Generation and input of data sets

1
Tutorial

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

2
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.
3
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.
4
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.
5
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 samples
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 is calculated for incremenal data sets
The corresponding slope of the most reliable data
set is calculated
Maximal R² value is determined
R² 0.9064 n 5
R² 0.9754 n 10
R² 0.9835 n 15
R² 0.9617 n 20
Slope 0.0815 ?OD600nm/min
7
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.
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Determination of the linear region by
1
Fixed linear regions
Maximizing R²
2
Subjective
3
4
Calculating corresponding slope
9
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.
10
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.
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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 replicas of the same
condition.
Different wells
Time
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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.
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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
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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.
15
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
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Calculating the corresponding slope
The corresponding slopes will be automatically
sorted as replicas of triplicate experiments on
the sheet Results. The average (Av.) and the
standard deviation (Stdev.) are calculated. Your
output will look like this
17
Calculating the corresponding slope
The colour code gives an overview of the
reproducibility of the replicas 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.
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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).
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Examples

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

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Additional remarks
To calculate the negative control (0 ng enzyme),
all data points are included because these
samples dont 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.
21
Additional remarks

• Sometimes false positives occur, therefore manual
  control is required.

Real maximum
False maximum
22
Additional remarks
A false positive can be easily recognized by
checking R² values

23
Additional remarks
If you delete the false positive, the correct one
(previous a local maximum) will be selected
automatically