On the Lambert W function and its utility in biochemical kinetics

Goličnik, Marko

doi:10.1016/j.bej.2012.01.010

Cited by 56 publications

(45 citation statements)

References 46 publications

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“…Fitting these type of data to an appropriate nonlinear curve, such as the solution to the Michaelis–Menten equation utilized in this account, would provide the flexibility to evaluate V 0 under a wider array of experimental conditions. Furthermore, as other have described [32,43], with enough data points it may be feasible to calculate Michaelis–Menten kinetic parameters directly from nonlinear analysis of a single initial concentration of substrate, a feature which would undoubtedly provide substantial time- and cost-savings when evaluating enzyme kinetics.…”

Section: Resultsmentioning

confidence: 99%

High-performance liquid chromatography-based method to evaluate kinetics of glucosinolate hydrolysis by Sinapis alba myrosinase

Vastenhout

Tornberg

Johnson

et al. 2014

Analytical Biochemistry

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Isothiocyanates (ITCs) are one of several hydrolysis products of glucosinolates, plant secondary metabolites which are substrates for the thioglucohydrolase myrosinase. Recent pursuits toward the development of synthetic, non-natural ITCs have consequently led to an exploration of generating these compounds from non-natural glucosinolate precursors. Evaluation of the myrosinase-dependent conversion of select non-natural glucosinolates to non-natural ITCs cannot be accomplished using established UV-Vis spectroscopic methods. To overcome this limitation, an alternative HPLC-based analytical approach was developed where initial reaction velocities were generated from non-linear reaction progress curves. Validation of this HPLC method was accomplished through parallel evaluation of three glucosinolates with UV-Vis methodology. The results of this study demonstrate that kinetic data is consistent between both analytical methods and that the tested glucosinolates respond similarly to both Michaelis–Menten and specific activity analyses. Consequently, this work resulted in the complete kinetic characterization of three glucosinolates with Sinapis alba myrosinase, with results that were consistent with previous reports.

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Section: Resultsmentioning

confidence: 99%

High-performance liquid chromatography-based method to evaluate kinetics of glucosinolate hydrolysis by Sinapis alba myrosinase

Vastenhout

Tornberg

Johnson

et al. 2014

Analytical Biochemistry

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“…Corless et al . ; Valluri, Jeffrey & Corless ; Goličnik ) and its mathematical properties have been studied in great depth (e.g. Corless et al .…”

Section: Discussionmentioning

confidence: 99%

“…Schnell & Mendoza ; Goudar et al . ; Helfgott & Seier ; Williams ; Goličnik ). This suggests similar applicability in ecology and evolution due to the resemblance in the mathematical structure of many problems: biochemical kinetics, predator–prey interactions, mate searching, fertilization kinetics, disease dynamics and many others are examples of coupled systems.…”

Section: Introductionmentioning

confidence: 99%

The Lambert W function in ecological and evolutionary models

Lehtonen

2016

Methods Ecol Evol

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Summary The Lambert W function is a mathematical function with a long history, but which was named and rigorously defined relatively recently. It is closely related to the logarithmic function and arises from many models in the natural sciences, including a surprising number of problems in ecology and evolution. I describe the basic properties of the function and present examples of its application to models of ecological and evolutionary processes. The Lambert W function makes it possible to solve explicitly several models where this is not possible with elementary functions. I present examples of such models from existing literature, as well as novel models. Solving models explicitly with the Lambert W function can provide deeper insight and a new point of view on a biological problem. Explicit solutions with the Lambert W function are easily amenable to further mathematical operations, such as differentiation and integration. These advantages apply to a wide range of models, from the marginal value theorem to population growth rates and disease epidemics.

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“…Here, W þ ðxÞ ¼ W 0 ðxÞ and W À ðxÞ ¼ W À 1 ðxÞ are the lower and upper branch of the Lambert W-function (Golicnik, 2012;Veberic, 2012;Williams, 2010), where the argument is in the range À e À 1 r x o 0.…”

Section: Flow In a Concentric Annulusmentioning

confidence: 99%

General pure convection residence time distribution theory of fully developed laminar flows in straight planar and axisymmetric channels

Wörner

2015

Chemical Engineering Science

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On the Lambert W function and its utility in biochemical kinetics

Cited by 56 publications

References 46 publications

High-performance liquid chromatography-based method to evaluate kinetics of glucosinolate hydrolysis by Sinapis alba myrosinase

High-performance liquid chromatography-based method to evaluate kinetics of glucosinolate hydrolysis by Sinapis alba myrosinase

The Lambert W function in ecological and evolutionary models

General pure convection residence time distribution theory of fully developed laminar flows in straight planar and axisymmetric channels

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