deletions | additions       diff --git a/Burst_Variance_Analysis.tex b/Burst_Variance_Analysis.tex  index bd7dc1a..09a057d 100644  --- a/Burst_Variance_Analysis.tex  +++ b/Burst_Variance_Analysis.tex 
...
\section{Implementing burst variance analysis (BVA)} Burst Variance Analysis}  \label{sec:bva}  In this section we describe how to implement the burst variance analysis (BVA)~\cite{Torella_2011}. 
...
a single peak cannot be a priori associated with a single FRET efficiency,  unless a detailed shot-noise analysis is carried out~\cite{Nir_2006,Antonik2006}.  The width of a FRET efficiency population distribution  has a typical lower boundary that set by shot noise, which  is causeddue to shot noise driven  by low number counting statistics. A broader the statistics of discrete photon-detection events.  FRET efficiency distribution distributions broader than the shot noise limit,  can be accounted for ascribed to  a static  mixture ofmultiple non-interconverting  species with slightly  different FRET efficiencies, and/or or to  a mixture of specie undergoing  dynamic species, interconverting transitions (e.g. interconversion between multiple states,  diffusion in a continuum of conformations, binding-unbinding events, etc...).  By simply looking  attimes comparable to  the diffusion time. Burst variance analysis (BVA) FRET histogram, in cases when there  isan analysis method for  single molecule FRET experiments, developed peak broader than shot-noise,   it is not possible  to detect molecular dynamics~\cite{Torella_2011}. It discriminate between the static and dynamic case.  The BVA method  has been successfully implemented developed  to identify heterogeneities address this issue of detecting the presence of dynamics  in FRET histograms due distributions~\cite{Torella_2011},   and has been successfully applied  to dynamic identify biomolecular  processes with   dynamics on the millisecond time-scale~\cite{Torella_2011, Robb_2013}.  The basic idea behind BVA is slicing bursts in sub-bursts with a fixed number  of biomolecules photons $n$,  and comparing the empirical variance of acceptor counts across all sub-bursts  in a burst   with  the milliseconds' time scale~\cite{Torella_2011, Robb_2013}. theoretical shot-noise limited variance, dictated by the Binomial distribution.  An empirical variance of sub-bursts larger than the shot-noise limited value indicates  the presence of dynamics. Naturally, 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 FRETefficiency  (sub-)population distribution  originating from a single static FRET efficiency has the minimum width and efficiency,  the sub-bursts acceptor counts ($N_a$) $N_a$  can be modeled as a binomial distribution, Binomial-distributed random variable  $N_a \sim \operatorname{Binom} \{n, E\}$, where $n$ is the number of photons in each sub-burst and   $E$ is the estimated population  FRET efficiency (In practice, efficiency. Note that, without approximation, we can replace   E with PR and use the uncorrected counts. This is possible because, regardless of the   molecula FRET efficiency, the detected counts are partitioned between donor and acceptor channel  according to a Binomila distribution whit a $p$ parameter equal to PR.  The only approximation done here and in the following paragraphs is neglecting the presence background.   We refer the interested reader to~\cite{Torella_2011} for further discussion.  the PR instead of the corrected The same considerations holds if, instead of $E$   we use the PR grated that we used the uncorrected acceptor counts in this case. and Note that, we can also substitute $E$ with $PR$  Proximity ratio is used as $E$, instead of FRET efficiency). Since, $N_a$ follow a binomial distribution, as modeled, and $E = N_a/n$, we expect the standard deviation of $E$ for the sub-bursts to be distributed according to eq.~\ref{eq:binom_std} ~\cite{Torella_2011}. This is an approximation because background counts (both from sample and detector's dark counts) add additional variance that is not taken into account. However, the approximation works well in practical cases because the background contribution  is normally a small fraction of the total number of counts (therefore it marginally contributes to the variance).