Showing papers on "Michaelis–Menten kinetics published in 1997"

Transport of Charged Dipeptides by the Intestinal H+/Peptide Symporter PepT1 Expressed in Xenopus laevis Oocytes

Abstract: The cloned intestinal peptide transporter is capable of electrogenic H+-coupled cotransport of neutral di- and tripeptides and selected peptide mimetics. Since the mechanism by which PepT1 transports substrates that carry a net negative or positive charge at neutral pH is poorly understood, we determined in Xenopus oocytes expressing PepT1 the characteristics of transport of differently charged glycylpeptides. Transport function of PepT1 was assessed by flux studies employing a radiolabeled dipeptide and by the two-electrode voltage-clamp-technique. Our studies show, that the transporter is capable of translocating all substrates by an electrogenic process that follows Michaelis Menten kinetics. Whereas the apparent K0.5 value of a zwitterionic substrate is only moderately affected by alterations in pH or membrane potential, K0.5 values of charged substrates are strongly dependent on both, pH and membrane potential. Whereas the affinity of the anionic dipeptide increased dramatically by lowering the pH, a cationic substrate shows only a weak affinity for PepT1 at all pH values (5.5–8.0). The driving force for uptake is provided mainly by the inside negative transmembrane electrical potential. In addition, affinity for proton interaction with PepT1 was found to depend on membrane potential and proton binding subsequently affects the substrate affinity. Furthermore, our studies suggest, that uptake of the zwitterionic form of a charged substrate contributes to overall transport and that consequently the stoichiometry of the flux-coupling ratios for peptide: H+/H3O+ cotransport may vary depending on pH.

Pre-steady-state study of recombinant sesquiterpene cyclases.

Abstract: An Escherichia coli expression system was used to generate hexahistidyl-tagged plant sesquiterpene cyclases, which were readily purified by a single affinity chromatographic step. Genes for Hyoscyamus muticus vetispiradiene synthase (HVS), a chimeric 5-epi-aristolochene synthase (CH3), and a chimeric sesquiterpene cyclase possessing multifunctional epi-aristolochene and vetispiradiene activity (CH4) were expressed in bacterial cells, which resulted in the sesquiterpene cyclases accumulating to 50% of the total protein and 35% of the soluble protein. From initial velocity experiments, the Michaelis constant for HVS was 3.5 microM, while CH3 and CH4 exhibited smaller values of 0.7 and 0.4 microM, respectively. Steady-state catalytic constants were from 0.02 to 0.04 s-1. A combination of pre-steady-state rapid quench experiments, isotope trapping experiments, and experiments to measure the burst rate constant as a function of substrate concentration revealed that turnover in all three cyclases is limited by a step after the initial chemical step involving rupture of the carbon-oxygen bond in farnesyl diphosphate (FPP). Rate constants for the limiting step were 10-70-fold smaller than for the initial chemical step. Dissociation constants for the enzyme-substrate complex (20-70 microM) were determined from the pre-steady-state experiments and were significantly larger than the observed Michaelis constants. A mechanism that involves an initial, rapid equilibration of enzyme with substrate to form an enzyme-substrate complex, followed by a slower conversion of FPP to an enzyme-bound hydrocarbon and a subsequent rate-limiting step, is proposed for the three enzymes. Interestingly, the multifunctional chimeric enzyme CH4 exhibited both a tighter binding of FPP and a faster conversion of FPP to products than either of its wild-type parents.

Substrate Kinetics of the Plant Mitochondrial Alternative Oxidase and the Effects of Pyruvate.

Abstract: The kinetics of alternative oxidase (AOX) of Arum italicum spadices and soybean (Glycine max L.) cotyledons were studied both with intact mitochondria and with a solubilized, partially purified enzyme. Ubiquinone analogs were screened for their suitability as substrates and ubiquinol-1 was found to be most suitable. The kinetics of ubiquinol-1 oxidation via AOX in both systems followed Michaelis-Menten kinetics, suggesting that the reaction is limited by a single-step substrate reaction. The kinetics are quite different from those previously described, in which the redox state of ubiquinone-10 was monitored and an increase in substrate was accompanied by a decrease in product. The difference between the systems is discussed. Pyruvate is a potent activator of the enzyme and its presence is essential for maximum activity. The addition of pyruvate to the solubilized enzyme increased the maximum initial velocity from 6.2 [plus or minus] 1.3 to 16.9 [plus or minus] 2.8 [mu]mol O2 mg-1 protein min-1 but had little effect on the Michaelis constant for ubiquinol-1, an analog of ubiquinol, which changed from 116 [plus or minus] 73 to 157 [plus or minus] 68 [mu]M. It is concluded that pyruvate (and presumably other keto acids) increases the activity of AOX but does not increase its affinity for its substrate. In agreement with this is the finding that removal of pyruvate (using lactate dehydrogenase and NADH) leads to an 80 to 90% decrease in the reaction rate, suggesting that pyruvate is important in the mechanism of reaction of AOX. The removal of pyruvate from the enzyme required turnover, suggesting that pyruvate is bound to the enzyme and is released during turnover.

[delta]1-Pyrroline-5-Carboxylate Dehydrogenase from Cultured Cells of Potato (Purification and Properties)

Abstract: [delta]1-Pyrroline-5-carboxylate (P5C) dehydrogenase (EC 1.5.1.12), the second enzyme in the proline catabolic pathway and a catalyst for the oxidation of P5C to glutamate, was purified from cultured potato (Solanum tuberosum L. var Desiree) cells. Homogeneous enzyme preparations were obtained by a three-step procedure that used anion-exchange, adsorption, and substrate elution chromatography. A 1600-fold purification was achieved, with a recovery of one-third of the initial activity. The purified enzyme was characterized with respect to structural, kinetic, and biochemical properties. It appeared to be an [alpha]-4 tetramer with subunits of an apparent molecular mass of about 60 kD and had a mildly acidic isoelectric point value. Potato P5C dehydrogenase had Michaelis constant values of 0.11 and 0.46 mM for NAD+ and P5C, respectively. Although NAD+ was the preferred electron acceptor, NADP+ also yielded an unusually high rate, and thus was found to serve as a substrate. Maximal activity was observed at pH values in the 7.3 to 8.3 range, and was progressively inhibited by chloride ions, a finding that strengthens recent suggestions that hyperosmotic stress negatively modulates in vivo proline oxidation.

Studies towards a tailor‐made catalyst for the Diels‐Alder reaction using the technique of molecular imprinting

Abstract: A tailor-made catalytically active polymer catalyzing the bimolecular Diels-Alder reaction is described. Kinetic studies carried out in acetonitrile at 82°C show a 270-fold rate acceleration (kcat/kuncat) for the Diels-Alder reaction between tetrachlorothiophene dioxide and maleic anhydride. The imprinted polymer induces Michaelis-Menten kinetics, with an apparent Km of 42.5 mM and an apparent kcat of 3.82 × 10−2 min−1, respectively. Substrate selectivity, accessible binding site analysis, dissociation constant determination, and inhibition study were also performed.

Effects of pH, temperature, and alcohols on the remarkable activation of thermolysin by salts.

Abstract: The activity of thermolysin in the hydrolysis of N-[3-(2-furyl)acryloyl] (FA)-dipeptide amides and N-carbobenzoxyl-L-aspartyl-L-phenylalanine methyl ester is remarkably enhanced by high concentrations (1-5 M) of neutral salts. The activation is due to an increase in the molecular activity, k(cat), while the Michaelis constant, K(m), is not affected by the addition of NaCl. In the present study, the effect of NaCl on the thermolysin-catalyzed hydrolysis of FA-glycyl-L-leucine amide (FAGLA) has been examined by changing the pH and temperature, and by adding alcohols to the reaction mixture. The enzyme activity, expressed by k(cat)/K(m), is pH-dependent, being controlled by two functional residues with pK(a) values of 5.4 and 7.8 in the absence of NaCl. The acidic pK(a) is shifted from 5.4 to 6.7 by the addition of 4 M NaCl, while the basic one is not changed. The degree of activation at a given concentration of NaCl is pH dependent in a bell-shaped manner with the optimum pH around 7. Although the activity increases in both the presence and absence of NaCl with increasing temperature from 5 to 35 degrees C, the degree of activation decreases. Alcohols inhibit thermolysin, and the degree of activation decreases with increasing alcohol concentration. The degree of activation tends to increase with increasing dielectric constant of the medium, although it varies considerably depending on the species of alcohol. Electrostatic interactions on the surface and at the active site of thermolysin are suggested to play a significant role in the remarkable activation by salts.

Studies on hydrolysis of chiral, achiral and racemic alcohol esters with pseudomonas cepacia lipase : mechanism of stereospecificity of the enzyme

Abstract: Steady-state kinetics of Pseudomonas cepacia lipase-catalysed hydrolysis of five analogous chiral and achiral substrates, i.e. (R)- and (S)-1-methyl-2-(4-phenoxyphenoxy)ethyl acetates (R)- and (S)-1a, (R)- and (S)-2-methyl-2-(4-phenoxyphenoxy)ethyl acetates (R)- and (S)-1b and 2-(4-phenoxyphenoxy)ethyl acetate 1c, were investigated in sufficiently emulsified reaction mixtures of water-insoluble substrates. The apparent Michaelis constant Km values were identical for all the esters, and no nonproductive binding was observed in these substrates. The apparent catalytic constants kcat were found to reflect the leaving abilities of the alcoholate ions for the fast-reacting enantiomers. These observations, based on the findings that acyl-enzyme intermediate formation was rate-determining in the overall reaction, strongly suggested that all the substrates are bound to the enzyme in the same manner whether or not the alcohol moiety has a medium-sized substituent LM at the stereocentre and that the breakdown of a tetrahedral intermediate is rate-determining in the acylation of the enzyme. Time courses were also studied for the hydrolysis of racemic 1-ethyl-2-(4-phenoxyphenoxy)ethyl acetate 1d together with 1a, 1b and 1c. The enzyme distinguished (R)-1d from its antipode perfectly and hydrolysed only the (R)-enantiomer. These results were interpreted to indicate that LM of the slow-reacting enantiomer is positioned close to the imidazole ring of the catalytic His and hinders NIµ2 of the residue from forming a weak interaction with O1 of the leaving alcohol and that the breakdown of the tetrahedral intermediate is thus inhibited.

A single amino acid substitution in the pleckstrin homology domain of phospholipase C δ1 enhances the rate of substrate hydrolysis

Abstract: The pleckstrin homology (PH) domain has been postulated to serve as an anchor for enzymes that operate at a lipid/water interface. To understand further the relationship between the PH domain and enzyme activity, a phospholipase C (PLC) delta1/PH domain enhancement-of-activity mutant was generated. A lysine residue was substituted for glutamic acid in the PH domain of PLC delta1 at position 54 (E54K). Purified native and mutant enzymes were characterized using a phosphatidylinositol 4,5-bisphosphate (PI(4, 5)P2)/dodecyl maltoside mixed micelle assay and kinetics measured according to the dual phospholipid model of Dennis and co-workers (Hendrickson, H. S., and Dennis, E. A. (1984) J. Biol. Chem. 259, 5734-5739; Carmen, G. M., Deems, R. A., and Dennis, E. A. (1995) J. Biol. Chem. 270, 18711-18714). Our results show that both PLC delta1 and E54K bind phosphatidylinositol bisphosphate cooperatively (Hill coefficients, n = 2.2 +/- 0.2 and 2.0 +/- 0.1, respectively). However, E54K shows a dramatically increased rate of (PI(4, 5)P2)-stimulated PI(4,5)P2 hydrolysis (interfacial Vmax for PLC delta1 = 4.9 +/- 0.3 micromol/min/mg and for E54K = 31 +/- 3 micromol/min/mg) as well as PI hydrolysis (Vmax for PLC delta1 = 27 +/- 3.4 nmol/min/mg and for E54K = 95 +/- 12 nmol/min/mg). In the absence of PI(4,5)P2 both native and mutant enzyme hydrolyze PI at similar rates. E54K also has a higher affinity for micellar substrate (equilibrium dissociation constant, Ks = 85 +/- 36 microM for E54K and 210 +/- 48 microM for PLC delta1). Centrifugation binding assays using large unilamelar phospholipid vesicles confirm that E54K binds PI(4,5)P2 with higher affinity than native enzyme. E54K is more active even though the interfacial Michaelis constant (Km) for E54K (0.034 +/- 0.01 mol fraction PI(4,5)P2) is higher than the Km for native enzyme (0.012 +/- 0.002 mol fraction PI(4,5)P2). D-Inositol trisphosphate is less potent at inhibiting E54K PI(4,5)P2 hydrolysis compared with native enzyme. These results demonstrate that a single amino acid substitution in the PH domain of PLC delta1 can dramatically enhance enzyme activity. Additionally, the marked increase in Vmax for E54K argues for a direct role of PH domains in regulating catalysis by allosteric modulation of enzyme structure.

Purification and characterization of phosphofructokinase from the yeast Kluyveromyces lactis

Abstract: Phosphofructokinase from Kluyveromyces lactis was purified by 180-fold enrichment, elaborating the following steps: cell disruption, polyethylene glycol precipitation, affinity chromatography, size exclusion chromatography on Sepharose 6B and on Bio-Sil SEC 400 and ion exchange chromatography. The homogeneous enzyme exhibits a molecular mass of 845 +/- 20 kDa as determined by sedimentation equilibrium measurements and a specific activity of 100 units/mg protein. The apparent sedimentation coefficient was found to be s20,c = 20.7 +/- 0.6 S and no significant dependence on the protein concentration was observed in a range from 0.2 to 8 mg protein/ml. Sodium dodecyl sulfate-polyacrylamide gel electrophoresis revealed two bands corresponding to molecular masses of 119 +/- 5 kDa and 102 +/- 5 kDa, respectively. Thus, the enzyme assembles as octamer composed of two types of subunits. From Western blot analysis applying subunit-specific monoclonal antibodies raised against Saccharomyces cerevisiae phosphofructokinase and from the determination of the N-terminal amino acid sequence, the conclusion was drawn that the 102 kDa-subunit corresponds to the beta-subunit of the S. cerevisiae enzyme. In contrast to bakers' yeast phosphofructokinase, the K. lactis enzyme exhibits no cooperativity with respect to the substrate fructose 6-phosphate. Both activators AMP and fructose 2,6-bisphosphate decrease the Michaelis constant with respect to this substrate. The enzyme from K. lactis is also inhibited by ATP. Fructose 2,6-bisphosphate or AMP diminish the ATP-inhibition. In contrast to the phosphofructokinase from S. cerevisiae, where fructose 2,6-bisphosphate turned out to be more efficient than AMP, both activators exert similar effects on the K. lactis enzyme.

Predicting the performance of immobilized enzyme reactors using reversible Michaelis–Menten kinetics

Abstract: A general mathematical model is developed in the present work for predicting the steady state performance of immobilized enzyme reactor performing reversible Michaelis - Menten kinetics. The model takes into account the effect of external diffusional limitations, the axial dispersion and the equilibrium constant on reactor performance quantified as relative substrate conversion and yield. The performance of reactor is characterized using the dimensionless parameters of Damkohler number, Stanton number, Peclet number, the equilibrium constant and the dimensionless input substrate concentration. The reactor performance is described for the two extreme cases of plug flow reactor (PFR) and continuous stirred tank reactor (CSTR) in addition to the intermediate case of dispersed plug flow reactor (DPFR). The performance of reactor is compared for the two cases of zero order and reversible first order kinetics.

Purification and characterization of a thermostable alkaline phosphatase produced by Thermus caldophilus GK24

Abstract: The thermophilic and thermostable alkaline phosphatase was purified to near homogeneity from the osmotic lysis of Thermus caldophilus GK24, The purified enzyme had an apparent molecular mass of 108, 000 Da and consisted of two subunits of 54,000 Da. lsoelectric-focusing analysis of the purified enzyme showed a pi of 7.3. The enzyme contained two Cys residues, and its amino acids composition was quite different from that of Thermus aquaticus YT-1 alkaline phosphatase and Escherichia coli alkaline phosphatase, The optimum pH and temperature of the enzyme were 11.0-11.5 and respectively. The enzyme was stable in the pH range of 9.0-12.0 at for 36 h. and the half-life at (pH 11.0) was 6 h. The enzyme was activated by and inhibited by EDTA. With as the substrate, the enzyme had a Michaelis constant of , The enzyme preferentially hydrolyzed the phosphomonoester bond of AMP in ribonucleotides and glycerophosphate.

A lung retention model based on Michaelis-Menten-like kinetics.

Abstract: A Michaelis-Menten (MM)-like kinetic model for pulmonary clearance and retention of insoluble dusts was developed and validated by comparing our predictions with experimental data from F344 rats. P...

Novel Immobilization of Enzyme in Molecular Assembly of Nonionic Surfactant Adsorbed on Silica Gel

Abstract: As a novel procedure to immobilize enzymes, lysozyme was dissolved in the molecular assembly of the nonionic surfactant Triton X-100 adsorbed on silica gel. The adsorption isotherms of Triton X-100 on silica gel, and of lysozyme in the molecular assembly of adsorbed Triton X-100 on silica gel, were obtained. The isotherm for the latter are significantly influenced by pH and buffering agents, while the isotherms for the former are not. Moreover, the adsorption of lysozyme was affected by the ionic strength of the buffering agents. Leakage of immobilized lysozyme is influenced by pH and temperature; it is found that much lysozyme leaked when pH and temperature were low. However, under limited conditions the immobilized enzyme is very stable. The immobilized lysozyme was used in the enzymatic hydrolysis reaction of the water-soluble chitin derivative glycol chitin. The enzymatic reaction obeys the Michaelis-Menten mechanism and the values of kinetic parameter, Michaelis constant Km and maximum velocity Vmax, are estimated. The apparent activation energy Ea is also obtained.

Acetylcholinesterase activity of normal and diabetic human erythrocyte membranes: The effect of oxidative agents

Abstract: The activity characteristics of membrane acetylcholinesterase from red blood cells of diabetic patients are very different from those of healthy donors: the limiting enzyme reaction rate is 17.2 +/- 0.8 mumol acetylthiocholine per ml packed cells per min compared with 13.1 +/- 0.8 mumol for control cells. This Michaelis constants for substrate are the same: 0.061 +/- 0.007 mM for diabetic and 0.061 +/- 0.004 mM for control cells. Cell exposure to oxidative agent (t-butyl hydroperoxide) significantly changes the enzyme activity parameters. The limiting enzyme reaction rate increases but the affinity for the substrate decreases at lower oxidant concentrations (up to 0.1 mM for the "diabetic" erythrocytes and up to 0.4 mM for the control ones). At higher oxidant concentrations both the limiting reaction rate and the Michaelis constant decrease. The susceptibility of erythrocyte membranes of diabetic patients to oxidative stress is much higher in comparison with control erythrocyte membranes.

A1-Pyrroline-5-Carboxylate Dehydrogenase from Cultured CeIIs of Potatol

Abstract: A1-Pyrroline-5-carboxylate (P5C) dehydrogenase (EC 1.5.1.1 2), the second enzyme in the proline catabolic pathway and a catalyst for the oxidation of P5C to glutamate, was purified from cultured potato (Solanum tuberosum L. var Desiree) cells. Homogeneous enzyme preparations were obtained by a three-step procedure that used anion-exchange, adsorption, and substrate elution chromatography. A 1600-fold purification was achieved, with a recovery of one-third of the initial activity. lhe purified enzyme was characterized with respect to structural, kinetic, and biochemical properties. It appeared to be an a-4 tetramer with subunits of an apparent molecular mass of about 60 kD and had a mildly acidic isoelectric point value. Potato P5C dehydrogenase had Michaelis constant values of 0.11 and 0.46 mM for NAD+ and PSC, respectively. Although NAD+ was the preferred electron acceptor, NADP+ also yielded an unusually high rate, and thus was found to serve as a substrate. Maximal activity was observed at pH values in the 7.3 to 8.3 range, and was progressively inhibited by chloride ions, a finding that strengthens recent suggestions that hyperosmotic stress negatively modulates in vivo proline oxidation. In a vast array of organisms ranging from bacteria to mammals, Pro is oxidized to glutamate through just two steps involving catalysis by Pro and P5C dehydrogenases (EC 1.4.3 and EC 1.5.1.12, respectively). In enterobacteria a multifunctional enzyme associated with the cytoplasmic membrane was shown to exert both activities (Brown and Wood, 1992; Ling et al., 1994), whereas for a11 other species tested so far, the activities depended on two distinct proteins. This discrepancy might reflect differences in Arg catabolism, which may take place via P5C directly from Orn, through pyrroline-2-carboxylate and Pro, or separately through the urea cycle (Fig. 1). Thus, the presence of a distinct P5C dehydrogenase could enable better, simultaneous regulation of the two convergent pathways (Mazelis, 1980; Phang, 1985). Subcellular fractionation studies and sequence analyses accounted for a mitochondrial localization of P5C dehydrogenase in higher plants, yeasts, and mammals (Elthon and Stewart, 1981; Brandriss and

Electrostatic effect on apparent kinetic parameters in a packed-bed immobilized enzyme reactor

Abstract: The effect of electrostatic field on apparent kinetic parameters in a packed-bed immobilized enzyme reactor was investigated using a mathematical model. The relationship between the dimensionless concentration of substrate consumed in the reactor and the logarithm of the unconverted fraction of substrate at the reactor outlet was nonlinear and changed remarkably according to the magnitude of electrostatic potential and the sign of charges that carry the support and substrate. For the opposite sign of these charges, the apparent Michaelis constant was less than its intrinsic value in the region of high substrate concentration, which reflects a promoting effect on the enzyme reaction by the electrostatic attraction.

Studies on Hydrolysis of Chiral, Achiral and Racemic Alcohol Esters with Pseudomonas cepacia Lipase: Mechanism of Stereospecificity of the Enzyme.

Abstract: Steady-state kinetics of Pseudomonas cepacia lipase-catalysed hydrolysis of five analogous chiral and achiral substrates, i.e. (R)- and (S)-1-methyl-2-(4-phenoxyphenoxy)ethyl acetates (R)- and (S)-1a, (R)- and (S)-2-methyl-2-(4-phenoxyphenoxy)ethyl acetates (R)- and (S)-1b and 2-(4-phenoxyphenoxy)ethyl acetate 1c, were investigated in sufficiently emulsified reaction mixtures of water-insoluble substrates. The apparent Michaelis constant Km values were identical for all the esters, and no nonproductive binding was observed in these substrates. The apparent catalytic constants kcat were found to reflect the leaving abilities of the alcoholate ions for the fast-reacting enantiomers. These observations, based on the findings that acyl-enzyme intermediate formation was rate-determining in the overall reaction, strongly suggested that all the substrates are bound to the enzyme in the same manner whether or not the alcohol moiety has a medium-sized substituent LM at the stereocentre and that the breakdown of a tetrahedral intermediate is rate-determining in the acylation of the enzyme. Time courses were also studied for the hydrolysis of racemic 1-ethyl-2-(4-phenoxyphenoxy)ethyl acetate 1d together with 1a, 1b and 1c. The enzyme distinguished (R)-1d from its antipode perfectly and hydrolysed only the (R)-enantiomer. These results were interpreted to indicate that LM of the slow-reacting enantiomer is positioned close to the imidazole ring of the catalytic His and hinders NIµ2 of the residue from forming a weak interaction with O1 of the leaving alcohol and that the breakdown of the tetrahedral intermediate is thus inhibited.

Acidic glutaminase and its use

Abstract: PROBLEM TO BE SOLVED: To provide a new enzyme produced by culturing a microorganism or from a commercially available enzyme preparation, etc, having characteristic action, optimum pH, stable pH range, substrate specificity, optimum temperature, stable temperature, etc, and effective for improving the taste of a glutamine- containing acidic food by the treatment of the food with the enzyme SOLUTION: The objective new acidic glutaminase hydrolyzes L-glutamine into L-glutamic acid and ammonia, has optimum pH of 3-6 and a stable pH range of 25-9, is active to decompose L- and D-glutamine and butoxycarbonylated glutamine and inactive for the decomposition of L- and D-asparagine, has a Km value (Michaelis constant) to L-glutamine of 32mM at 37 degC and pH40 (in acetic acid buffer solution) and an optimum temperature of 70 degC by the reaction at pH 40 for 30min and is stable up to 55 degC after 1hr The enzyme is useful eg for improving the taste of an acidic food such as tomato The enzyme can be produced either by culturing a microorganism capable of producing the enzyme or by separating from a commercially available enzymatic preparation and purifying the separated substance

Oxygen Diffusion in Tissue Preparations with Michaelis-Menten Kinetics

Abstract: A model is introduced for the oxygen consumption in thin vital tissue preparation. The steady uptake kinetics is modelled by a Michaelis-Menten form and for this case it proved that the resulting boundary value problem admits a unique solution for those parameter ranges typical of related physiological experiments. This solution is compared with Otto Warburg's hyperoxia model and with a hypoxra model. Uselul and easily computed approximations are derived for the minimum oxygen supply across the tissue and some numerical solutions of the governing equations are discussed. i' 1997 Academic Press Limired

Why nature has elected Michaelis‐Menten kinetics for enzymes: a tentative rationale from variational calculus

Abstract: The kinetic performance of enzymes, the catalysts designed by nature to accelerate the chemical reactions that support life, has traditionally been described in terms of a rate expression first derived by Michaelis and Menten in the beginning ofthis century. Why nature has selected such kinetic behaviour remains, however, a mystery. A tentative rationale based on Euler's equation was developed and, after having eliminated functional forms due to physico- chemical unfeasibility, a final open-form objective function (written as an infinite series and including dependencies on the substrate concentration, on the reaction rate, and on the derivative thereof with respect to concentration) is found. The integral of such an objective function is maximized by Michaelis- Menten kinetics and yields its maximum value when the upper integration limit is roughly equal to the Michaelis- Menten constant.