Simultaneous interaction of enzymes with two modifiers: Reappraisal of kinetic models and new paradigms

On the simultaneous activation of Agrobacterium tumefaciens ADP-glucose pyrophosphorylase by pyruvate and fructose 6-phosphate

Bacterial ADP-glucose pyrophosphorylases are allosterically regulated by metabolites that are key intermediates of central pathways in the respective microorganism. Pyruvate (Pyr) and fructose 6-phosphate (Fru6P) activate the enzyme from Agrobacterium tumefaciens by increasing V_max about 10- and 20-fold, respectively. Here, we studied the combined effect of both metabolites on the enzyme activation. Our results support a model in which there is a synergistic binding of these two activators to two distinct sites and that each activator leads the enzyme to distinct active forms with different properties. In presence of both activators, Pyr had a catalytically dominant effect over Fru6P determining the active conformational state. By mutagenesis we obtained enzyme variants still sensitive to Pyr activation, but in which the allosteric signal by Fru6P was disrupted. This indicated that the activation mechanism for each effector was not the same. The ability for this enzyme to have more than one allosteric activator site, active forms, and allosteric signaling mechanisms is critical to expand the evolvability of its regulation. These synergistic interactions between allosteric activators may represent a feature in other allosteric enzymes.

A Kinetic Process to Determine the Interaction Type Between Two Compounds, One of Which Is a Reaction Product, Using Alkaline Phosphatase Inhibition as a Case Study

This study describes the development of a new methodology based on a new integrated equation which allows the determination of the kinetic parameters for two mutually non-exclusive inhibitors when one of which is produced during the time-course reaction. Alkaline phosphatase simultaneously inhibited by phosphate and urea is used to illustrate this methodology, including the evaluation of interaction effects between them. Data analyses were carried out using two integrated velocity equations: exclusive linear mixed inhibition (EMI) and non-exclusive linear mixed inhibition (NEMI). Kinetic parameters are estimated using non-linear regression and results show that (i) the interaction between enzyme and the inhibitors urea and phosphate exhibit a mutually non-exclusive behavior; (ii) more specifically, these inhibitors are non-exclusive only in free enzyme (E) species; (iii) the inhibitors also show an interaction with enzyme classified as facilitation; (iv) phosphate is a competitive inhibitor and urea a mixed inhibitor; (v) the inhibition constant for phosphate is much lower than that determined for urea. In addition, a functional Excel Spreadsheet which can be adapted to any kinetic study is also included as a supplement.

Single-molecule theory of enzymatic inhibition

The classical theory of enzymatic inhibition takes a deterministic, bulk based approach to quantitatively describe how inhibitors affect the progression of enzymatic reactions. Catalysis at the single-enzyme level is, however, inherently stochastic which could lead to strong deviations from classical predictions. To explore this, we take the single-enzyme perspective and rebuild the theory of enzymatic inhibition from the bottom up. We find that accounting for multi-conformational enzyme structure and intrinsic randomness should strongly change our view on the uncompetitive and mixed modes of inhibition. There, stochastic fluctuations at the single-enzyme level could make inhibitors act as activators; and we state—in terms of experimentally measurable quantities—a mathematical condition for the emergence of this surprising phenomenon. Our findings could explain why certain molecules that inhibit enzymatic activity when substrate concentrations are high, elicit a non-monotonic dose response when substrate concentrations are low.

Single molecule approaches demonstrated that enzymatic catalysis is stochastic which could lead to deviations from classical predictions. Here authors rebuild the theory of enzymatic inhibition to show that stochastic fluctuations on the single enzyme level could make inhibitors act as activators.

Suppressive drug combinations and their potential to combat antibiotic resistance

Antibiotic effectiveness often changes when two or more such drugs are administered simultaneously and unearthing antibiotic combinations with enhanced efficacy (synergy) has been a longstanding clinical goal. However, antibiotic resistance, which undermines individual drugs, threatens such combined treatments. Remarkably, it has emerged that antibiotic combinations whose combined effect is lower than that of at least one of the individual drugs can slow or even reverse the evolution of resistance. We synthesize and review studies of such so-called 'suppressive interactions' in the literature. We examine why these interactions have been largely disregarded in the past, the strategies used to identify them, their mechanistic basis, demonstrations of their potential to reverse the evolution of resistance and arguments for and against using them in clinical treatment. We suggest future directions for research on these interactions, aiming to expand the basic body of knowledge on suppression and to determine the applicability of suppressive interactions in the clinic.

Representação do efeito de inibição enzimática reversível para o modelo cinético de Michaelis-Menten no estado transiente

ResumoOs processos enzimáticos que seguem o modelo cinético de Michaelis-Menten foram estudados a partir de diferentes propostas para descrever a etapa de inibição reversível. As propostas de inibição foram comparadas a partir de um processo genérico, onde as constantes cinéticas receberam valores unitários e o valor numérico da concentração de substrato foi dez (10) vezes superior ao valor numérico da concentração de enzima. Para cada proposta de modelo de inibição foram obtidas soluções numéricas a partir de sistema não linear de equações diferenciais ordinárias, gerando gráficos que apresentaram, separadamente, a variação das concentrações da enzima, dos complexos enzimáticos, do substrato e do produto da reação. Foi obtido um modelo, dentre as propostas avaliadas, com desempenho indicando comportamento similar ao verificado no modelo clássico de Michaelis-Menten, onde o complexo de reação é rapidamente formado e, ao longo do processo, decai até tender a zero. Em contrapartida, diferentemente do modelo clássico, na nova proposta de modelo o efeito de inibição começa em zero e, ao longo do processo, tende ao valor nominal da concentração inicial da enzima. Tais respostas mostraram-se válidas para valores distintos de concentração de enzima e de tempo de processo, mostrando robustez e indicando uma tendência do somatório do substrato e do produto atingir o valor nominal da concentração inicial do substrato ao longo do tempo de processamento.

Conformational flexibility and allosteric regulation of cathepsin K

The human cysteine peptidase cathepsin K is a key enzyme in bone homoeostasis and other physiological functions. In the present study we investigate the mechanism of cathepsin K action at physiological plasma pH and its regulation by modifiers that bind outside of the active site. We show that at physiological plasma pH the enzyme fluctuates between multiple conformations that are differently susceptible to macromolecular inhibitors and can be manipulated by varying the ionic strength of the medium. The behaviour of the enzyme in vitro can be described by the presence of two discrete conformations with distinctive kinetic properties and different susceptibility to inhibition by the substrate benzyloxycarbonyl-Phe-Arg-7-amino-4-methylcoumarin. We identify and characterize sulfated glycosaminoglycans as natural allosteric modifiers of cathepsin K that exploit the conformational flexibility of the enzyme to regulate its activity and stability against autoproteolysis. All sulfated glycosaminoglycans act as non-essential activators in assays using low-molecular-mass substrates. Chondroitin sulfate and dermatan sulfate bind at one site on the enzyme, whereas heparin binds at an additional site and has a strongly stabilizing effect that is unique among human glycosaminoglycans. All glycosaminoglycans stimulate the elastinolytic activity of cathepsin K at physiological plasma pH, but only heparin also increases the collagenolytic activity of the enzyme under these conditions. Altogether these results provide novel insight into the mechanism of cathepsin K function at the molecular level and its regulation in the extracellular space.

Paradoxical interactions between modifiers and elastase-2

The serine endopeptidase elastase-2 from human polymorphonuclear leukocytes is associated with physiological remodeling and pathological degradation of the extracellular matrix. Glycosaminoglycans bound to the matrix or released after proteolytic processing of the core proteins of proteoglycans are potential ligands of elastase-2. In vitro, this interaction results in enzyme inhibition at low concentrations of glycosaminoglycans. However, inhibition is reversed and even abolished at high concentrations of the ligands. This behavior, which can be interpreted by a mechanism involving at least two molecules of glycosaminoglycan binding the enzyme at different sites, may cause interference with the natural protein inhibitors of elastase-2, particularly the alpha-1 peptidase inhibitor. Depending on their concentration, glycosaminoglycans can either stimulate or antagonize the formation of the enzyme-inhibitor complex and thus affect proteolytic activity. This interference with elastase-2 inhibition in the extracellular space may be part of a finely-tuned control mechanism in the microenvironment of the enzyme during remodeling and degradation of the extracellular matrix.