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

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Thermodynamic analysis of enzyme catalysed reactions: new insights into the Michaelis-Menten equation

A simple thermodynamic analysis of the well-known Michaelis-Menten equation (MME) of enzyme catalysis is proposed that employs the chemical potential mu to follow the Gibbs free energy changes attending the formation of the enzyme-substrate complex and its turnover to the product. The main conclusion from the above analysis is that low values of the Michaelis constant KM and high values of the turnover number k(cat) are advantageous: this supports a simple algebraic analysis of the MME, although at variance with current thinking. Available data apparently support the above findings. It is argued that transition state stabilisation - rather than substrate distortion or proximity - is the key to enzyme catalysis.

On the Presumed Kinetic Consequences of Pre-equilibrium. Implications for the Michaelis-Menten Equation

The overall rate equation for a reaction sequence consisting of a pre-equilibrium and rate-determining steps should not be derived on the basis of the concentration of the intermediate product (X). This is apparently indicated by transition state theory (as the path followed to reach the highest energy transition state is irrelevant), but also proved by a straight-forward mathematical approach. The thesis is further supported by the equations of concurrent reactions as applied to the partitioning of X between the two competing routes (reversal of the pre-equilibrium and formation of product). The rate equation may only be derived rigorously on the basis of the law of mass action. It is proposed that the reactants acquire the overall activation energy prior to the pre-equilibrium, thus forming X in a high-energy state en route to the rate-determining transition state. (It is argued that conventional energy profile diagrams are misleading and need to be reinterpreted.) Also, these arguments invalidate the Michaelis-Menten equation of enzyme kinetics, and necessitate a fundamental revision of our present understanding of enzyme catalysis. (The observed ``saturation kinetics'' possibly arises from weak binding of a second molecule of substrate at the active site; analogous conclusions apply to reactions at surfaces).

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)

Estudo de processos redox enzimáticos confinados em eletrodos pelo concomitante monitoramento da variação de massa e da corrente: o caso da penicilinase como modelo

Pós-graduação em Biotecnologia - IQ

Conversão da lactose e síntese de galacto-oligossacarídeos: uma abordagem experimental e teórica

O presente trabalho avaliou, na etapa experimental, um processo simultâneo de catálise e fermentação láctica visando obter um iogurte com potenciais características nutracêuticas e, na sua etapa teórica, estabeleceu uma interlocução entre a vivência experimentalista e a teoria da cinética enzimática, no que se refere à conversão da lactose e à síntese de galactooligossacarídeos (GOS). Na abordagem experimental, para um substrato específico, avaliouse biocatálise conduzida simultaneamente à fermentação, defasando a adição da enzima em relação ao início do processo fermentativo. A fermentação foi realizada a partir de cultura láctica liofilizada comercial contendo dois micro-organismos probióticos, Bifidobacterium animalis e Lactobacillus acidophilus, associados aos micro-organismos característicos do iogurte, Lactobacillus bulgaricus e Streptococcus thermophilus. Foi utilizado um preparado enzimático contendo -galactosidases obtidas de duas origens distintas: Kluyveromyces lactis e Aspergillus niger. Foram avaliados os efeitos da concentração da enzima e do tempo de adição da enzima em um planejamento experimental 2 2 . As respostas foram às concentrações, ao final do processo, de lactose, de GOS, de glicose e de galactose e a hidrólise dos galactooligossacarídeos ao longo do tempo. No que se refere à abordagem teórica, o presente trabalho considerou modelos matemáticos de hidrólise de dissacarídeos e conversão da lactose, em que a inibição foi representada a partir do incremento da concentração dos produtos da reação. No que se refere à conversão da lactose e síntese de GOS, o presente trabalho buscou estabelecer um modelo matemático em que a inibição ocorreu por efeito do incremento das concentrações de glicose e de galactose, comparando-o com os modelos conhecidos na literatura. Verificou-se que o desempenho do modelo obtido no presente trabalho foi robusto em relação às premissas estabelecidas. Na comparação com resultados experimentais de conversão enzimática, o modelo mostrou-se capaz de minimizar o erro e de ajustar-se aos dados experimentais.

Caracterização in vitro do metabolismo e da absorção intestinal da casearina X

As principais propriedades farmacológicas da Casearia sylvestris, uma espécie de árvore cujas folhas são utilizadas na medicina popular, já foram descritas na literatura. Recentemente foi demonstrada a potente atividade citotóxica in vitro da casearina X (CAS X), o diterpeno clerodânico majoritário isolado das folhas de C. sylvestris, contra linhagens de células tumorais humanas. Apesar dos resultados promissores, sua potente atividade citotóxica in vitro não pode ser extrapolada para uma potente atividade in vivo, a menos que possua boa biodisponibilidade e duração desejável do seu efeito. Tendo em vista que o avanço nas pesquisas de produtos naturais requer a avaliação pré-clínica de propriedades farmacocinéticas, no presente trabalho foi realizada a caracterização in vitro do metabolismo e da absorção intestinal da CAS X, com o objetivo de prever sua biodisponibilidade in vivo. Para os estudos de metabolismo in vitro, foi utilizado o modelo microssomal hepático de ratos e de humanos. Foi desenvolvido um método analítico para a quantificação da CAS X em microssomas, empregando a precipitação de proteínas com acetonitrila no preparo das amostras e a cromatografia líquida de alta eficiência para as análises. O método foi validado de acordo com os guias oficiais da Agência Nacional de Vigilância Sanitária e da European Medicine Agency (EMA). A CAS X demonstrou ser substrato para as reações de hidrólise mediada pelas carboxilesterases (CES) e apresentou um perfil cinético de Michaelis-Menten. Foram estimados os parâmetros de Vmax e KM, demonstrando que o clearance intrínseco em microssomas hepático de humanos foi 1,7 vezes maior que o de ratos. O clearance hepático foi estimado por extrapolação in vitro-in vivo, resultando em mais de 90% do fluxo sanguíneo hepático em ambas as espécies. Um estudo qualitativo para a pesquisa de metabólitos foi feito utilizando espectrometria de massas, pelo qual foi possível sugerir a formação da casearina X dialdeído como produto de metabolismo. Nos estudos de absorção intestinal in vitro foi utilizado o modelo de monocamadas de células Caco-2. Um método analítico por cromatografia líquida acoplada a espectrometria de massas foi desenvolvido e validado de acordo com o EMA, para as etapas de quantificação da CAS X no sistema de células. Os parâmetros cinéticos de permeabilidade aparente absortiva e secretória da CAS X foram estimados em um sistema celular, no qual a atividade hidrolítica da CES foi inibida. Assim, a CAS X foi capaz de permear a monocamada de células Caco-2, provavelmente por transporte ativo, sem a ocorrência de efluxo, mas com significativa retenção do composto dentro das células. Em conjunto, os ensaios in vitro realizados demonstraram a susceptibilidade da CAS X ao metabolismo de primeira passagem, como substrato para as CES específicas expressas no fígado e intestino.

An analytical solution for diffusion and nonlinear uptake of oxygen in a spherical cell

We develop a new analytical solution for a reactive transport model that describes the steady-state distribution of oxygen subject to diffusive transport and nonlinear uptake in a sphere. This model was originally reported by Lin (Journal of Theoretical Biology, 1976 v60, pp449–457) to represent the distribution of oxygen inside a cell and has since been studied extensively by both the numerical analysis and formal analysis communities. Here we extend these previous studies by deriving an analytical solution to a generalized reaction-diffusion equation that encompasses Lin’s model as a particular case. We evaluate the solution for the parameter combinations presented by Lin and show that the new solutions are identical to a grid-independent numerical approximation.

Genomic organisation, activity and distribution analysis of the microbial putrescine oxidase degradation pathway

The catalytic action of putrescine specific amine oxidases acting in tandem with 4-aminobutyraldehyde dehydrogenase is explored as a degradative pathway in Rhodococcus opacus. By limiting the nitrogen source, increased catalytic activity was induced leading to a coordinated response in the oxidative deamination of putrescine to 4-aminobutyraldehyde and subsequent dehydrogenation to 4-aminobutyrate. Isolating the dehydrogenase by ion exchange chromatography and gel filtration revealed that the enzyme acts principally on linear aliphatic aldehydes possessing an amino moiety. Michaelis-Menten kinetic analysis delivered a Michaelis constant (KM=0.014mM) and maximum rate (Vmax=11.2μmol/min/mg) for the conversion of 4-aminobutyraldehyde to 4-aminobutyrate. The dehydrogenase identified by MALDI-TOF mass spectrometric analysis (E value=0.031, 23% coverage) belongs to a functionally related genomic cluster that includes the amine oxidase, suggesting their association in a directed cell response. Key regulatory, stress and transport encoding genes have been identified, along with candidate dehydrogenases and transaminases for the further conversion of 4-aminobutyrate to succinate. Genomic analysis has revealed highly similar metabolic gene clustering among members of Actinobacteria, providing insight into putrescine degradation notably among Micrococcaceae, Rhodococci and Corynebacterium by a pathway that was previously uncharacterised in bacteria.

Role of amine oxidase expression to maintain putrescine homeostasis in Rhodococcus opacus

While applications of amine oxidases are increasing, few have been characterised and our understanding of their biological role and strategies for bacteria exploitation are limited. By altering the nitrogen source (NH4Cl, putrescine and cadaverine (diamines) and butylamine (monoamine)) and concentration, we have identified a constitutive flavin dependent oxidase (EC 1.4.3.10) within Rhodococcus opacus. The activity of this oxidase can be increased by over two orders of magnitude in the presence of aliphatic diamines. In addition, the expression of a copper dependent diamine oxidase (EC 1.4.3.22) was observed at diamine concentrations>1mM or when cells were grown with butylamine, which acts to inhibit the flavin oxidase. A Michaelis-Menten kinetic treatment of the flavin oxidase delivered a Michaelis constant (KM)=190μM and maximum rate (kcat)=21.8s(-1) for the oxidative deamination of putrescine with a lower KM (=60μM) and comparable kcat (=18.2s(-1)) for the copper oxidase. MALDI-TOF and genomic analyses have indicated a metabolic clustering of functionally related genes. From a consideration of amine oxidase specificity and sequence homology, we propose a putrescine degradation pathway within Rhodococcus that utilises oxidases in tandem with subsequent dehydrogenase and transaminase enzymes. The implications of PUT homeostasis through the action of the two oxidases are discussed with respect to stressors, evolution and application in microbe-assisted phytoremediation or bio-augmentation.

Model-based analysis and optimization of bioreactor for hematopoietic stem cell cultivation

One of the problems to be solved in attaining the full potentials of hematopoietic stem cell (HSC) applications is the limited availability of the cells. Growing HSCs in a bioreactor offers an alternative solution to this problem. Besides, it also offers the advantages of eliminating labour intensive process as well as the possible contamination involved in the periodic nutrient replenishments in the traditional T-flask stem cell cultivation. In spite of this, the optimization of HSC cultivation in a bioreactor has been barely explored. This manuscript discusses the development of a mathematical model to describe the dynamics in nutrient distribution and cell concentration of an ex vivo HSC cultivation in a microchannel perfusion bioreactor. The model was further used to optimize the cultivation by proposing three alternative feeding strategies in order to prevent the occurrence of nutrient limitation in the bioreactor. The evaluation of these strategies, the periodic step change increase in the inlet oxygen concentration, the periodic step change increase in the media inflow, and the feedback control of media inflow, shows that these strategies can successfully improve the cell yield of the bioreactor. In general, the developed model is useful for the design and optimization of bioreactor operation.

Co-induction of sucrose transport and invertase activities in a thermophilic fungus,Thermomyces lanuginosus

The incorporation of sucrose into the thermophilic fungus,Thermomyces lanuginosus, occurred only in mycelia previously exposed to sucrose or raffinose. Sucrose uptake and invertase were inducible. Both activities appeared in sucrose-induced mycelia at about the same time. Both activities declined almost simultaneously following the exhaustion of sucrose in the medium. The sucrose-induced uptake system was specific for \beta -fructofuranosides as revealed by competition with various sugars. The induction of sucrose uptake system was blocked by cycloheximide, showing that it was dependent on new protein synthesis. Transport of sucrose did not seem to be dependent on ATP. Rather, uptake of this sugar seemed to be driven by a proton gradient across the plasma membrane. The uptake system showed Michaelis-Menten kinetics.

Partial purification and properties of a transamidinase from Lathyrus sativus seedlings. Involvement in homoarginine metabolism and amine interconversions

A transamidinase was purified 463-fold from Lathyrus sativus seedlings by affinity chromatography on homoarginine--Sepharose. The enzyme exhibited a wide substrate specificity, and catalysed the reversible transfer of the amidino groups from donors such as arginine, homoarginine and canavanine to acceptors such as lysine, putrescine, agmatine, cadaverine and hydroxylamine. The enzyme could not be detected in the seeds, and attained the highest specific activity in the embryo axis on day 10 after seed germination. Its thiol nature was established by strong inhibition by several thiol blockers and thiol compounds in the presence of ferricyanide. In the absence of an exogenous acceptor, it exhibited weak hydrolytic activity towards arginine. It had apparent mol.wt. 210000, and exhibited Michaelis--Menten kinetics with Km 3.0 mM for arginine. Ornithine competitively inhibited the enzyme, with Ki 1.0 mM in the arginine--hydroxylamine amidino-transfer reaction. Conversion experiments with labelled compounds suggest that the enzyme is involved in homoarginine catabolism during the development of plant embryo to give rise to important amino acids and amine metabolites. Presumptive evidence is also provided for its involvement in the biosynthesis of the guanidino amino acid during seed development. The natural occurrence of arcain in L. sativus and mediation of its synthesis in vitro from agmatine by the transamidinase are demonstrated.

Stochastic kinetics of ribosomes: Single motor properties and collective behavior

Syntheses of protein molecules in a cell are carried out by ribosomes.A ribosome can be regarded as a molecular motor which utilizes the input chemical energy to move on a messenger RNA (mRNA) track that also serves as a template for the polymerization of the corresponding protein. The forward movement, however, is characterized by an alternating sequence of translocation and pause. Using a quantitative model, which captures the mechanochemical cycle of an individual ribosome, we derive an exact analytical expression for the distribution of its dwell times at the successive positions on the mRNA track. Inverse of the average dwell time satisfies a Michaelis-Menten-type'' equation and is consistent with the general formula for the average velocity of a molecular motor with an unbranched mechanochemical cycle. Extending this formula appropriately, we also derive the exact force-velocity relation for a ribosome. Often many ribosomes each synthesizes a copy of the same protein. We extend the model of a single ribosome by incorporating steric exclusion of different individuals on the same track. We draw the phase diagram of this model of ribosome traffic in three-dimensional spaces spanned by experimentally controllable parameters. We suggest new experimental tests of our theoretical predictions.

Role of conformational dynamics in kinetics of an enzymatic cycle in a nonequilibrium steady state

Enzyme is a dynamic entity with diverse time scales, ranging from picoseconds to seconds or even longer. Here we develop a rate theory for enzyme catalysis that includes conformational dynamics as cycling on a two-dimensional (2D) reaction free energy surface involving an intrinsic reaction coordinate (X) and an enzyme conformational coordinate (Q). The validity of Michaelis-Menten (MM) equation, i.e., substrate concentration dependence of enzymatic velocity, is examined under a nonequilibrium steady state. Under certain conditions, the classic MM equation holds but with generalized microscopic interpretations of kinetic parameters. However, under other conditions, our rate theory predicts either positive (sigmoidal-like) or negative (biphasic-like) kinetic cooperativity due to the modified effective 2D reaction pathway on X-Q surface, which can explain non-MM dependence previously observed on many monomeric enzymes that involve slow or hysteretic conformational transitions. Furthermore, we find that a slow conformational relaxation during product release could retain the enzyme in a favorable configuration, such that enzymatic turnover is dynamically accelerated at high substrate concentrations. The effect of such conformation retainment in a nonequilibrium steady state is evaluated.