deletions | additions       diff --git a/Burst_Variance_Analysis.tex b/Burst_Variance_Analysis.tex  index 73b8c95..8900f4e 100644  --- a/Burst_Variance_Analysis.tex  +++ b/Burst_Variance_Analysis.tex 
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Single-molecule FRET histograms show more information than just mean FRET efficiencies.   While, in general, several peaks indicate the presence of multiple subpopulations,   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}. out~\cite{Nir_2006,Antonik2006}.  A broad FRET distribution might be attributed to a mixture of multiple species with static but different FRET efficiencies, single species with dynamic fluctuations between multiple FRET states, or a combination of the two cases. Burst Variance Analysis (BVA) is an analysis method for single molecule FRET experiments, developed to detect molecular dynamics~\cite{Torella_2011}. It has been successfully implemented to identify heterogeneities in FRET histograms due to dynamic processes of biomolecules in millisecond time scale~\cite{Torella_2011, Robb_2013}.  BVA analysis consists of four steps: 1) slicing bursts into sub-bursts containing \textit{n} consecutive photons, 2) computing FRET efficiencies of each sub-burst, 3) calculating the empirical standard deviation ($s_E$) of sub-burst FRET efficiencies over the whole burst, and 4) comparing $s_E$ to an expected standard deviation based on shot noise limited distribution~\cite{Torella_2011}.   A FRET peak originating from a single static FRET efficiency has the minimum width and   the sub-bursts acceptor counts ($n_a$) ($N_a$)  will ideally follow a binomial distribution of eq.~\ref{eq:binom_dist}, where $n$ is the number of photons in each sub-burst and   $E$ is the FRET efficiency. In practice, we use the proximity ratio peak position as $E$,  and we expect the standard deviation of the sub-bursts to be distributed according to  
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\begin{equation}  \label{eq:binom_std}  \operatorname{Std}(N_a) \operatorname{Var}(N_a)  = n E\,(1 - E) \end{equation}  If the observed broadening originates from different molecules having distinct FRET efficiencies without dynamics, $s_E$ of each burst is only affected by shot noise and will follow the expected standard deviation curve rationalized by a binomial distribution (see equation 4 in~\cite{Torella_2011}). However, if the observed broadness is due to millisecond dynamics of single species of biomolecules, $s_E$ of each burst is supposed to be larger than the expected standard deviation and sit above the expected standard deviation curve as shown in figure .