Analysis of spliceosome dynamics by maximum likelihood fitting of dwell time distributions

Abstract

Colocalization single-molecule methods can provide a wealth of information concerning the ordering and dynamics of biomolecule assembly. These have been used extensively to study the pathways of spliceosome assembly in vitro. Key to these experiments is the measurement of binding times-either the dwell times of a multi-molecular interaction or times in between binding events. By analyzing hundreds of these times, many new insights into the kinetic pathways governing spliceosome assembly have been obtained. Collections of binding times are often plotted as histograms and can be fit to kinetic models using a variety of methods. Here, we describe the use of maximum likelihood methods to fit dwell time distributions without binning. In addition, we discuss several aspects of analyzing these distributions with histograms and pitfalls that can be encountered if improperly binned histograms are used. We have automated several aspects of maximum likelihood fitting of dwell time distributions in the AGATHA software package.

Keywords: Dynamics; Fitting; Fluorescence; Single-molecule; Software; Spliceosome.

Figure 1.

Analysis of single-molecule binding dynamics of BBP on RNA substrates. (A) Cartoon schematic of the CoSMoS experiment described by Larson and Hoskins [21] in which green-labeled BBP binds to and dissociates from a surface-immobilized, red-labeled RNA substrate either containing (wild-type, WT) or lacking the BS sequence. (B) Single-molecule fluorescence intensity versus time plot showing multiple BBP binding events on a single WT RNA molecule. One of such binding event is magnified to highlight a single BBP dwell time. (C) Single-molecule fluorescence intensity versus time plot showing multiple BBP binding events on a single RNA molecule lacking the BS sequence. (D) Comparison between the probability density histograms of dwell times for BBP on either the WT RNA or the substrate lacking the BS.

Figure 2.

Fitting and statistical analysis of BBP dwell time histograms. (A) The log likelihood function, L(τ), for BBP binding times on RNAs without a BS is plotted as a function of parameter τ. The τ low and high values, where the L(τ_max) −0.5 line intersects the L(τ) curve, are the 0.5 unit intervals: 8.1 s and 9.1 s. Similarly, the 2 unit limits are 7.6 s and 9.6 s. (B) Contour plot of the log likelihood function, L(τ₁, τ₂)versus τ₁ and τ₂ for a₁ = 0.74. L(τ₁,τ₂) corresponds to the double exponential PDF with dwell times of BBP on WT RNA. (C) Probability density histogram of the ML estimates of τ that are obtained from 1000 random samples (Nboot=1000) of the dwell time dataset for BBP on RNA lacking a BS via bootstrapping. The histogram was fit with a Gaussian distribution to obtain a mean value, μ = 8.6 s, and the standard deviation, σ = 0.7 s. (D) Probability density histograms of the dwell times for BBP are fit with either a single (RNA without BS, black) or double exponential (WT RNA, red) PDFs. Fit parameters and their respective error estimates for both data sets are given in Table 1.

Figure 3.

Bin size-dependent comparison between ML and least squares fits of dwell time distributions. The probability density histograms for the dwell times of BBP on WT RNA with (A) 6, equally-sized bin widths, (B) 6, variably-sized bind widths, and (C) 9, variably sized bin widths. Lines represent the fits to the bin centers (black points) using least squares methods (blue) or fits of the unbinned data using ML methods (red). For both methods, the fit parameters and their corresponding confidence intervals are given in Tables 1 and 2.

Figure 4.

Screenshot of the startup screen for AGATHA software, a collection of programs designed to expedite analysis of dwell times and fluorescence intensity trajectories obtained from CoSMoS experiments.

Figure 5.

Screenshot of the Plotting Histogram GUI. Red numbers indicate widgets which require user input, and blue numbers indicate locations of the fitted parameters output. In addition, this program also outputs various histograms which are saved in a user-specified folder.