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...
The basic idea behind BVA is to subdivide bursts into contiguous burst chunks (sub-bursts)
comprising a fixed number $n$ of photons,
and to compare the empirical variance of acceptor counts across all sub-bursts in a burst
with the theoretical
shot-noise limited shot-noise-limited variance, as expected from a binomial distribution.
An empirical variance of sub-bursts larger than the 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
...
BVA analysis consists of 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
over the whole in each burst, and 4) comparing $s_E$ to the expected standard deviation
of a
shot-noise limited shot-noise-limited distribution~(eq.~\ref{eq:binom_std}).
If, as in figure~\ref{fig:bva_static}, the observed FRET efficiency distribution
originates from a static mixture of sub-populations (of different
non-interconverting molecules) characterized by distinct FRET efficiencies,
$s_E$ of each burst is only affected by
shot noise 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,
which interconverts between different FRET sub-populations (over times comparable to the diffusion
...
DexAem_mask_d = AemDex_mask[Dex_mask]
\end{lstlisting}
Here, the first two variables (\verb|Dex_mask| and \verb|DexAem_mask|)
are used to
select photon from the all-photons timestamps array,
while \verb|DexAem_mask_d|, selects A-emitted photons from the
array of photons emitted during D-excitation. As shown below,
the latter is needed to count acceptor photons in burst chunks.
Next,
the burst data relative we need to
express bursts start-stop data as indexes of the D-excitation photon stream
is needed
(by default burst start-stop
index indexes refer to all-photons timestamps array):
\begin{lstlisting}
ph_d = ds_FRET.get_ph_times(ph_sel=Ph_sel(Dex='DAem'))
...
\end{lstlisting}
Here, \verb|n| is the BVA parameter defining the number of photons in each burst chunk.
The outer loop iterates through bursts, while the inner loop iterates through
burst chunks. sub-bursts.
The variables \verb|startlist| and \verb|stoplist| are the list of start-stop indexes for
all
burst chunks sub-bursts in current burst.
In the inner loop, \verb|A_D| and \verb|E| contain the number of acceptor photons and
FRET efficiency for the current
burst chunk. sub-burst. Finally, for each burst, the standard deviation
of \verb|E| is appended to
the list \verb|E_sub_std|.
By plotting the 2D distribution of $s_E$ (i.e. \verb|E_sub_std|) versus the average (uncorrected) E
we obtain the BVA plots of figure~\ref{fig:bva_static} and~\ref{fig:bva_dynamic}.
