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\section{Introduction} \section*{Introduction}
\subsection{Open \subsection*{Open Science and Reproducibility}
Over the past 20 years, single molecule FRET (smFRET) has grown into one of the most
useful techniques in single-molecule spectroscopy~\cite{Weiss_1999,Hohlbein_2014}.
...
Together with all the aforementioned tools, FRETBursts contributes to the growing
ecosystem of open tools for reproducible science in the single-molecule field.
\subsection{Paper \subsection*{Paper Overview}
This paper is written as an introduction to smFRET burst analysis and
its implementation in FRETBursts.
The aim is illustrating the specificities and
...
(\href{https://github.com/tritemio/fretbursts_paper}{link}).
\section{FRETBursts \section*{FRETBursts Overview}
\label{sec:overview}
\subsection{Technical \subsection*{Technical Features}
FRETBursts can analyze smFRET measurements
from one or multiple excitation spots~\cite{Ingargiola_2013}. The supported
...
kernel density distribution estimator (2CDE)~\cite{Tomov_2012}
are available as FRETBursts notebooks.
\subsection{Software \subsection*{Software Availability}
FRETBursts is hosted and openly developed on GitHub. FRETBursts homepage
(\href{http://tritemio.github.io/FRETBursts}{link})
contains links to the various resources. Installation instructions can be found in the
...
without requiring any installation on the user's computer (\href{https://github.com/tritemio/FRETBursts_notebooks#run-online}{link}).
\section{Architecture \section*{Architecture and Concepts}
\label{sec:concepts}
In this section, we introduce some general burst analysis concepts
and notations used in FRETBursts.
\subsection{Photon \subsection*{Photon Streams}
\label{sec:ph_streams}
The raw data collected during a smFRET experiment consists in one or more arrays of
...
\caption{\label{tab:ph_sel_alex}Photon selection syntax (ALEX)}
\end{table}
\subsection{Background \subsection*{Background Definitions}
\label{sec:bg_intro}
An estimation of the background rates is needed to both select a proper threshold for
...
\end{figure}
\subsection{The \subsection*{The \texttt{Data} Class}
\label{sec:data_intro}
The \verb|Data| class
...
\end{table}
\paragraph{Python \paragraph*{Python details}
Many \verb|Data| attributes are lists of arrays (or scalars) with the length of the lists
equal to the number of excitation spots. This means that in
single-spot measurements, an array of burst-data
...
with an underscore, so that an equivalently syntax is
\verb|Data.nd_| instead of \verb|Data.nd[0]|.
\subsection{Introduction \subsection*{Introduction to Burst Search}
\label{sec:burstsearch_intro}
Identifying single-molecule fluorescence bursts in the stream of photons is
...
the burst selection based on burst size
with another criterion such as burst duration or brightness (see section~\nameref{sec:burstsel}).
\subsection{Corrected \subsection*{Corrected Burst Sizes and Weights}
\label{sec:burstsizeweights}
The number of photons detected during a burst --the ``burst size''--
...
and using weights, is possible to build a FRET histogram with well-defined FRET sub-populations peaks
without the need of searching an optimal burst-size threshold (\nameref{sec:burstweights_theory}).
\paragraph{Python \paragraph*{Python details}
FRETBursts has the option to weight bursts using $\gamma$-corrected
burst sizes which optionally include acceptor excitation photons \verb|naa|.
A weight proportional to the burst size is applied by passing the argument
...
However, using weights different from the size is not recommended
due to their less efficient use of burst information.
\section{smFRET \section*{smFRET Burst Analysis}
\label{sec:analysis}
\subsection{Loading \subsection*{Loading the Data}
\label{sec:dataload}
While FRETBursts can load several data files formats,
we encourage users to adopt the recently introduced Photon-HDF5
...
can be found in the \verb|loader| module's documentation
(\href{http://fretbursts.readthedocs.org/en/latest/loader.html}{link}).
\subsection{Alternation \subsection*{Alternation Parameters}
\label{sec:alternation}
For μs-ALEX and ns-ALEX data, Photon-HDF5 normally stores parameters defining
...
reloaded and the steps above repeated as described.
\subsection{Background \subsection*{Background Estimation}
\label{sec:bg_calc}
The first step of smFRET analysis involves estimating background rates.
...
These impurities tend to bleach on timescales of minutes resulting in
background variations during the course of the measurement.
\paragraph{Python \paragraph*{Python details}
The estimated background rates are stored in the \verb|Data| attributes
\verb|bg_dd|, \verb|bg_ad| and \verb|bg_aa|, corresponding to photon
...
\href{http://fretbursts.readthedocs.org/en/latest/background.html}{link}).
\subsection{Burst \subsection*{Burst Search}
\label{sec:burstsearch}
%\subsubsection{Burst %\subsubsection*{Burst Search in FRETBursts}
%\label{sec:burstsearch_code}
Following background estimation, burst search is the next step of
...
different copies of \verb|Data| objects, the memory usage is minimized, even when
several copies are created.
\paragraph{Python \paragraph*{Python details}
Note that, while \verb|.burst_search()| is a method of \verb|Data|,
\verb|burst_search_and_gate| is a function in the \verb|bext| module
taking a \verb|Data| object as a first argument and returning a new
...
collects ``plugin'' functions that provides additional algorithms
for processing \verb|Data| objects.
\subsection{Bursts \subsection*{Bursts Corrections}
\label{sec:corrcoeff}
In μs-ALEX, there are 3 important correction parameters: $\gamma$-factor,
...
can be found online as an interactive notebook (\href{http://nbviewer.jupyter.org/github/tritemio/notebooks/blob/master/Derivation%20of%20FRET%20and%20S%20correction%20formulas.ipynb}{link}).
\subsection{Burst \subsection*{Burst Selection}
\label{sec:burstsel}
After burst search, it is common to select bursts according to different
...
bursts in \verb|dsw|
will have sizes between 50 and 200 photons, and duration between 0.5 and 3~ms.
\paragraph{Burst \paragraph*{Burst Size Selection}
In the previous section, we selected bursts by size, using only
photons detected in both D and A channels during D excitation (i.e. Dex photons),
as in eq.~\ref{eq:burstsize_dex}.
...
\verb|select_bursts.size| documentation
(\href{http://fretbursts.readthedocs.org/en/latest/burst_selection.html#fretbursts.select_bursts.size}{link}).
\paragraph{Python \paragraph*{Python details}
To compute $\gamma$-corrected burst sizes (with or without addition of \verb|naa|)
the method \verb|Data.burst_sizes|
(\href{http://fretbursts.readthedocs.org/en/latest/data_class.html#fretbursts.burstlib.Data.burst_sizes}{link})
is used.
\paragraph{Select \paragraph*{Select the FRET Populations}
In smFRET-ALEX experiments, in addition to one or more FRET populations, there are always
donor-only (D-only) and acceptor-only (A-only) populations.
...
\end{center}
\end{figure}
\subsection{Population \subsection*{Population Analysis}
\label{sec:fretfit}
Typically, after bursts selection, E or S histograms are fitted to a model.
...
as well as the documentation for \verb|bursts_fitter| function
(\href{http://fretbursts.readthedocs.org/en/latest/plugins.html#fretbursts.burstlib_ext.bursts_fitter}{link}).
\paragraph{Python \paragraph*{Python details}
Models returned by FRETBursts's factory functions (\verb|mfit.factory_*|)
are \verb|lmfit.Model| objects (\href{https://lmfit.github.io/lmfit-py/model.html}{link}).
...
(\href{http://lmfit.github.io/lmfit-py/}{link}).
\section{Implementing \section*{Implementing Burst Variance Analysis}
\label{sec:bva}
In this section, we describe how to implement burst variance analysis (BVA)
...
FRETBursts provides well-tested, general-purpose functions for timestamps and burst data
manipulation and therefore simplifies implementing custom burst analysis algorithms such as BVA.
\subsection{BVA \subsection*{BVA Overview}
Single-molecule FRET histograms show more information than just mean FRET efficiencies.
While in general the presence of several peaks clearly indicates the existence of
multiple subpopulations, a single peak cannot a priori be associated with
...
\end{center}
\end{figure}
\subsection{BVA \subsection*{BVA Implementation}
The following paragraphs describe the low-level details involved in implementing the BVA using FRETBursts.
The main goal is to illustrate a real-world example of accessing and manipulating timestamps and burst data.
For a ready-to-use BVA implementation users can refer to the corresponding notebook included with FRETBursts
(\href{http://nbviewer.jupyter.org/github/tritemio/FRETBursts_notebooks/blob/master/notebooks/Example%20-%20Burst%20Variance%20Analysis.ipynb}{link}).
\paragraph{Python \paragraph*{Python details}
For BVA implementation, two photon streams are needed: all-photons during donor excitation (Dex)
and acceptor photons during donor excitation (DexAem).
These photon stream selections are obtained by computing boolean masks as follows
...
\section{Conclusions} \section*{Conclusions}
\label{sec:conclusions}
FRETBursts is an open source and openly developed (see~\nameref{sec:dev}) implementation % SI_link
...
Nesher Technologies and intellectual property used in the research
reported here. The work at UCLA was conducted in Dr. Weiss's Laboratory.
\beginsupplement
\section{Supporting \section*{Supporting Information}
\paragraph*{S1 Appendix.}
