Analysis of continuous enzyme kinetic data using ICEKAT

Abstract

ICEKAT (Interactive Continuous Enzyme Analysis Tool) is an interactive web-based program for calculating initial rates and kinetic parameters (e.g., $V_{\mathrm{m}\mathrm{a}\mathrm{x}},k_{\mathrm{c}\mathrm{a}\mathrm{t}},K_{\mathrm{M}},{\mathrm{E}\mathrm{C}}_{50},{\mathrm{I}\mathrm{C}}_{50}$) from continuous enzyme kinetic assay data that satisfy Michaelis–Menten and steady-state kinetic assumptions. ICEKAT is valuable in educational and research settings to consistently and accurately calculate initial rates and kinetic parameters, increasing assay veracity and reproducibility. Provided freely online to the scientific community, ICEKAT has been cited in at least 26 publications, and the initial journal article has been accessed nearly 9000 times since its debut in 2020 (Olp et al., 2020). Here, we provide in-depth instructions for software use, offer vital considerations for data analysis, and highlight updated software features for new and existing users. Through ICEKAT, we aim for the analysis of data from continuous enzyme kinetic studies worldwide to become more rapid, reliable, and repeatable. ICEKAT remains free of charge and available to all scientists at https://icekat.herokuapp.com/icekat; the source code for local use is found at https://github.com/SmithLabMCW/icekat.

1. Introduction

Under steady-state kinetic assumptions for an enzymatic reaction, the initial rate depends solely on the concentration and kinetic parameters of the enzyme (e.g., $V_{\mathrm{m}\mathrm{a}\mathrm{x}},k_{\mathrm{c}\mathrm{a}\mathrm{t}},K_{\mathrm{M}}$) (Cornish-Bowden, 2013; Michaelis, Menten, Johnson & Goody, 2011). Accordingly, initial rate calculations provide valuable insights into the mechanisms and biological roles of the enzyme. Initial rate calculations also mitigate several issues inherent in analyzing enzyme kinetics over extended periods, including chemical environment perturbations, enzyme stability, effects of reverse reactions on product concentration, and enzyme inhibition through product formation (i.e., product inhibition) (Cornish-Bowden, 2013; Michaelis et al., 2011). Initial rates can be determined through continuous and discontinuous enzyme kinetic assays; however, continuous assays are preferred for their greater sensitivity, accuracy, and experimental control (Kramer, 1980).

Initial rates are derived from continuous enzyme kinetic assays by many methods, including (a) calculating the slope of the linear portion of the assay data (Cornish-Bowden, 1975), (b) graphing the change in product formation over time $(\mathrm{\Delta }\mathrm{P}/t)$ versus total product formed $\left(\mathrm{\Delta }\mathrm{P}\right)$ and extrapolating backward to identify the y-intercept of this plot $\left(\mathrm{d}\mathrm{P}/\mathrm{d}{t}_0\right)$ (Boeker, 1982), (c) fitting assay data to integrated expressions of kinetic equations with more complex linear or nonlinear regressions (Cornish-Bowden, 1975; Duggleby, 1985; Jennings & Niemann, 1955; Lu & Fei, 2003; Nicholls, Jerfy, & Roy, 1974), or (d) fitting assay data to polynomials (Booman & Niemann, 1956; Cornish-Bowden, 1975; Elmore, Kingston, & Shields, 1963). The method of Boeker facilitates initial rate analysis for higher-order reaction mechanisms (Boeker, 1982). This method also avoids initial rate calculation errors introduced by eventual substrate depletion by excluding deviating later data points (Boeker, 1982). However, the Boeker method of initial rate determination is less suited for kinetics data derived from microplate assays, as correction for variable microplate background absorbances is difficult when extrapolating data backward to identify the initial rate from the y-intercept (Boeker, 1982). More complex methods of initial rate determination, especially those dealing with integrated forms of kinetic equations, suffer from substantial errors when enzyme kinetic parameters are derived from the entire kinetic trace (Cornish-Bowden, 1975; Cornish-Bowden, 2013). Additionally, satisfying steady-state kinetic assumptions in experimental conditions benefits analysis by ensuring data linearity (Cornish-Bowden, 1975). Thus, a simple calculation of the slope of the initial linear portion of the data suffices to confidently determine enzyme kinetic parameters from initial rates.

Several software programs exist for enzyme kinetic analyses, including DynaFit (Kuzmič, 1996), ENZO (Bevc et al., 2011), FITSIM (Zimmerle & Frieden, 1989), KinTek (Johnson, Simpson, & Blom, 2009), PCAT (Bäuerle, Zotter, & Schreiber, 2017), and renz (Aledo, 2022). Most of these programs rely on more elaborate analysis algorithms, so they are suited for analyzing data derived from enzymes with multifactorial reaction mechanisms or in situations where Michaelis–Menten kinetic criteria are not readily met (Hill, Waight, & Bardsley, 1977; Srinivasan, 2021). Conversely, many in vitro enzyme assays satisfy Michaelis–Menten and steady-state kinetic assumptions and do not require elaborate data analysis methods. In response to a lack of accessible computational programs focused on determining initial rates from continuous enzyme kinetic assay data, we developed ICEKAT, an interactive continuous enzyme kinetics analysis tool for the semi-automated calculation of initial rates (Olp, Kalous, & Smith, 2020). This tool circumvents the inaccuracies, user bias, and extensive time commitments inherent in manual data fitting and analysis with software programs like GraphPad Prism or Microsoft Excel (Olp et al., 2020). A comparison of ICEKAT to other existing enzyme kinetic analysis software programs demonstrates that ICEKAT meets multiple scientific needs in initial rate calculation from enzymatic studies (Table 1). Uniquely, ICEKAT is a web-based, real-time biochemistry teaching tool that demonstrates the importance of accurate enzyme kinetic data analysis by illustrating how fitting errors affect the determined steady-state parameters (Olp et al., 2020).

Table 1.

Comparison of ICEKAT to existing enzyme kinetic analysis software programs.

Software	Free and open source	No download required	Optimized for ${\mathbf{p}\mathbf{E}\mathbf{C}}_{\mathbf{50}}/\mathbf{p}{\mathbf{I}\mathbf{C}}_{\mathbf{50}}$ and HTS analysis	Visual teaching aid
ICEKAT	✓	✓	✓	✓
DYNAFIT	✓	✕	✕	✕
Enzo	✓	✓	✕	✕
FITSIM	✓	✕	✕	✕
KinTek	✕	✕	✕	✓
PCAT	✓	✕	✕	✕
renz	✓	✕	✕	✓

2. Program implementation

ICEKAT employs the Python NumPy package to calculate initial rates, where linear and non-linear regressions are performed using the lmfit Model class (Olp et al., 2020). Upon upload of continuous enzyme kinetic assay data in CSV or Text file format, data fitting proceeds under one of four user-determined models based on the nature of the experiment: (a) Michaelis–Menten, (b) $k_{\mathrm{c}\mathrm{a}\mathrm{t}}/K_{\mathrm{M}}$ (Johnson, 2019) (a new feature implemented since the original 2020 ICEKAT release), (c) ${\mathrm{p}\mathrm{E}\mathrm{C}}_{50}/\mathrm{p}{\mathrm{I}\mathrm{C}}_{50}$, where p represents the molar negative log₁₀ of the respective value (Baressi Šegota, Lorencin, Kovač, & Car, 2023), or (d) High-Throughput Screen (HTS). The Michaelis–Menten model focuses data analysis toward determining initial rates, $V_{\mathrm{m}\mathrm{a}\mathrm{x}}$, and $K_{\mathrm{M}}$. Users can also divide ICEKAT-generated $V_{\mathrm{m}\mathrm{a}\mathrm{x}}$ values by the enzyme concentration used in the assay to determine $k_{\mathrm{c}\mathrm{a}\mathrm{t}}$ values. The $k_{\mathrm{c}\mathrm{a}\mathrm{t}}/K_{\mathrm{M}}$ model focuses data analysis toward determining initial rates, $k_{\mathrm{c}\mathrm{a}\mathrm{t}}$, and $k_{\mathrm{c}\mathrm{a}\mathrm{t}}/K_{\mathrm{M}}$. The ${\mathrm{p}\mathrm{E}\mathrm{C}}_{50}/\mathrm{p}{\mathrm{I}\mathrm{C}}_{50}$ model focuses data analysis toward determining initial rates and ${\mathrm{p}\mathrm{E}\mathrm{C}}_{50}/\mathrm{p}{\mathrm{I}\mathrm{C}}_{50}$ values. As ${\mathrm{E}\mathrm{C}}_{50}/{\mathrm{I}\mathrm{C}}_{50}$ values exhibit skewed distributions (Ferreira et al., 2019; Singh, Mahadik, Surana, & Arora, 2022), measuring enzyme activation or inhibition in terms of ${\mathrm{p}\mathrm{E}\mathrm{C}}_{50}/\mathrm{p}{\mathrm{I}\mathrm{C}}_{50}$ values corrects this issue. The ${\mathrm{p}\mathrm{E}\mathrm{C}}_{50}/\mathrm{p}{\mathrm{I}\mathrm{C}}_{50}$ model also determines the values of the bottom and top of the fitted ${\mathrm{p}\mathrm{E}\mathrm{C}}_{50}/\mathrm{p}{\mathrm{I}\mathrm{C}}_{50}$ curve and the Hill slope of the fitted ${\mathrm{p}\mathrm{E}\mathrm{C}}_{50}/\mathrm{p}{\mathrm{I}\mathrm{C}}_{50}$ curve, which is the slope of the sigmoidal curve (Endrenyi, Fajszi, & Kwong, 1975). In the ${\mathrm{p}\mathrm{E}\mathrm{C}}_{50}/\mathrm{p}{\mathrm{I}\mathrm{C}}_{50}$ model, changes in initial rates and corresponding propagated errors are automatically reflected in the fit to the 4-parameter logistic model (Eq. (1)):

$$\mathit{y}=\mathit{b}\mathit{o}\mathit{t}\mathit{t}\mathit{o}\mathit{m}+\frac{\mathit{t}\mathit{o}\mathit{p}-\mathit{b}\mathit{o}\mathit{t}\mathit{t}\mathit{o}\mathit{m}}{1+{10}^{\mathit{H}\mathit{i}\mathit{l}\mathit{l}\mathit{S}\mathit{l}\mathit{o}\mathit{p}\mathit{e}\times \left(\mathit{p}\mathit{I}{\mathit{C}}_{50}-\mathit{x}\right)}}$$ (1)

The HTS model focuses data analysis toward determining initial rates for many samples (e.g., when screening many enzyme activators/inhibitors in a 96- or 384-well plate format; especially useful for pharmacological studies).

Data fitting is accomplished with one of four-user determined modes: (a) Maximize Slope Magnitude, (b) Linear Fit, (c) Logarithmic Fit, or (d) Schnell–Mendoza. All four modes require a minimum of five data points for fitting. In the default Maximize Slope Magnitude mode, uploaded data is automatically fit to a straight line that maximizes slope magnitude. The slope of this line corresponds to the initial rate. Through this fitting process, linear regression is used to maximize the first derivative of the data smoothed by cubic spline interpolation (Olp et al., 2020). In the Linear Fit mode, a straight line is fit to a user-specified data segment, and the slope of this straight line corresponds to the initial rate. In the Logarithmic Fit mode, data is fit to a logarithmic approximation of the integrated Michaelis–Menten equation (Eq. (2)):

$$\mathit{y}={\mathit{y}}_0+\mathit{b}\times \mathrm{l}\mathrm{n}(1+\frac{\mathit{t}}{{\mathit{t}}_0})$$ (2)

where $y_0$ is the background signal, $t_0>0$ is the scale of the logarithmic curve, and $b>0$ is a shape parameter (Lu & Fei, 2003; Olp et al., 2020). Here, the data slope corresponding to the initial rate equals the first derivative of the logarithmic fit at $t=0$. Logarithmic Fit mode is beneficial to avoid underestimation of initial rates in cases where a linear segment cannot be readily determined from early kinetic data. In the Schnell–Mendoza mode, all input data is globally fit to the closed-form solution of the Michaelis–Menten equation (Eq. (3)) (Schnell & Mendoza, 1997):

$$[\mathit{S}](\mathit{t})={\mathit{K}}_{\mathrm{M}}\mathit{W}\left(\frac{\left[{\mathit{S}}_0\right]}{{\mathit{K}}_{\mathrm{M}}}\mathrm{e}\mathrm{x}\mathrm{p}\left(\frac{-{\mathit{V}}_{\mathrm{m}\mathrm{a}\mathrm{x}}\mathit{t}+\left[{\mathit{S}}_0\right]}{{\mathit{K}}_{\mathrm{M}}}\right)\right)$$ (3)

where $\left[S_0\right]$ is the initial substrate concentration, [$S$] is the remaining substrate concentration at a particular point in time, $K_{\mathrm{M}}$ is the Michaelis constant, $W$ is the omega function (implemented in ICEKAT with the scipy.special.lambertw function), and $V_{\mathrm{m}\mathrm{a}\mathrm{x}}$ is the maximal reaction velocity (Fritsch, Shafer, & Crowley, 1973; Olp et al., 2020).

Note: Although ICEKAT does not save any uploaded data, users who desire to run the application locally can download the associated GitHub files at https://github.com/SmithLabMCW/icekat.

3. User’s guide to ICEKAT

3.1. Required materials

• Data from a continuous enzyme kinetic experiment

• Computer with Internet access

• Microsoft Excel or other spreadsheet programs (e.g., GraphPad Prism or Apple Numbers) capable of producing the Comma Separated Values (CSV) or Text file formats

• ICEKAT, available at https://icekat.herokuapp.com/icekat

Note: ICEKAT should only be used to calculate initial rates for data where steady-state assumptions (Eq. (4)) are satisfied:

$$\frac{\left[{\mathit{E}}_0\right]}{\left({\mathit{K}}_{\mathrm{M}}+\left[{\mathit{S}}_0\right]\right)}\ll 1$$ (4)

where $\left[E_0\right]$ is the initial enzyme concentration, $\left[S_0\right]$ is the initial substrate concentration, and $K_{\mathrm{M}}$ is the Michaelis constant (Olp et al., 2020; Schnell & Mendoza, 1997). Although there is no specific cutoff to the left-hand side of Eq. (4) for ICEKAT analysis to proceed, values approaching zero increase analysis validity.

3.2. Continuous enzyme kinetic assay data analysis in ICEKAT

3.2.1. Preparing and uploading data to ICEKAT

1. Arrange continuous enzyme kinetic assay data into columns in Microsoft Excel or another spreadsheet program. The first column should contain time data in integer or decimal format (Fig. 1, Concentration-dependent Data, Cell A1). Any additional columns should have time-dependent assay readout data separated by experimental conditions. For Michaelis–Menten, $k_{\mathrm{c}\mathrm{a}\mathrm{t}}/K_{\mathrm{M}}$, or pEC₅₀/pIC50 analyses, each column heading is labeled accordingly with numbers and units representing titrant (e.g., substrate, small molecule inhibitor, small molecule activator) concentration (Fig. 1, Concentration-dependent Data, Cell B1). For high-throughput screening analyses, any additional columns should have time-dependent assay readout data separated by well position on a 96- or 384-well plate, where each column heading is labeled with the well name (e.g., A1) (Fig. 1, High-throughput screening Data, Cell B1). If the data does not fit any analysis regimes described above, any generic heading may be used in the time-dependent assay readout data columns, and initial rates exported for further user-directed analysis outside ICEKAT.

   Note: ICEKAT uses the first continuous integer or float in each column heading of time-dependent assay readout data to determine substrate/inhibitor/activator concentration, so column headings should contain the appropriate information without other numbers preceding it. Additionally, ICEKAT does not differentiate between data presented with different units (e.g., μM vs. mM), so column headings should contain numbers in the same unit magnitude (e.g., μM only).

   Caution: Remove any extraneous metadata in the spreadsheet acquired from data collection, as this will cause errors in ICEKAT data upload/processing. Similar errors may arise with unsupported non-UTF-8 encoded characters in uploaded data files, especially from non-English languages (e.g., file names and column headings). To avoid this issue, use only UTF-8 encoded characters in uploaded data files. Special characters in uploaded data files are discouraged.

2. Save data in a Comma Separated Values (CSV) or Text file format. The file can be in any of the standard CSV or Text file formats: CSV (comma delimited), CSV UTF-8 (comma delimited), CSV (Macintosh), CSV (MS-DOS), Text (Tab delimited), Text (Macintosh), or Text (MS-DOS).

   Note: Text file formats must be used when uploading European-style data with commas denoting decimal points.

3. Access the ICEKAT graphical user interface through https://icekat.herokuapp.com/icekat.

4. Upload saved kinetic data in CSV or Text file format to ICEKAT by clicking the green ‘Upload Local File’ button (Fig. 2A) in the top left corner of the ICEKAT window and selecting the CSV or Text file from its location on the computer.

5. Upon data upload, note that the displayed data in the ICEKAT window should switch from the sample dataset to the user-uploaded dataset. The initial rate fit and model fit for the dataset are plotted as graphs (Fig. 2B, C) in the center of the ICEKAT window. Initial rates as slope values and additional model fit values with corresponding propagated errors are also displayed in results tables (Fig. 2D) to the right of the plots.

Fig. 1.

Preparing data for ICEKAT analysis. Concentration-dependent data: For standard data analysis, data should be formatted in a spreadsheet, where the first column contains time data, and the column heading specifies time units. All other columns in the spreadsheet should contain assay data, where the column headings specify titrant concentration numbers and units. High-throughput screening data: For HTS data analysis, data should be formatted in a spreadsheet, where the first column contains time data, and the column heading specifies time units. All other columns in the spreadsheet should contain assay data, where the column headings specify the name of a well (e.g., from a 96-well plate).

Fig. 2.

Getting started with ICEKAT. (A) Click the green ‘Upload Local File’ to upload user-generated kinetic data in CSV or Text file format. (B) With data upload, the initial rate fit for the dataset is plotted as a graph. (C) With data upload, the selected model fit for the dataset is plotted as a graph. (D) Initial rates as slope values and additional model fit values with corresponding propagated errors from the fitted data are displayed in results tables.

3.2.2. Semi-automated ICEKAT data analysis

1. Select the preferred model for data analysis (Michaelis–Menten, $k_{\mathrm{c}\mathrm{a}\mathrm{t}}/K_{\mathrm{M}},{\mathrm{p}\mathrm{E}\mathrm{C}}_{50}/\mathrm{p}{\mathrm{I}\mathrm{C}}_{50}$, or HTS) using the ‘Choose Model’ drop-down menu (Fig. 3A) under the ‘Upload Local File’ button.

   Caution: Be aware that each model for data analysis carries unique limitations (see Olp et al., 2020; for a discussion of these limitations).

2. Select the desired mode for data analysis (Maximize Slope Magnitude, Linear Fit, Logarithmic Fit, or Schnell–Mendoza) by clicking the appropriate button above the plots in the center of the ICEKAT window (Fig. 3B).

   Note: Uploaded data is automatically fit to the default Maximize Slope Magnitude mode if another mode is not selected.

   Note: Schnell–Mendoza mode can only be used if the data is analyzed under the Michaelis–Menten model.

3. To view the initial rate fit and model fit plots for the dataset of a particular experimental condition, select the experimental condition from the ‘Y-Axis Sample’ drop-down menu (Fig. 3C) located below the ‘Choose Model’ drop-down menu.

   Optional: To ensure that the most linear portion of the data is being fit, the user can manually adjust the range of data analyzed by entering start and end times in the corresponding text boxes (Fig. 3D) in the bottom center of the ICEKAT window and/or alter the x-axis range with the slider tool (Fig. 3E) below. Well-fit data will yield a random distribution of points (Mannervik, 1982) in the initial rate fit residuals plot (Fig. 3F) located under the initial rate fit and model data plots.

   Note: If needed, this optional step helps reduce errors derived from the inaccurate fitting of artifacts in the kinetic data.

   Critical: Avoid excessive manipulation of the time range analyzed, as this will yield artificially optimized fits to the Michaelis–Menten equation and introduce user bias into the data fits.

   Optional: To subtract the initial rate slope of a blank sample from the rest of the dataset, select the desired experimental condition for subtraction with the corresponding drop-down menu (Fig. 3G) located under the ‘Y-Axis Sample’ drop-down menu.

4. Select and adjust the fit for any remaining experimental conditions in the uploaded dataset, as necessary.

   Note: When kinetic data is re-fit by changing the experimental condition, model, mode, or time range used in the analyses, the corresponding initial rate fit and model data plots (Fig. 2B, C) and results tables (Fig. 2D) are automatically updated.

5. To convert the results table from initial rate slope values to actual initial rate values for a given enzyme concentration, enter a transform equation (e.g., Eq. (5)) in the ‘Enter Transform Equation’ text box (Fig. 3H), located under the ‘Select Blank Sample for Subtraction’ drop-down menu:

   $$\mathit{x}/(\mathit{\epsilon }\times \ell \times [\mathit{E}])$$ (5)

   where $x$ is the raw signal expressed as a function of time, $\epsilon$ is the enzyme extinction coefficient, $\ell$ is the path length, and $[E]$ is the enzyme concentration. When entering the equation into the text box, use ‘/’ for division and ‘*’ for multiplication functions.

   Note: If the enzyme mass is known instead of its concentration, this transform equation can instead be used to express initial rates in terms of the enzyme mass used (e.g., nmol/min/mg protein).

6. After completing the data analysis, export the calculated initial rates from ICEKAT by copying them to the clipboard or downloading them as a CSV file. Click the blue ‘Download Table to CSV’ or ‘Copy Table to Clipboard’ buttons (Fig. 3I) in the top right corner of the ICEKAT window. Data will export in three columns, where x (first column) = experimental condition, y (second column) = initial rate as the slope of the fitted data (or as initial rate value if transformed), and e (third column) = fit error.

Fig. 3.

Basic functions of ICEKAT data analysis. (A) Select the desired model for data analysis with the ‘Choose Model’ drop-down menu. (B) Select the desired mode for data analysis by clicking the corresponding button above the initial rate fit and model fit plots. (C) Select a specific experimental condition from the ‘Y-Axis Sample’ drop-down menu to view the corresponding fit plots. (D) Optional step: Manually adjust the x-axis range of data analyzed by entering start and end times in the corresponding text boxes under the initial rate fit and model data plots. (E) Alternatively, adjust the x-axis range of data analyzed with the slider tool. (F) An indication of well-fit data is a random distribution of points in the initial rate fit residuals plot. (G) Optional step: To select a desired experimental condition as a blank for subtraction from the rest of the dataset, use the corresponding ‘Select Blank Sample for Subtraction’ drop-down menu. (H) Convert initial rate slope values in the results table to true initial rate values by entering a transform equation in the ‘Enter Transform Equation’ text box. (I) Export calculated initial rate slope values from the results tables by clicking the blue ‘Download Table to CSV’ or ‘Copy Table to Clipboard’ buttons. (J) If there was a time delay between reaction mixing and reaction initiation, enter a time value into the ‘Enter Time Between Mixing and First Read’ text box in Logarithmic Fit mode to extrapolate initial rate calculations back to the precise reaction start time.

3.3. Special considerations for specific ICEKAT analysis models

3.3.1. pEC₅₀/pIC₅₀ model

1. If titrant (e.g., small molecule activator or inhibitor) concentration is not already in a log₁₀ scale in the CSV or Text file uploaded to ICEKAT, navigate to the ‘Advanced Settings for pEC50/pIC50 Analysis’ section (Fig. 4A) in the lower-left corner of the ICEKAT window. Switch the x-axis of the model data plot to a log₁₀ scale by clicking the ‘Transform X-Axis to Log10 Scale’ button (Fig. 4B).

2. If the data fit must be constrained, set the bottom and top of the fitted ${\mathit{p}\mathrm{E}\mathrm{C}}_{50}/\mathrm{p}{\mathrm{I}\mathrm{C}}_{50}$ curve and/or assign the Hill slope of the fitted ${\mathrm{p}\mathrm{E}\mathrm{C}}_{50}/\mathrm{p}{\mathrm{I}\mathrm{C}}_{50}$ curve as a fixed value. The Hill slope may be set to 1 unless positive or negative cooperativity is anticipated (Roy & Horovitz, 2022). To make any of these changes, input the appropriate values into the ‘Fix pEC50/pIC50 Bottom’ (Fig. 4C), ‘Fix pEC50/pIC50 Top’ (Fig. 4D), or ‘Fix pEC50/pIC50 Hill Slope’ (Fig. 4E) text boxes located under the ‘Advanced Settings for pEC50/pIC50 Analysis’ heading (Fig. 4A).

   Caution: ${\mathrm{E}\mathrm{C}}_{50}/{\mathrm{I}\mathrm{C}}_{50}$ values generated by ICEKAT are empirical because they strongly depend on kinetic assay conditions and enzyme inhibition mechanisms (Olp et al., 2020). For the greatest rigor and reproducibility, users should employ Cheng-Prusoff equations to transform ${\mathrm{I}\mathrm{C}}_{50}$ values to less empirical $K_{\mathrm{i}}$ values (Cheng & Prusoff, 1973; Kalliokoski, Kramer, Vulpetti, & Gedeck, 2013).

Fig. 4.

Considerations for specific ICEKAT data analysis models. (A) When analyzing data with the ${\mathrm{p}\mathrm{E}\mathrm{C}}_{50}/\mathrm{p}{\mathrm{I}\mathrm{C}}_{50}$ model, the ‘Advanced Settings for ${\mathrm{p}\mathrm{E}\mathrm{C}}_{50}/\mathrm{p}{\mathrm{I}\mathrm{C}}_{50}$ Analysis’ section may be used. (B) Click the ‘Transform X-Axis to Log10 Scale’ button to convert the x-axis of the model data plot to a log₁₀ scale in the ${\mathrm{p}\mathrm{E}\mathrm{C}}_{50}/\mathrm{p}{\mathrm{I}\mathrm{C}}_{50}$ model. (C) Set the bottom of the fitted ${\mathrm{p}\mathrm{E}\mathrm{C}}_{50}/\mathrm{p}{\mathrm{I}\mathrm{C}}_{50}$ curve to a particular value with the ‘Fix pEC50/pIC50 Bottom’ text box. (D) Set the top of the fitted ${\mathrm{p}\mathrm{E}\mathrm{C}}_{50}/\mathrm{p}{\mathrm{I}\mathrm{C}}_{50}$ curve to a particular value with the ‘Fix pEC50/pIC50 Top’ text box. (E) Set the Hill slope of the ${\mathrm{p}\mathrm{E}\mathrm{C}}_{50}/\mathrm{p}{\mathrm{I}\mathrm{C}}_{50}$ curve to a particular value with the ‘Fix pEC50/pIC50 Hill Slope’ text box. (F) When analyzing data with the HTS model, use the ‘HTS Hit Threshold (Standard Deviation)’ slider tool to adjust the user-defined HTS hit standard deviation threshold. (G) In the HTS model, a horizontal line on the model data plot represents the mean initial rate value of the dataset. Initial rate values above (red dots), below (blue dots), or within (gray dots) the HTS hit standard deviation threshold are highlighted on the model data plot. (H) Initial rate values above (red cell), below (blue cell), or within (white cell) the HTS hit standard deviation threshold are highlighted in the results table.

3.3.2. HTS model

1. To adjust the user-defined HTS hit standard deviation threshold (i.e., a specified number of standard deviations above or below the mean), use the ‘HTS Hit Threshold (Standard Deviation)’ slider tool (Fig. 4F) below the results tables.

   Note: In the HTS model, ICEKAT overlays a horizontal line representing the mean initial rate value of the dataset on the model data plot (Fig. 4G). ICEKAT thereby highlights sample hits with initial rate values either above (red) or below (blue) the user-defined HTS hit threshold in both the model data plot (Fig. 4G) and the results table (Fig. 4H).

3.4. Special considerations for specific ICEKAT analysis modes

3.4.1. Schnell–Mendoza mode

1. Unlike other modes, the Schnell–Mendoza mode requires that data be plotted as a decrease in substrate concentration over time. Ensure this is the case when setting up the CSV or Text file before uploading it into ICEKAT.

2. Because data is plotted as a decrease in substrate concentration over time, input of a transform equation in the ‘Enter Transform Equation’ text box (Fig. 3H) is required when selecting this mode. If the raw data output is measured in terms of increasing values (e.g., absorbance) over time, invert the transform equation with an input of − $x$ in the numerator of the transform equation. If the raw data output is already measured in decreasing substrate concentration over time, enter $x$ as the transform equation.

   Note: In this setting, if the ‘Select Blank Sample for Subtraction’ drop-down menu is used, a straight line derived from the trace selected in the drop-down menu is subtracted from the data globally fit to the closed-form solution of the Michaelis–Menten equation.

   Caution:As the Schnell–Mendoza mode plots data as a decrease in substrate concentration over time and extrapolates back to $t=0$, data correction for variable microplate background absorbances is difficult. To mitigate this concern, use high-quality microplates with negligible absorbance differences at the wavelength(s) used for the enzyme assay(s).

3.4.2. Logarithmic Fit mode

1. If a significant time delay was present between reaction initiation and the first valid data point resulting from that reaction, enter a time value into the ‘Enter Time Between Mixing and First Read’ text box (Fig. 3J) located under the ‘Enter Transform Equation’ text box to extrapolate initial rate calculations back to the precise reaction initiation time.

   Note: This value is only used for initial rate calculations made in the Logarithmic Fit mode and is ignored if entered for all other modes.

4. Data processing

Since ICEKAT analyzes data under four modes (Maximize Slope Magnitude, Linear Fit, Logarithmic Fit, and Schnell–Mendoza mode), understanding which mode is most appropriate to achieve the best outcomes from data analysis is essential. Maximize Slope Magnitude is the default ICEKAT analysis mode and is recommended when the user is unsure which analysis mode to select or needs more information about the enzyme system under study. However, users must be cautious when using the Maximize Slope Magnitude analysis mode in settings with large measurement errors (e.g., where recorded absorbance values dramatically fluctuate across the time interval). In this scenario, cubic spline interpolation of the first derivative of the kinetics data may result in spline-interpolated data that lies outside the actual values from the original measured data, greatly overestimating initial rates (North & Livingstone, 2013). Such concerns can be minimized by carefully designing and performing kinetic experiments, especially regarding enzyme concentration, to provide high-quality data.

Linear Fit mode is recommended when the user is confident in the quality of the obtained enzyme kinetic data in terms of data linearity and satisfaction of steady-state assumptions. The Linear Fit and Maximize Slope Magnitude analysis modes may underestimate initial rates at high enzyme-to-substrate concentration ratios when insufficient data is collected during the initial quasi-steady-state phase of the reaction under investigation (Lu & Fei, 2003). Evaluation of initial rates is further complicated by the susceptibility of early data points to measurement artifacts (e.g., lag phases in enzyme-coupled systems) (Boeker, 1982; Hanes, 1932). These limitations can be addressed by extrapolating to $t=0$ to determine an initial rate that more closely approximates reality (Boeker, 1982; Hanes, 1932; Lu & Fei, 2003). Such extrapolation is accomplished by the Logarithmic Fit and Schnell–Mendoza modes in ICEKAT.

Logarithmic Fit mode is recommended when a linear segment of the initial portion of a kinetic trace cannot be easily delineated since the Logarithmic Fit mode fits the kinetic data to a logarithmic approximation of the Michaelis–Menten equation (Lu & Fei, 2003; Olp et al., 2020). Compared to other ICEKAT analysis modes, the Logarithmic Fit mode also has the unique advantage of correcting time delays between reaction initiation and data collection with the ‘Enter Time Between Mixing and First Read’ box. However, the Logarithmic Fit mode still has difficulty identifying an appropriately linear segment with high enzyme-to-substrate concentration ratios (Lu & Fei, 2003). Additionally, since the Logarithmic Fit mode uses a logarithmic approximation of the Michaelis–Menten equation, the use of integrated forms of the Michaelis–Menten equation can underestimate initial rates when high substrate concentrations are not substantially decreased during an experiment (Duggleby, 1985; Lu & Fei, 2003; Nicholls et al., 1974). As a result, the Schnell–Mendoza mode is recommended when collected assay data can be accurately represented as a decrease in substrate concentration over time. Because the Schnell–Mendoza mode fits data to the closed-form solution of the Michaelis–Menten equation, the Schnell–Mendoza mode can account for changes in reactant concentrations, regardless of magnitude, over the course of an entire enzymatic reaction (Schnell & Mendoza, 1997). However, because analysis in Schnell–Mendoza mode involves data extrapolation back to $t=0$, data correction for variable microplate background absorbances may be challenging. This concern can readily be addressed using high-quality microplates with negligible absorbance differences at the specific wavelength(s) of data collection. In addition, enzymes with potent product inhibition or low stability under assay conditions and the experimental time course will yield underestimated initial rates for all analysis modes. This is a particular concern when using the Logarithmic and Schnell–Mendoza modes, where an initial rate is not determined by maximizing the initial slope magnitude. This issue can be addressed by optimizing assay conditions to enhance enzyme stability or establishing a system with negligible product inhibition.

Although kinetic parameter uncertainties are challenging to determine (Eisenthal & Cornish-Bowden, 1974), ICEKAT incorporates several features to facilitate rigorous yet convenient statistical treatment of initial rate determinations and downstream kinetic parameter calculations. To account for inevitable outliers in assay data (Cornish-Bowden & Eisenthal, 1974), the analyzed data range can be fine-tuned with either the ICEKAT slider tool or the ‘Enter Start Time’ and ‘Enter End Time’ text boxes. Each point in the residuals plot is the difference between the observed rate and the calculated rate at a given time (Mannervik, 1982); users can visually evaluate for normality of residuals as data analysis proceeds, where well-fit data is evidenced by a random residual distribution with no correlation to any variable in the system (Mannervik, 1982). In addition, standardized errors associated with calculated initial rates are automatically propagated during the calculation of Michaelis–Menten and ${\mathrm{p}\mathrm{E}\mathrm{C}}_{50}/\mathrm{p}{\mathrm{I}\mathrm{C}}_{50}$ parameters. These are crucial statistical considerations that are challenging to implement when performing analysis manually with general-purpose software like Apple Numbers, GraphPad Prism, or Microsoft Excel.

5. Expected outcomes, advantages, and limitations

ICEKAT facilitates convenient, intuitive, and statistically rigorous analysis of continuous enzyme kinetic experiments performed under conditions compatible with Michaelis–Menten assumptions. Other available software packages, including DYNAFIT (Kuzmič, 1996), FITSIM (Zimmerle & Frieden, 1989), KinTek (Johnson et al., 2009), and ENZO (Bevc et al., 2011), allow modeling of more complex kinetic systems, such as those encountered in complex cellular environments. However, these sophisticated approaches are often unnecessary when analyzing the output of carefully designed in vitro enzyme kinetic experiments. They are also less intuitive and computationally efficient than simple initial rate calculations. In addition, ICEKAT is explicitly designed for analyzing standard enzyme kinetics experiment outputs, offering a significant advantage over general-purpose software like Apple Numbers, GraphPad Prism, or Microsoft Excel, in efficiency and ease of use. ICEKAT is also uniquely accessible as a free online web-based application. In contrast, other similarly intuitive progress curve analysis tools like renz (Aledo, 2022) and PCAT (Bäuerle et al., 2017) require local installation and the relevant programming platform (R, MATLAB, or Python). Together, these advantages allow ICEKAT users with varying experience levels to analyze substantial amounts of kinetic data quickly and accurately. Furthermore, the interactive nature and pre-populated example data of ICEKAT serve as an intuitive teaching aid for demonstrating the effects of accurate and poor initial rate fits on the calculation of downstream kinetic parameters.

Many kinetic analysis programs like DYNAFIT, ENZO, FITSIM, and KinTek are capable of analyzing data from an entire kinetic trace and thus advantageous to use in scenarios with more complex mechanisms and reaction intermediates (Bevc et al., 2011; Johnson et al., 2009; Kuzmič, 1996; Zimmerle & Frieden, 1989). ICEKAT is not well-suited to analyze such complex data, especially in the context of cellular enzyme kinetics, where available substrate and product concentrations may uncontrollably vary over time (e.g., due to competitive substrate use by another enzyme) (Dourado, Mori, Hwa, & Lercher, 2021). The analysis of entire kinetic traces requires elaborate mathematical schemes to fit kinetic assay data to differential integrated rate equations (Bevc et al., 2011; Johnson et al., 2009; Kuzmič, 1996; Zimmerle & Frieden, 1989), which are often more complicated than needed for analysis of well-controlled in vitro enzyme kinetics assays. Furthermore, the errors inherent in analyzing an entire kinetic trace are well-documented (Cornish-Bowden, 1975; Cornish-Bowden, 2013). In contrast, ICEKAT relies on more straight-forward mathematical solutions to Michaelis–Menten-derived equations and the initial segment of a kinetic trace where steady-state assumptions hold true (Olp et al., 2020).

Compared to other kinetic analysis programs, ICEKAT also has a significant advantage in terms of analysis speed and consistency. DYNAFIT has been noted to use inconsistent iterations for data fitting across computer types and compilers (Kuzmič, 1996). Similarly, ENZO suffers from lengthy computational times if convergence between the proposed and actual kinetic traces is not reached (Bevc et al., 2011). Additionally, computational time and accuracy vary across analysis models in PCAT (Bäuerle et al., 2017). In contrast, kinetic data analysis with any ICEKAT analysis model is accomplished in seconds.

ICEKAT is also an accessible teaching tool to help biochemistry students understand the importance of accurate kinetic trace analysis for the validity of the initial rate and kinetic parameters calculated from such analysis. Analogous to ICEKAT, KinTek can model the effects of changing reaction parameters, such as reactant starting concentration, on the overall shape of the simulated kinetic traces and is a helpful teaching tool (Johnson et al., 2009). However, the full version of the KinTek software requires a paid subscription (Johnson et al., 2009), which is detrimental to accessible data processing and student learning. Similarly, renz facilitates tractable analysis of the early linear portion of the kinetic trace with several methods to calculate initial rates and kinetic parameters (Aledo, 2022). However, renz must be downloaded and requires a working knowledge of coding in R (Aledo, 2022). ICEKAT, in contrast, is freely and fully available through a web interface for teachers, students, and researchers alike.

Additionally, ICEKAT holds significant advantages in the versatility of its different data analysis models. Enzyme $K_{\mathrm{M}}$ values can be calculated under both the Michaelis–Menten and the $k_{\mathrm{c}\mathrm{a}\mathrm{t}}/K_{\mathrm{M}}$ analysis models, and either model can be used to calculate additional kinetic parameters. Among all existing enzyme kinetics analysis programs, ICEKAT is the only program optimized to determine the modulatory effects of a specific compound or a library of compounds on enzymatic activity through the ${\mathrm{p}\mathrm{E}\mathrm{C}}_{50}/\mathrm{p}{\mathrm{I}\mathrm{C}}_{50}$ and HTS analysis models, respectively. The ICEKAT analysis models cannot globally fit replicate data acquired at different start times or data collected at multiple inhibitor and substrate concentrations to determine mechanisms of inhibition (e.g., competitive, non-competitive, uncompetitive, and mixed) and associated $K_{\mathrm{i}}$ values. However, both concerns can be addressed by exporting initial rates and/or kinetic parameters calculated by ICEKAT for use in other programs like GraphPad Prism that are capable of global model fitting to determine mechanisms of inhibition and $K_{\mathrm{i}}$ values. Here, any further data analysis required will be more manageable, as the total computational effort is reduced by first processing the continuous enzyme kinetics data through ICEKAT. Continuous enzyme kinetic data analysis with ICEKAT is intended to yield rapid determination of the initial rate and multiple kinetic parameters (e.g., $k_{\mathrm{c}\mathrm{a}\mathrm{t}},K_{\mathrm{M}},V_{\mathrm{m}\mathrm{a}\mathrm{x}},{\mathrm{E}\mathrm{C}}_{50},{\mathrm{I}\mathrm{C}}_{50}$) of an enzyme-catalyzed reaction. With a variety of user-selected data analysis models and modes, ICEKAT allows continuous enzyme kinetic data analysis to proceed in a manner conducive to basic science research and biochemistry teaching.

6. Conclusions

ICEKAT is a free, interactive, and web-based tool for the semi-automated analysis of continuous enzyme kinetics assay data and determining initial rates. ICEKAT uniquely mitigates errors and biases introduced by manual data analysis and simplifies the overcomplicated analysis process used by other enzyme kinetic analysis software programs. ICEKAT is one of the only enzyme kinetic analysis software programs that requires no download, installation, or computer program file space. ICEKAT can be effectively used to calculate initial rates from kinetics assay datasets for research or education purposes. As the enzymology field suffers from issues with data reproducibility (Halling et al., 2018), the routine use of semi-automated enzyme kinetic analysis tools like ICEKAT will increase data reproducibility through consistent models and modes of data analysis. To address the issue of data reproducibility and related concerns, the National Institutes of Health recently published a new Data Management and Sharing Policy (NOT-OD-21-013) that aims to advance scientific research through more robust data-sharing practices. Therefore, when coupled with faithful adherence to the Standards for Reporting Enzymology Data (STRENDA) guidelines (Tipton et al., 2014) (https://www.beilstein-institut.de/en/projects/strenda/guidelines) and uniform deposition of kinetics assay data in the STRENDA DB database (Swainston et al., 2018) (https://www.beilstein-strenda-db.org/strenda), the newest version of ICEKAT will allow scientists to continue to analyze and publish enzyme kinetics data with enhanced reliability and speed.

Key Resources Table.

Reagent or Resource	Source	Identifier
ICEKAT kinetic analysis program	https://icekat.herokuapp.com/icekat	N/A
Spreadsheet program	Apple Numbers, GraphPad Prism, Microsoft Excel, etc.	N/A

Abbreviations

CSV

Comma Separated Values

HTS

High-Throughput Screening

ICEKAT

Interactive Continuous Enzyme Kinetics Analysis Tool

${\mathrm{I}\mathrm{C}}_{50}$

half-maximal inhibitory concentration

${\mathit{k}}_{\mathrm{c}\mathrm{a}\mathrm{t}}$

enzyme catalysis rate

${\mathit{k}}_{\mathrm{c}\mathrm{a}\mathrm{t}}/{\mathit{K}}_{\mathrm{M}}$

catalytic efficiency

${\mathit{K}}_{\mathrm{M}}$

Michaelis constant

${\mathrm{p}\mathrm{E}\mathrm{C}}_{50}$

negative log of the half-maximal effective concentration

$\mathrm{p}{\mathrm{I}\mathrm{C}}_{50}$

negative log of the half-maximal inhibitory concentration

STRENDA DB

Standards for Reporting Enzymology Data Database

${\mathit{V}}_{\mathrm{m}\mathrm{a}\mathrm{x}}$

maximal reaction velocity