Investigations of reaction kinetics for immobilized enzymes--identification of parameters in the presence of diffusion limitation

A method is proposed for identification of kinetic parameters when diffusion of substrates is limiting in reactions catalyzed by immobilized enzymes. This method overcomes conventional sequential procedures, which assume immobilization does not affect the conformation of the enzyme and, thus, consider intrinsic and inherent kinetics to be the same. The coupled equations describing intraparticle mass transport are solved simultaneously using numerical methods and are used for direct estimation of kinetic parameters by fitting modeling results to time-course measurements in a stirred tank reactor. While most traditional procedures were based on Michaelis-Menten kinetics, the method presented here is applicable to more complex kinetic mechanisms involving multiple state variables, such as ping-pong bi-bi. The method is applied to the kinetic resolution of (R/S)-1-methoxy-2-propanol with vinyl acetate catalyzed by Candida antarctica lipase B. A mathematical model is developed consisting of irreversible ping-pong bi-bi kinetics, including competitive inhibition of both enantiomers. The kinetic model, which fits to experimental data over a wide range of both substrates (5-95%) and temperatures (5-56 degrees C), is used for simulations to study typical behavior of immobilized enzyme systems.     

A Maxwell's Demon type of membrane transport: possibility for active transport by ABC-type transporters?

ATP-binding-cassette (or ABC)-type transporters constitute one of the largest family of membrane transporters in nature. Many of its members move substrates "actively", i.e. in an ATP-dependent manner against an electrochemical gradient. No consensus is available about the mechanism. Therefore, a novel class of transport mechanisms is proposed based on Maxwell's demon idea. This transport mechanism consists of a gated pore that selectively opens for substrates from one, but not the other side. Thermoenergy (Brownian motion) would suffice for substrate translocation across the membrane; energy for synchronizing gate opening with substrate arrival would come from ATP hydrolysis. Simulations demonstrate that such a mechanism would be thermodynamically and kinetically feasible. It exhibits "active", unidirectional transport, saturation, and other typical features of protein-catalysed reactions. It also shows pore behavior with charged substrates moving under the influence of electrical potentials. Its efficiency depends on a diffusion time constant of the substrate in solution that is slower than the transit time through the membrane, a situation that can realistically be achieved at millimolar or lower substrate concentrations. Features of the novel mechanism that differ significantly from P- or F-type ATPases are: (1) transport cannot be run in "reverse" to synthesize ATP even if sufficient energy is available in the gradient of the transported solute and (2) unidirectional and net substrate fluxes through the transporter diverge with increasing substrate concentration.     

A family of models for the elimination of substrate in the liver

A family of models describing the elimination of substrates from the blood by the liver is proposed. It is shown how it contains some previously proposed models for elimination in the liver, diffusion through the capillaries and absorption in the intestine, where the elimination is assumed to follow either first-order or simple Michaelis-Menten kinetics.Applications to allosteric reactions are suggested.     

Real-time measurements of DNA hybridization on microparticles with fluorescence resonance energy transfer

When capture oligonucleotides are tethered on planar surfaces, mass transport limitations influence the kinetics of solid-phase nucleic acid hybridizations. By diffusion theory, however, hybridization of oligonucleotides on microparticles should be reaction-rate limited. In an initial effort to understand the kinetics of microparticle hybridization reactions, we developed a fluorescence resonance energy transfer method for monitoring oligonucleotide hybridization on microparticles. Microparticles were coated with a fluoresceinated oligomer at surface densities of 20, 40, and 80% saturation, hybridized to a complementary oligonucleotide labeled with tetramethylrhodamine, and monitored over time for quenching of the fluorescein signal as hybridization occurred on the particle surface. Association rate constants were compared for microparticle-based hybridization and solution-phase hybridization. Rate constants for hybridizations on the particle surface were about an order of magnitude less than those for hybridization in solution, but decreasing the surface density of the capture oligonucleotide to 20% saturation improved particle hybridization rates. Although a bimolecular reaction model adequately described solution-phase hybridization kinetics, oligonucleotide hybridization on microparticles did not fit this model but exhibited biphasic reaction kinetics. Based on two different lines of reasoning, we argue that microparticle-based oligonucleotide hybridization was indeed reaction-rate limited in our system and not diffusion-rate limited.     

Kinetic mechanism of the Cu(II) enzyme galactose oxidase

The steady-state kinetics of four redox reactions catalyzed by galactose oxidase have been determined. The alcohol substrate used in each case was galactose; the four oxidant substrates used were O₂, IrCl₆^2?, porphyrexide, and Fe(CN)₆^3?. With the exception of the last reagent, saturation behavior is exhibited by all substrates. Double reciprocal plots of rate data obtained varying one substrate at various concentrations of the other are intersecting for all pairs that exhibited saturation behavior. Thus, these reactions are kinetically sequential processes involving single central complexes. These complexes involve enzyme, galactose, and one molecule of oxidant, whether or not the oxidant is a one- or two-electron acceptor. This result indicates that for one-electron oxidants, an enzyme-alcohol-derived radical species may exist as a transient prior to the reaction of the second electron equivalent of oxidant. A similar substrate

transient is postulated in the reaction involving O₂. The inhibition by H₂O₂ has also been studied in detail. H₂O₂ apparently binds to the enzyme at two sites. The nature of alcohol and O₂ binding to the enzyme Cu(II) is discussed in light of these kinetic results.     

Concentration multiplicity in a draft tube fluidized-bed bioreactor involving two limiting substrates

Concentration multiplicity in a two-phase or three-phase draft tube fluidized-bed bioreactor containing biofloc particles is studied. The kinetics of biological reactions considered involve two limiting substrates. The necessary and sufficient conditions for concentration multiplicity in both the biofilm and bioreactor are examined in terms of effectiveness factor, inlet and bulk concentration of substrates, and liquid flow rate. Hysteresis behavior in both the biofilm and bioreactor and multiplicity of concentration profiles in the biofilm are also discussed.     

Construction of a novel guest biomimetic glutathione peroxidase with solvent-dependent catalytic behavior by incorporating the active center into adamantyl molecule

A novel guest biomimetic glutathione peroxidase(3,3′-tellurobis(propane-3,1-diyl) diadamantanecarboxylate, denoted as ADA-Te-ADA) was synthesized. ADA-Te-ADA functioned to overcome the disadvantages in the construction of building block for giant supramolecular biomimetic enzyme. To reveal the catalytic property of hydrophobic ADA-Te-ADA, the catalytic mechanism was investigated using PBS (phosphate buffer (pH = 7.0, 50 mM))/methanol solvent mixture as assay solution. It indicated that ADA-Te-ADA exhibited typical enzyme catalytic behavior by saturation kinetics measurement. Importantly, ADA-Te-ADA exhibited the typical solvent-dependent catalytic behavior. And the highest catalytic rate 4.29 μM × min^?1 was obtained when the volume ratio of PBS: methanol was 5: 5. Especially, the catalytic rates obtained based on various substrates proved that ADA-Te-ADA slightly displayed special substrate selectivity, which was the ideal catalytic characterization of building block for giant supramolecular biomimetic enzyme. The success-fully synthesis of ADA-Te-ADA might highlight for the understanding of the catalytic mechanism of hydrophobic guest biomimetic glutathione peroxidase. And it also might provide the basement for the construction of giant supramolecular biomimetic enzyme.     

Kinetic analysis of the mechanism for subtilisin in essentially anhydrous organic solvents

Steady-state kinetic analysis has been used to confirm the catalytic mechanism of lyophilized subtilisin suspended in a variety of organic solvents. Specifically, this article demonstrates that partial reactions can occur between subtilisin and ester substrates in organic solvents. Partitioning of common intermediates between competing acceptors at a constant ratio of products has also been described. The decomposition of a common intermediate formed from different substrates at the same rate is also further evidence of an acyl-enzyme mechanism for subtilisin suspended in anhydrous solvents. Partitioning of a common intermediate to give two products at a constant total rate, and saturation kinetics at varying substrate concentrations, complete a kinetic investigation of the enzyme mechanism. All the data generated support the formation of a stable acyl enzyme during the transesterification reaction catalzyed by subtilisin in the solvents used.     

Generalized rate equation for single-substrate enzyme catalyzed reactions

The most widely used rate expression for single-substrate enzyme catalyzed reactions, namely the Michaelis-Menten kinetics is based upon the assumption that enzyme concentration is in excess of the substrate in the medium and the rate is mainly limited by the substrate concentration according to saturation kinetics. However, this is only a special case and the actual rate expression varies depending on the initial enzyme/substrate ratio (E₀/S₀). When the substrate concentration exceeds the enzyme concentration the limitation is due to low enzyme concentration and the rate increases with the enzyme concentration according to saturation kinetics. The maximum rate is obtained when the initial concentrations of the enzyme and the substrate are equal. A generalized rate equation was developed in this study and special cases were discussed for enzyme catalyzed reactions.     

Kinetics of collagen-bound sorbitol dehydrogenase in the rotating membrane reactor: Opposite variations of affinity constants under diffusional limitations

Sorbitol dehydrogenase was bound to the surface of acyl-azide-activated collagen membranes and its kinetics was investigated as a model of two-substrate or cofactor-requiring enzyme reactions. The study was performed with the “rotating membrane reactor” especially designed to obtain a precise variation of the external mass-transfer coefficient, and thus the direct visualization of diffusional effects on the bound enzyme behavior. Diffusional limitations for NADH were found to decrease the apparent affinity for NADH, but to increase the apparent affinity for fructose. Such opposite effects of diffusional limitations on apparent affinities are generally applicable to reactions involving two substrates or a substrate and a cofactor of widely different affinities.     

Nitrate Utilization by the Diatom Skeletonema costatum: I. Kinetics of Nitrate Uptake

Nitrate uptake has been studied in nitrogen-deficient cells of the marine diatom Skeletonema costatum. When these cells are incubated in the presence of nitrate, this ion is quickly taken up from the medium, and nitrite is excreted by the cells. Nitrite is excreted following classical saturation kinetics, its rate being independent of nitrate concentration in the incubation medium for nitrate concentration values higher than 3 micromolar. Nitrate uptake shows mixed-transfer kinetics, which can be attributed to the simultaneous contributions of mediated and diffusion transfer. Cycloheximide and p-hydroxymercuribenzoate inhibit the carrier-mediated contribution to nitrate uptake, without affecting the diffusion component. When cells are preincubated with nitrate, the net nitrogen uptake is increased.     

Mechanisms of alveolar protein clearance in the intact lung

Transport of protein across the alveolar epithelial barrier is a critical process in recovery from pulmonary edema and is also important in maintaining the alveolar milieu in the normal healthy lung. Various mechanisms have been proposed for clearing alveolar protein, including transport by the mucociliary escalator, intra-alveolar degradation, or phagocytosis by macrophages. However, the most likely processes are endocytosis across the alveolar epithelium, known as transcytosis, or paracellular diffusion through the epithelial barrier. This article focuses on protein transport studies that evaluate these two potential mechanisms in whole lung or animal preparations. When protein concentrations in the air spaces are low, e.g., albumin concentrations <0.5 g/100 ml, protein transport demonstrates saturation kinetics, temperature dependence indicating high energy requirements, and sensitivity to pharmacological agents that affect endocytosis. At higher concentrations, the protein clearance rate is proportional to protein concentration without signs of saturation, inversely related to protein size, and insensitive to endocytosis inhibition. Temperature dependence suggests a passive process. Based on these findings, alveolar albumin clearance occurs by receptor-mediated transcytosis at low protein concentrations but proceeds by passive paracellular mechanisms at higher concentrations. Because protein concentrations in pulmonary edema fluid are high, albumin concentrations of 5 g/100 ml or more, clearance of alveolar protein occurs by paracellular pathways in the setting of pulmonary edema. Transcytosis may be important in regulating the alveolar milieu under nonpathological circumstances. Alveolar degradation may become important in long-term protein clearance, clearance of insoluble proteins, or under pathological conditions such as immune reactions or acute lung injury. acute respiratory distress syndrome; endocytosis; diffusion; protein transport pulmonary edema     

Human glutathione transferase A1-1 demonstrates both half-of-the-sites and all-of-the-sites reactivity

A study of the kinetics of a heterodimeric variant of glutathione transferase (GST) A1-1 has led to the conclusion that, although the wild-type enzyme displays all-of-the-sites reactivity in nucleophilic aromatic substitution reactions, it demonstrates half-of-the-sites reactivity in addition reactions. The heterodimer, designed to be essentially catalytically inactive in one subunit due to a single point mutation (D101K), and the two parental homodimers were analyzed with seven different substrates, exemplifying three types of reactions catalyzed by glutathione transferases (nucleophilic aromatic substitution, addition, and double-bond isomerization reactions). Stopped-flow kinetic results suggested that the wild-type GST A1-1 behaved with half-of-the-sites reactivity in a nucleophilic aromatic substitution reaction, but steady-state kinetic analyses of the GST A1-D101K heterodimer revealed that this was presumably due to changes to the extinction coefficient of the enzyme-bound product. In contrast, steady-state kinetic analysis of the heterodimer with three different substrates of addition reactions provided evidence that the wild-type enzyme displayed half-of-the-sites reactivity in association with these reactions. The half-of-the-sites reactivity was shown not to be dependent on substrate size, the level of saturation of the enzyme with glutathione, or relative catalytic rate.     

Diffusion and redistribution of lipid-like molecules between membranes in virus-cell and cell-cell fusion systems.

The kinetics of redistribution of lipid-like molecules between the membranes of two fused spherical vesicles is studied by solving the time-dependent diffusion equation of the system. The effects on the probe redistribution rate of pore size at the fusion junction and the relative sizes of the vesicles are examined. It is found that the redistribution rate constant decreases significantly, but not drastically, as the relative size of the pore to that of the vesicles decreases (the bottleneck effect). In general, the time scale of the probe redistribution rate is determined by the size of the vesicles that is loaded with the probe before the activation of the fusion. For a pore size 50 A in diameter and a typical diffusion coefficient of 10(-8) cm2/s for lipids, the mixing half times for typical virus-cell and cell-cell fusion systems are less than 30 ms and above 200 s, respectively. Thus, although the redistribution of lipid-like probes by diffusion is not rate limiting in virus-cell fusion, redistribution by diffusion is close to rate limiting in spike-protein mediated cell-cell fusion.     

Iron binding by phosvitin: variation of rate of iron release as a function of the degree of saturation of iron binding sites

The rate of iron release from Fe(III)-phosvitin complexes, at varied degrees of saturation, was studied. Iron release was induced by reduction in the presence of the ferrous ion chelator, o-phenanthroline. If iron release was induced photochemically (without a chemical reductant), the reactions proceeded in zero order fashion, independently of the degree of saturation but with a strong dependence on the concentration of phenanthroline. When hydroquinone was added and the reactions were conducted in the dark, iron release followed first-order kinetics and the rate constants showed a clear dependence on the degree of saturation of the protein, which was most marked at lower levels of saturation. The results imply control of iron release by binding site differences produced by different intramolecular environments as the protein provides different combinations of its phosphoserine groups as ligands depending on the number of iron atoms to be accommodated per protein molecule.     

Formation of enzyme-bound carbanion intermediate in the isocitrate lyase-catalyzed reaction: enzymatic reaction of tetranitromethane with substrates and its dependence on effector, pH, and metal ions

Isocitrate lyase of germinating castor seed endosperm catalyzes the reactions of succinate and of isocitrate (but not of glyoxylate) with tetranitromethane (TNM), giving rise to the nitroform anion (C-(NO2)3), analogous to the reaction of TNM with carbanions (O.P. Malhotra and U.N. Dwivedi, 1984, Ind. J. Biochem. Biophys. 21, 65-67). The kinetics of this reaction have been investigated under a variety of conditions. At a fixed TNM concentration, the initial rate of reaction exhibits a hyperbolic saturation of the enzyme with isocitrate. The reaction with succinate, however, shows "negative cooperativity" in succinate saturation and the data are consistent with the existence of two sets of succinate binding sites of unequal affinity ("tight" and "loose" sites). Equal reaction rates are observed at enzyme-saturating concentrations of succinate and isocitrate. In every case, the rate of reaction is proportional to the TNM concentration. In the presence of alpha-ketoglutarate, hyperbolic saturation curves are obtained for all the substrates (TNM and succinate or TNM and isocitrate). In the presence of this effector the Km of succinate and TNM are independent of the concentration of the second substrate. On the other hand, sets of parallel straight lines are obtained in the double-reciprocal plots for the enzymatic reaction of TNM with isocitrate in the presence of alpha-ketoglutarate. Studies on the effect of pH on the isocitrate lyase-catalyzed reactions of TNM with succinate, TNM with isocitrate, and succinate with glyoxylate in the absence as well as in the presence of alpha-ketoglutarate show that the proton behaves as an uncompetitive inhibitor in all these reactions, suggesting the presence of a "masked" basic group at the enzyme site, which is protonated in the presence of substrate only. The pKa value of this group lies in the range 6.7-6.9. The enzymatic reactions of TNM with succinate and isocitrate exhibit identical Mg2+ ion dependence. From a comparison of the data on the enzymatic reactions of TNM with the corresponding results on the physiological reaction catalyzed by this enzyme, it has been suggested that an ion pair intermediate (E+ X S-, in which E, S, and S- stand for enzyme, succinate, and succinate carbanion, respectively) lies on the pathway of catalysis by isocitrate lyase.     

External and internal diffusion in heterogeneous enzymes systems

The intrusion of diffusion in heterogeneous enzyme reactions, which follow. Michaelis-Menten kinetics, is quantitatively characterized by dimensionless parameters that are independent of the substrate concentration. The effects of these parameters on the overall rate of reaction is illustrated on plots commonly employed in enzyme kinetics. The departure from Michaelis-Menten kinetics due to diffusion limitations can be best assessed by using Hofstee plots which are also suitable to distinguish between internal and external transport effects. A graphical method is described for the evaluation of the reaction rate as a function of the surface concentration of the substrate from measured data.     

Quantitative measurements of NO reaction kinetics with a Clark-type electrode.

Nitric oxide (NO) plays important physiological roles in the body. Knowledge regarding the kinetics of NO catabolism is important for understanding the biological functions of NO. Clark-type NO electrodes have been frequently employed in measuring the kinetics of NO reactions; however, the slow response time of these electrodes can cause measurement errors and limit the application of the electrode in measurements of fast NO reactions. In this study, a simplified diffusion model is given for describing the response process of the NO electrode to the change of NO concentration. The least-square method is used in fitting the currents calculated from the diffusion equation to the experimental curves for determining the diffusion parameters and rate constants. The calculated currents are in excellent accordance with the experimental curves for different NO reaction kinetics. It has been demonstrated that when using an NO electrode with a response time of approximately 6 s to measure fast NO reactions with a half-life of approximately 1s, the response currents of the electrode have large differences compared to the curve of actual NO concentration in the solution; however, the rate constant of NO decay can still be accurately determined by computer simulations with the simplified diffusion model. Theoretical analysis shows that an NO electrode with a response time of 6 s (D/L2=0.06 s-1) and the lowest detection limit of 1 nM NO can be used in measuring kinetics of extremely rapid NO reactions with a half-life below 10 ms.     

Enzymatic elimination of substrates flowing through the intact liver

Enzymatic elimination of a class of substrates by the liver is analyzed in terms of a convective model of the microcirculation carrying the substrates. The elimination generates concentration gradients of the substrates which in turn affect the elimination rate through Michaelis-Menten saturation kinetics. The interplay of biochemical, anatomical and haemo-dynamic factors results in a variety of limiting regimes of elimination which are given a quantitative discussion and classification. The kinetic parameters of the enzymatic elimination reaction are expressed in terms of quantities observable on the intact liver. An overall elimination efficiency is defined by comparison with a homogenous process and evaluated for all elimination regimes, with clinical implications. Examples of two types of experiments supporting the validity of the model are presented.