Easy Kinetics: a novel enzyme kinetic characterization software Easy Kinetics: a novel enzyme kinetic characterization software Gabriele Morabito 1,2 * Correspondence: g.morabito@age.mpg.de 1 Department of Biology, University of Pisa, Pisa, Italy Keywords: computational enzymology, enzyme’s kinetic 2 Max Planck Institute for Biology of Ageing, Cologne, Germany doi: 10.5281/zenodo.3242785 Abstract Here will be presented the software Easy Kinetics, a publicly available graphical interface that allows rapid evaluation of the main kinetics parameters in an enzyme catalyzed reaction. In contrast to other similar commercial software using algorithms based on non-linear regression models to reach these results, Easy Kinetics is based on a completely different original algorithm, requiring in input the spectrophotometric measurements of ∆Abs/min taken twice at only two different substrate concentrations. The results generated show however a significant concordance with those ones obtained with the most common commercial software used for enzyme kinetics characterization, GraphPad Prism 8Ó, suggesting that Easy Kinetics can be used for routine tests in enzyme kinetics as an alternative valid software. Introduction The continuous and rapid evolution of modern biochemical methods make the study of enzyme’s kinetic very useful both in academic research, to test how interesting polypeptidic chain’s variation impact on enzymes functionality, and in industrial processes, to optimize the production processes of the molecules of interest in enzymatic reactors [2]. The Michaelis-Mentem reaction mechanism was proposed almost a century ago to describe how the reaction speed of enzymes is affected by the substrate’s concentration [3], and it’s still the core reference model to describe enzymes kinetics. This model however requires a few parameters to fit the raw data: "#, Km and Vmax. Several methods were developed by biochemists during years to evaluate these parameters from the raw data, the most used of which allow software like GraphPad Prism 8Ó [1] to apply linear or non-linear regression model [4]. Original alternative methods for Km and Vmax determination were proposed, which graphically determine these values [5], but like the previous ones they require multiple spectrophotometric measurements of ∆Abs/min (at least 6 conducted in duplicate) at different substrate concentrations to precisely determine the main kinetic parameters. In this paper will be presented an alternative method implemented in the software Easy Kinetics, which allows determination of the main kinetics parameters of an enzyme catalyzed reaction and the corresponding kinetics graphs, by the spectrophotometric measurements of ∆Abs/min taken twice at only two different substrate concentrations. Materials and methods Algorithm used in evaluation of Km and Vmax: The evaluation of Km and Vmax by the spectrophotometric measurements of ∆Abs/min taken twice at only two different substrate concentrations, is based on a trigonometric demonstration (Fig.1). Briefly the algorithm transforms the mean of the duplicates at the two measurements in their reciprocal values, considering the Lineweaver-Burk reciprocal plot. Known two points of this graph, it’s universally accepted that they can be joined by one and only one straight line. This line will have an unknown inclination "a" and will intersect the Cartesian axes in points %&'() and - % *' , also unknown. However by tracing the projections of the two known .CC-BY 4.0 International licenseavailable under a not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which wasthis version posted January 2, 2021. ; https://doi.org/10.1101/674051doi: bioRxiv preprint https://doi.org/10.1101/674051 http://creativecommons.org/licenses/by/4.0/ points (x1,y1) and (x2,y2) on the Cartesian plane, it is evident that the parallel lines y = y2 and y = 0 intersect the studied straight line. By the Alternate Interior Angles theorem [6], if two parallel lines are cut by a transversal one, then the pairs of alternate interior angles are congruent: so, by Fig.1, "a" = "a1". Considering instead the lines y = y2 and y = y1, which are also parallel and intersected by the studied straight line, for the same theorem discussed before, their internal alternate angles are congruent: so, by Fig.1, "a1" = "a2". This implies that: tan(/) = 23 − 2% 53 − 5% But also 6 78 = tan(/), with 9 = 23 − % &'() , so: 1 ;<=7 = 23 − z = 23 − (tan(/) ∗ 53) = 23 − 53 ∗ (23 − 2%) 53 − 5% Once calculated % &'() , the value of % *' can be determined as follow: @− 1 A< @ = 1 ;<=7 tan(/) Inverting the two previous values, A<(? ∗@ [A] B? C 9: D< ;,9: .,EFG = HI ∗ JK L∗ M U = OPQRGSR = TU TV D ∗ W ∗ X YZ = AbsZ^E_`Ga − AbsbF0ac 0.064 ∗ O i0j_GkG_l = U YZ +j0_ = P.M ∗ .,01 X ∗ W ∗ YZ Y`ooGjG`ajl = $%&>/ ;pqr ;s Equation used for the generation of the kinetic graph Equation used for the evaluation of the V0 at a set chosen substrate Equation used to switch the previously evaluated V0, expressed in ∆Abs/min, into a new V0 value expressed in μmoli of reporter product generated per minute Equation used for the evaluation of the enzymatic units in the sample Equation used for the evaluation of the protein concentration during the Bradford assay Equation used for the evaluation of the enzyme’s specific activity Equation used for the evaluation of the enzyme’s Kcat Equation used for the evaluation of the enzyme’s catalytic efficiency Equation used for the evaluation of the Hill coefficient .CC-BY 4.0 International licenseavailable under a not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which wasthis version posted January 2, 2021. ; https://doi.org/10.1101/674051doi: bioRxiv preprint https://doi.org/10.1101/674051 http://creativecommons.org/licenses/by/4.0/ where [S] represents the substrate’s concentration; Si can be 1, if substrate’s inhibition is present or 0, if substrate’s inhibition is absent; Ki represents the inhibition’s constant evaluated at a very high substrate’s concentration as: +G = (>//∗ ;s)t (uII∗ Bs)∗ vsqw xyz(uII∗Bs){Bs{ (uII∗ Bs) when substrate inhibition is present +G = 1 when substrate inhibition is absent Lf represents the final volume of the sample; Li represents the starting volume of the sample; ε represents the extinction molar coefficient of the product; O represents the optical path of the spectrophotometer; Abshigh represents the absorbance measured at a very high substrate’s concentration; Absprotein represents the absorbance of the protein’s solution; Absblank represents the absorbance measured for the previous solution without proteins inside; P.M. represents the molecular weight of the reporter product. Enzyme’s ∆Abs/min raw data for several concentrations of tested limiting substrates: Tab.1 Experimentally measured ∆Abs/min values for several substrate’s concentrations in the enzyme’s catalyzed reactions tested. .CC-BY 4.0 International licenseavailable under a not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made The copyright holder for this preprint (which wasthis version posted January 2, 2021. ; https://doi.org/10.1101/674051doi: bioRxiv preprint https://doi.org/10.1101/674051 http://creativecommons.org/licenses/by/4.0/