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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
IntroductionIntroductionMost 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.
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IntroductionIntroductionAccurate 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.
IntroductionIntroduction
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.
IntroductionIntroductionR² 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.
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R² = 0.9064n = 5
R² = 0.9754n = 10
R² = 0.9835n = 15
R² = 0.9617n = 20
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45 min
n = 15
Slope = 0.0815 OD600nm/min
R² is calculated for incremenal data setsMaximal R² value is determinedThe corresponding slope of the most reliable data set is calculated
IntroductionIntroduction
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.
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Subjective
Maximizing R²
Fixed linear
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R²
Determinationof the linear
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Calculating corresponding
slope
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Need for objective criterion
IntroductionIntroduction
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.
IntroductionIntroduction
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 setsGeneration of data setsUse 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 Input of data setsof 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 Maximizing R² of incremental data setsincremental 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 ofMaximizing R² of incremental data sets 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 Calculating the corresponding slopecorresponding 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 Calculating the corresponding slopecorresponding 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 Calculating the corresponding slopecorresponding 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 Calculating the corresponding slopecorresponding 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’).
ExamplesExamplesHere 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)
2. Activity of hen egg white lysozyme on Micrococcus lysodeikticus cells (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)
Click here to open the ActivityCalculator
Additional remarksAdditional 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 remarksAdditional remarksSometimes false positives occur, therefore manual control is required. Sometimes false positives occur, therefore manual control is required.
False maximum Real maximum
Additional remarksAdditional remarksA false positive can be easily recognized by checking R²
values:
Additional remarksAdditional remarksIf you delete the false positive, the correct one (previous a local
maximum) will be selected automatically
