Kinetic analysis of a Michaelis-Menten mechanism in which the enzyme is unstable.
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ABSTRACT:
SUBMITTER: Garrido-del Solo C
PROVIDER: S-EPMC1134476 | biostudies-other | 1993 Sep
REPOSITORIES: biostudies-other
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Project description:Examining enzyme kinetics is critical for understanding cellular systems and for using enzymes in industry. The Michaelis-Menten equation has been widely used for over a century to estimate the enzyme kinetic parameters from reaction progress curves of substrates, which is known as the progress curve assay. However, this canonical approach works in limited conditions, such as when there is a large excess of substrate over enzyme. Even when this condition is satisfied, the identifiability of parameters is not always guaranteed, and often not verifiable in practice. To overcome such limitations of the canonical approach for the progress curve assay, here we propose a Bayesian approach based on an equation derived with the total quasi-steady-state approximation. In contrast to the canonical approach, estimates obtained with this proposed approach exhibit little bias for any combination of enzyme and substrate concentrations. Importantly, unlike the canonical approach, an optimal experiment to identify parameters with certainty can be easily designed without any prior information. Indeed, with this proposed design, the kinetic parameters of diverse enzymes with disparate catalytic efficiencies, such as chymotrypsin, fumarase, and urease, can be accurately and precisely estimated from a minimal amount of timecourse data. A publicly accessible computational package performing such accurate and efficient Bayesian inference for enzyme kinetics is provided.
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Project description:Many computational models for analyzing and predicting cell physiology rely on in vitro data collected in dilute and controlled buffer solutions. However, this can mislead models because up to 40% of the intracellular volume-depending on the organism, the physiology, and the cellular compartment-is occupied by a dense mixture of proteins, lipids, polysaccharides, RNA, and DNA. These intracellular macromolecules interfere with the interactions of enzymes and their reactants and thus affect the kinetics of biochemical reactions, making in vivo reactions considerably more complex than the in vitro data indicates. In this work, we present a new, to our knowledge, type of kinetics that captures and quantifies the effect of volume exclusion and other spatial phenomena on the kinetics of elementary reactions. We further developed a framework that allows for the efficient parameterization of these kinetics using particle simulations. Our formulation, entitled generalized elementary kinetics, can be used to analyze and predict the effect of intracellular crowding on enzymatic reactions and was herein applied to investigate the influence of crowding on phosphoglycerate mutase in Escherichia coli, which exhibits prototypical reversible Michaelis-Menten kinetics. Current research indicates that many enzymes are reaction limited and not diffusion limited, and our results suggest that the influence of fractal diffusion is minimal for these reaction-limited enzymes. Instead, increased association rates and decreased dissociation rates lead to a strong decrease in the effective maximal velocities Vmax and the effective Michaelis-Menten constants KM under physiologically relevant volume occupancies. Finally, the effects of crowding were explored in the context of a linear pathway, with the finding that crowding can have a redistributing effect on the effective flux responses in the case of twofold enzyme overexpression. We suggest that this framework, in combination with detailed kinetics models, will improve our understanding of enzyme reaction networks under nonideal conditions.
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Project description:Nearly 100 years ago Michaelis and Menten published their now classic paper [Michaelis, L., and Menten, M. L. (1913) Die Kinetik der Invertinwirkung. Biochem. Z. 49, 333-369] in which they showed that the rate of an enzyme-catalyzed reaction is proportional to the concentration of the enzyme-substrate complex predicted by the Michaelis-Menten equation. Because the original text was written in German yet is often quoted by English-speaking authors, we undertook a complete translation of the 1913 publication, which we provide as Supporting Information . Here we introduce the translation, describe the historical context of the work, and show a new analysis of the original data. In doing so, we uncovered several surprises that reveal an interesting glimpse into the early history of enzymology. In particular, our reanalysis of Michaelis and Menten's data using modern computational methods revealed an unanticipated rigor and precision in the original publication and uncovered a sophisticated, comprehensive analysis that has been overlooked in the century since their work was published. Michaelis and Menten not only analyzed initial velocity measurements but also fit their full time course data to the integrated form of the rate equations, including product inhibition, and derived a single global constant to represent all of their data. That constant was not the Michaelis constant, but rather V(max)/K(m), the specificity constant times the enzyme concentration (k(cat)/K(m) × E(0)).
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Project description:Biochemical transformation kinetics is based on the formation of enzyme-substrate complexes. We developed a robust scheme based on unit productions of enzymes and reactants in cyclic events to comply with mass action law to form enzyme-substrate complexes. The developed formalism supports a successful application of Michaelis-Menten kinetics in all biochemical transformations of single parameters. It is an essential tool to overcome some challenging healthcare and environmental issues. In developing the formalism, we defined the substrate [S]= [Product]3/4 and rate of reaction based on rate and time perspectives. It allowed us to develop two quadratic equations. The first, represents a body entity that gave a useful relationship of enzyme E?=?2S0.33, and the second nutrients/feed, each giving [Enzymes] and [Enzyme-substrate complexes], simulating rate of reaction, [substrate], and their differentials. By combining [Enzymes] and [Enzyme-substrate complexes] values, this quadratic equation derives a Michaelis-Menten hyperbolic function. Interestingly, we can derive the proportionate rate of reaction and [Enzymes] values of the quadratics resulting in another Michaelis-Menten hyperbolic. What is clear from these results is that between these two hyperbolic functions, in-competitive inhibitions exist, indicating metabolic activities and growth in terms of energy levels. We validated these biochemical transformations with examples applicable to day to day life.
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Project description:An analytic solution to enzyme kinetics expressed by the Michaelis-Menten-Monod mathematical framework is presented. The analytic solution describes the implicit problem with the independent variable, normally time, substituted with the concentration of the reaction product. The analytic solution provides the substrate, enzyme, and microbial biomass concentration instantaneously and over all time domains without the use of numerical integration schemes or iterative solvers required to overcome transcendental functions. Experiments of NO2 - nitrification by Candidatus Nitrospira defluvii at temperatures ranging between 10 and 32 °C were used for validation tests with the numerical solution by finite differences and the implicit analytic solution presented here. Results showed that both finite differences and analytic solutions matched the experiments particularly well, with a correlation coefficient greater than 0.99 and residuals smaller than 2.75%.
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Project description:It is shown here that a suitable form for estimation and inference using the Michaelis-Menten [(1913) Biochem Z. 49, 333-369] model for simple enzymic reactions is one in which the two parameters appear in the denominator of the equation. In this form, convergence to the least-squares estimates using the Gauss-Newton method [see Kennedy & Gentle (1980) Statistical Computing, Marcel Dekker, New York] is virtually ensured, or, as the model in this form is a member of the class of 'generalized linear models', it may be fitted by packages such as those of Rothamsted Experimental Station [(1977) GENSTAT (A General Statistical Program), Rothamsted Experimental Station, Harpenden] and the Numerical Algorithms Group [(1978) GLIM (Generalised Linear Interactive Modeling), Numerical Algorithms Group, Oxford]. Furthermore, the parameters-in-denominator principle is readily extended to more complicated catalytic models. With all parameters in the denominator, the least-squares estimators are close to being unbiased and normally distributed, whereas severe bias and non-normality may result from use of the standard formulations.
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Project description:The Michaelis-Menten equation provides a hundred-year-old prediction by which any increase in the rate of substrate unbinding will decrease the rate of enzymatic turnover. Surprisingly, this prediction was never tested experimentally nor was it scrutinized using modern theoretical tools. Here we show that unbinding may also speed up enzymatic turnover--turning a spotlight to the fact that its actual role in enzymatic catalysis remains to be determined experimentally. Analytically constructing the unbinding phase space, we identify four distinct categories of unbinding: inhibitory, excitatory, superexcitatory, and restorative. A transition in which the effect of unbinding changes from inhibitory to excitatory as substrate concentrations increase, and an overlooked tradeoff between the speed and efficiency of enzymatic reactions, are naturally unveiled as a result. The theory presented herein motivates, and allows the interpretation of, groundbreaking experiments in which existing single-molecule manipulation techniques will be adapted for the purpose of measuring enzymatic turnover under a controlled variation of unbinding rates. As we hereby show, these experiments will not only shed first light on the role of unbinding but will also allow one to determine the time distribution required for the completion of the catalytic step in isolation from the rest of the enzymatic turnover cycle.
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Project description:The driving force for active physical and biological systems is determined by both the underlying landscape and nonequilibrium curl flux. While landscape can be experimentally quantified from the histograms of the collected real-time trajectories of the observables, quantifying the experimental flux remains challenging. In this work, we studied the single-molecule enzyme dynamics of horseradish peroxidase with dihydrorhodamine 123 and hydrogen peroxide (H2O2) as substrates. Surprisingly, significant deviations in the kinetics from the conventional Michaelis-Menten reaction rate were observed. Instead of a linear relationship between the inverse of the enzyme kinetic rate and the inverse of substrate concentration, a nonlinear relationship between the two emerged. We identified nonequilibrium flux as the origin of such non-Michaelis-Menten enzyme rate behavior. Furthermore, we quantified the nonequilibrium flux from experimentally obtained fluorescence correlation spectroscopy data and showed this flux to led to the deviations from the Michaelis-Menten kinetics. We also identified and quantified the nonequilibrium thermodynamic driving forces as the chemical potential and entropy production for such non-Michaelis-Menten kinetics. Moreover, through isothermal titration calorimetry measurements, we identified and quantified the origin of both nonequilibrium dynamic and thermodynamic driving forces as the heat absorbed (energy input) into the enzyme reaction system. Furthermore, we showed that the nonequilibrium driving forces led to time irreversibility through the difference between the forward and backward directions in time and high-order correlations were associated with the deviations from Michaelis-Menten kinetics. This study provided a general framework for experimentally quantifying the dynamic and thermodynamic driving forces for nonequilibrium systems.
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Project description:Procedures to define kinetic mechanisms from catalytic activity measurements that obey the Michaelis-Menten equation are well established. In contrast, analytical tools for enzymes displaying non-Michaelis-Menten kinetics are underdeveloped, and transient-state measurements, when feasible, are therefore preferred in kinetic studies. Of note, transient-state determinations evaluate only partial reactions, and these might not participate in the reaction cycle. Here, we provide a general procedure to characterize kinetic mechanisms from steady-state determinations. We described non-Michaelis-Menten kinetics with equations containing parameters equivalent to kcat and Km and modeled the underlying mechanism by an approach similar to that used under Michaelis-Menten kinetics. The procedure enabled us to evaluate whether Na+/K+-ATPase uses the same sites to alternatively transport Na+ and K+ This ping-pong mechanism is supported by transient-state studies but contradicted to date by steady-state analyses claiming that the release of one cationic species as product requires the binding of the other (ternary-complex mechanism). To derive robust conclusions about the Na+/K+-ATPase transport mechanism, we did not rely on ATPase activity measurements alone. During the catalytic cycle, the transported cations become transitorily occluded (i.e. trapped within the enzyme). We employed radioactive isotopes to quantify occluded cations under steady-state conditions. We replaced K+ with Rb+ because 42K+ has a short half-life, and previous studies showed that K+- and Rb+-occluded reaction intermediates are similar. We derived conclusions regarding the rate of Rb+ deocclusion that were verified by direct measurements. Our results validated the ping-pong mechanism and proved that Rb+ deocclusion is accelerated when Na+ binds to an allosteric, nonspecific site, leading to a 2-fold increase in ATPase activity.
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Project description:The Michaelis-Menten (MM) rate law has been the dominant paradigm of modeling biochemical rate processes for over a century with applications in biochemistry, biophysics, cell biology, systems biology, and chemical engineering. The MM rate law and its remedied form stand on the assumption that the concentration of the complex of interacting molecules, at each moment, approaches an equilibrium (quasi-steady state) much faster than the molecular concentrations change. Yet, this assumption is not always justified. Here, we relax this quasi-steady state requirement and propose the generalized MM rate law for the interactions of molecules with active concentration changes over time. Our approach for time-varying molecular concentrations, termed the effective time-delay scheme (ETS), is based on rigorously estimated time-delay effects in molecular complex formation. With particularly marked improvements in protein-protein and protein-DNA interaction modeling, the ETS provides an analytical framework to interpret and predict rich transient or rhythmic dynamics (such as autogenously-regulated cellular adaptation and circadian protein turnover), which goes beyond the quasi-steady state assumption.
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