Graphpad Enzyme Kinetics

[Fe Kittner]

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Enzymes are nature's catalysts, mediating chemical processes in living systems. The study of enzyme function and mechanism includes defining the maximum catalytic rate and affinity for substrate/s (among other factors), referred to as enzyme kinetics. Enzyme kinetics is a staple of biochemistry curricula and other disciplines, from molecular and cellular biology to pharmacology. However, because enzyme kinetics involves concepts rarely employed in other areas of biology, it can be challenging for students and researchers. Traditional graphical analysis was replaced by computational analysis, requiring another skill not core to many life sciences curricula. Computational analysis can be time-consuming and difficult in free software (e.g., R) or require costly software (e.g., GraphPad Prism). We present Enzyme Kinetics Analysis (EKA), a web-tool to augment teaching and learning and streamline EKA. EKA is an interactive and free tool for analyzing enzyme kinetic data and improving student learning through simulation, built using R and RStudio's ShinyApps. EKA provides kinetic models (Michaelis-Menten, Hill, simple reversible inhibition models, ternary-complex, and ping-pong) for users to fit experimental data, providing graphical results and statistics. Additionally, EKA enables users to input parameters and create data and graphs, to visualize changes to parameters (e.g., K M or number of measurements). This function is designed for students learning kinetics but also for researchers to design experiments. EKA (enzyme-kinetics.shinyapps.io/enzkinet_webpage/) provides a simple, interactive interface for teachers, students, and researchers to explore enzyme kinetics. It gives researchers the ability to design experiments and analyze data without specific software requirements.

The kinetics of lysozyme was measured as a function of concentration of its substrate NAM-NAG, a disaccharide found as a major structural component in many bacterial cell walls. Lysozyme will hydrolyze the bond between the two sugar components of this disaccharide.

The assay is done as follows: the enzyme produces product at an initial rate that is approximately linear for a short period after the start of the reaction. As the reaction proceeds and substrate is consumed, the rate continuously slows. To measure the initial rate, enzyme assays are carried out while the reaction has progressed only a few percent.

In our case, initial rates were measured for a range of substrate concentrations (0 mM - 9.0 mM NAM-NAG). The enzyme was then assayed over the same concentration range, but in the presence of 2 mM inhibitor X and 5 mM inhibitor Y. The data are available as a csv file.

Open the file in WordPad.

The first column shows the substrate concentrations.

The next columns show the initial reaction rates in the three conditions that have been tested.

To analyze the data we need to plot the initial rate of the reaction in function of the substrate concentration.

The initial rate of the reaction (v0) increases as the substrate concentration (S) increases. However, as the substrate concentration gets higher, the enzyme becomes saturated with substrate and the rate reaches a maximum (Vmax). So the relation between V0 and S is not linear.

Continuous enzyme kinetic assays are often used in high-throughput applications, as they allow rapid acquisition of large amounts of kinetic data and increased confidence compared to discontinuous assays. However, data analysis is often rate-limiting in high-throughput enzyme assays, as manual inspection and selection of a linear range from individual kinetic traces is cumbersome and prone to user error and bias. Currently available software programs are specialized and designed for the analysis of complex enzymatic models. Despite the widespread use of initial rate determination for processing kinetic data sets, no simple and automated program existed for rapid analysis of initial rates from continuous enzyme kinetic traces.

An Interactive Continuous Enzyme Kinetics Analysis Tool (ICEKAT) was developed for semi-automated calculation of initial rates from continuous enzyme kinetic traces with particular application to the evaluation of Michaelis-Menten and EC50/IC50 kinetic parameters, as well as the results of high-throughput screening assays. ICEKAT allows users to interactively fit kinetic traces using convenient browser-based selection tools, ameliorating tedious steps involved in defining ranges to fit in general purpose programs like Microsoft Excel and Graphpad Prism, while still maintaining simplicity in determining initial rates. As a test case, we quickly analyzed over 500 continuous enzyme kinetic traces resulting from experimental data on the response of the protein lysine deacetylase SIRT1 to small-molecule activators.

ICEKAT allows simultaneous visualization of individual initial rate fits and the resulting Michaelis-Menten or EC50/IC50 kinetic model fits, as well as hits from high-throughput screening assays. In addition to serving as a convenient program for practicing enzymologists, ICEKAT is also a useful teaching aid to visually demonstrate in real-time how incorrect initial rate fits can affect calculated Michaelis-Menten or EC50/IC50 kinetic parameters. For the convenience of the research community, we have made ICEKAT freely available online at

In cases where complex kinetic programs are not required, scientists often resort to manual inspection, selection, and fitting of a linear range from each individual kinetic trace using graphing programs such as Microsoft Excel or GraphPad Prism. This approach is time-consuming and susceptible to human error or bias, particularly when low substrate concentrations result in significant curvature of the observed continuous kinetic trace. For our own studies, we unsuccessfully searched for programs that expedited determination of initial rates from continuous enzyme kinetic traces. To fill this void, we developed an Interactive Continuous Enzyme Kinetics Analysis Tool (ICEKAT) for semi-automated initial rate calculations that maintains simplicity while allowing rapid and user-interactive visualization of initial rate fits. For the convenience of the research community, we converted ICEKAT into a publicly-available, browser-based program ( ) to which users can upload series of kinetic traces in comma separated values (CSV) format and download the resulting table of initial rates for further analysis and plotting. ICEKAT has several advantages over other available programs for analyzing enzyme kinetics experiments in that it is free, open source, and does not require any downloads or installations prior to use (Table 1). In addition, ICEKAT includes a plot of the Michaelis-Menten (or IC50/EC50) fit for the uploaded experiment that is automatically updated based on user interaction with the time ranges used to calculate initial rates (Table 1). As a result, we have found that ICEKAT also serves as a useful teaching aid when demonstrating how incorrect fitting of initial rates from kinetic traces can affect the Michaelis-Menten or IC50/EC50 parameters calculated from an experiment.

All calculations are carried out in Python using numpy, and both linear and non-linear regression is performed using the Model and curve_fit functions from the lmfit and scipy.optimize modules, respectively. Measured signal can be converted to substrate concentration according to a user-defined transform equation entered into a text box. In linear mode, slopes corresponding to initial rates are determined using a straight line fit to a user-specified segment of the kinetic trace. In logarithmic mode, selected kinetic traces are fit to a logarithmic approximation of the integrated Michaelis-Menten equation defined by

where yo is the background signal, to > 0 is the scale of the logarithmic curve, and b > 0 is a shape parameter [3]. The kinetic trace slope corresponding to the initial rate is equal to the first derivative of the logarithmic fit when t = 0. In Schnell-Mendoza mode, kinetic data is globally fit to the closed form solution to the Michaelis-Menten equation for uncompetitive enzymatic reactions previously described by Schnell and Mendoza [11]

where [S] is the substrate concentration, KM is the Michaelis constant, W is the omega function [12] (implemented using the lambertw function from scipy.special), [S0] is the initial substrate concentration, and Vmax is the maximum reaction velocity. The source code for ICEKAT is freely available at

Continuous enzyme kinetic traces are uploaded in CSV format using the green button labeled "Upload Local File" at the top of the page (Fig. 1a). While no uploaded data is saved by ICEKAT, users concerned about privacy can download the associated GitHub repository ( ) and run the application locally. Each CSV file should have one column containing time in seconds or minutes. The remaining CSV columns should contain time-course data, where each column heading contains a number corresponding to titrant concentration (an example CSV file for Michaelis-Menten fitting is included as Appendix C and at ). Depending on the type of experiment being analyzed, users can choose to fit datasets in Michaelis-Menten, EC50/IC50, or high-throughput screening (HTS) modes using the dropdown menu labeled "Choose Model" (Fig. 1b). Upon file upload, all kinetic traces are automatically fit to a straight line that maximizes slope magnitude (Fig. 1c), the model fit for the dataset (Fig. 1e) is plotted to the right of the selected trace (Fig. 1d), and the initial rate and model fit values with propagated errors are listed in data tables (Fig. 1f). Users can select individual kinetic traces using the dropdown menu "Y Axis Sample" (Fig. 1b) and manually refit subsets of the time-course data to obtain random residual distributions by entering start and end times in the "Enter Start Time" and "Enter End Time" text boxes and fine tuning the x-axis range using the slider tool (Fig. 1g). Upon refitting an individual kinetic trace, the model fit plot (Fig. 1e) and the data tables (Fig. 1f) are automatically updated. Users may subtract the slope of a blank sample from the rest of the dataset using the "Select Blank Sample for Subtraction" dropdown menu (Fig. 1b). Users can also transform measured signal into meaningful substrate concentrations by entering a transform equation (signal as a function of time "x", e.g. "x/(extinction coefficient path length enzyme concentration)") in the "Enter Transform Equation" box (Fig. 1b). Finally, the initial rates listed in the table at the right can be copied to the clipboard by clicking the blue button labeled "Copy Table to Clipboard" or downloaded as a CSV file using the blue button labeled "Download Table to CSV" (Fig. 1f). To encourage wide adoption of ICEKAT, we have created a tutorial (Appendix B).

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