Extending the kinetic solution of the classic Michaelis-Menten model of enzyme action

The principal aim of studies of enzyme-mediated reactions has been to provide comparative and quantitative information on enzyme-catalyzed reactions under distinct conditions. The classic Michaelis-Menten model (Biochem Zeit 49:333, 1913) for enzyme kinetic has been widely used to determine important parameters involved in enzyme catalysis, particularly the Michaelis-Menten constant (K (M) ) and the maximum velocity of reaction (V (max) ). Subsequently, a detailed treatment of the mechanisms of enzyme catalysis was undertaken by Briggs-Haldane (Biochem J 19:338, 1925). These authors proposed the steady-state treatment, since its applicability was constrained to this condition. The present work describes an extending solution of the Michaelis-Menten model without the need for such a steady-state restriction. We provide the first analysis of all of the individual reaction constants calculated analytically. Using this approach, it is possible to accurately predict the results under new experimental conditions and to characterize and optimize industrial processes in the fields of chemical and food engineering, pharmaceuticals and biotechnology.

Enzyme deactivation in fixed bed reactors with michaelis-menten kinetics

Rate expression for enzyme poisoning which are consistent with a Michaelis-Menten main reaction are used to analyze the performance of a fixed bed reactor containing immobilized enzyme. When enzyme deactivation results from the irreversible bonding of a product molecule to an existing substrate-enzyme complex, it is shown that minimum enzyme activity can occur in the interior of the bed, well away from the ends. This suggests that bed sectioning techniques may enable direct evaluation of fundamental poisoning mechanisms.

A finite integral transform technique for solving the diffusion-reaction equation with Michaelis-Menten kinetics

An approximate analytical technique employing a finite integral transform is developed to solve the reaction diffusion problem with Michaelis-Menten kinetics in a solid of general shape. A simple infinite series solution for the substrate concentration is obtained as a function of the Thiele modulus, modified Sherwood number, and Michaelis constant. An iteration scheme is developed to bring the approximate solution closer to the exact solution. Comparison with the known exact solutions for slab geometry (quadrature) and numerically exact solutions for spherical geometry (orthogonal collocation) shows excellent agreement for all values of the Thiele modulus and Michaelis constant.

Modelling the uptake and growth kinetics of Penicillium glabrum in a tannic acid-containing solid-state fermentation for tannase production

A mathematical growth model for the batch solid-state fermentation process for fungal tannase production was developed and tested experimentally. The unstructured model describes the uptake and growth kinetics of Penicillium glabrum in an impregnated polyurethane foam substrate system. In general, good agreement between the experimental data and model simulations was obtained. Biomass, tannase and spore production are described by logistic kinetics with a time delay between biomass production and tannase and spore formation. Possible induction mechanisms for the latter are proposed. Hydrolysis of tannic acid, the main carbon source in the substrate system, is reasonably well described with Michaelis-Menten kinetics with time-varying enzyme concentration but a more complex reaction mechanism is suspected. The metabolism of gallic acid, a tannase-hydrolysis product of tannic acid, was shown to be growth limiting during the main growth phase. (c) 2004 Elsevier Ltd. All rights reserved.

In vitro metabolism study of a new nitrosyl ruthenium complex [Ru(NH center dot NHq)(terpy)NO](3+) nitric oxide donor using rat microsomes

A new nitrosyl ruthenium complex [Ru(NH center dot NHq)(terpy)NO](3+) nitric oxide donor was recently developed and due to its excellent vasodilator activity, it has been considered as a potential drug candidate. Drug metabolism is one of the main parameters that should be evaluated in the early drug development, so the biotransformation of this complex by rat hepatic microsomes was investigated. In order to perform the biotransformation study, a simple, sensitive and selective HPLC method was developed and carefully validated. The parameters evaluated in the validation procedure were: linearity, recovery, precision, accuracy, selectivity and stability. Except for the stability study, all the parameters evaluated presented values below the recommended by FDA guidelines. The stability study showed a time-dependent degradation profile. After method validation, the biotransformation study was accomplished and the kinetic parameters were determined. The biotransformation study obeyed the Michaelis-Menten kinetics. The V(max) and K(m) were, respectively, 0.1625 +/- 0.010 mu mol/mg protein/min and 79.97 +/- 11.52 mu M. These results indicate that the nitrosyl complex is metabolized by CYP450. (C) 2009 Elsevier Inc. All rights reserved.

Approximate analytical solutions for porous catalysts with nonuniform activity

Using a novel finite integral transform technique, the problem of diffusion and chemical reaction in a porous catalyst with general activity profile is investigated theoretically. Analytical expressions for the effectiveness factor are obtained for pth order and Michaelis-Menten kinetics. Perturbation methods are employed to provide useful asymptotic solutions for large or small values of Thiele modulus and Biot number.

Development of a method to investigate the hydrolysis of xenobiotic esters by a Mycobacterium smegmatis homogenate.

One of the main problems in combating tuberculosis is caused by a poor penetration of drugs into the mycobacterial cells. A prodrug approach via activation inside mycobacterial cells is a possible strategy to overcome this hurdle and achieve efficient drug uptake. Esters are attractive candidates for such a strategy and we and others communicated previously the activity of esters of weak organic acids against mycobacteria. However very little is known about ester hydrolysis by mycobacteria and no biological model is available to study the activation of prodrugs by these microorganisms. To begin filling this gap, we have embarked in a project to develop an in vitro method to study prodrug activation by mycobacteria using Mycobacterium smegmatis homogenates. Model ester substrates were ethyl nicotinate and ethyl benzoate whose hydrolysis was monitored and characterized kinetically. Our studies showed that in M. smegmatis most esterase activity is associated with the soluble fraction (cytosol) and is preserved by storage at 5°C or at room temperature for one hour, or by storage at -80°C up to one year. In the range of homogenate concentrations studied (5-80% in buffer), k(obs) varied linearly with homogenate concentration for both substrates. We also found that the homogenates showed Michaelis-Menten kinetics behavior with both prodrugs. Since ethyl benzoate is a good substrate for the mycobacterial esterases, this compound can be used to standardize the esterasic activity of homogenates, allowing results of incubations of prodrugs with homogenates from different batches to be readily compared.

Catabolic ornithine carbamoyltransferase of Pseudomonas aeruginosa. Importance of the N-terminal region for dodecameric structure and homotropic carbamoylphosphate cooperativity.

Pseudomonas aeruginosa has an anabolic (ArgF) and a catabolic (ArcB) ornithine carbamoyltransferase (OTCase). Despite extensive sequence similarities, these enzymes function unidirectionally in vivo. In the dodecameric catabolic OTCase, homotropic cooperativity for carbamoylphosphate strongly depresses the anabolic reaction; the residue Glu1O5 and the C-terminus are known to be essential for this cooperativity. When Glu1O5 and nine C-terminal amino acids of the catabolic OTCase were introduced, by in vitro genetic manipulation, into the closely related, trimeric, anabolic (ArgF) OTCase of Escherichia coli, the enzyme displayed Michaelis-Menten kinetics and no cooperativity was observed. This indicates that additional amino acid residues are required to produce homotropic cooperativity and a dodecameric assembly. To localize these residues, we constructed several hybrid enzymes by fusing, in vivo or in vitro, the E. coli argF gene to the P. aeruginosa arcB gene. A hybrid enzyme consisting of 101 N-terminal ArgF amino acids fused to 233 C-terminal ArcB residues and the reciprocal ArcB-ArgF hybrid were both trimers with little or no cooperativity. Replacing the seven N-terminal residues of the ArcB enzyme by the corresponding six residues of E. coli ArgF enzyme produced a dodecameric enzyme which showed a reduced affinity for carbamoylphosphate and an increase in homotropic cooperativity. Thus, the N-terminal amino acids of catabolic OTCase are important for interaction with carbamoylphosphate, but do not alone determine dodecameric assembly. Hybrid enzymes consisting of either 26 or 42 N-terminal ArgF amino acids and the corresponding C-terminal ArcB residues were both trimeric, yet they retained some homotropic cooperativity. Within the N-terminal ArcB region, a replacement of motif 28-33 by the corresponding ArgF segment destabilized the dodecameric structure and the enzyme existed in trimeric and dodecameric states, indicating that this region is important for dodecameric assembly. These findings were interpreted in the light of the three-dimensional structure of catabolic OTCase, which allows predictions about trimer-trimer interactions. Dodecameric assembly appears to require at least three regions: the N- and C-termini (which are close to each other in a monomer), residues 28-33 and residues 147-154. Dodecameric structure correlates with high carbamoylphosphate cooperativity and thermal stability, but some trimeric hybrid enzymes retain cooperativity, and the dodecameric Glu1O5-->Ala mutant gives hyperbolic carbamoylphosphate saturation, indicating that dodecameric structure is neither necessary nor sufficient to ensure cooperativity.

Expression of the gene encoding the high-Km glucose transporter 2 by the early postimplantation mouse embryo is essential for neural tube defects associated with diabetic embryopathy.

AIMS/HYPOTHESIS: Excess glucose transport to embryos during diabetic pregnancy causes congenital malformations. The early postimplantation embryo expresses the gene encoding the high-Km GLUT2 (also known as SLC2A2) glucose transporter. The hypothesis tested here is that high-Km glucose transport by GLUT2 causes malformations resulting from maternal hyperglycaemia during diabetic pregnancy. MATERIALS AND METHODS: Glut2 mRNA was assayed by RT-PCR. The Km of embryo glucose transport was determined by measuring 0.5-20 mmol/l 2-deoxy[3H]glucose transport. To test whether the GLUT2 transporter is required for neural tube defects resulting from maternal hyperglycaemia, Glut2+/- mice were crossed and transient hyperglycaemia was induced by glucose injection on day 7.5 of pregnancy. Embryos were recovered on day 10.5, and the incidence of neural tube defects in wild-type, Glut2+/- and Glut2-/- embryos was scored. RESULTS: Early postimplantation embryos expressed Glut2, and expression was unaffected by maternal diabetes. Moreover, glucose transport by these embryos showed Michaelis-Menten kinetics of 16.19 mmol/l, consistent with transport mediated by GLUT2. In pregnancies made hyperglycaemic on day 7.5, neural tube defects were significantly increased in wild-type embryos, but Glut2+/- embryos were partially protected from neural tube defects, and Glut2-/- embryos were completely protected from these defects. The frequency of occurrence of wild-type, Glut2+/- and Glut2-/- embryos suggests that the presence of Glut2 alleles confers a survival advantage in embryos before day 10.5. CONCLUSIONS/INTERPRETATIONS: High-Km glucose transport by the GLUT2 glucose transporter during organogenesis is responsible for the embryopathic effects of maternal diabetes.

The cataract and glucosuria associated monocarboxylate transporter MCT12 is a new creatine transporter.

Creatine transport has been assigned to creatine transporter 1 (CRT1), encoded by mental retardation associated SLC6A8. Here, we identified a second creatine transporter (CRT2) known as monocarboxylate transporter 12 (MCT12), encoded by the cataract and glucosuria associated gene SLC16A12. A non-synonymous alteration in MCT12 (p.G407S) found in a patient with age-related cataract (ARC) leads to a significant reduction of creatine transport. Furthermore, Slc16a12 knockout (KO) rats have elevated creatine levels in urine. Transport activity and expression characteristics of the two creatine transporters are distinct. CRT2 (MCT12)-mediated uptake of creatine was not sensitive to sodium and chloride ions or creatine biosynthesis precursors, breakdown product creatinine or creatine phosphate. Increasing pH correlated with increased creatine uptake. Michaelis-Menten kinetics yielded a Vmax of 838.8 pmol/h/oocyte and a Km of 567.4 µm. Relative expression in various human tissues supports the distinct mutation-associated phenotypes of the two transporters. SLC6A8 was predominantly found in brain, heart and muscle, while SLC16A12 was more abundant in kidney and retina. In the lens, the two transcripts were found at comparable levels. We discuss the distinct, but possibly synergistic functions of the two creatine transporters. Our findings infer potential preventive power of creatine supplementation against the most prominent age-related vision impaired condition.

Estudo da dissolução oxidativa microbiológica de uma complexa amostra mineral contendo pirita (FeS2), Pirrotita (Fe1-xS) e Molibdenita (MoS2)

This work aims to study the oxidation of a complex molybdenite mineral which contains pyrite and pyrrotite, by Acidithiobacillus ferrooxidans. This study was performed by respirometric essays and bioleaching in shake flasks. Respirometric essays yielded the kinetics of mineral oxidation. The findings showed that sulfide oxidation followed classical Michaelis-Menten kinetics. Bioleaching in shake flasks allowed evaluation of chemical and mineralogical changes resulting from sulfide oxidation. The results demonstrated that pyrrotite and pyrite were completely oxidized in A. ferrooxidans cultures whereas molybdenite was not consumed. These data indicated that molybdenite was the most recalcitrant sulfide in the sample.

Delineamentos experimentais eficientes para estudos de cinética química

In this paper we show how to obtain efficient designs of experiments for fitting Michaelis-Menten and Hill equations useful in chemical studies. The search of exact D-optimal designs by using local and pseudo-Bayesian approaches is considered. Optimal designs were compared to those commonly used in practice using an efficiency measure and theoretical standard errors of the kinetic parameter estimates. In conclusion, the D-optimal designs based on the Hill equation proved efficient for estimating the parameters of both models. Furthermore, these are promising with respect to practical issues, allowing efficient estimation as well as goodness-of-fit tests and comparisons between some kinetic models.

The regulation of oat coleoptile phosphoenolpyruvate carboxylase and malic enzyme by Hâ ½ and metabolites : kinetic evidence for and against a cytosolic pH-stat

Phosphoenolpyruvate carboxylase (PEPC) and malic enzyme activities in soluble protein extracts of Avena coleoptiles were investigated to determine whether their kinetics were consistent with a role in cytosol pH regulation. Malic enzyme activity was specific for NADP+ and Mn2+. Maximal labelled product formation from [14C]-substrates required the presence of all coenzymes, cofactors and substrates. Plots of rate versus malate concentration, and linear transformations there- 2 of, indicated typical Michaelis-Menten kinetics at non-saturating malate levels and substrate inhibition at higher malate levels. pH increases between 6.5 and 7.25 increased near-optimal activity, decreased the degree of substrate inhibition and the Kmapp(Mn2+) but did not affect the Vmax or Kmapp(malate). Transformed data of PEPC activity demonstrated non-linear plots indicative of non-Michaelian kinetics. pH increases between 7.0 and 7.6 increased the Vmax and decreased the Km app (Mg2+) but did not affect the Kmapp(PEP). Various carboxylic acids and phosphorylated sugars inhibited PEPC and malic enzyme activities, and these effects decreased with pH increases. Metabolite inhibited malic enzyme activity was non-competitive and resulted mainly from Mn2+ chelation. In contrast, metabolite inhibited PEPC activity was unique for each compound tested, being variously dependent on the PEP concentration and the pH employed. These results indicate that fluctuations in pH and metabolite levels affect PEPC and malic enzyme activities similarly and that 3 the in vitro properties of PEPC are consistent with its proposed role in a pH-stat, whereas the in vitro properties of the malic enzyme cannot be interpreted in terms of a role in pH regulation.

Kinetic Parameters of Thymidine Kinase and DNA Synthesis During Liver Regeneration: Role Ofthyroid Hormones

The role of thyroid hormones in DNA synthesis and in the activity of Thymidille kinase (TK), a key regulatory enzyme of DNA synthesis was studied in proliferating hepatocytes in vivo. Liver regeneration after partial hepatectomy was used as a model for controlled cell division in rats having different thyroid status - euthyroid, hypothyroid and 3,3',5'-triiodo-L-thyronine (T))-heated hypothyroid. Partial hepatectomy caused a significant elevation of DNA synthesis (p<0.01) in all the three groups compared to their sham-operated counterparts. Hypothyroid liepatectomised animals showed significantly lower (p<0.01) level of DNA synthesis than euthyroid hepatectomised animals. A single subcutaneous close of 1'3 to hypothyroid shamoperated animals resulted in a significant increase (p<0.01) of DNA synthesis in the intact liver. 17tis was comparable to the level of DNA synthesis occurring in regenerating liver of euthyroid animals. In hypothyroid hepatectomised animals, "1'3 showed an additive effect on l)NA synthesis and this group exhibited maximum level of DNA synthesis (p<0.0I ). Studies of the kinetic parameters of TK show that the Michelis-Menten constant, (K111) of TK for thymidine was altered by the thyroid status. K11 increased significantly (p<0.01) in untreated hypothyroid animals when compared to the euthyroid rats. '13 treatment of hypothyroid animals reversed this effect and this group showed the lowest value for K111 (p<0.01). Thus our results indicate that thyroid hormones can influence DNA synthesis during liver regeneration and they may regulate the activity of enzymes such as 17rymidine kinase which are important for DNA synthesis and hence cell division.

Modelling the movement and survival of the root-feeding clover weevil, Sitona lepidus, in the root-zone of white clover

White clover (Trifolium repens) is an important pasture legume but is often difficult to sustain in a mixed sward because, among other things, of the damage to roots caused by the soil-dwelling larval stages of S. lepidus. Locating the root nodules on the white clover roots is crucial for the survival of the newly hatched larvae. This paper presents a numerical model to simulate the movement of newly hatched S. lepidus larvae towards the root nodules, guided by a chemical signal released by the nodules. The model is based on the diffusion-chemotaxis equation. Experimental observations showed that the average speed of the larvae remained approximately constant, so the diffusion-chernotaxis model was modified so that the larvae respond only to the gradient direction of the chemical signal but not its magnitude. An individual-based lattice Boltzmann method was used to simulate the movement of individual larvae, and the parameters required for the model were estimated from the measurement of larval movement towards nodules in soil scanned using X-ray microtomography. The model was used to investigate the effects of nodule density, the rate of release of chemical signal, the sensitivity of the larvae to the signal, and the random foraging of the larvae on the movement and subsequent survival of the larvae. The simulations showed that the most significant factors for larval survival were nodule density and the sensitivity of the larvae to the signal. The dependence of larval survival rate on nodule density was well fitted by the Michealis-Menten kinetics. (c) 2005 Elsevier B.V All rights reserved.