On enzymatic clotting processes. II. The colloidal instability of chymosin-treated casein micelles.

The enzymatic clotting of casein micelles dispersed in 0.01 M CaCl₂ was monitored by turbidimetry and electrophoresis. The relation between the duration of the lag phase and the enzyme concentration, (e), can be represented by t = K(e)^?γ, where K is a constant and the exponent γ is found to vary between 0.92 and 1.00. This result is interpreted in terms of a flocculation rate constant increasing with the concentration of the enzyme. It is shown that the colloidal instability of chymosin-treated casein micelles cannot be explained on the basis of the well-known theory of the stability of lyophobic colloids, but that clotting is achieved through short-range interactions. The short-range effects that most probably account for the clotting are: hydrophobic bond formation, Ca-bridgas and electrostatic interactions. Under typica'. experimental conditions (33°C; maximum rate of enzymatic product formation about 1.8 × 10^?10 mol ml^?1 s^?1) the flocculation rate constant of clotting micelles was found to be 5 × 10⁵ mlmol^?1s^?1. Various factors, which could be responsible for this low value, are discussed. In the initial stages of the clotting process the turbidity of the system passes through a shallow minimum, which is ascribed to the cleavage of a macropeptide from K-casein by the clotting enzyme. The condition for the minimum has been derived.     

Kinetics of milk coagulation: III. Mathematical modeling of the kinetics of curd formation following enzymatic hydrolysis of kappa-casein--parameter estimation

A step function model of milk micelle agglomeration is proposed to explain the observed kinetics of milk clotting following rennet addition. The model ties together the primary and secondary phases of coagulation. The basis of the model is that no micelle flocculation takes place until ca. 75% of the kappa-casein in the milk is hydrolyzed, at which time flocculation occurs rapidly and the rate limiting step for the clotting process shifts to the kappa-casein hydrolysis reaction. Using such a model, it is possible to explain the clotting kinetics for both rapidly denaturing enzymes and stable enzyme systems. The average rate of the flocculation reaction can be obtained from clotting time-versus-reciprocal-enzyme-concentration data by extrapolating the data to infinite enzyme concentration. The critical conversion required for imminent flocculation can be found by extrapolating the enzyme concentration to zero. This approach indicates that the critical conversion necessary for gelation is temperature dependent changing from a limiting value of essentially 100% hydrolysis at temperatures below 15 degrees C to only 60% conversion at temperatures above 30 degrees C.     

The influence of temperature on the flocculation rate of renneted casein micelles

The flocculation rate constant of completely renneted casein micelles in milk ultrafiltrate was measured by Rayleigh light scattering between 20 and 35 degrees C. In this temperature range an apparent energy of activation of 103 kJ mol (+/-11 kJ mol : n = 50) was measured. At 15 degrees C clotting was not longer perceptible. The activation of the flocculation between 20 and 35 degrees C is explained not so much by the height of the energy barrier separating the clotting micelles, as by the very negative temperature coefficient of that barrier. In line with this conclusion it is suggested that renneted micelles adhere through hydrophobic bonding. The flocculation rate constant of renneted casein micelles is independent of micelle size at the four temperature levels studied.     

Kinetic manifestations of slow isomerization of allosteric enzyme for the model of Monod, Wyman and Changeux]

A shape of the curves of a product accumulation in time (t) is analysed for the variant of Monod, Wyman and Changeux model which is characterized by comparable rates of equilibration between R and T enzyme forms on the one hand and the enzymatic process on the other hand. It is assumed that the complex of R and T forms with substrate are in rapid equilibrium with the free components. The character of the dependences of effective constant of R denoting T isomerization and the value of tau on substrate concentration are analysed (tau is the intercept of t-axis for linear asymptota of the curve of product concentration versus time at t leads to infinity). It is also shown that the low rate of R denoting T isomerization may be manifested by the shape of the plot of initial reaction rate versus substrate concentration unusual for the model of Monod et al. (the plots with intermediate plateau and ones with Hill's coefficient of cooperativity less than unity).     

Affinity labeling of rabbit muscle pyruvate kinase by 5'-p-fluorosulfonylbenzoyladenosine.

Rabbit muscle pyruvate kinase is irreversibly inactivated upon incubation with the adenine nucleotide analogue, 5'-p-fluorosulfonylbenzoyladenosine. A plot of the time dependence of the logarithm of the enzymatic activity at a given time divided by the initial enzymatic activity(logE/Eo) reveals a biphasic rate of inactivation, which is consistent with a rapid reaction to form partially active enzyme having 54% of the original activity, followed by a slower reaction to yield totally inert enzyme. In addition to the pyruvate kinase activity of the enzyme, modification with 5'-p-fluorosulfonylbenzoyladenosine also disrupts its ability to catalyze the decarboxylation of oxaloacetate and the ATP-dependent enolization of pyruvate. In correspondence with the time dependence of inactivation, the rate of incorporation of 5'-p-[14C]fluorosulfonylbenzoyladenosine is also biphasic. Two moles of reagent per mole of enzyme subunit are bound when the enzyme is completely inactive. The pseudo-first-order rate constant for the rapid rate is linearly dependent on reagent concentration, whereas the constant for the slow rate exhibits saturation kinetics, suggesting that the reagent binds reversibly to the second site prior to modification. The adenosine moiety is essential for the effectiveness of 5'-p-fluorosulfonylbenzoyladenosine, since p-fluorosulfonylbenzoic acid does not inactivate pyruvate kinase at a significant rate. Thus, the reaction of 5'-p-fluorosulfonylbenzoyladenosine with pyruvate kinase exhibits several of the characteristics of affinity labeling of the enzyme. Protection against inactivation by 5'-p-fluorosulfonylbenzoyladenosine is provided by the addition to the incubation mixture of phosphoenolpyruvate. Mg-ADP or Mg2+. In contrast, the addition of pyruvate, Mg-ATP, or ADP and ATP alone has no effect on the rate of inactivation. These observations are consistent with the postulate that the 5'-p-fluorosulfonylbenzoyladenosine specifically labels amino acid residues in the binding region of Mg2+ and the phosphoryl group of phosphoenolpyruvate which is transferred during the catalytic reaction. The rate of inactivation increases with increasing pH, and k1 depends on the unprotonated form of an amino acid residue with pK = 8.5. On the basis of the pH dependence of the reaction of pyruvate kinase with 5'-p-fluorosulfonylbenzoyladenosine and the elimination of cysteine residues as possible sites of reaction, it is postulated that lysyl or tyrosyl residues are the most probably candidates for the critical amino acids.     

A model for enzymatic isomerization of D-glucose to D-fructose in a batch reactor.

Using whole cells containing glucose isomerase, mathematical models for the enzymatic conversion of D-glucose to D-fructose and for the inactivation of the enzyme catalyst have been postulated and verified experimentally. The heat of reaction, the equilibrium constant, and the individual rate constants and their activation energies have been estimated. The model can be used to predict the time course for the enzymatic production of fructose in a batch reactor within the tested experimental range of 40-80 degrees C.     

Enzyme reactions at the surface of living cells. I. Electric repulsion of charged ligands and recognition of signals from the external milieu

The dynamic behaviour of a polyelectrolyte-bound enzyme is studied when diffusion of substrate or diffusion of product is coupled to electric repulsion and to Michaelis-Menten enzyme reaction. The definition of the classical concepts of electric partition coefficients and Donnan potential of a polyelectrolyte membrane has been extended under global non-equilibrium conditions. This extension is permissible when a strong repulsion exists of substrate and product by the fixed negative charges of the membrane. Coupling between product diffusion, electric repulsion and enzyme reaction at constant advancement may result in a hysteresis loop of the partition coefficient as the product concentration is increased in the reservoir. This hysteresis loop vanishes as the rate of product diffusion increases. No hysteresis loop may occur when electric repulsion effects are coupled to substrate diffusion and reaction. The existence of multiple values of the partition coefficient for a fixed concentration of product implies that the membrane may store short-term memory of the former product concentration present in the external milieu. The occurrence of hysteresis generated by coupling enzyme reaction, product diffusion, electric partition effects at constant advancement of the reaction may be viewed as a sensing device of product concentration in the external milieu. Surprisingly, non-linearities required to generate this sensing device come from electrostatic effects and not from enzyme kinetics.     

On enzymic clotting processes V: Rate equations for the case of arbitrary rate of production of the clotting species

The rate theory for enzyme-triggered coagulation reactions, such as the clotting of fibrin or casein, is extended to the case of an arbitrary rate of production of the clotting species. It is shown that the general expression for the growth of the weight-average molecular weight of the clotting product, -M_w, is given by -M_w = M₁{1 + k_s {∫₀^tP(t)² dt}/P(t)}, where M₁ is the “monomer” molecular weight, k_s the smoluchowskian flocculation rate constant and P(t) the total number of monomers produced by the enzyme in t. In the purely smoluchowskian case P(t) stands for the total number of monomers at the beginning of the clotting process. Numerical examples in which the rate of enzymic production is governed by complete Michaelis-Menten kinetics, are compared to cases in which this rate equals V_max- It is shown that after exhaustion of the substrate the system continues to coagulate in a purely smoluchowskian way. Turbidimetric experiments on the clotting of micelles of whole and κ-casein are presented which suggest inactivation of the enzyme by non-productive binding in the flocs formed.     

Kinetic analysis of the mechanism of Escherichia coli dihydrofolate reductase

A kinetic mechanism is presented for Escherichia coli dihydrofolate reductase which describes the full time course of the enzymatic reaction over a wide range of substrate and enzyme concentrations at pH 7.2 and 20 degrees C. Specific rate constants were estimated by computer simulation of the full time course of single turnover, burst, and steady-state experiments using both nondeuterated and deuterated NADPH. The mechanism involves the random addition of substrates, but the substrates and enzyme are not at equilibrium prior to the chemical transformation step. The rate-limiting step follows the chemical transformation, and the maximum velocity of the reaction is limited by the release of the product tetrahydrofolate. The full time course of the reaction is markedly affected by the formation of the enzyme-NADPH-tetrahydrofolate abortive complex, but not by the enzyme-NADP-dihydrofolate abortive complex.     

Kinetic behavior of slowly equilibrating association-dissociation enzyme systems]

The shape of the plots of product accumulation versus time (t) has been analysed for slowly equilibrating association-dissociation enzyme systems of the types 2p in equilibrium P (P is enzyme oligomer which is able to dissociate reversibly forming two identical halves p) and M in equilibrium M2 in equilibrium M2 in equilibrium... (M is monomer which has two association sites overlapping with active sites). It is assumed that the rate of equilibration between oligomeric forms is comparable with the rate of over-all enzymatic reaction and that substrate-oligomer complexes are in rapid equilibrium with free components. It has been shown that characteristic feature of kinetic behavior of slowly equilibrating association-dissociation enzyme systems is that the value of tau depends on enzyme concentration (tau is the intercept on t-axis for linear asymptota of the curve of product concentration versus time at t leads to infinity).     

Evolutionary optimization of the catalytic efficiency of enzymes.

1. The rate equation for a generalized Michaelian type of enzymic reaction mechanism has been analyzed in order to establish how the mechanism should be kinetically designed in order to optimize the catalytic efficiency of the enzyme for a given average magnitude of true and apparent first-order rate constants in the mechanism at given concentrations of enzyme, substrate and product. 2. As long as on-velocity constants for substrate and product binding to the enzyme have not reached the limiting value for a diffusion-controlled association process, the optimal state of enzyme operation will be characterized by forward (true and apparent) first-order rate constants of equal magnitude and reverse rate constants of equal magnitude. The drop in free energy driving the catalysed reaction will occur to an equal extent for each reaction step in the mechanism. All internal equilibrium constants will be of equal magnitude and reflect only the closeness of the catalysed reaction to equilibrium conditions. 3. When magnitudes of on-velocity constants for substrate and product binding have reached their upper limits, the optimal kinetic design of the reaction mechanism becomes more complex and has to be established by numerical methods. Numerical solutions, calculated for triosephosphate isomerase, indicate that this particular enzyme may or may not be considered to exhibit close to maximal efficiency, depending on what value is assigned to the upper limit for a ligand association rate constant. 4. Arguments are presented to show that no useful information on the evolutionary optimization of the catalytic efficiency of enzymes can be obtained by previously taken approaches that are based on the application of linear free-energy relationships for rate and equilibrium constants in the reaction mechanism.     

Enzyme--substrate interaction in lipid monolayers. III. A study of the variation of the surface concentration with lipolysis.

Monolayers of a diacylglycerol were submitted to the action of lipase, keeping the area constant. The variation of lipase, keeping the area constant. The variation of the surface concentration gamma of the substrate with time was derived from the recorded reduction of the surface pressure pi (the isotherm of the monolayer being previously established). The rate -d gamma/dt was determined both as a function of the surface concentration gamma of the substrate and as a function of the bulk concentration C of the enzyme in the underlying solution. The rate depends on the quantity of enzyme ze adsorbed on the monolayer and on the enzymatic specific activity alpha of these adsorbed enzyme molecules. Both ze and alpha vary with gamma. The two variations have been quantitatively dissociated. The curves of ze and of alpha as functions of gamma coincide with those previously established in the study of hydrolysis under constant surface pressure.     

Enzymatic breakdown of threonine by threonine aldolase

1. The enzyme which splits threonine to acetaldehyde and glycine has been partially purified from rat liver (five- to sixfold purification) and the name threonine aldolase proposed for it. 2. The general properties of threonine aldolase have been studied. The enzyme is unstable to a pH below 5. The pH optimum of the enzyme reaction is at 7.5-7.7. The initial rate of production of acetaldehyde is proportional to the enzyme concentration, and when the enzyme concentration is constant, the production of acetaldehyde is proportional to the time, provided that the substrate is in excess. The enzyme is inhibited by the carbonyl group reagent, hydroxylamine. Attempts to demonstrate that pyridoxal phosphate is a cofactor were unsuccessful. 3. The enzyme splits only L-allothreonine and L-threonine and is inactive against the D-forms of these amino acids. 4. The enzyme reaction on DL-allothreonine follows first order kinetics. From the first order velocity constants and the initial rates of the rates of the reaction at various substrate concentrations the Michaelis constant, Ks, for this substrate has been evaluated. Michaelis constants have also been determined for threonine. 5. The optimum temperature for the enzymatic breakdown of DL-allothreonine at pH 7.65 was found to be 50 degrees C. in phosphate buffer and 48 degrees C. in tris-maleate buffer. The rate of thermal inactivation of the enzyme threonine aldolase obeys a first order reaction. The heat of thermal inactivation was calculated by the aid of the van't Hoff-Arrhenius equation to be 43,000 cal. per mole for the temperature range 41.2-46.6 degrees C. 6. Equivalent amounts of acetaldehyde and glycine were formed from DL-allothreonine and the enzymatic breakdown of DL-allothreonine was found to be irreversible.     

Systems approach to the study of drug transport across membranes using suspension cultures of mammalian cells V. Simultaneous passive transport and biosynthesis

A physical model is described for the simultaneous enzymatic bioconversion of a nonelectrolyte solute and the passive transport of both the solute and product of the enzymatic reaction out of cells in culture suspension. The plasma membrane is assumed to be the rate-determining transport barrier. This model provides the basis for the experimental design and analysis of the Michaelis-Menten kinetic parameters of simple enzymatic reactions in situ, the phenomenological transport parameters and other factors. The primary set of differential equations describing the quasisteady state rate of change in the concentration of the solute and product within the cell due to enzyme reaction and transport are given. These are nonlinear and must be solved by numerical methods. However, analytical mathematical expressions have been derived for various cases in the limit when the rate of enzymatic reaction is first or zero order.     

The substrate reactivity of mu-monothiopyrophosphate with pyrophosphate-dependent phosphofructokinase: evidence for a dissociative transition state in enzymatic phosphoryl group transfer.

mu-Monothiopyrophosphate (MTP), an analogue of pyrophosphate (PPi) with sulfur in place of oxygen in the bridge position, is a substrate for the enzyme pyrophosphate-dependent phosphofructokinase. At pH 9.4 and 6 degrees C, the maximal velocity for the phosphorylation of fructose 6-phosphate (F6P) by MgMTP is about 2.8% of that with MgPPi as the phosphoryl donor. The kinetic mechanism is equilibrium random with rate-limiting transformation of the substrate ternary complex to the product when either MgMTP or MgPPi is the phosphoryl donor. This is known from independent studies to be kinetic mechanism at pH 8.0 and 25 degrees C [Bertagnolli, B. L., & Cook, P. F. (1984) Biochemistry 23, 4101-4108]. The dissociation constant of MgPPi is 14 microM, that of MgMTP is 64 microM, and that of F6P from the enzyme is about 5 mM. The Km values for MgPPi and MgMTP are 14.5 and 173 microM, respectively. MgMTP competes with MgPPi for binding to the enzyme. The values of kcat are 3.4 s-1 and 140 s-1 for MgMTP and MgPPi, respectively, at pH 9.4 and 6 degrees C. The estimated rate enhancement factors are 3.6 x 10(5) and 1.4 x 10(14) for the reactions of MgMTP and MgPPi, respectively. Therefore, MgMTP is a reasonably good substrate for PPi-dependent PKF, on the basis of comparisons of kcat. However, the rate enhancement factors show that the enzyme is a poor catalyst for the reaction of MgMTP. Lesser enzymatic catalysis in the reaction of MgMTP compared with MgPPi is largely compensated for by the greater intrinsic reactivity of MgMTP. Thus, the larger substrate MgMTP is well accommodated in the active site, and the dissociative reaction of MgMTP is well accommodated in the transition state. The results are interpreted to indicate a dissociative transition state for phosphoryl group transfer by PPi-dependent PFK. A modified synthesis and purification of MTP are described, in which (trimethylsilyl)trifluoromethanesulfonate and tetra-N-butylammonium iodide are used in place of iodotrimethylsilane to dealkylate tetramethyl-MTP.     

Optimization of batch processes involving simultaneous enzymatic and microbial reactions

Two general models for batch simultaneous enzymatic and microbial reaction (SEMR) processes are presented, the second derived from and simpler than the first and accounting for enzyme denaturation. Using the second model and parameter values from the literature, simulation was used to examine a range of enzyme addition rate strategies (in which the rate was a linear function of time) for a relatively fast ethanol fermentation and for a longer duration citric acid fermentation, both using cellulose as the substrate. For the ethanol process it is optimal (for a specific objective function which accounts for product value and enzyme cost) to add all the enzyme at the beginning of the process. But for the citric acid process a linearly decreasing enzyme addition rate, coupled with the addition of a small fraction of the enzyme at time zero, is better than pure batch operation or operation with the best constant enzyme feed rate.     

Compound X. An intermediate in enzymatic halogenation.

Previous studies have shown that chlorite serves as a halogenation substrate for horseradish peroxidase. In its substrate role, chlorite serves both as a halogen donor and as a source of oxidizing equivalents in the chlorination reaction. We now show that a new spectral intermediate, which we have termed Compound X, can be detected as the initial product of the reaction of chlorite with horseradish peroxidase. The reaction of chlorite with horseradish peroxidase to form Compound X is a relatively fast reaction especially at acidic pH values. The second order rate constant (Kf) for the formation of Compound X at pH 4.5 (optimum pH) is 0.9 X 10(6) M-1 S-1. Compound X, in the absence of a halogen acceptor, decomposes to Compound I and chloride ion. The first order rate constant (Kd) for the decay of Compound X to Compound I is 0.2 s-1 at pH 4.5. The pH optimum for enzymatic chlorination with chlorite compares favorably with the pH profile for the lifetime of Compound X (Kf/Kd). These observations indicate that Compound X is the halogenating intermediate in the chlorite reaction and that the rate of enzymatic chlorination is directly related to the stability of Compound X. We propose an -OCl ligand on a ferric heme as the most likely structure for Compound X.     

Modification of lipoxygenase by hydrogen peroxide and photooxidation.

The kinetic study of fluorescence stopped-flow method suggested that the interaction between lipoxygenase and H2O2 is consistent with a simple irreversible one-step mechanism. The activation energy of the reaction was 7.2 kcal/mol. Participation of an ionizable group with pK about 8.8, possibly a histidine residue, was suggested from the pH-dependence of the rate constant. No further fluorescence quenching of lipoxygenase was observed when the product was added to the lipoxygenase solution before mixing the lipoxygenase and H2O2 solutions. The fluorescence quenching of lipoxygenase by H2O2 was in parallel with the inactivation of the enzyme. Hydroperoxylinoleic acid strongly protects the inactivation of lipoxygenase caused by H2O2. These results are consistent with an interpretation that OH- and/or O- - are produced when the iron of the enzyme is oxidized by H2O2, which in turn will attack some amino acid essential for the enzyme activity. The pH-dependence of the inactivation rate constant of photooxidation of lipoxygenase sensitized by methylene blue indicated that an ionizable group with pK about 8.8 is concerned with the enzymatic activity. In contrast to the inactivation of lipoxygenase by H2O2, the product protected the inactivation of the enzyme by photooxidation only at high concentration.     

The effect of electrochemical regeneration upon the enzymatic catalysis of a thermodynamically unfavorable reaction

The association between enzymatic and electrochemical reactions, enzymatic electrocatalysis, had proven to be a very powerful tooth in both analytical and synthetic fields. However, most of the combinations studied have involved enzymatic catalysis of irreversible or quasi-irreversible reaction. In the present work, we have investigated the possibility of applying enzymatic electrocatalysis to a case where the electrochemical reaction drives a thermodynamically unfavorable reversible reaction. Such thermodynamically unfavorable reactions include most of the oxidations catalyzed by dehydrogenases. Yeast alcohol dehydrogenase (E.C. 1.1.1.1) was chosen as a model enzyme because the oxidation of ethanol is thermodynamically very unfavorable and because its kinetics are well known. The electrochemical reaction was the oxidation of NADH which is particularly attractive as a method of cofactor regeneration. Both the electrochemical and enzymatic reactions occur in the same batch reactor in such a way that electrical energy is the only external driving force. Two cases were experimentally and theoretically developed with the enzyme either in solution or immobilized onto the electrode's surface. In both cases, the electrochemical reaction could drive the enzymatic reaction by NADH consumption in solution or directly in the enzyme's microenvironment. However even for a high efficiency of NADH consumption, the rate of enzymatic catalysis was limited by product (acetaldedehyde) inhibition. Extending this observation to the subject of organic synthesis catalyzed by dehydrogenases, we concluded that thermodynamically unfavorable reaction and can only be used in a process if efficient NAD regeneration and product elimination are simultaneously carried out within the reactor.