Interpretation of concentration-dependence in aggregation kinetics

Aggregation processes are analyzed by two kinetic models, the random polymerization model and the nucleation-dependent polymerization model. A kinetic equation for the random polymerization model can be derived analytically, revealing the relation between the initial monomer concentration ([M]0), the rate constant (k(a)), time (t), the yield of detectable aggregate ([F]), and the critical aggregation number (m). However, time-course curves for the nucleation-dependent polymerization model can be obtained by numerical calculation. It is found that lag time (t(d)) and half-time (t1/2) are proportional to [M](-1) in the random polymerization model, while t(d) and t1/2 are proportional to [M1](-s) (1 < s < n; n is nucleus size) at the lower concentration and are less dependent on [M1] at the higher concentration in the nucleation-dependent polymerization model.     

Activation of nitrite reductase from Escherichia coli K12 by oxidized nicotinamide-adenine dinucleotide.

Nitrite reductase from Escherichia coli K12 requires the presence of NAD+, one of the products of the reduction of NO2-by NADH, for full activity. The effect is observed with both crude extracts and purified enzyme. NAD+ also acts as a product inhibitor at high concentrations, and plots of initial rate against NAD+ concentration are bell-shaped. The maximum occurs at about 1 mM-NAD+, but increases with increasing NADH concentration. In the presence of 1 mM-NAD+ and saturating NO2-(2mM) the Michaelis constant for NADH is about 16 micron. The Michaelis constant for NO2-is about 5 micron and is largely independent of the NAD+ concentration. Similar but more pronounced effects of NAD+ are observed with hydroxylamine as electron acceptor instead of NO2-. The maximum rate of NADH oxidation by hydroxylamine is about 5.4 times greater than the maximum rate of NADH oxidation by NO2- when assayed with the same volume of the same preparation of purified enzyme. The Michaelis constant for hydroxylamine is 5.3 mM, however, about 1000 times higher than for NO2-. These results are consistent with a mechanism in which the same enzyme-hydroxylamine complex occurs as an intermediate in both reactions.     

The effect of hypertonic urea solution on Na+ and K+ transport through the smooth muscle membrane.

The aim of this work was to examine the effect of a hypertonic solution (Krebs solution + 290 mM urea) on K+ and Na+ transport. The experiments were carried out on the guinea-pig taenia coli preparations using the method of Na-24 and K-24 loading and washout. The efflux curves were analysed by means of the digital computer technique. The following parameters were determined: efflux rate constant k2, influx rate constant k1, intracellular ion concentration C1 ion flux M and permeability P. Any significant difference between PNa/PK ratio in hypertonic urea and isotonic Krebs solutions was found.     

Kinetics on the turbidity change of wheat starch during its retrogradation

Wheat starch dispersions of 10–40% (w/w) were gelatinized and the change in turbidity of each solution during storage was measured in the 400–1100 nm wavelength range. The relative transmittance, defined as the ratio of transmittance at any storage time to that at the initial time, decreased when the solutions were stored at 5 and 30 °C; the decrease, reflecting the progress of retrogradation, was larger at 5 °C than at 30 °C. Most of the changes in relative transmission taking place over 14 days were achieved during the first 90 min. The change in the relative transmittance is inversely proportional to the energy required for deformation. The kinetics on change in relative transmittance can be expressed by Weibull equation. The larger rate constant at higher starch concentration could be ascribed to the state of the starch granules, which depended on starch concentration.     

Formation kinetics of insulin-based amyloid gels and the effect of added metalloporphyrins

The kinetics of insulin-based amyloid gel formation has been studied using extinction and fluorescence detection. The process is treated as autocatalytic, and the kinetic profiles are fit using a nonconventional analysis involving a time-dependent rate constant (factor): k(t) = k(o) + k(c)(k(c)t)(n). The dependence of the kinetic parameters on initial solution conditions of concentration, pH, and ionic strength has been investigated. A mechanism is proposed in which the rate-determining step involves the activation of insulin solute species into partially unfolded, structurally modified monomers, which then aggregate. The influence of added metalloporphyrins on the rate and extent of gel formation is described. Metal derivatives of tetrakis(4-sulfonatophenyl)porphine prove effective at inhibiting the aggregation of insulin via pathways that depend on concentration and identity of the incorporated metal.     

胰酶对皮肤角质细胞分离和传代的影响

考察不同的胰酶浓度及其作用时间对角质细胞分离和传代的影响。实验发现在胰酶浓度 0.25%时作用5min可获得的总活细胞量和有克隆形成能力的细胞量均优于其它培养条件 ;而在胰酶浓度0.05%时作用 5min可获得最大的原代角质细胞贴壁率。随着胰酶浓度的提高 ,传代角质细胞的贴壁率和贴壁速率常数以及克隆形成率均随之增加 ,因此在传代培养时使用 0.25%胰酶浓度进行消化较为适宜.     

Mechanism of actomyosin adenosine triphosphatase. Evidence that adenosine 5'-triphosphate hydrolysis can occur without dissociation of the actomyosin complex.

We have investigated the steps in the actomyosin ATPase cycle that determine the maximum ATPase rate (Vmax) and the binding between myosin subfragment one (S-1) and actin which occurs when the ATPase activity is close to Vmax. We find that the forward rate constant of the initial ATP hydrolysis (initial Pi burst) is about 5 times faster than the maximum turnover rate of the actin S-1 ATPase. Thus, another step in the cycle must be considerably slower than the forward rate of the initial Pi burst. If this slower step occurs only when S-1 is complexed with actin, as originally predicted by the Lymn-Taylor model, the ATPase activity and the fraction of S-1 bound to actin in the steady state should increase almost in parallel as the actin concentration is increased. As measured by turbidity determined in the stopped-flow apparatus, the fraction of S-1 bound to actin, like the ATPase activity, shows a hyperbolic dependence on actin concentration, approaching 100% asymptotically. However, the actin concentration required so that 50% of the S-1 is bound to actin is about 4 times greater than the actin concentration required for half-maximal ATPase activity. Thus, as previously found at 0 degrees C, at 15 degrees C much of the S-1 is dissociated from actin when the ATPase is close to Vmax, showing that a slow first-order transition which follows the initial Pi burst (the transition from the refractory to the nonrefractory state) must be the slowest step in the ATPase cycle. Stopped-flow studies also reveal that the steady-state turbidity level is reached almost instantaneously after the S-1, actin, and ATP are mixed, regardless of the order of mixing. Thus, the binding between S-1 and actin which is observed in the steady state is due to a rapid equilibrium between S-1--ATP and acto--S-1--ATP which is shifted toward acto-S-1--ATP at high actin concentration. Furthermore, both S-1--ATP and S-1--ADP.Pi (the state occurring immediately after the initial Pi burst) appear to have the same binding constant to actin. Thus, at high actin concentration both S-1--ATP and S-1--ADP.Pi are in rapid equilibrium with their respective actin complexes. Although at very high actin concentration almost complete binding of S-1--ATP and S-1--ADP.Pi to actin occurs, there is no inhibition of the ATPase activity at high actin concentration. This strongly suggests that both the initial Pi burst and the slow rate-limiting transition which follows (the transition from the refractory to the nonrefractory state) occur at about the same rates whether the S-1 is bound to or dissociated from actin. We, therefore, conclude that S-1 does not have to dissociate from actin each time an ATP molecule is hydrolyzed.     

Heme transfer between phospholipid membranes and uptake by apohemoglobin

The incorporation of CO-heme into single bilayer, egg lecithin vesicles was examined by following the spectral changes that occur when the porphyrin becomes embedded in the membranes. The rate of CO-heme uptake by liposomes is extremely fast (t1/2 less than or equal to 20 ms at 10 degrees C), and the maximum extent is roughly 1 heme/5 phospholipid molecules. This limiting stoichiometry is due to unfavorable electrostatic interactions between the propionate groups of the bound CO-heme. This effect was treated theoretically by attenuating the intrinsic heme partitioning equilibrium constant with an exponential term reflecting the surface potential of the membranes. The surface potential was assumed to be proportional to the concentration of CO-heme in the membranes, and the final expression is Kp = Kop exp[-AHb/VpCp], where Kp is the observed partition constant; Kop, the intrinsic constant; Hb, the concentration of bound heme in the suspension; Vp, the partial molar volume of egg lecithin; Cp, the concentration of lipid phosphate; and A, an empirical constant representing the capacitance of the membrane for heme. For the analysis of kinetic data, the electrostatic term is assumed to apply only to the membrane dissociation rate constant, k-1, and not the association rate constant, k1. The dissociation rate was measured independently either by following the transfer of CO-heme from one vesicle fraction to another or by monitoring heme efflux from the membranes and incorporation into apohemoglobin at high protein concentrations. The data for all three sets of experiments, heme uptake, transfer, and incorporation into globin at 10 degrees C, were fitted quantitatively to the partitioning mechanism using A = 15 M-1, Kop = 5 X 10(5), k1 = 2 X 10(6) s-1, and k0(-1) = 4 s-1. Thus, heme can spontaneously migrate across lipid-water interfaces and hence diffuse rapidly from the mitochondrial inner membrane where it is synthesized to the rough endoplasmic reticulum where it is incorporated into hemoglobin.     

Hydrogen ion currents in rat alveolar epithelial cells.

Alveolar epithelial cells isolated from rats and maintained in primary culture were studied using the whole-cell configuration of the "patch-clamp" technique. After other ionic conductances were eliminated by replacing permeant ions with N-methyl-D-glucamine methanesulfonate, large voltage-activated hydrogen-selective currents were observed. Like H+ currents in snail neurons and axolotl oocytes, those in alveolar epithelium are activated by depolarization, deactivate upon repolarization, and are inhibited by Cd2+ and Zn2+. Activation of H+ currents is slower in alveolar epithelium than in other tissues, and often has a sigmoid time course. Activation occurs at more positive potentials when external pH is decreased. Saturation of the currents suggests that diffusion limitation may occur; increasing the pipette buffer concentration from 5 to 120 mM at a constant pH of 5.5 increased the maximum current density from 8.7 to 27.3 pA/pF, indicating that the current amplitude can be limited in 5 mM buffer solutions by the rate at which buffer molecules can supply H+ to the membrane. These data indicate that voltage-dependent H+ currents exist in mammalian cells.     

Re-interpretation of the logistic equation for batch microbial growth in relation to Monod kinetics

Aims:  To determine the underlying substrate utilization mechanism in the logistic equation for batch microbial growth by revealing the relationship between the logistic and Monod kinetics. Also, to determine the logistic rate constant in terms of Monod kinetic constants.
Methods and Results:  The logistic equation used to describe batch microbial growth was related to the Monod kinetics and found to be first-order in terms of the substrate and biomass concentrations. The logistic equation constant was also related to the Monod kinetic constants. Similarly, the substrate utilization kinetic equations were derived by using the logistic growth equation and related to the Monod kinetics.
Conclusion:  It is revaled that the logistic growth equation is a special form of the Monod growth kinetics when substrate limitation is first-order with respect to the substrate concentration. The logistic rate constant ( k ) is directly proportional to the maximum specific growth rate constant ( μ _m) and initial substrate concentration ( S ₀) and also inversely related to the saturation constant ( K _s).
Significance and Impact of the Study:  The semi-empirical logistic equation can be used instead of Monod kinetics at low substrate concentrations to describe batch microbial growth using the relationship between the logistic rate constant and the Monod kinetic constants.     

Cell-mass maximization in fed-batch cultures

Complete solutions are provided for cell-mass maximization for free and fixed final times and constant and variable yields. The optimal feed rate profile is a concatenation of maximum, minimum and singular feed rates. The exact sequence and duration of each feed rate depends primarily on the initial substrate concentration, and degenerate cases arise due to the magnitude constraint on the feed rate and the length of final time t _f. When the final time is free and not in the performance index, it is infinite for constant yield so that any form of feed rate leads to the same amount of cells, while for variable yield the singular feed rate is exponential and maximizes the yield. For fixed final time the singular feed rate for constant yield is exponential and maximizes the specific growth rate by maintaining the substrate concentration constant, while for variable yield, it is semi-exponential and the substrate concentration starts near the maximum specific growth rate and moves toward the maximum yield. A simple sufficient condition for existence of singular feed rate requires an existence of a region bounded by the maxima of specific growth and cellular yield. Otherwise, the optimal feed rate profile is a bang-bang type and the bioreactor operates in batch mode.     

Theory and simulation of the time-dependent rate coefficients of diffusion-influenced reactions.

A general formalism is developed for calculating the time-dependent rate coefficient k(t) of an irreversible diffusion-influenced reaction. This formalism allows one to treat most factors that affect k(t), including rotational Brownian motion and conformational gating of reactant molecules and orientation constraint for product formation. At long times k(t) is shown to have the asymptotic expansion k(infinity)[1 + k(infinity) (pie Dt)-1/2 /4 pie D + ...], where D is the relative translational diffusion constant. An approximate analytical method for calculating k(t) is presented. This is based on the approximation that the probability density of the reactant pair in the reactive region keeps the equilibrium distribution but with a decreasing amplitude. The rate coefficient then is determined by the Green function in the absence of chemical reaction. Within the framework of this approximation, two general relations are obtained. The first relation allows the rate coefficient for an arbitrary amplitude of the reactivity to be found if the rate coefficient for one amplitude of the reactivity is known. The second relation allows the rate coefficient in the presence of conformational gating to be found from that in the absence of conformational gating. The ratio k(t)/k(0) is shown to be the survival probability of the reactant pair at time t starting from an initial distribution that is localized in the reactive region. This relation forms the basis of the calculation of k(t) through Brownian dynamics simulations. Two simulation procedures involving the propagation of nonreactive trajectories initiated only from the reactive region are described and illustrated on a model system. Both analytical and simulation results demonstrate the accuracy of the equilibrium-distribution approximation method.     

Kinetic characteristics of extracellular catalase from Penicillium piceum F-648 and variants of fungi,adapted to hydrogen peroxide

A comparative kinetic study of extracellular catalases produced by Penicillium piceum F-648 and their variants adapted to H2O2 was performed in culture liquid filtrates. The specific activity of catalase, the maximum rate of catalase-induced H2O2 degradation (Vmax),Vmax/KM ratio, and the catalase inactivation rate constant in the enzymatic reaction (kin, s-1) were estimated in phosphate buffer (pH 7.4) at 30 degrees C. The effective constant representing the rate of catalase thermal inactivation (kin*, s-1) was determined at 45 degrees C. In all samples, the specific activity and KM for catalase were maximum at a protein concentration in culture liquid filtrates of 2.5-3.5 x 10(-4) mg/ml. The effective constants describing the rate of H2O2 degradation (k, s-1) were similar to that observed in the initial culture. These values reflected a twofold decrease in catalase activity in culture liquid filtrates. We hypothesized that culture liquid filtrates contain two isoforms of extracellular catalase characterized by different activities and affinities for H2O2. Catalases from variants 5 and 3 with high and low affinities for H2O2, respectively, had a greater operational stability than the enzyme from the initial culture. The method of adaptive selection for H2O2 can be used to obtain fungal variants producing extracellular catalases with improved properties.     

Kinetics of peroxidation of linoleic acid incorporated into DPPC vesicles initiated by the thermal decomposition of 2,2'-azobis(2-amidinopropane) dihydrochloride

In a previous work [Chem. Phys. Lipids 2000 104, 49], we have derived the following rate law for the oxidation of lipids in compartmentalized systems: R(T)=(k(1)/k(t))(0.5) k(p) [In](0.5) c(0.5) [LH], where, R(T) is the total rate of oxidation, k(1) is the rate constant for the production of free radicals, k(t) and k(p) are the intra-particle rate constants for the termination and propagation sets, respectively, [In] is the concentration of a water-soluble initiator, c is the concentration of particles, and [LH] is the intra-particle concentration of oxidable lipid. In the present work, we have investigated on the applicability of the proposed kinetic rate law for a system where it takes place the oxidation of a reactive lipid incorporated into an inert matrix. With this purpose, we have measured the rate of oxidation of linoleic acid incorporated into dipalmitoylphosphatidylcholine vesicles initiated by the thermal decomposition of 2,2'-azobis(2-amidinopropane) dihydrochloride as a function of the initiator, particles, and intra-particle LH concentrations. The experimentally determined kinetic orders obtained were 0.54+/-0.02, 0.48+/-0.05 and 0.83+/-0.04 for the dependence of the oxidation rate with initiator, particles, and LH intra-particle concentrations, respectively, in agreement with those theoretically predicted. The lower value obtained for the kinetic order in LH is attributed to a change in k(t) with the increase in oxidable lipid intra-particle concentration. The main point to be emphazised from the results here obtained is that the kinetic rate law for the oxidation of lipids in compartmentalized systems can be significantly different than that observed when to the oxidation takes place in homogeneous solution.     

Kinetics of the hydrolysis of cellobiose and p-nitrophenyl-beta-D-glucoside by cellobiase of Trichoderma viride.

Cellobiase has been isolated from the crude cellulase mixture of enzymes of Trichoderma viride using column chromatographic and ion-exchange methods. The steady-state kinetics of the hydrolysis of cellobiose have been investigated as a function of cellobiose and glucose concentrations, pH of the solution, temperature, and dielectric constant, using isopropanol-buffer mixtures. The results show that (i) there is a marked activation of the reaction by initial glucose concentrations of 4 X 10(-3) M to 9 X 10(-2) M and strong inhibition of the reaction at higher initial concentrations, (ii) the log rate -pH curve has a maximum at pH 5.2 and enzyme pK values of 3.5 and 6.8, (iii) the energy of activation at pH 5.1 is 10.2 kcal mol-1 over the temperature range 5-56 degrees C, and (iv) the rate decreases from 0 to 20% (v/v) isopropanol. The hydrolysis by cellobiase (EC 3.2.1.21) of p-nitrophenyl-beta-D-glucoside was examined by pre-steady-state methods in which [enzyme]0 greater than [substrate]0, and by steady-state methods as a function of pH and temperature. The results show (i) a value for k2 of 21 S-1 at pH 7.0 (where k2 is the rate constant for the second step in the assumed two-intermediate mechanism (formula: see text), (ii) a log rate -pH curve, significantly different from that for hydrolysis of cellobiose, in which the rate increases with decreasing pH below pH 4.5, is constant in the region pH 4.5-6, and decreases above pH 6 (exhibiting an enzyme pK value of 7.3), and (iii) an activation energy of 12.5 kcal mol-1 at pH 5.7 over the temperature range 10-60 degrees C.     

Stepwise Kinetic Equilibrium Models of Quantitative Polymerase Chain Reaction

ABSTRACT: BACKGROUND: Numerous models for use in interpreting quantitative PCR (qPCR) data are present in recent literature. The most commonly used models assume the amplification in qPCR is exponential and fit an exponential model with a constant rate of increase to a select part of the curve. Kinetic theory may be used to model the annealing phase and does not assume constant efficiency of amplification. Mechanistic models describing the annealing phase with kinetic theory offer the most potential for accurate interpretation of qPCR data. Even so, they have not been thoroughly investigated and are rarely used for interpretation of qPCR data. New results for kinetic modeling of qPCR are presented. RESULTS: Two models are presented in which the efficiency of amplification is based on equilibrium solutions for the annealing phase of the qPCR process. Model 1 assumes annealing of complementary targets strands and annealing of target and primers are both reversible reactions and reach a dynamic equilibrium. Model 2 assumes all annealing reactions are nonreversible and equilibrium is static. Both models include the effect of primer concentration during the annealing phase. Analytic formulae are given for the equilibrium values of all single and double stranded molecules at the end of the annealing step. The equilibrium values are then used in a stepwise method to describe the whole qPCR process. Rate constants of kinetic models are the same for solutions that are identical except for possibly having different initial target concentrations. Analysis of qPCR curves from such solutions are thus analyzed by simultaneous non-linear curve fitting with the same rate constant values applying to all curves and each curve having a unique value for initial target concentration. The models were fit to two data sets for which the true initial target concentrations are known. Both models give better fit to observed qPCR data than other kinetic models present in the literature. They also give better estimates of initial target concentration. Model 1 was found to be slightly more robust than model 2 giving better estimates of initial target concentration when estimation of parameters was done for qPCR curves with very different initial target concentration. Both models may be used to estimate the initial absolute concentration of target sequence when a standard curve is not available. CONCLUSIONS: It is argued that the kinetic approach to modeling and interpreting quantitative PCR data has the potential to give more precise estimates of the true initial target concentrations than other methods currently used for analysis of qPCR data. The two models presented here give a unified model of the qPCR process in that they explain the shape of the qPCR curve for a wide variety of initial target concentrations.     

Temperature and driving force dependence of the folding rate of reduced horse heart cytochrome c

Utilizing the stability difference between the ferro and ferri forms of horse heart cytochrome c (cyt c), folding of reduced cyt c was triggered by laser-induced reduction of unfolded oxidized cyt c. Measurements were made of the kinetics of the main folding phase (1 ms-10 s) in which collapsed reduced cyt c transforms to the native conformation. The folding rates were studied extensively as a function of temperature (5-75 degrees C) and guanidine hydrochloride (GdnHCl) concentration (1.6-4.9 M). At constant [GdnHCl], the Arrhenius plot of the folding rate constant (k) is nonlinear. At temperatures above 40 degrees C, the decrease in protein stability counteracts the expected increase in folding rate. Introducing free energy (DeltaG), derived from protein stability data, into the Eyring and Arrhenius equations leads to: ln k = ln(k(b)T/h) + DeltaS()/R - DeltaH()/RT - theta(m)DeltaG/RT = ln A - E(a)/RT - theta(m)DeltaG/RT, where theta(m) is the ratio between the denaturant dependence of the folding rate and the stability. By using this equation at constant DeltaG [or constant equilibrium constant (K)], linear Arrhenius plots are obtained. For the main folding phase of reduced cyt c, a positive DeltaS() is obtained indicating that the transition state is less ordered than the reactant. A model is proposed in which reduced cyt c first collapses into a compact intermediate, which needs to expand to reach the transition state of the rate-limiting folding reaction.     

Effect of chlorpromazine on the relation between temperature and the binding of ANS by human erythrocytes

It has been shown that under the effect of chlorpromazin (concentration to 2.10(-5) M) breaks observed on Arrhenius graphs of the rate constant of ANS binding with erythrocytes (k) at 28 and 36 degrees C are shifted to the region of low temperatures approximately to a similar interval (14-15 degrees C). The value k measured at 22 degrees C is not changed within the pH range of 5-7. It is concluded that breaks characterised the initial and final stages of temperature transition initiated in the zone of acid phospholipid of membranes.     

Refined evaluation of the exponential curve parameters and initial exchange rate constant for 22Na+ washout in cultured human skin fibroblasts

A technique is proposed to evaluate the exponential curve parameters and the initial exchange rate constant (kie) for 22Na+ washout from cultured human skin fibroblasts. After loading with the isotope, the cells were subjected to cold washing and warming steps. A desaturation curve for 22Na+ washout was developed including the activity in the warming medium that corresponded to t = 0 min. Using nonlinear regression analysis, a general three exponential function adequately described the 22Na+ washout in the time interval of 0-70 min. A back extrapolation was performed to estimate the initial time (ti; a negative number) when the total activity was present in the cells. The ti was substituted into the first derivative function of the three exponents to yield the kie. Calculated from the equilibrium distribution of 22Na+ and the specific activity of the medium, the concentration of Na+ (in mM; mean +/- SD) for fibroblasts of two individuals were 13.3 +/- 2.3, n = 3, and 19.0 +/- 5.2, n = 4. This indicates that the washout originated mainly or exclusively from the cellular milieu. Therefore, the kie represents the equilibrium exchange rate constant for Na+ washout from an inhomogeneous cell-related space. Multiple experiments demonstrated that the kie value for the two subjects were significantly higher than the initial slopes of the washout curves (kA), a commonly used parameter to characterize Na+ washout, and significantly lower than the slopes of the fastest exponential components (k3): kie = 0.531 +/- 0.017, kA = 0.502 +/- 0.019, and k3 = 0.557 +/- 0.017 min-1 (n = 3) for one subject, and kie = 0.567 +/- 0.065, kA = 0.479 +/- 0.031, and k3 = 0.667 +/- 0.094 min-1 (n = 6) for the other subject. The respective equilibrium exchange rates for these cells, namely the products of kie and cellular Na+ contents, were 1.10 +/- 0.16 and 1.19 +/- 0.24 nmole/10(5) cells. Using the exponential curve parameters, analytical solutions of a serial model and a parallel model with three compartments were performed. According to these analyses the major portion of the cellular Na+ comprises a fast exchangeable cellular compartment. The relative size of this compartment (expressed as a fraction of total cellular Na+ content) for fibroblasts of the two subjects was 96.2 and 89.2% for the serial model and 96.1 and 89.3% according to the parallel model.(ABSTRACT TRUNCATED AT 250 WORDS)     

Equilibrium and kinetic studies of oxygen binding to the haemocyanin from the freshwater snail Lymnaea stagnalis.

The binding of oxygen by the haemocyanin of the gastropod Lymnaea stagnalis was studied by equilibrium and kinetic methods. The studies were performed under conditions in which the haemocyanin molecule was in the native state. Over the pH range 6.8-7.6, in the presence of 10mM-CaCl2 the haemocyanin bound O2 cooperatively. Over this pH range the haemocyanin molecule displayed a normal Bohr effect whereby the O2 affinity of the molecule decreased with a fall in the pH of the solution. The maximum slope of the Hill plot (hmax.) was 3.5, obtained at pH 7.5. An increase in the CaCl2 concentration from 5 to 20 mM at pH 6.8 resulted in a slight increase in the oxygen affinity, with hmax. remaining virtually unchanged. At constant pH and CaCl2 concentration, an increase in NaCl concentration from 0 to 50 mM resulted in a small decrease in O2 affinity, but a significant increase in the value of hmax. from 3.5 to 8.6. Temperature-jump relaxation experiments over a range of O2 concentrations produced single relaxation times. The dependence of the relaxation time on the reactant concentrations indicated a simple bimolecular binding process. The calculated association and dissociation rate constants for this process at pH 7.5 are 29.5 X 10(6) M-1 X S-1 and 49 S-1 respectively. The association rate constant kon was found to be essentially independent of pH and CaCl2 concentration. The dissociation rate constant, koff, however, increased with a decrease in the pH, but was also independent of CaCl2 concentration. These results indicate that the stability of the haemocyanin-O2 complex is determined by the dissociation rate constant.