deletions | additions
diff --git a/Burst_Variance_Analysis.tex b/Burst_Variance_Analysis.tex
index 485125d..f1c34a2 100644
--- a/Burst_Variance_Analysis.tex
+++ b/Burst_Variance_Analysis.tex
...
comprising a fixed number $n$ of photons,
and to compare the empirical variance of acceptor counts of all sub-bursts in a burst,
with the theoretical shot-noise-limited variance.
An empirical variance of sub-bursts larger than the
shot-noise limited shot-noise-limited value indicates
the presence of dynamics.
Since the estimation of the sub-bursts variance is affected
by uncertainty, BVA analysis provides and indication of an higher or lower probability
of observing dynamics.
In a FRET (sub-)population originating from a single static FRET efficiency,
the sub-bursts acceptor counts $n_a$ can be modeled as a binomial-distributed random variable
...
\operatorname{Std}(E_{\textrm{sub}}) = \left( \frac{E_p\,(1 - E_p)}{n} \right)^{1/2}
\end{equation}
BVA analysis consists
of in four steps: 1) dividing bursts into consecutive sub-bursts
containing a constant number of consecutive photons~\textit{n}, 2) computing the PR
of each sub-burst, 3) calculating the empirical standard deviation ($s_E$) of sub-bursts
PR in each burst, and 4) comparing $s_E$ to the expected standard deviation
...
non-interconverting molecules) characterized by distinct FRET efficiencies,
$s_E$ of each burst is only affected by shot-noise and will follow the expected
standard deviation curve based on eq.~\ref{eq:binom_std}.
Conversely, if the observed distribution originates from biomolecules belonging to a single
specie, species,
which interconverts between different FRET sub-populations (over times comparable to the diffusion
time), as in figure~\ref{fig:bva_dynamic}, $s_E$ of each burst will be larger than the expected
shot-noise-limited standard deviation, and will be located above the shot-noise standard
diff --git a/bibliography/biblio.bib b/bibliography/biblio.bib
index 14622e4..72b6ee6 100644
--- a/bibliography/biblio.bib
+++ b/bibliography/biblio.bib
...
author = {Kou, S. C. and Sunney Xie, X. and Liu, Jun S.},
month = jun,
year = {2005},
keywords = {Bayes factor, Brownian diffusion, Continuous time Markov chain, Cox process, Energy barrier, freely-diffusing, Likelihood,
OrnsteinâUhlenbeck Ornstein-Uhlenbeck process, Scale transformation update, smFRET},
pages = {469--506},
}
...
url = {http://dx.doi.org/10.1073/pnas.95.4.1556},
year = {1998},
month = {feb},
publisher =
{Proceedings of the National {National Academy of
Sciences}, Sciences USA},
volume = {95},
number = {4},
pages = {1556--1561},
author = {C. Eggeling and J. R. Fries and L. Brand and R. Gunther and C. A. M. Seidel},
title = {{Monitoring conformational dynamics of a single molecule by selective fluorescence spectroscopy}},
journal = {Proceedings of the National Academy of
Sciences}, Sciences USA},
}
...
title = {
8-spot smFRET analysis using two 8-pixel SPAD arrays
},
publisher =
{{SPIE}}, {SPIE},
volume = {8590},
pages = {85900E-85900E-11},
year = {2013},
doi = {10.1117/12.2003704},
URL = { http://dx.doi.org/10.1117/12.2003704},
booktitle journal =
{{Single Molecule Spectroscopy and Superresolution Imaging VI}}, {Proceedings of SPIE},
note = {doi:\href{http://dx.doi.org/10.1117/12.2003704}{10.1117/12.2003704}}
}
...
@article{Laurence_2005,
author = {Laurence, Ted A. and Kong, Xiangxu and Jäger, Marcus and Weiss, Shimon},
title = {{Probing structural heterogeneities and fluctuations of nucleic acids and denatured proteins}},
journal = {Proceedings of the National Academy of
Sciences}, Sciences USA},
volume = {102},
number = {48},
pages = {17348-17353},
...
doi = {10.1117/12.2212085},
url = {http://dx.doi.org/10.1117/12.2212085},
year = {2016},
publisher =
{{SPIE}}, {SPIE},
volume = {971405},
author = {Antonino Ingargiola and Ted Laurence and Robert Boutelle and Shimon Weiss and Xavier Michalet},
title = {{Photon-{HDF}5: open data format and computational tools for timestamp-based single-molecule experiments}},
booktitle journal =
{Single Molecule Spectroscopy and Superresolution Imaging {IX}}, {Proceedings of SPIE},
note = {\href{http://dx.doi.org/10.1117/12.2212085}{doi:10.1117/12.2212085}},
}
...
url = {http://dx.doi.org/10.1073/pnas.96.7.3670},
year = {1999},
month = {mar},
publisher =
{Proceedings of the National {National Academy of
Sciences}, Sciences USA},
volume = {96},
number = {7},
pages = {3670--3675},
author = {A. A. Deniz and M. Dahan and J. R. Grunwell and T. Ha and A. E. Faulhaber and D. S. Chemla and S. Weiss and P. G. Schultz},
title = {{Single-pair fluorescence resonance energy transfer on freely diffusing molecules: Observation of Forster distance dependence and subpopulations}},
journal = {Proceedings of the National Academy of
Sciences}, Sciences USA},
}
...
url = {http://dx.doi.org/10.1073/pnas.93.13.6710},
year = {1996},
month = {jun},
publisher =
{Proceedings of the National {National Academy of
Sciences}, Sciences USA},
volume = {93},
number = {13},
pages = {6710--6715},
author = {L. Edman and U. Mets and R. Rigler},
title = {{Conformational transitions monitored for single molecules in solution.}},
journal = {Proceedings of the National Academy of
Sciences}, Sciences USA},
}
...
url = {http://dx.doi.org/10.1073/pnas.0401690101},
year = {2004},
month = {jun},
publisher =
{Proceedings of the National {National Academy of
Sciences}, Sciences USA},
volume = {101},
number = {24},
pages = {8936--8941},
author = {A. N. Kapanidis and N. K. Lee and T. A. Laurence and S. Doose and E. Margeat and S. Weiss},
title = {{Fluorescence-aided molecule sorting: Analysis of structure and interactions by alternating-laser excitation of single molecules}},
journal = {Proceedings of the National Academy of
Sciences}, Sciences USA},
}
diff --git a/figures/ALEX_BVA_dynamic/caption.tex b/figures/ALEX_BVA_dynamic/caption.tex
index 52a2ed3..959eacc 100644
--- a/figures/ALEX_BVA_dynamic/caption.tex
+++ b/figures/ALEX_BVA_dynamic/caption.tex
...
\label{fig:bva_dynamic} \textbf{BVA distribution for a hairpin sample undergoing dynamics.}
The left panel shows the E-S histogram for a single stranded DNA sample ($A_{31}$-TA, see in~\cite{Tsukanov_2013}), designed to form a transient hairpin in 400mM NaCl. The right panel shows the corresponding BVA plot. Since the transition between hairpin and open structure causes a significant change in FRET efficiency, $s_E$ lies largely above the static standard deviation curve (\textit{red curve}).
Data courtesy of XXX.
diff --git a/fitting_2.tex b/fitting_2.tex
index b97ded8..f78ce43 100644
--- a/fitting_2.tex
+++ b/fitting_2.tex
...
Unfortunately, the method is not of straightforward application for
freely-diffusing data as it requires a special selection
criterion for filtering bursts with quasi-Poisson rates.
Santoso~\cite{santoso_probing_2009} Santoso et al.~\cite{santoso_probing_2009} and
Kalinin~\cite{Kalinin2010} Kalinin et al.~\cite{Kalinin2010}
extended the PDA approach to estimate conversion rates between different
states by comparing FRET histograms as a function of the time-bin size.
In addition, Gopich and Szabo~\cite{Gopich2009, gopich_theory_2011} developed
...
In case of measurement including lifetime, the multiparameter fluorescence
detection (MFD) method allows to identify dynamics from the deviation
from the linear relation between lifetime and E~\cite{sisamakis_accurate_2010}.
Hoffman~\cite{hoffmann_quantifying_2011} Hoffman et al.~\cite{hoffmann_quantifying_2011} proposed a method
called RASP (recurrence analysis of single particles) to extend
the timescale of detectable kinetics.
Hoffman
computes et al. compute the probability that two nearby bursts are due to
the same molecule and therefore allows setting a time-threshold
for considering consecutive bursts as the same single-molecule event.
...
Finally, two related methods for discriminating between static heterogeneity
and sub-millisecond dynamics are Burst Variance Analysis
(BVA) proposed by
Torella~\cite{Torella_2011} Torella et al.~\cite{Torella_2011} and
two-channel kernel density estimator (2CDE) proposed by
Tomov~\cite{Tomov_2012}. Tomov et al.~\cite{Tomov_2012}. The BVA method is described in the next section.
The 2CDE method, which has been implemented in FRETBursts, computes local
photon rates from timestamps within bursts using
Kernel Density Estimation (KDE)
(FRETBursts includes general-purpose functions
to compute KDE of photon timestamps in the \verb|phrates| module,
(\href{http://fretbursts.readthedocs.io/en/latest/phrates.html}{link})).
From time variations of local
rates rates, it is possible to
detect infer the
occurrence presence of
some dynamics. In
particular particular, the 2CDE method
builds, for each burst, a quantity $(E)_D$ (or
$(1-E)_A$) $(1-E)_A$), which is equal
to the burst average $E$ when no dynamics is present, but
it is biased
toward an higher (or lower) value in presence of dynamics. From these
quantities quantities, a burst ``estimator''
(called FRET-2CDE) is derived. For a
user user, the 2CDE method
consists
in amounts
to plotting the 2-D histogram of $E$ versus
FRET-2CDE
in FRET-2CDE, and assessing the vertical position of the various populations:
populations centered around FRET-2CDE=10
have undergo
no
dynamics dynamics, while population biased towards higher FRET-2CDE values
have undergo dynamics.
The BVA and 2CDE methods are implemented
in two notebooks included with FRETBursts
...
and run the anaysis therein.
The other methods mentioned in this section are not currently
implemented in FRETBursts.
However, users can
easily implement
their any additional
favorite method
taking advantage of FRETBursts functions for methods
in FRETBursts, using its built-in burst analysis
and timestamps/bursts
manipulation.
To facilitate this task, in manipulation functions.
In the next section,
we show how to perform low-level analysis of timestamps and bursts data
by implementing the BVA method from scratch.
An additional example showing how to split bursts in constant time-bins
