Kinetics of [³H]neurotoxin‐receptor complex formation (A) and dissociation (B) for low degrees of receptor saturation. A: on‐rate. The reaction was performed in a total volume of 1.105 ml. Aliquots of 0.15 ml were taken after the indicated times and diluted into 1 ml of buffer solution containing 0.5 mg of unlabeled toxin in order to stop the reaction; the aliquots were then assayed for the content of receptor‐[³H]neurotoxin complexes. Receptor concentration R₀ = 6.33 × 10⁻⁸ M, toxin concentration T₀ = 1.45 × 10⁻⁹ M, final equilibrium concentration of receptor‐toxin complex M as calculated from experimental points after 60 min. A second‐order rate constant k₂ = 4.3 × 10⁶ M⁻¹ min⁻¹ was calculated from the slope of Fig. 1A. First half‐time τ = 2.54 min. Rate law . B: off‐rate. In a total volume of 6.05 ml, receptor (2.6 × 10⁻⁸ M) and [³H]neurotoxin (3.64 × 10⁻⁹ M) were incubated for 95 min at 25°C, and 1,000 ml of buffer at 25°C was added. Aliquots of 50 ml were taken at the indicated times and analyzed for their content of remaining receptor‐toxin complexes. From the slope of Fig. 1B a first‐order rate constant k₁ = 1.4 × 10⁻⁴ min⁻¹ was calculated. Dissociation constant calculated from k₂ of Fig. 1A and k₁ of Fig. 1B is K_D = 3.3 × 10⁻¹¹ M.

Dissociation of [³H]toxin‐receptor complex. In a total volume of 2.07 ml, receptor (2.66 × 10⁻⁸ M) and [³H]neurotoxin (4.12 × 10⁻⁸ M) were incubated for 30 min at 25°C, and 250 ml of buffer at 25°C was then added. Aliquots of 10 ml were taken at the indicated times and analyzed for their content of remaining toxin‐receptor complexes. Equilibrium concentrations before and after dilution were calculated to be 2.52 × 10⁻⁸ M and 5.3 × 10⁻¹¹ M. Fast component (after correction for the contribution of the slow component) k₁ = 4 × 10⁻³ min⁻¹ (τ = 3 h), slow component k₁ = 9 × 10⁻⁵ min⁻¹ (τ = 125 h). Inset: off‐rate in presence of decamethonium chloride; 50 ml of the initial reaction mixture (see above) was taken after 45 h and 71 h, respectively, mixed with 60 ml of 2.65 × 10⁻³ M decamethonium chloride, and 20 ml aliquots were analyzed by filtration at the indicated times. Concentrations of remaining receptor‐toxin complex were normalized to 100%. k₁ (decamethonium) = 6.6 × 10⁻³ min⁻¹, τ = 1.75 h.

A: dissociation of [³H]toxin‐receptor complexes in presence of unlabeled toxin. Neurotoxin‐receptor complexes were prepared as follows: separate reaction mixtures in a final volume of 75.25 ml standard buffer contained receptor (4 × 10⁻¹⁰ M) and [³H]neurotoxin (9.2 × 10⁻⁹M). These were preincubated for different time periods at 25°C before the addition of a 3,500‐fold excess of unlabeled toxin (2 ml of a solution containing 10 mg/ml). Aliquots (5 ml) were taken at appropriate intervals thereafter and analyzed for residual [³H]toxin‐receptor complexes. Each reaction mixture yielded a curve like that in the inset: the dissociation of preformed complexes revealed the existence of two complexes, the relative proportions of which were determined by extrapolation to zero time as shown. The logarithm of the percentage of rapidly dissociating complex (RT) was then plotted as a function of the length of preincubation preceding addition of unlabeled toxin. At longer times of incubation the slowly dissociating complex (RT)* increases at the expense of the rapid component (RT). B: change in dissociation constant (K_D) of [³H]neurotoxin‐receptor complexes with increasing time of incubation, the usual binding assay was performed and results organized in the form of double‐reciprocal plots; the K_D was obtained by extrapolation in the normal way for different periods of incubation in the range 3.3–48 h. The logarithm of the K_D was then plotted as a function of the incubation time (inset: K_D as a function of time). In all these experiments the concentration of receptor was 1.0 × 10⁻⁹ M and the concentration of neurotoxin was in the range 3.1 × 10⁻¹⁰ to 2.2 × 10⁻⁸ M.

A schematic model for receptor‐neurotoxin interaction. With a large excess of receptor and low saturation with neurotoxin, the single complex of high affinity —(RT)* —is formed. The toxin molecule bound at one site initially blocks an optimal “fit” for another toxin molecule interacting at the second site of a pair. Further toxin binding, leading to high degrees of receptor saturation, thus yields a lower affinity complex (RT) in addition to (RT)*. The affinity characteristic of the two complexes can oscillate between them. The lower affinity species (RT) is converted to the single population (RT)* by a slow first‐order process (k₄) with a half‐time of approximately 30 h. The model represents one way to visualize the slow, time‐dependent accommodation of a second toxin molecule in the form of (RT)*; a conformational change in the receptor would enlarge the toxin‐ binding region and allow both toxin residues to bind without mutual obstruction.

Competitive binding of a small ligand, dimethyl‐d‐tubocurarine, and [³H]α‐cobra toxin to the receptor. A: double‐reciprocal plot: C_l, dimethyl‐d‐tubocurarine concentrations. (•) C_l = 0; (□) C_l = 4.10 × 10⁻⁸ M; (▵) C_l = 4.55 × 10⁻⁷ M; (○) C_l = 4.17 × 10⁻⁶ M. C_B is concentration of bound ligand, C_F is concentration of free ligand. Inset: replot of the apparent dissociation constants as a function of the concentration (×), and of the square root of the concentration (○), of dimethyl‐d‐tubocurarine. Intrinsic dissociation constant per site of dimethyl‐d‐tubocurarine calculated from the linear replot is K_l = 1.2 × 10⁻⁷ M. Note that the experimental point is the same for both functions, and it is represented only by a single symbol. B: logarithmic plot of the binding of dimethyl‐d‐tubocurarine to the receptor. Receptor concentration 4.9 × 10⁻⁹ M. Toxin concentration (fixed) 3.55 × 10⁻⁸ M. The toxin concentration was sufficient to saturate more than 99% of the receptor binding sites even in the absence of dimethyl‐d‐tubocurarine. Sample volumes without dimethyl‐d‐tubocurarine totaled 1,020 μl. (RI), concentration of receptor inhibitor complex; (RT), concentration of receptor‐toxin complex; T, free toxin concentration; K_D, dissociation constant of the receptor‐toxin complex in absence of inhibitor; I, concentration of free inhibitor. Slope m = n = 0.58; K_l, per mole of inhibitor K_l = 1.0 × 10⁻⁷ M.

A: competitive binding of |³H]neurotoxin and decamethonium to the receptor at 20°C. Concentrations of decamethonium: (○) I = 0; (•) I = 1.08 × 10⁻⁶ M; (▵) I = 4.32 × 10⁻⁶ M; (□) I = 2.16 × 10⁻⁵ M. B: competitive binding of decamethonium to the receptor at 25°C in presence of constantly high concentration of [³H]α‐neurotoxin. R₀ = 1.23 × 10⁻⁹ M; T₀ = 4.06 × 10⁻⁸ M; all other conditions as in Fig. 5. Initial slope at low decamethonium concentrations m = n = 0.52. Initial dissociation constant per mole of decamethonium K_l = 1.0 × 10⁻⁸ M.

Competitive binding of [³H]neurotoxin and bis‐methonium compounds to the receptor at 22°C. Compounds and concentrations are: (•) toxin alone; (□) tetramethonium 1.0 × 10⁻⁴ M; (+) pentamethonium 9 × 10⁻⁵ M; (○) hexamethonium 9 × 10⁻⁶ M; (▪) heptamethonium 8 × 10⁻⁵ M; (×) octamethonium 8 × 10⁻⁵ M; (▿) enneamethonium 4.9 × 10⁻⁵ M; (▴) decamethonium 2.16 × 10⁻⁵ M.

Dissociation of [³H]toxin‐receptor complexes after addition of benzoquinonium. In a total volume of 0.5 ml, 2.9 × 10⁻¹¹ mol of receptor and 8.5 × 10⁻¹² mol of [⁻³H]cobra neurotoxin were incubated in standard buffer for 21 h at 20°C. The reaction mixture was then mixed with 50 ml of the appropriate benzoquinonium solution in standard buffer, and 2.5‐ml aliquots were analyzed for their content of remaining receptor‐toxin complexes by filtration at the indicated times. The molar concentrations of receptor and toxin after dilution were 5.8 × 10 M and 1.7 × 10⁻¹⁰ M, respectively. The initial concentration of receptor‐toxin complexes was 1.68 × 10⁻¹⁰ M, the equilibrium concentration after distribution 1.62 × 10⁻¹⁰ M. Hence spontaneous dissociation of receptor‐toxin complexes resulting from dilution is negligible. (▾) standard buffer without benzoquinonium (illustrates the small extent of denaturation of receptor‐toxin complexes); (▵) 2 × 10⁻⁷ M; (▪) 6.7 × 10⁻⁷ M; (○) 2 × 10⁻⁶ M; (+) 7 × 10⁻⁶ M; and (•) 2.2 × 10⁻⁴ M benzoquinonium. K_l¹ calculated from initial rates K_l¹ = 2.7 × 10⁻⁵ M.

Dissociation of [³H]toxin‐receptor complexes in presence of benzoquinonium. Equilibrium shift by addition of benzoquinonium (•). In a total volume of 0.5 ml, receptor (4 × 10⁻¹¹ mol) and toxin (1.45 × 10⁻¹¹ mol) were incubated in standard buffer for 20.5 h at 21°C; 50 ml of a benzoquinonium solution in standard buffer (4.5 × 10⁻⁶ M) was added, and 2.5‐ml aliquots were analyzed for their content of remaining receptor‐toxin complexes by filtration at the indicated times. The molar concentrations of receptor and toxin after dilution were 8 × 10⁻¹⁰ M and 2.9 × 10⁻¹⁰ M, respectively. Spontaneous dissocation of receptor‐toxin complexes due to dilution is therefore negligible. Rate constant of the initial linear part k = 8.67 × 10⁻³ min⁻¹; equilibrium concentration of bound toxin C_eq = 2.4 × 10⁻¹¹ M. Inset: initial rate constants k for various concentrations of benzoquinonium under comparable experimental conditions. k_max = 0.065 obtained by extrapolation, benzoquinonium concentration for half‐maximal rate constant k_{i max} = 2.4 × 10⁻⁵ M. Equilibrium shift by dilution and addition of benzoquinonium (▿). Receptor (1.2 × 10⁻¹¹ mol) and toxin (9 × 10⁻¹² mol) in a total volume of 3.1 ml were incubated for 3 h at 21°C, and 2,000 ml of buffer 8 × 10⁻⁸ M in benzoquinonium was then added. Aliquots of 50 ml were taken at the indicated times and analyzed as described above. Rate constant of initial linear part k = 1.6 × 10⁻³ min⁻¹; rate constant of final linear part k₁ = 1.6 × 10⁻⁴ min^−1.