[8] Kinetic analysis of progress curves

Enzymatic assays are widely employed to characterize important allosteric and enzyme modulation effects. The high sensitivity of these assays can represent a serious problem if the occurrence of experimental errors surreptitiously affects the reliability of enzyme kinetics results. We have addressed this problem and found that hidden assay interferences can be unveiled by the graphical representation of progress curves in modified reaction coordinates. To render this analysis accessible to users across all levels of expertise, we have developed a webserver, interferENZY, that allows (i) an unprecedented tight quality control of experimental data, (ii) the automated identification of small and major assay interferences, and (iii) the estimation of bias-free kinetic parameters. By eliminating the subjectivity factor in kinetic data reporting, interferENZY will contribute to solving the “reproducibility crisis” that currently challenges experimental molecular biology. The interferENZY webserver is freely available (no login required) at https://interferenzy.i3s.up.pt.

Enzymes are among the most important drug targets in the pharmaceutical industry. The bioassays used to screen enzyme modulators can be affected by unaccounted interferences such as time-dependent inactivation and inhibition effects. Using procaspase-3, caspase-3, and α-thrombin as model enzymes, we show that some of these effects are not eliminated by merely ignoring the reaction phases that follow initial-rate measurements. We thus propose a linearization method (LM) for detecting spurious changes of enzymatic activity based on the representation of progress curves in modified coordinates. This method is highly sensitive to signal readout distortions, thereby allowing rigorous selection of valid kinetic data. The method allows the detection of assay interferences even when their occurrence is not suspected a priori. By knowing the assets and liabilities of the bioassay, enzymology results can be reported with enhanced reproducibility and accuracy. Critical analysis of full progress curves is expected to help discriminating experimental artifacts from true mechanisms of enzymatic inhibition.

To determine initial velocities of enzyme catalyzed reactions without theoretical errors it is necessary to consider the use of the integrated Michaelis–Menten equation. When the reaction product is an inhibitor, this approach is particularly important. Nevertheless, kinetic studies usually involved the evaluation of other inhibitors beyond the reaction product. The occurrence of these situations emphasizes the importance of extending the integrated Michaelis–Menten equation, assuming the simultaneous presence of more than one inhibitor because reaction product is always present. This methodology is illustrated with the reaction catalyzed by alkaline phosphatase inhibited by phosphate (reaction product, inhibitor 1) and urea (inhibitor 2). The approach is explained in a step by step manner using an Excel spreadsheet (available as a template in Appendix). Curve fitting by nonlinear regression was performed with the Solver add-in (Microsoft Office Excel). Discrimination of the kinetic models was carried out based on Akaike information criterion. This work presents a methodology that can be used to develop an automated process, to discriminate in real time the inhibition type and kinetic constants as data (product vs. time) are achieved by the spectrophotometer.

In beating hearts, phosphorylation of myosin regulatory light chain (RLC) at a single site to 0.45 mol of phosphate/mol by cardiac myosin light chain kinase (cMLCK) increases Ca²⁺ sensitivity of myofilament contraction necessary for normal cardiac performance. Reduction of RLC phosphorylation in conditional cMLCK knock-out mice caused cardiac dilation and loss of cardiac performance by 1 week, as shown by increased left ventricular internal diameter at end-diastole and decreased fractional shortening. Decreased RLC phosphorylation by conventional or conditional cMLCK gene ablation did not affect troponin-I or myosin-binding protein-C phosphorylation in vivo. The extent of RLC phosphorylation was not changed by prolonged infusion of dobutamine or treatment with a β-adrenergic antagonist, suggesting that RLC is constitutively phosphorylated to maintain cardiac performance. Biochemical studies with myofilaments showed that RLC phosphorylation up to 90% was a random process. RLC is slowly dephosphorylated in both noncontracting hearts and isolated cardiac myocytes from adult mice. Electrically paced ventricular trabeculae restored RLC phosphorylation, which was increased to 0.91 mol of phosphate/mol of RLC with inhibition of myosin light chain phosphatase (MLCP). The two RLCs in each myosin appear to be readily available for phosphorylation by a soluble cMLCK, but MLCP activity limits the amount of constitutive RLC phosphorylation. MLCP with its regulatory subunit MYPT2 bound tightly to myofilaments was constitutively phosphorylated in beating hearts at a site that inhibits MLCP activity. Thus, the constitutive RLC phosphorylation is limited physiologically by low cMLCK activity in balance with low MLCP activity.

The coupling kinetics of phenylalanine amide and the carbamoylmethyl ester of N-protected phenylalanine in near-anhydrous tetrahydrofuran were investigated. This coupling was catalyzed by Alcalase covalently immobilized onto macroporous acrylic beads; these immobilized enzymes were hydrated prior to use. Near-anhydrous conditions (i.e. extremely low water activity) were maintained by a carefully chosen amount of molecular sieve powder. Kinetic characteristics were determined from reaction time courses up to full conversion at various initial concentrations of substrate and product. These progress curve data were fitted with different kinetic models to determine which of these models best approximates the kinetic properties of the immobilized Alcalase with respect to the coupling under study. An appropriate model of the coupling reaction is necessary in order to design a reactor and predict its performance adequately leading to the practical implementation of biocatalyic peptide synthesis. The kinetics of the coupling were found to be complex and to obey a two-substrate kinetic model with two competitive product inhibition terms. To reduce the effect of the product inhibition on immobilized Alcalase, a reactor should be designed in which at least glycolamide is selectively removed as this was found to be the strongest inhibitor.

Enzyme kinetic parameters are usually determined from initial rates nevertheless, laboratory instruments only measure substrate or product concentration versus reaction time (progress curves). To overcome this problem we present a methodology which uses integrated models based on Michaelis–Menten equation. The most severe practical limitation of progress curve analysis occurs when the enzyme shows a loss of activity under the chosen assay conditions. To avoid this problem it is possible to work with the same experimental points utilized for initial rates determination. This methodology is illustrated by the use of integrated kinetic equations with the well-known reaction catalyzed by alkaline phosphatase enzyme. In this work nonlinear regression was performed with the Solver supplement (Microsoft Office Excel). It is easy to work with and track graphically the convergence of SSE (sum of square errors). The diagnosis of enzyme inhibition was performed according to Akaike information criterion.