Diffusional and electrostatic effects on apparent kinetic parameters of reactions catalyzed by enzyme immobilized on the external surface of a support

Diffusional and electrostatic effects on the apparent maximum reaction rate V_m^app and the apparent Michaelis constant K_m^app were investigated theoretically for a system in which an enzyme immobilized on the external surface of a solid support catalyzes a reaction according to Michaelis-Menten kinetics. In such a system, the dependence of V_m^app and K_m^app on the substrate concentration can be expressed analytically. When the support and substrate carry charges of the same sign, resulting in a repulsive force between them, both V_m^app and K_m^app decrease with increasing substrate concentration, but they never decrease below the respective intrinsic values. On the other hand, when the support and substrate carry charges of opposite sign and therefore an attractive force occurs, V_m^app decreases towards its intrinsic value, while K_m^app decreases to values below its intrinsic value in the region of high substrate concentration.     

Influences of nonuniform activity distributions on the apparent maximum reaction rate and apparent Michaelis constant of immobilized enzyme reactions

The influences of nonuniform activity distribution within a porous solid support on the apparent kinetic parameters, V_m^app and K_m^app, of immobilized enzyme reactions following the Michaelis-Menten kinetics were theoretically investigated. As the enzyme is distributed to the neighborhood of the external surface of the support, V_m^app and K_m^app approach their respective intrinsic values over a wide range of substrate concentration. There is a close relationship between the nonuniform distribution and internal diffusional resistance. Changes in these two factors provide similar effects on V_m^app and K_m^app. As long as the immobilized enzyme reaction follows Michaelis-Menten kinetics, the nonuniform activity distribution never makes K_m^app less than its intrinsic value.     

Chlorophyllase in citrus leaves. Kinetic aspects of the reaction

The reaction: Chlorophyll + Enzyme → Chlorophyllide + Phytol follows a first order kinetics with regard to the quantity of enzyme, when it is saturated by substrate. K_m and V_m were determined from the average reaction rates for the substrates: Chlorophylla andb, pheophytina andb, methylchlorophyllidea and methylpheophorbide a: The lowest K_m corresponded to chlorophylla and the highest V_m to methylpheophorbidea. For a substrate of chlorophyll (a + b), K_m and V_m were determined also using the initial reaction rates. “Enzyme efficiency” was calculated using both methods of determination. The reaction products partially inhibit the hydrolytic process.     

Activation of the β-galactoside transport system in escherichia coli ML-308 by n-alkanols. Modification of lipid-protein interaction by a change in bilayer fluidity

The net rate of transport of $\text{o-}\text{nitrophenyl}\text{-β-}\text{d}\text{-}\text{galactopyranoside}$ by Escherichia coli ML-308 is increased at temperatures below the apparent phase transition of the lipid bilayer in the presence of n-alkanols. The degree of activation produced is determined both by the concentration and chain length of the n-alkanol used. At low concentrations n-alkanols “activate” transport, but do not cause either cell lysis or denaturation of β-galactosidase.Arrhenius plots of the kinetic constants for transport indicate the K_m shows discontinuity with increasing temperature, while the slope for V changes only gradually. The presence of 10.5 mM n-hexanol increases the value of both K_m and V at low temperature. A comparison of these data to those obtained at a single substrate concentration (1.85 mM o-nitrophenyl-β-d-galactopyranoside) suggests the biphasic behavior of Arrhenius plots at that concentration may be attributed to changes in the K_m for the transport process.     

Estimation of kinetic parameters for substrate and inhibitor in a reaction with an enzyme sample containing different types of inhibitor

The method of kinetic analysis is developed to obtain the maximum velocity (V_m), the Michaelis constant (K_m) and the parameters characterizing the inhibitors in an impure enzyme reaction, contaminated with one of four types of inhibitor (competitive, noncompetitive, uncompetitive and mixed-type). Although the reaction rate decreases with the increasing concentration of the enzyme sample containing an inhibitor, the double-reciprocal plot of the rate against the sample concentration becomes linear. The slopes of these linear plots at several different concentrations of substrate provide K_m and the specific enzyme activity, which is proportional to V_m, in the sample. These linear straight lines intersect in a point, of which the coordinates give the unique parameters for the inhibitor. To prove the validity of this kinetic method, the model experiments were carried out with acetylcholinesterase and its inhibitors, phenyltrimethylammonium and trimethylammonium. The present method was applied to the measurement of the specific activity of galactosylceramide galactosidase in the mouse cerebral homogenate. In addition, a kinetic method is indicated for the inhibition of an enzymatic reaction by a contaminant which binds the substrate to reduce the fraction available to the enzyme.     

NMR for direct determination of Km and Vmax of enzyme reactions based on the Lambert W function-analysis of progress curves

¹H NMR spectroscopy was used to follow the cleavage of sucrose by invertase. The parameters of the enzyme's kinetics, K_m and V_max, were directly determined from progress curves at only one concentration of the substrate. For comparison with the classical Michaelis-Menten analysis, the reaction progress was also monitored at various initial concentrations of 3.5 to 41.8 mM. Using the Lambert W function the parameters K_m and V_max were fitted to obtain the experimental progress curve and resulted in K_m = 28 mM and V_max = 13 μM/s. The result is almost identical to an initial rate analysis that, however, costs much more time and experimental effort. The effect of product inhibition was also investigated. Furthermore, we analyzed a much more complex reaction, the conversion of farnesyl diphosphate into (+)-germacrene D by the enzyme germacrene D synthase, yielding K_m = 379 μM and k_cat = 0.04 s^− 1. The reaction involves an amphiphilic substrate forming micelles and a water insoluble product; using proper controls, the conversion can well be analyzed by the progress curve approach using the Lambert W function.     

Steady-state kinetics of ADP-arsenate and ATP-synthesis in Rhodospirillum rubrum chromatophores

(1) Rates of ATP synthesis and ADP-arsenate synthesis catalyzed by Rhodospirillum rubrum chromatophores were determined with the firefly luciferase method and by a coupled enzyme assay involving hexokinase and glucose-6-phosphate dehydrogenase. (2) V_m for ADP-arsenate synthesis was about 2-times lower than V_m for ATP-synthesis. With saturating [ADP], K(As_i) was about 20% higher than K(P_i). With saturating [anion], K(ADP) was during arsenylation about 20% lower than during phosphorylation. (3) Plots of $\text{1}\text{v}$ vs. $\text{1}\text{[}\text{substrate}\text{]}$ were non-linear at low concentrations of the fixed substrate. The non-linearity was such as to suggest a positive cooperativity between sites binding the variable substrate, resulting in an increased $\text{V}{}_{\mathrm{<mtext>m</mtext>}}\text{K}{}_{\mathrm{<mtext>m</mtext>}}$ ratio. High concentrations of the fixed substrate cause a similar increase in $\text{V}{}_{\mathrm{<mtext>m</mtext>}}\text{K}{}_{\mathrm{<mtext>m</mtext>}}$, but abolish the cooperativity of the sites binding the variable substrate. (4) Low concentrations of inorganic arsenate (As_i) stimulate ATP synthesis supported by low concentrations of P_i and ADP about 2-fold. (5) At high ADP concentrations, the apparent K_i of As_i for inhibition of ATP-synthesis was 2–3-times higher than the apparent K_m of As_i for arsenylation; the apparent K_i of P_i for inhibition of ADP-arsenate synthesis was about 40% lower than the apparent K_m of P_i for ATP synthesis. (6) The results are discussed in terms of a model in which P_i and As_i compete for binding to a catalytic as well as an allosteric site. The interaction between these sites is modulated by the ADP concentration. At high ADP concentrations, interaction between these sites occurs only when they are occupied with different species of anion.     

Purification and kinetic studies on a porphobilinogen deaminase from the unicellular green alga Scenedesmus obliquus

Porphobilinogen deaminase, the enzyme condensing four molecules of porphobilinogen, was isolated and purified from light grown Scenedesmus obliquus (wild type). The purification procedure included heat treatment, ammonium sulphate fractionation, gel filtration, high-resolution anion-exchange chromatography and hydrophobic interaction chromatography. The enzyme was purified 1368-fold, compared to the initial crude extract. Its final specific activity was 6812 units · (mg · protein)^?1 at pH 7.4 with a recovery of 44%. The relative molecular mass was 33000, as determined by Sephadex G-100 gel filtration, and 35900 by lithium dodecyl sulfate-polyacrylamide-gel electrophoresis, indicating that the enzyme is a monomer. Studies of initial reaction velocities showed a linear progress curve for hydroxymethylbilane formation and a hyperbolic dependence of the initial reaction rate on substrate concentration, consistent with a sequential displacement mechanism. Apparent kinetic constants (K _m and V _max) for the conversion of porphobilinogen to hydroxymethylbilane at 37 ° C, pH 7.4, were 79 μM and 176 pmol · min^?1, respectively. Variation of both V _max and K _max with pH indicated the presence of ionizable groups in the enzyme-substrate complex(es), showing a single ionization (pK 7.15) in V _max/K _m plots. A sharp pH-profile for V _max was interpreted as a positive cooperative proton dissociation. In spite of the two pathways existing for 5-aminolevulinate biosynthesis in Scenedesmus, currently there is no indication of the existence of two porphobilinogen deaminases or even of isoenzymes.     

The application of flow microcalorimetry to the study of enzyme kinetics

The use of flow microcalorimetry to measure velocities for enzyme-catalyzed reactions is described. Studies are presented involving the enzymes chymotrypsin, trypsin, and ribonuclease A. In determining the Michaelis-Menten parameters, V_m and K_m, for these systems complications arise due to substrate depletion and product inhibition. By employing an integrated Michaelis-Menten equation, V_m and K_m can be determined.     

The hydrolysis of 3-(2-furylacryloyl)-glycyl-l-leucine amide by thermolysin

The kinetics of the hydrolysis of 3-(2-furylacryloyl)-glycycl-l-leucine amide by thermolysin has been reinvestigated. It was found that the K_m for the enzyme substrate interaction is 2.5 × 10^?3m at pH 7.2. This K_m is an order of magnitude less than what has been previously assumed to be the K_m for the enzyme-substrate interaction. The normally recommended assay has 1–3 × 10^?3m substrate and is based on the assumption that the substrate concentration is much less than the K_m. Our data indicate that this assumption appears to be invalid. The hydrolysis of 3-(2-furylacryloyl)-glycyl-l-leucine amide results in a maximum decrease in absorbance at 322 nm. The change in absorbance is nearly 10-fold greater at 322 nm than the change in absorbance at 345 nm where the hydrolysis has been customarily followed. By following the hydrolysis of the substrate at 10^?4m at 322 nm it is possible to work under conditions where the substrate concentration is much less than the K_m.     

Kinetics of the ion-sensitive Mg, Ca-adenosinetriphosphatase (ATPase) from Escherichia coli.

The Mg, Ca-ATPase from Escherichia coli is activated by KCl at low concentration and inhibited at high ion concentration. The optimum is at 30 mm KCl. The anion has a major effect, the monovalent cation a minor effect. The activation by Cl^? shows positive cooperativity with a Hill coefficient n_H= 2. The activation is accompanied by a decrease in K_m, leaving V unchanged. Thus the activation is seen especially at low substrate [MgATP] concentration. Trypsin-treated ATPase is also activated by KCl. An allosteric transition by anions is assumed.     

Choline sulfokinase of Penicillium chrysogenum: partial purification and kinetic mechanism.

Choline sulfokinase (3′-phosphoadenosine 5′-phosphosulfate (PAPS):choline sulfotransferase, EC 2.8.2.6) was purified approximately 30-fold from the mycelium of Penicillium chrysogenum. The K_m for PAPS is 12 μm. The enzyme is remarkably specific for the adenosine 3′,5′ (or 2′-5′)-diphosphate moiety. 3′,5′-ADP (PAP) has a K_i of 2.5 to 14 μm (depending on the choline concentration) whereas the K_i values of 3′-AMP, 5′-AMP, and 5′-ADP are at least 300-fold higher. The enzyme is also highly specific for choline (K_m = 17 μM). Of a number of other amino alcohols tested, none were potent inhibitors and only dimethylaminoethanol served as a reasonably good substrate (K_m = 800 μmV = 35% of V with choline). Triethylaminoethanol was a significantly poorer substrate (K_m = 2800 μM; V = 2% of V with choline). The purified enzyme is relatively stable when stored frozen in the presence of 25% sucrose. In the absence of sucrose, the maximum activity decreases and the K_m for choline increases. (The K_m for PAPS remains constant.) The age-inactivated enzyme can be restored to full activity (original V and K_m for choline) by a 10-min preincubation with 50 mm mercaptoethanol. However, prolonged incubation (24 h) with 50 mm mercaptoethanol results in irreversible denaturation. Initial velocity studies established that the enzyme follows a sequential kinetic mechanism. Product inhibition studies suggest a rapid equilibrium random binding sequence. Choline-O-phosphate (a dead-end inhibitor) is linearly competitive with choline and a linear mixed type inhibitor with respect to PAPS. Choline analogs lacking the alcohol (or ester) group (e.g., trimethylammonium, neurine, chlorocholine) are competitive dead-end inhibitors with respect to choline but are uncompetitive with respect to PAPS. Thiocholine is a linear mixed type inhibitor with respect to PAPS, but the reciprocal plots are almost parallel. These results suggest that the analogs lacking an oxygen atom have a negligible affinity for the free enzyme and bind predominantly to the enzyme-PAPS complex.     

Single-channel analysis of the anion channel-forming protein from the plant pathogenic bacterium Clavibacter michiganense ssp. nebraskense

The anion channel protein from Clavibacter michiganense ssp. nebraskense (Schürholz, Th. et al. 1991, J. Membrane Biol. 123: 1-8) was analyzed at different concentrations of KCl and KF. At 0.8 M KCl the conductance G(V_m) increases exponentially from 21 pS at 50 mV up to 53 pS at V_m = 200 mV, 20°C. The concentration dependence of G(V_m) corresponds to a Michaelis-Menten type saturation function at all membrane voltage values applied (0-200 mV). The anion concentration K_0.5, where G(V_m) has its half-maximum value, increases from 0.12 M at 50 mV to 0.24 M at 175 mV for channels in a soybean phospholipid bilayer. The voltage dependence of the single channel conductance, which is different for charged and neutral lipid bilayers, can be described either by a two-state flicker (2SF) model and the Nernst-Planck continuum theory, or by a two barrier, one-site (2B1S) model with asymmetric barriers. The increase in the number of open channels after a voltage jump from 50 mV to 150 mV has a time constant of 0.8 s. The changes of the single-channel conductance are much faster (<1 ms). The electric part of the gating process is characterized by the (reversible) molar electrical work ΔG^θ_el = ρZ_gFV_m ≈ -1.3 RT, which corresponds to the movement of one charge of the gating charge number |Z_g| = 1 across the fraction ρ = ΔV_m/V_m = 0.15 of the membrane voltage V_m = 200 mV. Unlike with chloride, the single channel conductance of fluoride has a maximum at about 150 mV in the presence of the buffer PIPES (≥5 mM, pH 6.8) with K_0.5 ≈ 1 M. It is shown that the decrease in conductance is due to a blocking of the channel by the PIPES anion. In summary, the results indicate that the anion transport by the Clavibacter anion channel (CAC) does not require a voltage dependent conformation change of the CAC.     

Role of cysteine in activation and allosteric regulation of maize phosphoenolpyruvate carboxylase

The effect of 5-5′-dithiobis-2-nitrobenzoate (DTNB) on the kinetic parameters and structure of phosphoenolpyruvate carboxylase purified from maize (Zea mays L.) has been studied. The V_max is found to be independent of the presence of this thiol reagent. The K_m is increased upon oxidation of cysteines by DTNB. At a substrate concentration higher than K_m (3.1 millimolar Mgphosphoenolpyruvate), a significant reversible decrease of the activity is observed. Malate has little effect in preventing the modification of these cysteines. The V type inhibition by malate was also studied at a saturating phosphoenolpyruvate level (9.3 millimolar Mgphosphoenolpyruvate). In the presence of 50 micromolar DTNB, up to 60% inhibition is caused by 15 millimolar malate; however, in the presence of both 50 micromolar DTNB and 50 millimolar dithiothreitol (DTT) this inhibition is reduced to 20%. The presence of DTT alone increases the size of the phosphoenolpyruvate carboxylase molecule as determined by light scattering. The activity at nonsaturating substrate concentration is increased by 36% in the presence of DTT. The oligomerization equilibrium between the dimer and the tetrameric form of the enzyme is affected by cysteine. The K_m for the substrate, the sensitivity toward malate, and the size of the enzyme are found to be modified upon incubation in the presence of DTT.     

Catalytic properties of enzymes from Erwinia carotovora involved in transamination of phenylpyruvate

K _m for L-phenylalanine, L-glutamic acid, L-aspartic acid, and the corresponding keto acids were calculated, as well as V _max was measured for the following pairs of substrates: L-phenylalanine-2-ketoglutarate, L-phenylalanine-oxaloacetate, L-glutamic acid-phenylpyruvate, and L-aspartic acid-phenylpyruvate for aminotransferases PAT1, PAT2, and PAT3 from Erwinia carotovora catalyzing transamination of phenylpyruvate. The ping-pong bi-bi mechanism was shown for the studied aminotransferases. The substrate inhibition (K _s) of PAT3 with 2-ketoglutarate and oxaloacetate was 10.23 ± 3.20 and 3.73 ± 1.99 mM, respectively. It was shown that L-β-(N-benzylamino)alanine was a competitive inhibitor with respect to L-phenylalanine for PAT1 (K _i = 0.32 ± 0.07 mM, K _m = 0.45 ± 0.1 mM, V _max = 11. 6 ± 0.4 U/mg) at 25 mM concentration of 2-ketoglutarate in the reaction medium. L-β-(N-methylamino)alanine is a noncompetitive inhibitor with respect to L-phenylalanine for PAT3 (K _I = 138.4 ± 95.4 mM, K _m = 13.7 ±3.9 mM, V _max = 18.6 ± 4.1 U/mg) at 2 mM concentration of 2-ketoglutarate in the reaction medium. L-stereo isomers of nonprotein analogues of aromatic amino acids were studied as substrates for PAT1, PAT2, and PAT3. L-β-(2-Br-phenyl)alanine, L-β-(4-Br-phenyl)alanine, L-β-(2-F-phenyl)alanine, and L-(2-F)tryptophan were good substrates for all three aminotransferases; L-α-methyl-β-(2-Br-phenyl)alanine and L-O-benzyltyrosine were substrates only for PAT3; L-β-(4-F-phenyl)alanine was a substrate for PAT1 and PAT3. Thus, these analogues of aromatic amino acids can be stereoselectively synthesized using the studied aminotransferases in the presence of the corresponding keto acids.     

Calculation of Km and Vmax from Substrate Concentration Versus Time Plot

A simple method for the calculation of kinetic parameters (K_m, V_max) under conditions of changing substrate concentrations is presented. An application of the method to detect shifts in groups involved in the utilization of a substrate in a mixed microbial culture is given.     

Voltage dependent potassium fluxes and the significance of action potentials in Acetabularia

Membrane potential, V_m, and K⁺(⁸⁶Rb⁺) fluxes have been measured simultaneously on individual cells of Acetabularia mediterranea. During resting state (resting potential approx. ?170 mV) the K⁺ influx amounts to 0.24–0.6 pmol · cm^?2 · s^?1 and the K⁺ efflux to 0.2–1.5 pmol · cm^?2 s^?1. According to the K⁺ concentrations inside and outside the cell (40 : 1) the voltage dependent K⁺ flux (zero at V_m = E_K = ?90 mV) is stimulated approx. 40-fold for V_m more positive than E_K.It is calculated that during one action potential (temporary depolarization to V_m more positive than E_K) a cell looses the same amount of K⁺, which leaks in during 10–20 min in the resting state (V_m = ?170 mV). Since action potentials occur spontaneously in Acetabularia, they are therefore suggested to have a significant function for the K⁺ balance of this alga.     

α-d-Galactosidase immobilized on a soluble polymer

α-d-Galactosidase (α-d-galactoside galactohydrolase, EC 3.2.1.22) from green coffee beans has been immobilized by attachment to cyanogen bromide-activated Dextran T-70. Since this represents the first reported example of the preparation of a water-soluble derivative of an enzyme showing substrate inhibition, the kinetic properties, thermal stability and pH optima were investigated and compared with those of the free enzyme. The K_m, K_s, K_i, V_max, optimum substrate concentration and optimum pH were all lower than those of free enzyme. The enzyme conjugate showed greater resistance than the free enzyme to thermal inactivation. These data, although obtained with the synthetic substrate 4-nitrophenyl-α-d-galactoside, suggest some advantages in using the enzyme conjugate for the removal of terminal α-d-galactopyranosyl groups from the erythrocyte cell surface.     

Simultaneous Measurements of Cytoplasmic K Concentration and the Plasma Membrane Electrical Parameters in Single Membrane Samples of Chara corallina

The electrophysiological properties of cytoplasm-rich fragments (single membrane samples) prepared from internodal cells of Chara corallina were explored in conjunction with K⁺-sensitive microelectrode and current-voltage (I-V) measurements. This system eliminated the problem of the inaccessible cytoplasmic layer, while preserving many of the electrical characteristics of the intact cells. In 0.1 millimolar external K concentration (K_o⁺), the resting conductance (membrane conductance G_m, 0.85 ± 0.25 Siemens per square meter (±standard error)) of the single membrane samples, was dominated by the proton pump, as suggested by the response of the near-linear I-V characteristic to changes in external pH. Initial cytoplasmic K⁺ activities (a_K+), judged most reliable, gave values of 117 ± 67 millimolar; stable a_K+ values were 77 ± 31 millimolar. Equilibrium potentials for K⁺ (Nernst equilibrium potential) (E_K) calculated, using either of these data sets, were near the mean membrane potential (V_m). On a cell-to-cell basis, however, E_K was generally negative of the V_m, despite an electrogenic contribution from the Chara proton pump. When K_o⁺ was increased to 1.0 millimolar or above, G_m rose (by 8- to 10-fold in 10 millimolar K_o⁺), the steady state I-V characteristics showed a region of negative slope conductance, and V_m followed E_K. These results confirm previous studies which implicated a K_o⁺-induced and voltage-dependent permeability to K⁺ at the Chara plasma membrane. They provide an explanation for transitions between apparent K_o⁺-insensitive and K_o⁺-sensitive (`K⁺ electrode') behavior displayed by the membrane potential, as recorded in many algae and higher plant cells.     

Degradation of cellulose by thermophilic bacteria

Degradation of 1—.10% crystalline cellulose and concentration of:free reducing sugars in the medium, were studied during cultivation of a wild coculture of obligately thermphilic bacteria in 3-L fermentors at 60^°C and pH 7.0 under anaerobic conditions. The coculture was composed of five different species ofBacillus and a single cellulolytic species lof Clostridium. The proportion of degraded substrate was inversely proportional to the initial concentration of cellulose. The higher the initial substrate concentration the lower the proportion of its.degradation. Cellulose at 1 — 2 % concentration is best degraded (98 % in:5.d). The fermentation time increases with increasing cellulose concentration, the level of reducing saccharides increases together with the initial rate of substrate degradation. In the presence of 10 %) cellulose the rate of degradation within a period of a 1-d fermentation is close toV, being 0.455 g L^-1 h^-1withK _m of 12.5 g/L. However, during further cultivation (1—3 d) the rate of degradation of 4—10 % cellulose decreases, probably due to the effect of accumulated reducing saccharides whose levels reach 55—60 mg/L.