# Tutorial Introduction Generation and input of data sets Maximizing R² of incremental data sets Calculating the corresponding slope Examples Additional.

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Tutorial Introduction Generation and input of data sets Maximizing R² of incremental data sets Calculating the corresponding slope Examples Additional remarks

Introduction Most common assay to determine the enzymatic activity of murein hydrolases is based on the drop in turbidity of a substrate suspension upon addition of the enzyme. Initially, the turbidity of the suspension will drop linearly. The slope is a direct measure for the activity of the enzyme. After depletion of the enzyme and/or inferior substrate concentration, the slope will gradually decrease.

Introduction Accurate determination of this linear region is necessary to enable reliable comparison between the activities measured under different conditions. The criterion to demarcate this linear region is often not specified, it is determined in a subjective manner or the linear region is calculated over a fixed period. E.g. if you want to compare activities of very different curve shapes, there is a clear need for a criterion how to decide which data points you have to include in the linear region, because this decision has a strong influence on your outcome. Here we introduce a simple principle to determine this region.

Introduction To pinpoint the region of linear descent in an objective way, we calculated different linear regressions for an incremental data set (n = number of measurements in time, starting from n = 5, 6, 7…). The corresponding determination coefficient (R²) indicates the degree of linear relation between optical density and time and it is a measure of how well the linear regression represents the selected data set.

Introduction R² will maximize, as more data points of the linear region are included, but will decrease beyond the linear region. The data set with the maximized R² value ensures the most reliable linear regression and corresponds to the most reliable data set to determine the sample’s activity. When the appropriate data set is determined by maximizing R², the corresponding slope of the linear regression is a direct measure for activity. The principle is illustrated with an example in the next slide.

R² = 0.9064 n = 5 R² = 0.9754 n = 10 R² = 0.9835 n = 15 R² = 0.9617 n = 20 45 min n = 15 Slope = 0.0815  OD 600nm /min R² is calculated for incremenal data sets Maximal R² value is determined The corresponding slope of the most reliable data set is calculated

Introduction In the next slide, the need for a criterion for the determination of the linear region is illustrated by the large variability that arises if you choose fixed periods or choose the linear region in a subjective way. The third calculation gives the results according to the method of maximizing R² values.

Fixed after 6 min Fixed after 18 min Fixed after 30 min Subjective Maximizing R² Fixed linear regions Subjective Maximizing R² Determination of the linear region by Calculating corresponding slope 1 2 3 4 Need for objective criterion

Introduction This method is especially suited for experiments where individual curves differ extensively from each other (e.g. low versus high activity conditions). The introduction of this objective criterion will enhance the interpretation of experiments that investigate various conditions. It offers a handy tool to analyze your results, whereas previously the decision to pinpoint the linear region has impact on your outcome.

Introduction To increase efficiency in processing large variable data sets statistically, an Excel spreadsheet is available which automatically calculates maximized R² data sets and corresponding slopes. Experimental data of up to 200 samples/conditions from the raw output can be handled. In the next slides, a step-by-step protocol is described for the use of this spreadsheet.

Generation of data sets Use a spectrophotometer that measures the optical density of multiwell plates in regular intervals. The output of these measurements must be arranged in vertical columns with the time scale in column A. The data will be processed as a triplicate experiment. Therefore, column B-C-D (and E-F-G and …) should be replica’s of the same condition. Time Different wells

Input of data sets Copy/paste these data on the sheet ‘Data’ of the Activitycalculator Then, fill in the number of measurements and the number of wells on the sheet ‘Info’ to demarcate the range of calculations.

Maximizing R² of incremental data sets Use the hotkey ‘CTRL + r’ to calculate the determination coefficient R² of incremental data sets. Your output at sheet ‘RSQ’ will look like this :

Maximizing R² of incremental data sets A red color indicates the maximum R² value. A green color indicates a local maximum (range 5 measurements). R² values of less than 5 measurements are not calculated to prevent fals positives.

Calculating the corresponding slope Use the hotkey ‘CTRL + s’ to calculate the slope of the optimized data set. Your output at sheet ‘Slope’ will look like this:

Calculating the corresponding slope The corresponding slopes will be automatically sorted as replica’s of triplicate experiments on the sheet ‘Results’. The average (Av.) and the standard deviation (Stdev.) are calculated. Your output will look like this:

Calculating the corresponding slope The colour code gives an overview of the reproducibility of the replica’s: a standard deviation smaller or equal than 10 % of the average is coloured green, between 10 and 30 % is coloured orange and above or equal than 30 % is coloured red.

Calculating the corresponding slope Hotkey ‘CTRL + t’ combines the maximization of R² and the calculation of the corresponding results. All results will be automatically grouped on the last sheet (‘Results’).

Examples Here you can find example data sets and their corresponding analyses: 1.Activity of hen egg white lysozyme on permeabilized P. aeruginosa PA01 cells (input – output)input output 2.Activity of hen egg white lysozyme on Micrococcus lysodeikticus cells (input – output)input output 3.Kinetic stability of hen egg white lysozyme after heat treatments (1 hour) between 25 and 95°C – substrate permeabilized P. aeruginosa PA01 cells (input - output)input output Click here to open the ActivityCalculatorhere

Additional remarks To calculate the negative control (0 ng enzyme), all data points are included because these samples don’t show a typical curved shape as when murein hydrolase is added. To detect activity of samples with very low amounts of a murein hydrolase (just above the detection level), all data points also have to be included to enable activity detection. These curves are quite linear as well.

Additional remarks Sometimes false positives occur, therefore manual control is required. False maximum Real maximum

Additional remarks A false positive can be easily recognized by checking R² values:

Additional remarks If you delete the false positive, the correct one (previous a local maximum) will be selected automatically

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