FRETBursts - μs-ALEX smFRET burst analysis¶
This notebook is part of a tutorial series for the FRETBursts burst analysis software.
In this notebook, we present a typical FRETBursts workflow for μs-ALEX smFRET burst analysis. Briefly, we show how to perform background estimation, burst search, burst selection, compute FRET histograms and ALEX histograms, do sub-population selection and finally, FRET efficiency fit.
Before running the notebook, you can click on menu Cell -> All Output -> Clear to clear all previous output. This will avoid mixing output from current execution and the previously saved one.
Loading the software¶
We start by loading FRETBursts:
from fretbursts import *
Note that FRETBursts version string tells you the exact FRETBursts version (and revision) in use. Storing the version in the notebook helps with reproducibility and tracking software regressions.
Next, we initialize the default plot style for the notebook (under the hood it uses seaborn):
sns = init_notebook()
Note that the previous command has no output. Finally, we print the version of some dependencies:
import lmfit; lmfit.__version__
import phconvert; phconvert.__version__
Downloading the data file¶
The full list of smFRET measurements used in the FRETBursts tutorials can be found on Figshare.
This is the file we will download:
url = 'http://files.figshare.com/2182601/0023uLRpitc_NTP_20dT_0.5GndCl.hdf5'
url variable above to download your own data file.
This is useful if you are executing FRETBursts online and you want to use
your own data file. See
First Steps.
Here, we download the data file and put it in a folder named data,
inside the notebook folder:
download_file(url, save_dir='./data')
NOTE: If you modified the
urlvariable providing an invalid URL the previous command will fail. In this case, edit the cell containing theurland re-try the download.
Selecting the data file¶
Use one of the following 2 methods to select a data file.
Option 1: Paste the file-name¶
Here, we can directly define the file name to be loaded:
filename = "./data/0023uLRpitc_NTP_20dT_0.5GndCl.hdf5"
filename
Now filename contains the path of the file you just selected.
Run again the previous cell to select a new file. In a following cell
we will check if the file actually exists.
See First Steps.
Option 2: Use an "Open File" dialog¶
Alternatively, you can select a data file with an "Open File" windows. Note that, since this only works in a local installation, the next commands are commented (so nothing will happen when running the cell).
If you want to try the File Dialog, you need to remove the # signs:
# filename = OpenFileDialog()
# filename
Check that the data file exists¶
Let's check that the file exists:
import os
if os.path.isfile(filename):
print("Perfect, file found!")
else:
print("Sorry, file:\n%s not found" % filename)
Load the selected file¶
We can finally load the data and store it in a variable called d:
d = loader.photon_hdf5(filename)
If you don't get any message, the file is loaded successfully.
We can also set the 3 correction coefficients:
- leakage or bleed-through:
leakage - direct excitation:
dir_ex(ALEX-only) - gamma-factor
gamma
d.leakage = 0.11
d.dir_ex = 0.04
d.gamma = 1.
NOTE: at any later moment, after burst search, a simple reassignment of these coefficient will update the burst data with the new correction values.
μs-ALEX parameters¶
At this point, timestamps and detectors numbers are contained in the ph_times_t and det_t attributes of d. Let's print them:
d.ph_times_t, d.det_t
We need to define some ALEX parameters:
d.add(det_donor_accept = (0, 1),
alex_period = 4000,
offset = 700,
D_ON = (2180, 3900),
A_ON = (200, 1800))
Here the parameters are:
det_donor_accept: donor and acceptor channelsalex_period: length of excitation period (in timestamps units)D_ONandA_ON: donor and acceptor excitation windowsoffset: the offset between the start of alternation and start of timestamping (see also Definition of alternation periods).
To check that the above parameters are correct, we need to plot the histogram of timestamps (modulo the alternation period) and superimpose the two excitation period definitions to it:
bpl.plot_alternation_hist(d)
If the previous alternation histogram looks correct, the corresponding definitions of the excitation periods can be applied to the data using the following command:
loader.alex_apply_period(d)
If the previous histogram does not look right, the parameters in the d.add(...) cell can be modified and checked by running the histogram plot cell until everything looks fine. Don't forget to apply the
parameters with loader.usalex_apply_period(d) as a last step.
NOTE: After applying the ALEX parameters a new array of timestamps containing only photons inside the excitation periods is created (name
d.ph_times_m). To save memory, by default, the old timestamps array (d.ph_times_t) is deleted. Therefore, in the following, when we talk about all-photon selection we always refer to all photons inside both excitation periods.
Measurement infos¶
The entire measurement data is now stored in the variable d. Printing it
will give a compact representation containing the file-name and additional parameters:
d
To check the measurement duration (in seconds) run:
d.time_max
Plotting basics¶
In this section basic concepts of plotting with FRETBursts using the timetrace plot as an example.
To plot a timetrace of the measurement we use:
dplot(d, timetrace);
Here, dplot is a generic wrapper (the same for all plots)
that takes care of setting up the figure, title and axis
(in the multispot case dplot creates multi-panel plot).
The second argument, timetrace, is the actual plot function.
All the eventual additional arguments passed to dplot are,
in turn, passed to the plot function (e.g. timetrace).
If we look at the documentation for timetrace
function we notice that it accepts a long list of arguments.
In python, when an argument is not specified, it will take the default
value specified in the function definition (see previus link).
As an example, to change the bin size (i.e. duration) of the timetrace histogram,
we can look up in the timetrace documentation
and find that the argument we need to modify is binwidth
(we can also see that the default value is 0.001 seconds).
We can then re-plot the timetrace using a bin of 0.5 ms:
dplot(d, timetrace, binwidth=0.5e-3);
The timetrace is computed between tmin and tmax (by default 0 and 200s),
but as you can see is displayed only between 0 an 1 second, just because these
are the default x-axis limits. The axis limits can be changes by using the
standard matplotlib command plt.xlim().
On the other hand, to change the range where the timetrace is computed,
we pass the additional arguments tmin and tmax as follows:
dplot(d, timetrace, binwidth=0.5e-3, tmin=50, tmax=150)
plt.xlim(51, 52);
When using FRETBursts in a notebook, all plots are static by default.
This is because we use the so called inline backend of matplotlib.
If you want to manipulate figures interactively, you can switch
to the interactive notebook backend with:
%matplotlib notebookto go back to inline use:
%matplotlib inlineNOTE: Currently, the notebook backend is incompatible with the QT backend.
If in a session you activate the notebook backend, then switching to the QT backend requires
restarting the notebook. Conversely, you can switch between inline and notebook
or between inline and qt4 backends in the same session wihtou issues.
See also:¶
- bpl.timetrace function documentation
- bpl.ratetrace function documentation
- Intensity timetrace and Rate-timetrace, a later section in this tutorial.
Background estimation¶
As a first step of the analysis, we need to estimate the background. Here we will compute the background using the recommended approach of using the auto-threshold.
For more details see Background estimation.
Automatic threshold¶
It is a good practice to monitor background rates as a function of time. Here, we compute background in adjacent 30s windows (called background periods) and plot the estimated rates as a function of time.
d.calc_bg(bg.exp_fit, time_s=30, tail_min_us='auto')
dplot(d, timetrace_bg)
NOTE: All background data is stored in
d.bg. For details on how to to export it see the Background estimation notebook.
Burst analysis¶
The first step of burst analysis is the burst search.
We will use the sliding-window algorithm on all photons. Note that "all photons", as mentioned before, means all photons selected in the alternation histogram. An important variation compared to the classical sliding-windows is that the threshold-rate for burst start is computed as a function of the background and changes when the background changes during the measurement.
To perform a burst search evaluating the photon rate with
10 photons (m=10), and selecting a minimum rate 6 times larger than
the background rate (F=6) calculated with all photons (default):
d.burst_search(L=10, m=10, F=6)
The previous command performs the burst search, corrects the bursts sizes for background, spectral leakage and direct excitation, and computes $\gamma$-corrected FRET and Stoichiometry.
See the
burst_search documentation for more details.
We can plot the resulting FRET histogram using the following command:
dplot(d, hist_fret);
All pre-defined plots follow this pattern:
call the generic dplot() function, passing 2 parameters:
- the measurement data (
din this case) - the plot function (
hist_fret)
In some case we can add other optional parameters to tweak the plot.
All plot functions start with hist_ for histograms,
scatter_ for scatter-plots or timetrace_ for plots as a function
of measurement time. You can use autocompletion to find all
plot function or you can look in bursts_plot.py where
all plot functions are defined.
Instead of hist_fret we can use hist_fret_kde to add a KDE overlay. Also, we can plot a weighted histogram by passing an additional parameter weights:
dplot(d, hist_fret, show_kde=True);
dplot(d, hist_fret, show_kde=True, weights='size');
You can experiment with different weighting schema (for all
supported weights see get_weigths() function in fret_fit.py).
Burst selection¶
When we performed the burst search, we specified L=10 without
explaining what this parameter means. L is traditionally the minimum size
(number of photons) for a burst: smaller bursts will be rejected.
By setting L=m (10 in this case) we are deciding to not discard
any burst (because the smallest detected burst has at least m counts).
Selecting the bursts in a second step, by applying a minimum burst size criterion, results in a more accurate and unbiased selection.
For example, we can select bursts with more than 30 photons (after
background, gamma, leakage and direct excitation corrections)
and store the result in a new
Data() variable ds:
ds = d.select_bursts(select_bursts.size, th1=30)
By defaults the burst size includes donor and acceptor photons
during donor excitation. To add acceptor photons during
acceptor excitation (naa), we add the parameter add_naa=True:
ds = d.select_bursts(select_bursts.size, add_naa=True, th1=30)
Similar to plot functions, all selection functions
are defined in select_bursts.py and you can access them by typing
select_bursts. and using the TAB key for autocompletion.
See also:
- Burst selection in the documentation. In particular the function
select_bursts.sizeandData.select_bursts.
To replot the FRET histogram after selection (note that now
we are passing ds to the plot function):
dplot(ds, hist_fret);
Note how the histogram exhibits much more clearly defined peaks after burst selection.
Histogram fitting and plotting style¶
Under the hood the previous hist_fret plot creates a MultiFitter
object for $E$ values. This object, stored as ds.E_fitter, operates
on multi-channel data and computes the histogram, KDE and can fit
the histogram with a model (lmfit.Model).
Now, just for illustration purposes, we fit the previous histogram with 3 Gaussians, using the already created ds.E_fitter object:
ds.E_fitter.fit_histogram(mfit.factory_three_gaussians(), verbose=False)
dplot(ds, hist_fret, show_model=True);
The bin width can be changed with binwidth argument. Alternatively,
an arbitrary array of bin edges can be passed in bins
(overriding binwidth).
We can customize the appearance of this plot (type
hist_fret? for the complete set of arguments).
For example to change from a bar plot to a line-plot
we use the hist_style argument:
dplot(ds, hist_fret, show_model=True, hist_style='line')
We can customize the line-plot, bar-plot, the model plot and the KDE plot by passing dictionaries with matplotlib style. The name of the arguments are:
hist_plot_style: style for the histogram line-plothist_bar_style: style for the histogram bar-plotmodel_plot_style: style for the model plotkde_plot_style: style for the KDE plot
As an example:
dplot(ds, hist_fret, show_model=True, hist_style='bar', show_kde=True,
kde_plot_style = dict(linewidth=5, color='orange', alpha=0.6),
hist_plot_style = dict(linewidth=3, markersize=8, color='b', alpha=0.6))
plt.legend();
Other plots¶
Similarly, we can plot the burst size using all photons
(type hist_size? to learn about all plot options):
dplot(ds, hist_size, add_naa=True);
Or plot the burst size histogram for the different components:
dplot(ds, hist_size_all);
NOTE: The previous plot may generate a benign warning due to the presence of zeroes when switching to log scale. Just ignore it.
A scatterplot of Size vs FRET is created by:
dplot(ds, scatter_fret_nd_na)
xlim(-1, 2)
We can further select only bursts smaller than 300 photons to get rid of multi-molecule events:
ds2 = ds.select_bursts(select_bursts.size, th2=300)
and superimpose the two histograms before and after selection to see the difference:
ax = dplot(ds2, hist_fret, hist_style='bar', show_kde=True,
hist_bar_style = dict(facecolor='r', alpha=0.5,
label='Hist. no large bursts'),
kde_plot_style = dict(lw=3, color='m',
label='KDE no large bursts'))
dplot(ds, hist_fret, ax=ax, hist_style='bar', show_kde=True,
hist_bar_style = dict(label='Hist. with large bursts'),
kde_plot_style = dict(lw=3, label='KDE with large bursts'))
plt.legend();
NOTE: It is not necessarily true that bursts with more that 300 photons represents multiple molecules. To asses the valididty of this assumption it can be useful to plot the peak count rates in each burst. See
hist_burst_phratefor this kind of plot.
Fit and plot peak positions¶
We can find the KDE peak position in a range (let say 0.2 ... 0.6):
ds.E_fitter.find_kde_max(np.r_[0:1:0.0002], xmin=0.2, xmax=0.6)
and plot it with show_kde_peak=True, we also use show_fit_value=True to show a box with the fitted value:
dplot(ds, hist_fret, hist_style='line',
show_fit_value=True,
show_kde=True, show_kde_peak=True);
Instead of using the KDE, we can use the peak position as fitted from a gaussian model.
ds.E_fitter.fit_histogram(mfit.factory_three_gaussians(), verbose=False)
To select which peak to show we use fit_from='p1_center':
dplot(ds, hist_fret, hist_style='line',
show_fit_value=True, fit_from='p2_center',
show_model=True);
The string 'p2_center' is the name of the parameter of the
gaussian fit that we want to show in the text box. To see all
the parameters of the model we look in:
ds.E_fitter.params # <-- pandas DataFrame, one row per channel
ALEX plots¶
We can create a simple E-S scatter plot with scatter_alex:
dplot(ds, scatter_alex, figsize=(4,4), mew=1, ms=4, mec='black', color='purple');
We can also plot the ALEX histogram with a scatterplot overlay using hist2d_alex:
dplot(ds, hist2d_alex);
Finally we can also plot an ALEX histogram and marginals (joint plots) as follow (for more options see: Example - usALEX histogram):
alex_jointplot(ds);