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\title{Walkthrough:\Hardware and software for single-molecule fluorescence analysis} \author[1]{Ben Gamari} \author[2]{Laura Dietz} \author[1]{Lori Goldner} \affil[1]{Department of Physics, University of Massachussetts, Amherst} \affil[2]{Department of Computer Science, University of Massachussetts, Amherst}


In this document describe how to carry out a small experimental data analysis using the tools provided in our submission. In the submission package we have provided two datasets from a single-molecule fluorescence experiment taken with our time-stamping hardware. The datasets\footnote{experimental data due to Peker Milas of the Goldner group}, taken for our recent publication [@Milas2013], examine FRET in an RNA 16-mer (Figure \ref{fig:rna}) labelled terminally with Cy3 and Cy5 dyes for comparison against predictions derived from molecular dynamics simulations.

The RNA 16-mer under study. Here we see the RNA backbone along with the two terminal Cyanine dyes.\label{fig:rna}


The tools used are provided by four packages, each of which have associated documentation including installation instructions. The firmware for the timestamping hardware is provided by the timetag-fx2 and timetag-fpga packages. The tools for interacting with the hardware are provided in the timetag-tools package. Installation and usage of these tools is described in the tutorial.

The photon-tools package provides a variety of utilities for working with fluorescence timestamp data and computing and analyzing fluorescence correlation functions.

Finnally, the hphoton package provides an end-to-end FRET analysis package.

We will be focusing on the tools provided by these last two packages.

First steps

We will begin by examining the first dataset, donor-only.timetag, which is a measurement of the 16-mer labelled with only the donor dye for calibration purposes. We will begin by examining the binned intensity timeseries of this dataset using the plot-bins utility provided by photon-tools,

$ plot-bins donor.timetag
Average rates:
              acceptor:    125.666360 / second
                 donor:    222.855797 / second

This will display a plot similar to that shown in Figure \ref{fig:plot-bins}. Each row shows roughly 10 seconds of the experiments where we see a number intensity bursts from labelled RNA passing through the observation volume. As this is a donor-only sample, we see that nearly all of the fluorescence is in the donor (green) channel. In contrast, we can examine the doubly-labelled sample,

$ plot-bins fret.timetag

Here we see more sparse bursts (due to lower sample concentration) but find that a substantial amount of fluorescence is being detected in the acceptor (red) channel. We see that neither of the samples show any indication of long, intense bursts, which are a common sign of contamination.

For reference, passing the -­help option to plot-bins gives a help message describing the various flags supported by the tool.

Bin timeseries showing roughly two minutes of the donor-only dataset\label{fig:plot-bins}.

Correlation analysis

Next we can compute a correlation function to characterize the diffusive characteristics of the samples, using fcs-corr, also provided by photon-tools. We will ignore lags beneath 5 µs to avoid seeing photophysical effects,

$ fcs-corr --plot -­min-lag=5e-5 donor.timetag

This will produce six files in the current directory: three correlation functions (donor and acceptor autocorrelation, and the donor-acceptor cross-correlation, in tab-separated format) along with a plot of each. Nex, we fit a three-dimensional diffusion model to, for instance, the donor (channel 0) auto-correlation function to extract a characteristic diffusion time from which we can infer the molecule's hydrodynamic radius,

$ fcs-fit ­­plot donor.timetag.acorr-0

This shows a plot of the correlation function along with a fit, its parameters, and a variety of goodness-of-fit metrics. Most importantly, we see that the diffusion time, tau_d has a value of 292 μs. As a sanity check, we can compare this fit against that of fret.timetag, where we see that the diffusion times are within the parameter uncertainty of one another. Furthermore, looking at the $α$ parameter, we can validate that the alignment of the instrument's optics has not changed as the day progressed.

Further uses of the photon-tools are described in the package documentation.

FRET analysis

Have verified that the sample is clear of contamination and contains the expected species, we can now extract a FRET efficiency. We begin by examining the donor-only sample, fitting the resulting FRET distribution to a single Beta distribution with 5 ms bin width, and a burst acceptance threshold of 10 photons,

$ fret-analysis --fit-comps=1 --bin-width=5e-3 --burst-size=10 --nbins=10 donor.timetag

This produces a few tab-separated files describing the above-threshold bins, a variety of plots, as well as an HTML file summarizing the analysis. We see in the summary that the donor-only sample contains a single population exhibiting low FRET efficiency. Althouhg there are no true acceptor emissions (as there is no acceptor dye), the peak is shifted away from $E=0$ due to spectral crosstalk. The magnitude of this shift can be later used to correct the histogram FRET dataset.

Next we can examine the doubly-labelled FRET sample. Here we will use two fit components (one for the donor-only population and another for the doubly-labelled population) and a higher threshold due to the second dye. Further, we can indicate that the software should correct for crosstalk and gamma, inferring the correction parameters from the donor-only dataset,

$ fret-analysis --fit-comps=2 --burst-size=20 --nbins=20 --donly-file=donor.timetag
--crosstalk=auto --gamma=auto --bin-width=5e-3 fret.timetag

We see, the FRET histogram, the inferred fit for the FRET distribution, and a variant of the fit which shows the distribution that would be expected in the case of a shot-noise limited FRET population exhibiting no slow dynamics.

Bayesian burst detection

While sometimes effective, the bin-threshold technique imposes an arbitrary timescale on the data and there struggles to isolate bursts shorter than the significantly shorter than the bin width, as is common in solution FRET experiments like the one described above.

To overcome this, we provide a novel Bayesian inference for burst identification. In contrast to the bin-threshold method, our approach exploits the exponential distribution of Poissonian interarrival times in conjunction with an assumption of the smoothness on the fluorescence intensity as a function of time. This allows bursts with duration shorter than one bin width to be isolated and examined. We include an implementation of this technique in the hphoton package which can be easily used to support a simple FRET analysis as seen in \ref{fig:burstfind}.

An IPython notebook session showing the easy integration between tools provided in the submission.\label{fig:burstfind}