A novel method of determination of the internal enzyme distribution within porous solid supports and the deactivation rate constant

This article presents a method for determining the rate constant for deactivation and the internal distribution of immobilized enzyme. This method makes use of the parallel deactivation process in a diffusion-controlled regime, in which the internal activity profile behaves like a penetration front. This front basically traces through the initial active enzymatic profile, and one can determine the internal profile and the rate constant for deactivation from the experimentally observable bulk concentration versus time. This method is applied to the experimental data of the system of hydrogen-peroxide-immobilized catalase on controlled pore glass and Si-Al particles.     

On true and apparent Michaelis constants in enzymology. I. Differences

Differences between both true and apparent rate constants and Michaelis constants have been examined. Rate constants of elementary stages of real mechanisms are true ones. True Michaelis constant Km is expressed by equation Km = (k(-1) + k2)/k. True constants may be determined for reliable mechanism only for which the equation of initial rate was obtained which displays physical sense of these constants and permits to find the method of their calculation. The true constant values are independent of concentration of reactants, activators, inhibitors, extraneous agents and pH. The apparent rate constants are such constants of the composite reaction which are observed when this reaction is described by the equation of simple reaction. Michaelis constant calculated by a half of the ultimate constant is an apparent constant. The apparent constants may be functions of several true rate constants and/or concentrations of reacting substances. The evident physical sense of apparent constants being absent, only formal relation between the reaction rate and reactant concentration independent of the investigated mechanism is provided.     

Theory and experimental method for determining individual kinetic constants of fast-acting, irreversible proteinase inhibitors

A theory and experimental method are presented to characterize the kinetics of fast-acting, irreversible proteinase inhibitors. The theory is based upon formal analysis of the case of an irreversible inhibitor competing with a substrate for the active-site of a proteinase. From this theory, an experimental method is described by which the individual microscopic kinetic constants for the interaction of the inhibitor with the proteinase can be determined. These are, for a two-step inhibition reaction sequence, the equilibrium dissociation constant and the first-order rate constant for inhibition, and, for a one-step inhibition reaction sequence, the second-order rate constant for inhibition. The theory and experimental method were validated by an analysis of the inhibition of trypsin by the two-step synthetic inhibitor p-nitrophenyl p-guanidinobenzoate and the one-step protein inhibitor bovine pancreatic trypsin inhibitor. The substrate used in these experiments is a new, fluorogenic substrate for trypsin-like serine proteinases (Cbz-Ile-Pro-Arg-NH)2-Rhodamine, the synthesis and properties of which are described.     

Controlling the soil moisture environment of transpiring plants

Summary A method of growing plants under constant soil moisture conditions when the transpiration rate is constant is presented. This method uses the principles of unsaturated flow through a porous media to arrive at values for the design variables. If the transpiration rate is not constant, the maximum possible fluctuation in the soil moisture content can be determined.     

Optimization of Protease-Catalyzed Acyl Transfer Reactions. Determination of the Partition Constant Characterizing Nucleophile Efficiency

The partitioning of the acyl-enzyme between aminolysis by an added nucleophile and hydrolysis plays a key-role in protease-catalyzed acyl transfer reactions. It can be characterized by the partition constant, which is equal to the nucleophile concentration for which aminolysis and hydrolysis proceed at the same velocity. We describe a method for calculation of the partition constant from the product ratio which is based on the integrated rate equation. Therefore, it can be applied to reactions performed under synthesis-like conditions, i.e. a high degree of nucleophile consumption during the reaction. In principle, the dependence of the partition constant on nucleophile concentration can be determined from a single reaction. V8-protease-catalyzed acyl transfer reactions using Z-Glu-OMe as acyl donor and amino acid amides as nucleophiles were investigated as an application of the method. The central role of the partition constant in optimization of preparative protease-catalyzed acyl transfer reactions is discussed.     

Optimization of Protease-Catalyzed Acyl Transfer Reactions. Determination of the Partition Constant Characterizing Nucleophile Efficiency

The partitioning of the acyl-enzyme between aminolysis by an added nucleophile and hydrolysis plays a key-role in protease-catalyzed acyl transfer reactions. It can be characterized by the partition constant, which is equal to the nucleophile concentration for which aminolysis and hydrolysis proceed at the same velocity. We describe a method for calculation of the partition constant from the product ratio which is based on the integrated rate equation. Therefore, it can be applied to reactions performed under synthesis-like conditions, i.e. a high degree of nucleophile consumption during the reaction. In principle, the dependence of the partition constant on nucleophile concentration can be determined from a single reaction. V8-protease-catalyzed acyl transfer reactions using Z-Glu-OMe as acyl donor and amino acid amides as nucleophiles were investigated as an application of the method. The central role of the partition constant in optimization of preparative protease-catalyzed acyl transfer reactions is discussed.     

An exact procedure for the analysis of heterogeneous kinetics in polyclonal antibody populations

Antibody populations with heterogeneous binding properties exhibit complex first-order dissociation kinetics. An analytical method has been developed to determine the average dissociation rate constant and the heterogeneity index of a specific antibody population. This procedure was based on Laplace transformation of the gamma distribution function, which yielded an exact, macroscopic rate law for the entire antibody population. Linearization of the macroscopic rate law is achieved by plotting data points versus their numerical derivatives using log-log axes. Linear regression of such plots yields the average dissociation rate constant from the Y-intercept, and heterogeneity index from the slope. This analytic method is transparent to the antibody system and kinetic assay employed, requiring only a programmable calculator to perform the necessary calculations. The usefulness of this analytic method was demonstrated by the evaluation of dissociation kinetics in murine monoclonal and rabbit polyclonal anti-fluorescyl-IgG antibody populations.     

Rate constants for binding, dissociation, and internalization of EGF: effect of receptor occupancy and ligand concentration

We measured the kinetic parameters for interaction of epidermal growth factor (EGF) with fetal rat lung (FRL) cells under two sets of experimental conditions and applied sensitivity analysis to see which parameters were well-defined. In the first set of experiments (method 1), the kinetics of internalization and dissociation of radiolabeled EGF were measured with a temperature-shift protocol in medium initially devoid of free ligand. The initial concentration of radiolabeled EGF bound to the cell surface corresponded to levels of receptor occupancy ranging from approximately 200 receptors per cell to approximately 18,000 receptors per cell, a level at which EGF binding approaches saturation. In the second set of experiments (method 2), carried out at a constant temperature, we began with no surface-bound or internalized ligand. The initial free ligand concentration was varied from 0.2 to 50 ng/mL. In both sets of experiments, we measured surface-bound, internalized, and free 125I-EGF as functions of time and evaluated the parameters of a mathematical model of endocytosis. Sensitivity analysis showed that three rate constants were well-defined in this combination of two experimental approaches: ke, the endocytic rate constant; ka, the association rate constant; and kd, the dissociation rate constant. The endocytic parameter ke was found to be independent of initial surface receptor occupancy (method 1); there was some indication that it increased with initial free ligand concentration in method 2. Neither kd nor ka was found to change with extent of initial surface receptor occupancy or initial free ligand concentration, respectively, a finding of significance, since diffusion theory predicts these parameters will vary with surface receptor occupancy.(ABSTRACT TRUNCATED AT 250 WORDS)     

Some characteristics of the kinetics of enzymatic reactions based on the example of catalase]

A method of kinetic analysis for quickly acting enzymes, which are characterized with substrate inhibition, on the catalase model is proposed. Catalase kinetics was shown to be full described, considering changes in the maximal reaction rate and Michaelis constant, by four parameters instead of two usual ones (Vmax, Km equals const.). The method described makes possible to calculate the change the Michaelis constant in time and to estimate real dependencies of the reaction rate on time and on the substrate concentration. Moreover, the enzyme concentration and its inactivation rate at any reaction moment can be calculated under saturation conditions. It is supposed that experimental dependencies of Km on t and of Vmax on t are the results of residual conformation changes accumulated by the enzyme in the reaction process.     

Shear breakage of nylon membrane microcapsules in a turbine reactor

The breakage of nylon membrane microcapsules is proposed as a new method to study and quantify shear effects in biological systems. A critique of this method shows that a narrower particle size distribution may be an important improvement in the breakage study as well as breakage control in many bioreactor and biotechnological applications. In a turbine reactor, it was shown that the primary process which determines the microcapsule breakage is the shear effect. The breakage kinetics are first order with regard to the microcapsule concentration. The breakage kinetic constant was ob served to be dependent on the temperature and the particle size, and proportional to the average shear rate and the third power of the turbine angular velocity. Decrease of the breakage kinetic constant with temperature can be explained by a decrease of fluid viscosity and a change in nylon membrane properties. An increase in the breakage kinetic constant with the microcapsule diameter can be due to a lowering of internal pressure and a reduction of the membrane resistance with size. Proportionality between the breakage kinetic constant and the shear rate shows that shear is the main process which leads to microcapsule breakage. The additional intervention in the shear rate expression of the turbine angular speed in the form of the turbine and particle velocities, results in the dependence of the breakage kinetic constant on the third power of the angular velocity.     

Kinetic evidence for a two-step mechanism for the binding of chymotrypsin to alpha 1-proteinase inhibitor.

We have used the proflavin displacement method and a stopped-flow apparatus to measure the rate constant for the binding of 2 microM-chymotrypsin to 20-125 microM-alpha 1-proteinase inhibitor. The observed pseudo-first-order constant showed a hyperbolic dependence on alpha 1-proteinase inhibitor concentration, suggesting a reaction mechanism in which a fast pre-equilibrium (K = 0.19 mM) is followed by a first-order formation of the final complex (k = 252 s-1).     

STUDIES OF THE GROWTH OF PENICILLIUM CHRYSOGENUM IN CONTINUOUS FLOW CULTURE WITH REFERENCE TO PENICILLIN PRODUCTION

SUMMARY: A filamentous mould was cultured by the continuous flow method in which medium is supplied at a constant rate and the culture volume is kept constant. Flow rates up to 0·1 culture volumes/hr were used. The mycelial dry weight concentration and the yield of mycelium/g of carbon source used were equal to or slightly greater than the maximum obtained in batch culture. With glucose concentrations up to 80 g/1. at a flow rate of 0·05 culture volumes/hr, about 45% of the substrate carbon was converted into mycelial carbon and the remainder oxidized to CO₂.
With unlimited amounts of all nutrients available growth of the mould followed the exponential law, as does bacterial growth, and therefore the mould had a constant doubling time.
The oxygen demand of the mould as function of growth rate was determined.
Conditions were found under which the rate of penicillin production/g of mycelium remained at its maximum value for 1000 hr.     

A step toward the prediction of the fluorescence lifetimes of tryptophan residues in proteins based on structural and spectral data

A method is presented that allows the calculation of the lifetimes of tryptophan residues on the basis of spectral and structural data. It is applied to two different proteins. The calcium binding protein from the sarcoplasm of the muscles of the sand worm Nereis diversicolor (NSCP) changes its conformation upon binding of Ca2+ or Mg2+. NSCP contains three tryptophan residues at position 4, 57, and 170, respectively. The fluorescence lifetimes of W57 are investigated in a mutant in which W4 and W170 have been replaced. The time resolved fluorescence properties of W57 are linked to its different microconformations, which were determined by a molecular dynamics simulation map. Together with the determination of the radiative rate constant from the wavelength of maximum intensity of the decay associated spectra, it was possible to determine an exponential relation between the nonradiative rate constant and the distance between the indole CE3 atom and the carbonyl carbon of the peptide bond reflecting a mechanism of electron transfer as the main determinant of the value for the nonradiative rate constant. This result allows the calculation of the fluorescence lifetimes from the protein structure and the spectra. This method was further tested for the tryptophan of Ha-ras p21 (W32) and for W43 of the Tet repressor, which resulted in acceptable values for the predicted lifetimes.     

The Effect of Nonspecific Binding of Lambda Repressor on DNA Looping Dynamics

The λ repressor (CI) protein-induced DNA loop maintains stable lysogeny, yet allows efficient switching to lysis. Herein, the kinetics of loop formation and breakdown has been characterized at various concentrations of protein using tethered particle microscopy and a novel, to our knowledge, method of analysis. Our results show that a broad distribution of rate constants and complex kinetics underlie loop formation and breakdown. In addition, comparison of the kinetics of looping in wild-type DNA and DNA with mutated o3 operators showed that these sites may trigger nucleation of nonspecific binding at the closure of the loop. The average activation energy calculated from the rate constant distribution is consistent with a model in which nonspecific binding of CI between the operators shortens their effective separation, thereby lowering the energy barrier for loop formation and broadening the rate constant distribution for looping. Similarly, nonspecific binding affects the kinetics of loop breakdown by increasing the number of loop-securing protein interactions, and broadens the rate constant distribution for this reaction. Therefore, simultaneous increase of the rate constant for loop formation and reduction of that for loop breakdown stabilizes lysogeny. Given these simultaneous changes, the frequency of transitions between the looped and the unlooped state remains nearly constant. Although the loop becomes more stable thermodynamically with increasing CI concentration, it still opens periodically, conferring sensitivity to environmental changes, which may require switching to lytic conditions.     

On true and apparent Michaelis constants in enzymology. III. Is it linear dependence between apparent michaelis constant and limiting rate and is it possible to determine the substrate constant value using this dependence?

The Slater-Bonner method which is used for graphic determination of substrate constant (Ks) by linear dependence of apparent Michaelis constant (Km(app)) on the limiting rate (V(app)) of enzyme-catalysed reactions with activator participation has been critically analysed. It has been shown that although it is possible to record the mechanisms of such reactions as a scheme similar to Michaelis-Menten model which allow to find correlation Km(app) and V(app) as equation Km(app) = Ks + V(app)/k1[E]0 ([E]0 is a total enzyme concentration, k1 is a rate constant of enzyme-substrate complex formation from free enzyme and substrate) in order to calculate Ks and individual rate constants (k1, k(-1)), but this approach for investigation of all reactions with activator participation ought not to be used. The above equation is not obeyed in general, it may be true for some mechanisms only or under certain ratios of kinetic parameters of enzyme-catalysed reactions.     

A Theoretical and Experimental Study of Competition Between Solution and Surface Receptors for Ligand in a Biacore Flow Cell

Rate constants that characterize the kinetics of binding and dissociation between biomolecules carry fundamental information about the biological processes these molecules are involved in. An instrument that is widely used to determine these rate constants is the Biacore. In a Biacore experiment, one of the reactants, which we will call the receptor, is immobilized on a sensor chip. During the binding phase of the experiment the other reactant flows past the chip. After binding, buffer alone is introduced into the flow cell and dissociation is monitored. Often surface-based binding assays are influenced by the transport of the reactant in solution, complicating the determination of the chemical rate constants from the observed binding kinetics. We propose a new way to determine the dissociation rate constant by adding soluble receptor during dissociation. The method is tested first on simulated data and then on Biacore experiments where the lac repressor protein binds and dissociates from a stretch of double stranded DNA containing the lac repressor binding site. With this method we find a dissociation rate constant k_d=0.075 ± 0.005s^-1, a value that is faster than previously obtained from Biacore experiments. In developing our method to analyze these experiments we obtain an expression for the transport limited rate constant for a Biacore experiment when soluble receptor is present during dissociation.     

Kinetic study of lipoxygenase-hydroperoxylinoleic acid interaction.

Interaction of lipoxygenase with hydroperoxylinoleic acid, which is the product of this enzyme reaction and acts as an activator, was studied kinetically by the fluorescence stopped-flow method. The kinetic features are consistent with a two-step mechanism involving a fast bimolecular association process followed by a slow unimolecular process. The dissociation constant of the bimolecular process was 3 (+/-2) - 10(-5) M, which was appreciably dependent on temperature and pH, in contrast to the rate constant of the latter process. The enthalpy and the entropy of activation for the unimolecular process were estimated to be 21 kcal/mol and 20 e.u., respectively. The pH dependence of the rate constant indicated that an ionizable group with pK of about 8.6 is involved in the interaction. Linoleic acid, the substrate of lipoxygenase, and oleic acid inhibited the interaction between the lipoxygenase and the hydroperoxylinoleic acid by reducing the rate. A series of saturated monohydric alcohols also reduced the rate of the interaction as the chain length of the alcohols increases, though methanol and ethanol increased the rate of the interaction.     

How fast does the gamma-aminobutyric acid receptor channel open? Kinetic investigations in the microsecond time region using a laser-pulse photolysis technique.

The gamma-aminobuytric acid(A) (GABA(A)) receptor is a membrane-bound protein that mediates signal transmission between neurons through formation of chloride ion channels. GABA is the activating ligand, which upon binding to the receptor triggers channel opening in the microsecond time domain and reversible desensitization of the receptor in the millisecond time region. We have investigated the channel-opening mechanism for this receptor in rat hippocampal neurons before the protein desensitizes by using a rapid flow method (cell-flow) with a 10 ms time resolution and a laser-pulse photolysis technique with a approximately 30 micros time resolution to determine the rate and equilibrium constants for channel opening and closing. Two different forms of the receptor, namely, a rapidly and a slowly desensitizing form, exist in the rat hippocampal cells and are characterized by their different rates for desensitization. At 250 microM GABA the rate constant for desensitization was 2.3 +/- 0.4 s(-)(1) for the rapidly desensitizing form and 0.4 +/- 0.1 s(-)(1) for the slowly desensitizing form. The dissociation constant of GABA from the site controlling channel opening was 100 +/- 40 microM for the rapidly desensitizing form and 120 +/- 60 microM for the slowly desensitizing form. The rate constants for channel closing did not differ significantly for the two forms, 85 +/- 20 s(-)(1) for the rapidly desensitizing and 100 +/- 60 s(-)(1) for the slowly desensitizing form. However, the channel-opening rate constant differed by a factor of 3, 1840 +/- 160 s(-)(1) for the rapidly desensitizing and 6700 +/- 330 s(-)(1) for the slowly desensitizing form. This difference in the rate constant for channel opening for the two forms, determined by the laser-pulse photolysis technique, is reflected as a shift in the channel-opening equilibrium constant, which is 7 +/- 5 and 20 +/- 15 for the rapidly and slowly desensitizing forms respectively, determined by the cell-flow method. These constants, together with the concentration of GABA and the concentration of receptor sites in the membrane, determine the number of channels that open as a function of GABA concentration, and the rate at which they open and close. These constants play an important role in determining the rate of the transmembrane ion flux and, therefore, the receptor-controlled changes in transmembrane voltage that trigger signal transmission.     

Dimerization kinetics of violamycin BI anthracycline--the influence of ionic strength

Violamycin BI is an anthracycline derivative with two sugars hanging on, each of them carries one positive charge. It dimerizes under conditions, which depend on the concentration of the antibiotic, pH and the ionic strength of the solution. By keeping a constant pH in a phosphate-EDTA buffer, the rate constants of violamycin BI dimerization were determined at various ionic strengths by temperature jump method. The dimerization constant Kd, resulting from the ratio of these rate constants, confirmed the values obtained spectrophotometrically in this study or elsewhere. The influence of ionic strength (0.02-0.2 M) on the rate constant values suggested to us some speculations on the reaction mechanism of the dimerization, in which, the specific mutual orientation of the monomers in the encounter, and perhaps a specific conformation of their side groups is required before a stabilizing action of the binding forces sets in.