3H2O].was investigated on the O2 evolution activity of photsystem II particles. Lanthanum (La)-crown inhibited the electron flow at the reducing side of PS II complex. Short duration (1-2 min) treatment of PS II membranes with trypsin partly developed resistance to La-crown inhibition. However, longer proteolytic treatment (>2 min) appeared to expose newer site(s) for La-crown inhibition. The inhibitory constant (Ki) for La-crown was nearly 0.17 | μᴍ . This inhibitory capacity is about 4 to 5 times less than the potent PS II inhibitor diuron which also binds at the acceptor side of PS II. The number of binding sites for La-crown was found to be 1 per 20 chlorophyll molecules. The Hill plot analysis showed the presence of three distinct straight lines suggesting that the compound acts at least at three sites. Furthermore, from the slope value (Hill coefficient) it is suggested that two of these sites provide minimum of two binding domains for the inhibitor.

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Voltage Dependence of the Apparent Affinity for External Na+ of the Backward-Running Sodium Pump

The Journal of General Physiology ◽

10.1085/jgp.117.4.315 ◽

2001 ◽

Vol 117 (4) ◽

pp. 315-328 ◽

Cited By ~ 25

Author(s):

Paul De Weer ◽

David C. Gadsby ◽

R.F. Rakowski

Keyword(s):

Steady State ◽

Sodium Pump ◽

Channel Model ◽

Pump Current ◽

Hill Coefficient ◽

Access Channel ◽

Electrogenic Sodium Pump ◽

The Difference ◽

Loligo Pealei ◽

The Hill

The steady-state voltage and [Na+]o dependence of the electrogenic sodium pump was investigated in voltage-clamped internally dialyzed giant axons of the squid, Loligo pealei, under conditions that promote the backward-running mode (K+-free seawater; ATP- and Na+-free internal solution containing ADP and orthophosphate). The ratio of pump-mediated 42K+ efflux to reverse pump current, Ipump (both defined by sensitivity to dihydrodigitoxigenin, H2DTG), scaled by Faraday's constant, was −1.5 ± 0.4 (n = 5; expected ratio for 2 K+/3 Na+ stoichiometry is −2.0). Steady-state reverse pump current-voltage (Ipump-V) relationships were obtained either from the shifts in holding current after repeated exposures of an axon clamped at various Vm to H2DTG or from the difference between membrane I-V relationships obtained by imposing Vm staircases in the presence or absence of H2DTG. With the second method, we also investigated the influence of [Na+]o (up to 800 mM, for which hypertonic solutions were used) on the steady-state reverse Ipump-V relationship. The reverse Ipump-V relationship is sigmoid, Ipump saturating at large negative Vm, and each doubling of [Na+]o causes a fixed (29 mV) rightward parallel shift along the voltage axis of this Boltzmann partition function (apparent valence z = 0.80). These characteristics mirror those of steady-state 22Na+ efflux during electroneutral Na+/Na+ exchange, and follow without additional postulates from the same simple high field access channel model (Gadsby, D.C., R.F. Rakowski, and P. De Weer, 1993. Science. 260:100–103). This model predicts valence z = nλ, where n (1.33 ± 0.05) is the Hill coefficient of Na binding, and λ (0.61 ± 0.03) is the fraction of the membrane electric field traversed by Na ions reaching their binding site. More elaborate alternative models can accommodate all the steady-state features of the reverse pumping and electroneutral Na+/Na+ exchange modes only with additional assumptions that render them less likely.

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The oxygen-linked zinc-binding site of human haemoglobin

Biochemical Journal ◽

10.1042/bj1690625 ◽

1978 ◽

Vol 169 (3) ◽

pp. 625-632 ◽

Cited By ~ 28

Author(s):

J G Gilman ◽

G J Brewer

Keyword(s):

Binding Sites ◽

Zinc Ion ◽

Bohr Effect ◽

Zinc Binding ◽

Hill Coefficient ◽

Human Haemoglobin ◽

Equilibrium Binding ◽

Zinc Binding Site ◽

Alkaline Bohr Effect ◽

The Hill

Zn2+ is known to increase the 02 affinity of human haemoglobin. Previous data suggested that Zn2+ exerts its effect by directly binding to haemoglobin, rather than by competing with or binding to 2,3-bisphosphoglycerate. It was also shown that there are two 02-linked zinc-binding sites in haemoglobin, and that Zn2+ does not significantly alter haemoglobin co-operativity or the alkaline Bohr effect. The effect of Zn2+ on 02 affinity of haemoglobin can also be observed for other haemoglobins as diverse as those of cow and chicken. This paper presents new data on the haemoglobin-zinc interaction for normal haemoglobin, des-His146beta-haemoglobin and N-ethylsuccinimide-haemoglobin of humans. For normal haemoglobin (0.05 mM in tetramers), at 20 degrees C in buffer containing 0.1 M-Cl-, 02-dissociation-curve experiments showed that the addition of 0.4-0.5 mM-ZnS04 did not change the Bohr effect between pH 6.71 and 7.29. Similar experiments, with “zinc-ion buffers”, showed that the value of the Hill coefficient, h, decreased only slightly if the concentration of free Zn2+ was held constant. For N-ethylsuccinimide-haemoglobin, Zn2+ caused less increase in O2 affinity than for normal haemoglobin. These studies, together with data on the equilibrium binding of Zn2+ to oxy-, deoxy- and des-His146beta-haemoglobins, suggest that zinc is chelated in oxyhaemoglobin by at least three amino acids, two of which are histidine-146beta and cysteine-93beta.

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The Estimation of the Number of Binding Sites for Antibody on Antigen Molecules with Reference to Factor VIII and its Antibody

Thrombosis and Haemostasis ◽

10.1055/s-0038-1647956 ◽

1976 ◽

Vol 35 (02) ◽

pp. 274-288 ◽

Cited By ~ 2

Author(s):

Judith Pool ◽

Rosemary Biggs ◽

R. G Miller

Keyword(s):

Factor Viii ◽

Binding Sites ◽

Theoretical Basis ◽

Human Antibody ◽

Rabbit Antibody ◽

Number Of Binding Sites ◽

Theoretical Considerations

SummaryThe theoretical basis for determining the number of antibody sites on antigen molecules is examined. The theoretical considerations are applied to factor VIII molecules. Examples based on data available at the Oxford Haemophilia Centre are calculated to illustrate the approach. It is concluded that there are few sites on each factor VIII molecule for human antibody. The three antibodies for which reasonable data were available suggest 1–3 sites for human antibody. The data for rabbit antibody suggest 5–6 sites per factor VIII molecule.

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