Notes & TipsExplicit analytic approximations for time-dependent solutions of the generalized integrated Michaelis–Menten equation
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Acknowledgment
This study was supported by the Slovenian Research Agency (Grant P1-170).
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Mechanistic insights on novel small molecule allosteric activators of cGMP-dependent protein kinase PKG1α
2022, Journal of Biological ChemistryDrug discovery for enzymes
2021, Drug Discovery TodayCitation Excerpt :The study of full progress curves has several advantages, such as automatic and continuous variation of the substrate concentration with progression of the reaction beyond the initial linear phase, stoichiometric formation of the genuine product, and the potential to obtain kinetic properties from fewer experiments [28]. Although several approaches to solving integrated rate equations have been described [28–33], only the advent of explicit analytical reformulations of the integrated rate equations made this analysis broadly applicable in a drug discovery environment [34–36]. A recent example of the application of integrated rate equations in HTS assays for drug discovery is the determination of drug residence time for inhibitors of protein kinases [37].
Selection and optimization of enzyme reporters for chemical cytometry
2019, Methods in EnzymologyCitation Excerpt :The additional parameter kcat (turnover number) of an enzyme-substrate reaction is a measure of how quickly a given amount of enzyme can convert substrate to product in a given unit of time, with high kcat values indicating rapid turnover. In the procedure described below, KM and kcat are estimated by generating progress curves of substrate phosphorylation by recombinant enzyme and fitting the curves with the time-dependent Michaelis-Menten equation using an analytical approximation of the Lambert function (Goličnik, 2011; Yun & Suelter, 1977). Benefits of this method over the more commonly used initial velocities method include savings in cost, time, and reagents consumed as well as being able to use more data gathered over the entirety of the progress curve, enabling a better fit of the overall data to estimate the kinetic parameters.
On the Lambert W function and its utility in biochemical kinetics
2012, Biochemical Engineering JournalCitation Excerpt :The main advantage of these solutions is that global progress-curve analysis explicitly shows the reliability of the results. Although this review is mainly focused on problems considering the Lambert W function that appear in the biochemical and biotechnological disciplines [22–29,34–39], and in chemical engineering [13–19], other applications of W of practical import have been discovered in various engineering and life sciences, and I cite here only recently published literature. Thus, W appears in solutions to a large family of equations that describes situations in physiology [40,41], hydrology [42,43], colloid and interface science [44,45], materials and transport research [46–48], electrochemistry [49], and droplet microfluidics [50].