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.
We start by loading
from fretbursts import *
- Optimized (cython) burst search loaded. - Optimized (cython) photon counting loaded. -------------------------------------------------------------- You are running FRETBursts (version 0.5.7+0.g7267863.dirty). If you use this software please cite the following paper: FRETBursts: An Open Source Toolkit for Analysis of Freely-Diffusing Single-Molecule FRET Ingargiola et al. (2016). http://dx.doi.org/10.1371/journal.pone.0160716 --------------------------------------------------------------
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__
url = 'http://files.figshare.com/2182601/0023uLRpitc_NTP_20dT_0.5GndCl.hdf5'
urlvariable 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
inside the notebook folder:
URL: http://files.figshare.com/2182601/0023uLRpitc_NTP_20dT_0.5GndCl.hdf5 File: 0023uLRpitc_NTP_20dT_0.5GndCl.hdf5 File already on disk: /Users/anto/src/FRETBursts/notebooks/data/0023uLRpitc_NTP_20dT_0.5GndCl.hdf5 Delete it to re-download.
NOTE: If you modified the
urlvariable providing an invalid URL the previous command will fail. In this case, edit the cell containing the
urland re-try the download.
Use one of the following 2 methods to select a data file.
Here, we can directly define the file name to be loaded:
filename = "./data/0023uLRpitc_NTP_20dT_0.5GndCl.hdf5" filename
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.
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
# filename = OpenFileDialog() # filename
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)
Perfect, file found!
We can finally load the data and store it in a variable called
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:
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.
At this point, timestamps and detectors numbers are contained in the
det_t attributes of
d. Let's print them:
([array([ 146847, 188045, 294124, ..., 47999863658, 47999877783, 47999955353])], [array([0, 1, 1, ..., 1, 1, 0], dtype=uint32)])
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 channels
alex_period: length of excitation period (in timestamps units)
A_ON: donor and acceptor excitation windows
offset: 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:
If the previous alternation histogram looks correct, the corresponding definitions of the excitation periods can be applied to the data using the following command:
# Total photons (after ALEX selection): 2,259,522 # D photons in D+A excitation periods: 721,537 # A photons in D+A excitation periods: 1,537,985 # D+A photons in D excitation period: 1,434,842 # D+A photons in A excitation period: 824,680
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
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.
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:
data_0023uLRpitc_NTP_20dT_0.5GndCl G1.000 Lk11.000 dir4.0
To check the measurement duration (in seconds) run:
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 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
in turn, passed to the plot function (e.g.
If we look at the documentation for
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
and find that the argument we need to modify is
(we can also see that the default value is
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
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
On the other hand, to change the range where the timetrace is computed,
we pass the additional arguments
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:
to go back to inline use:
NOTE: 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
qt4 backends in the same session wihtou issues.
As a first step of the analysis, we need to estimate the background.
The assumption is that the background is a Poisson process and therefore
the corresponding inter photon delays are exponentially distributed. Since the
background can change during the measurement, a new estimation is
time_s seconds (this time is called the background period).
The inter photon delay distribution contains both single-molecule signal and background, the latter being the only one we are interested in and the former being in general much shorter. Therefore, a threshold is needed to discriminate between the exponential tail and the single-molecule peak.
Choosing a threshold and fitting the exponential tail are two different problems. FRETBursts provides several ways to specify the minimum threshold and different functions to fit the exponential tail.
We will go over three different methods in increasing order of complexity (and recommendability)
For more information see:
Let start with a standard Maximum Likelihood (ML) background fit with a minimum tail threshold of 500μs:
d.calc_bg(bg.exp_fit, time_s=1000, tail_min_us=500)
- Calculating BG rates ... [DONE]
We can look at how the fit looks with:
dplot(d, hist_bg, show_fit=True)
<matplotlib.axes._subplots.AxesSubplot at 0x1042f54e0>
Note that the fits are not very good. This is understandable because we used a single threshold for all the photon streams, each one having a quite different background.
To improve the fit, we can try specifying a threshold for each channel. This method is bit ad-hoc but it may work well when the thresholds are properly choosen.
d.calc_bg(bg.exp_fit, time_s=1000, tail_min_us=(800, 4000, 1500, 1000, 3000))
- Calculating BG rates ... [DONE]
dplot(d, hist_bg, show_fit=True);
For ALEX measurements, the tuple passed to
tail_min_us in order to define the thresholds needs to contain
5 values corresponding the 5 distinct photon streams (the all-photon stream
[Ph_sel(Dex='DAem', Aex='DAem'), Ph_sel(Dex='Dem', Aex=None), Ph_sel(Dex='Aem', Aex=None), Ph_sel(Dex=None, Aex='Dem'), Ph_sel(Dex=None, Aex='Aem')]
Finally, is possible to let FRETBursts infer the threshold automatically with:
d.calc_bg(bg.exp_fit, time_s=1000, tail_min_us='auto', F_bg=1.7)
- Calculating BG rates ... [DONE]
Which results in the following fit plot:
dplot(d, hist_bg, show_fit=True);
Under the hood, this method estimates the threshold automatically according to this formula:
threshold_auto = F_bg / coarse_background_rate
F_bg is the fit function input argument (by default 1.7)
coarse_background_rate is an initial background estimation
performed with fixed threshold. This method is concemptually an
iterative method to compute the threshold that is stopped
after the second iteration (this is usually more than enough for
Of the three methods here described, the latter is the recommended one since it works well and without user intervention in a wide range of experimental conditions.
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', F_bg=1.7)
- Calculating BG rates ... [DONE]
<matplotlib.axes._subplots.AxesSubplot at 0x1246163c8>
The background rates are stored in
bg_aa. These contain all the
fitted background rates for each channel and period.
We can also get the average background for each channel:
d.rate_m, d.rate_dd, d.rate_ad, d.rate_da, d.rate_aa
([2212.6520253589342], [592.2024909931622], [994.39404281480734], [74.737849340892041], [564.86449968607053])
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)
- Performing burst search (verbose=False) ...[DONE] - Calculating burst periods ...[DONE] - Counting D and A ph and calculating FRET ... - Applying background correction. - Applying leakage correction. - Applying direct excitation correction. [DONE Counting D/A]
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.
burst_search documentation for more details.
We can plot the resulting FRET histogram using the following command:
All pre-defined plots follow this pattern:
call the generic
dplot() function, passing 2 parameters:
din this case)
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
all plot functions are defined.
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
dplot(d, hist_fret, show_kde=True); dplot(d, hist_fret, show_kde=True, weights='size');
- Overwriting the old E_fitter object with the new weights.
You can experiment with different weighting schema (for all
supported weights see
get_weigths() function in
When we performed the burst search, we specified
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
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
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.
To replot the FRET histogram after selection (note that now
we are passing
ds to the plot function):
Note how the histogram exhibits much more clearly defined peaks after burst selection.
Under the hood the previous
hist_fret plot creates a
object for $E$ values. This object, stored as
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
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
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
dplot(ds, hist_fret, show_model=True, hist_style='line')
<matplotlib.axes._subplots.AxesSubplot at 0x120a132e8>
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-plot
hist_bar_style: style for the histogram bar-plot
model_plot_style: style for the model plot
kde_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();
Similarly, we can plot the burst size using all photons
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:
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.
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.
To select which peak to show we use
dplot(ds, hist_fret, hist_style='line', show_fit_value=True, fit_from='p2_center', show_model=True);
'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
We can create a simple E-S scatter plot with
dplot(ds, scatter_alex, figsize=(4,4), mew=1, ms=4, mec='black', color='purple');
/Users/anto/miniconda3/lib/python3.5/site-packages/matplotlib/cbook.py:2644: UserWarning: Saw kwargs ['ms', 'markersize'] which are all aliases for 'markersize'. Kept value from 'markersize' seen=seen, canon=canonical, used=seen[-1])) /Users/anto/miniconda3/lib/python3.5/site-packages/matplotlib/cbook.py:2644: UserWarning: Saw kwargs ['mew', 'markeredgewidth'] which are all aliases for 'markeredgewidth'. Kept value from 'markeredgewidth' seen=seen, canon=canonical, used=seen[-1])) /Users/anto/miniconda3/lib/python3.5/site-packages/matplotlib/cbook.py:2644: UserWarning: Saw kwargs ['mec', 'markeredgecolor'] which are all aliases for 'markeredgecolor'. Kept value from 'markeredgecolor' seen=seen, canon=canonical, used=seen[-1]))