Explicit Probability and Rate Transition (ExPRT) Plots

smFRET allows for the monitoring the distances between single Cy3 – Cy5 pairs on single molecules in real time. Therefore, single events such as binding interactions, conformational changes, and protein translocation can be observed explicitly. Analyses that quantify the probabilities and rates of these events can be used to provide a detailed characterization of the dynamics being observed. There are several programs available to perform analyses on smFRET data [208, 209, 212, 213]. These programs rely on using Hidden Markov modeling programs, such as HaMMY and vbFRET to fit data to ideal states [207, 209]. The analysis programs then use the ideal state fits to the raw data to generate transition plots, where the initial FRET value (the FRET state preceding the transition) is on the x-axis, and the final FRET value (the FRET state transitioned into) is on the y-axis. For example, the Transition Density Plot (TDP) program created by the Ha laboratory uses ideal state fits to each individual trace and visualizes all transitions from all traces as heat map [209, 212]. Heterogeneity within the transitions can be visualized and qualitative comparison of transition probability can be visualized, but features that provide explicit quantification of the data directly on the plot are lacking [209, 212]. Another analysis program is the Probability and Kinetically Indexed Transition (POKIT) Plot program developed by the Walter laboratory [208, 213]. This program relies on fitting all traces as one stitched trace, which allows for the analysis of the transition rate and probability between the

data into bins diminishes the power of single-molecule methods to determine the explicit parameters such as probability and rates based on single-molecule events. There are limitations and shortcomings for all analysis programs. The currently available analyses either cannot visualize both probability and kinetic information on a single plot or rely on binning data into ranges of values in order to do so. We sought to overcome some of these limitations by creating our own smFRET analysis program termed Explicit Probability and Rate Transition (ExPRT) plots.

Figure 2-3: smFRET Analysis of WT and Mutant SsoSSB bound to DNA.

A) A histogram of all single-molecule FRET data collected for the DNA3050 substrate alone, with WT SsoMCM, and SsoMCM (K323D/R440D). B) and C) show the ExPRT plots for WT SsoMCM and SsoMCM (K323D/R440D), respectively. D) The legend for the ExPRT plots: Transition Probability and Dwell Times. smFRET time traces for E) WT and F) K323D/R440D showing Cy3 (green) and Cy5 (red) intensities and FRET efficiencies (blue). The red line is a fit to ideal FRET states.

The ExPRT analysis program is a Matlab executable program that produces ExPRT plots from raw smFRET values. The ExPRT program follows an initial data processing and analysis approach similar to the POKIT program, where the raw data that is collected must be stitched together and fit to ideal states using software such as vbFRET [207]. That ideal stitched trace is then unstitched to avoid analyzing ‘false transitions’ and to generate single-trace statistics. The unstitched traces can then be fed into the ExPRT program. Figure 2.3E-F show examples of unstitched traces for WT SsoMCM and SsoMCM (K323D/R440D) on the DNA3050 fork. The upper panel shows the raw Cy3 donor and Cy5 acceptor intensities, and the lower panel shows the FRET efficiency calculated from the raw data. The overlaid red line is the ideal state fit to calculated FRET values. The program goes through each trace and collects all transitions that occur in addition to the dwell time of each state between transitions. Once all traces have been analyzed, the ExPRT program generates the transition plots (Figure 2.3B-C). Each transition is plotted as a marker based on its initial FRET state on the x-axis and the final FRET state on the y-axis. The size of the circle corresponds to the probability of that transition occurring within a measured single trace. We define probability as the fraction of analyzed traces that exhibit the given transition at least once. The color of the filled circle corresponds to the time spent in the initial state before transitioning (Figure 2.3D). Although the ExPRT plots resemble POKIT plots in that they both use circular markers to denote transitions, ExPRT plots use and visualize the explicit probabilities and dwell time values rather than displaying the data in bins. In addition, the ExPRT program also plots the dwell times of each transition in the form of a survival curve, and fits the subsequent curve to single and double exponential decay functions. The user is then able to determine which fit is appropriate based on the differences in R² values between fits. If a double exponential decay is selected, then the resulting marker on the ExPRT plot will be

concentric, containing two colors where each color corresponds to the dwell time based on the rates given by the exponential fit. For SsoMCM (K323D/R440D), there is an increase in the number of FRET states, an increase in the probability of a transition, and a decrease in the dwell times in each state compared with WT (Figure 2.3B-C). In all, this mutation is responsible for a large increase in excluded strand binding dynamics.

The ExPRT program illustrates all observed dynamics on a single plot, which allows the reader to more easily gain greater insight into the measured interactions. When altering the length of the excluded strand or when studying mutants designed to disrupt the interaction, the ExPRT plots capture changes in FRET states, transitions, and kinetics. ExPRT analysis is the only single-molecule FRET analysis program that produces transition plots that simultaneously display explicit transitions, probability of transitions, and dwell times on a single plot. Moreover, the ExPRT program tests for and can display multiple rates that govern a transition.

Visualization of the data is a critical aspect of analysis, and interpretation and comparison between data sets necessitates concise representation of the data. We believe that the ExPRT plots provide the most detailed description of dynamics on a single plot, which is advantageous for comparison between experimental conditions and interpretation of results.For these reasons, we believe that the ExPRT program may be a preferable method of analyzing and displaying data compared to other smFRET analysis programs [208, 209, 212, 213].