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.

Experimental design methodologies for the identification of Michaelis-Menten type kinetics

The main objective of this work was to investigate the application of experimental design techniques for the identification of Michaelis-Menten kinetic parameters. More specifically, this study attempts to elucidate the relative advantages/disadvantages of employing complex experimental design techniques in relation to equidistant sampling when applied to different reactor operation modes. All studies were supported by simulation data of a generic enzymatic process that obeys to the Michaelis-Menten kinetic equation. Different aspects were investigated, such as the influence of the reactor operation mode (batch, fed-batch with pulse wise feeding and fed-batch with continuous feeding) and the experimental design optimality criteria on the effectiveness of kinetic parameters identification. The following experimental design optimality criteria were investigated: 1) minimization of the sum of the diagonal of the Fisher information matrix (FIM) inverse (A-criterion), 2) maximization of the determinant of the FIM (D-criterion), 3) maximization of the smallest eigenvalue of the FIM (E-criterion) and 4) minimization of the quotient between the largest and the smallest eigenvalue (modified E-criterion). The comparison and assessment of the different methodologies was made on the basis of the Cramér-Rao lower bounds (CRLB) error in respect to the parameters vmax and Km of the Michaelis-Menten kinetic equation. In what concerns the reactor operation mode, it was concluded that fed-batch (pulses) is better than batch operation for parameter identification. When the former operation mode is adopted, the vmax CRLB error is lowered by 18.6 % while the Km CRLB error is lowered by 26.4 % when compared to the batch operation mode. Regarding the optimality criteria, the best method was the A-criterion, with an average vmax CRLB of 6.34 % and 5.27 %, for batch and fed-batch (pulses), respectively, while presenting a Km’s CRLB of 25.1 % and 18.1 %, for batch and fed-batch (pulses), respectively. As a general conclusion of the present study, it can be stated that experimental design is justified if the starting parameters CRLB errors are inferior to 19.5 % (vmax) and 45% (Km), for batch processes, and inferior to 42 % and to 50% for fed-batch (pulses) process. Otherwise equidistant sampling is a more rational decision. This conclusion clearly supports that, for fed-batch operation, the use of experimental design is likely to largely improve the identification of Michaelis-Menten kinetic parameters.

Uso de equações lineares na determinação dos parâmetros de Michaelis-Menten

The Michaelis-Menten equation is used in many biochemical and bioinorganic kinetic studies involving homogeneous catalysis. Otherwise, it is known that determination of Michaelis-Menten parameters K M, Vmax, and k cat by the well-known Lineweaver-Burk double reciprocal linear equation does not produce the best values for these parameters. In this paper we present a discussion on different linear equations which can be used to calculate these parameters and we compare their results with the values obtained by the more reliable nonlinear least-square fit.

Electrogravimetric Real-Time and in Situ Michaelis-Menten Enzimatic Kinetics: Progress Curve of Acetylcholinesterase Hydrolysis

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Delineamentos D-ótimos para os modelos de Michaelis-Menten e de Hill

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Extraction, purification and biochemical characterization of a peroxidase from Copaifera langsdorffii leaves

The aim of this work is to obtain, purify and characterize biochemically a peroxidase from Copaifera langsdorffii leaves (COP). COP was obtained by acetone precipitation followed by ion-exchange chromatography. Purification yielded 3.5% of peroxidase with the purification factor of 46.86. The COP optimum pH is 6.0 and the temperature is 35 ºC. COP was stable in the pH range of 4.5 to 9.3 and at temperatures below 50.0 ºC. The apparent Michaelis-Menten constants (Km) for guaiacol and H2O2 were 0.04 mM and 0.39 mM respectively. Enzyme turnover was 0.075 s-1 for guaiacol and 0.28 s-1 for hydrogen peroxide. Copaifera langsdorffii leaves showed to be a rich source of active peroxidase (COP) during the whole year. COP could replace HRP, the most used peroxidase, in analytical determinations and treatment of industrial effluents at low cost.

Ensaio in vitro da enzima nitrato redutase e efeito da disponibilidade de nitrato e fosfato em variantes pigmentares de Hypnea musciformis (Wulfen) J. V. Lamour. (Gigartinales, Rhodophyta)

A enzima nitrato redutase (NR) catalisa a redução do nitrato a nitrito e controla a taxa de assimilação do nitrato. O ensaio in vitro da nitrato redutase foi otimizado para a linhagem selvagem (marrom, MA) e para a linhagem deficiente em ficoeritrina (verde-clara, VC) de Hypnea musciformis. As duas linhagens foram cultivadas em temperatura de 23 ± 2°C, fotoperíodo de 14 horas, irradiância de 60-90µmol fótons m-2s-1, e meio composto por água do mar esterilizada (30ups) enriquecida com a solução de von Stosch na concentração de 50% (VSES/2). As condições ótimas de ensaio para ambas as linhagens foram: 40µM de NADH; 10min de incubação do extrato bruto (EB) e 100µL de EB. A atividade ótima da NR ocorreu em 4 e 2mM de nitrato para a linhagem VC e MA, respectivamente. As linhagens VC e MA apresentaram, respectivamente, constante aparente de Michaelis-Menten (K M) para NADH de 0,2068 e 0,0837 µM, e K M para nitrato de 0,0492 e 0,0294mM. Os resultados indicam que a NR da linhagem MA tem maior afinidade pelo substrato do que a NR da linhagem VC de H. musciformis. Os experimentos para avaliar os efeitos da disponibilidade de nitrato (5 a 105µM) e nitrato e fosfato (0,5 a 25,5µM, com a relação N:P de 4:1) mostraram que a atividade da NR das linhagens VC e MA não aumentou com a adição de nitrato no meio, o que pode estar relacionado com o estado nutricional dessas algas. A atividade da NR foi maior nos tratamentos com adição de fosfato do que naqueles com adição de apenas nitrato, indicando que esse nutriente é importante para os processos metabólicos relacionados a atividade da NR.

The development of an immobilized enzyme reactor containing glyceraldehyde-3-phosphate dehydrogenase from Trypanosoma cruzi: the effect of species' specific differences on the immobilization

Glyceraldehyde-3-phosphate dehydrogenase (GAPDH) plays an important role in the life cycle of the Trypanosoma cruzi, and an immobilized enzyme reactor (IMER) has been developed for use in the on-line screening for GAPDH inhibitors. An IMER containing human GAPDH has been previously reported; however, these conditions produced a T. cruzi GAPDH-IMER with poor activity and stability. The factors affecting the stability of the human and T. cruzi GAPDHs in the immobilization process and the influence of pH and buffer type on the stability and activity of the IMERs have been investigated. The resulting T. cruzi GAPDH-IMER was coupled to an analytical octyl column, which was used to achieve chromatographic separation of NAD+ from NADH. The production of NADH stimulated by D-glyceraldehyde-3-phosphate was used to investigate the activity and kinetic parameters of the immobilized T. cruzi GAPDH. The Michaelis-Menten constant (K-m) values determined for D-glyceraldehyde-3-phosphate and NAD(+) were K-m = 0.5 +/- 0.05 mM and 0.648 +/- 0.08 mM, respectively, which were consistent with the values obtained using the non-immobilized enzyme.

Pseudomonas fluorescens lipase immobilization on polysiloxane-polyvinyl alcohol composite chemically modified with epichlorohydrin

The technique based on sol-gel approach was used to generate silica matrices derivatives by hydrolysis of silane compounds. The present work evaluates a hybrid matrix obtained with tetraethoxysilane (TEOS) and polyvinyl alcohol (PVA) on the immobilization yield of lipase from Pseudomonas fluorescens. The resulting polysiloxane-polyvinyl alcohol (POS-PVA) matrix combines the property of PVA as a suitable polymer to retain proteins with an excellent optical, thermal and chemical stability of the host silicon oxide matrix. Aiming to render adequate functional groups to the covalent binding with the enzyme the POS-PVA matrix was chemically modified using epichlorohydrin. The results were compared with immobilized derivative on POS-PVA activated with glutaraldehyde. Immobilization yield based on the recovered lipase activity depended on the activating agent and the highest efficiency (32%) was attained when lipase was immobilized on POS-PVA activated with epichlorohydrin, which, probably, provided more linkage points for the covalent bind of the enzyme on the support. This was confirmed by determining the morphological properties using different techniques as X-ray diffraction and scanning electron microscopy (SEM). Comparative studies were carried out to attain optimal activities for free lipase and immobilized systems. For this purpose, a central composite experimental design with different combinations of pH and temperature was performed. Enzymatic hydrolysis with the immobilized enzyme in the framework of the Michaelis-Menten mechanism was also reported. Under optimum conditions, the immobilized derivative on POS-PVA activated with epichlorohydrin showed to have more affinity for the substrate in the hydrolysis of olive oil, with a Michaelis-Menten constant value (K-m) of 293 mM, compared to the value of 401 mM obtained for the immobilized lipase on support activated with glutaraldehyde. Data generated by DSC showed that both immobilized derivatives have similar thermal stabilities. (C) 2007 Elsevier B.V. All rights reserved.

Ammonia volatilization in soil treated with tannery sludge

The utilization of tannery sludge in agricultural areas can be an alternative for its disposal and recycling. Despite this procedure may cause the loss of nitrogen by ammonia volatilization, there is no information about this process in tropical soils. For two years a field experiment was carried out in Rolandia (Parana State, Brazil), to evaluate the amount of NH(3) volatilization due to tannery sludge application on agricultural soil. The doses of total N applied varied from zero to 1200 kg ha(-1), maintained at the surface for 89 days, as usual in this region. The alkalinity of the tannery sludge used was equivalent to between 262 and 361 g CaCO(3) per kg. Michaelis-Menten equation was adequate to estimate NH(3)-N volatilization kinetics. The relation between total nitrogen applied as tannery sludge and the potentially volatilized NH(3)-N, calculated by the chemical-kinetics equation resulted in an average determination coefficient of 0.87 (P > 0.01). In this period, the amount of volatilized NH(3) was more intense during the first 30 days; the time to reach half of the maximum NH(3) volatilization (K(m)) was 13 an 9 days for the first and second experiments, respectively. The total loss as ammonia in the whole period corresponded in average to 17.5% of the total N applied and to 35% of the NH(4)(+)-N present in the sludge. If tannery sludge is to be surface applied to supply N for crops, the amounts lost as NH(3) must be taken into consideration. (C) 2010 Elsevier Ltd. All rights reserved.

In vitro characterization of rosiglitazone metabolites and determination of the kinetic parameters employing rat liver microsomal fraction

Rosiglitazone (RSG), a thiazolidinedione antidiabetic drug, is metabolized by CYP450 enzymes into two main metabolites: N-desmethyl rosiglitazone (N-Dm-R) and rho-hydroxy rosiglitazone (rho-OH-R). In humans, CYP2C8 appears to have a major role in RSG metabolism. On the other hand, the in vitro metabolism of RSG in animals has not been described in literature yet. Based on these concerns, the kinetic metabolism study of RSG using rat liver microsomal fraction is described for the first time. Maximum velocity (V (max)) values of 87.29 and 51.09 nmol/min/mg protein were observed for N-Dm-R and rho-OH-R, respectively. Michaelis-Menten constant (K (m)) values were of 58.12 and 78.52 mu M for N-Dm-R and rho-OH-R, respectively. Therefore, these results demonstrated that this in vitro metabolism model presents the capacity of forming higher levels of N-Dm-R than of rho-OH-R, which also happens in humans. Three other metabolites were identified employing mass spectrometry detection under positive electrospray ionization: ortho-hydroxy-rosiglitazone (omicron-OH-R) and two isomers of N-desmethyl hydroxy-rosiglitazone. These metabolites have also been observed in humans. The results observed in this study indicate that rats could be a satisfactory model for RSG metabolism.

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.