Precisely and Accurately Inferring Single-Molecule Rate Constants

Abstract

The kinetics of biomolecular systems can be quantified by calculating the stochastic rate constants that govern the biomolecular state versus time trajectories (i.e., state trajectories) of individual biomolecules. To do so, the experimental signal versus time trajectories (i.e., signal trajectories) obtained from observing individual biomolecules are often idealized to generate state trajectories by methods such as thresholding or hidden Markov modeling. Here, we discuss approaches for idealizing signal trajectories and calculating stochastic rate constants from the resulting state trajectories. Importantly, we provide an analysis of how the finite length of signal trajectories restrict the precision of these approaches, and demonstrate how Bayesian inference-based versions of these approaches allow rigorous determination of this precision. Similarly, we provide an analysis of how the finite lengths and limited time resolutions of signal trajectories restrict the accuracy of these approaches, and describe methods that, by accounting for the effects of the finite length and limited time resolution of signal trajectories, substantially improve this accuracy. Collectively, therefore, the methods we consider here enable a rigorous assessment of the precision, and a significant enhancement of the accuracy, with which stochastic rate constants can be calculated from single-molecule signal trajectories.

Observation and Analysis of RAD51 Nucleation Dynamics at Single-Monomer Resolution

“…, the RAD51 nucleoprotein filament in the current case) taken at consecutive time points. Analysis of these signal trajectories involves correlating the values of the signal at different time points to the underlying conformational dynamics of the individual molecule (Kinz-Thompson et al, 2016). Unfortunately, despite being sensitive enough to report on individual molecules, the signal trajectories collected using most single-molecule techniques are relatively noisy, and this confounds the ability to correlate the signal values to the underlying dynamics.…”

“…For the rate constant for the transition from generic states i to j , denoted $k_{ij}$, this calculation can be performed with the formula $k_{ij}=-ln(1-P_{ij})/\tau$, where $P_{ij}$ is the transition probability for the transition from state i to j , which is an element of the transition matrix located in Transition_Matrix entry of the Analysis Summary , and $\tau$ is the time resolution of the dataset in units of seconds (see (Kinz-Thompson et al, 2016) for additional details). Further insights relating to the kinetic mechanism of interest can be obtained by generating a transition density plot (TDP).…”

The formation of intramolecular secondary structure brings mRNA ends in close proximity

“…3). Using GAPDH mRNA as an example, we further explored the statistics of fluctuations between FRET states via Hidden Markov Model (HHM) and Transition Density Plot analyses 20,21 . Consistent with FRET distribution histograms, individual GAPDH mRNA molecules predominantly fluctuated between ~0.4, 0.6 and 0.8 FRET states at frequencies of ~0.1 -0.03 s -1 ( Fig.…”

Increasing the time resolution of single-molecule experiments with Bayesian inference

“…Notably, when the rate constants for transitions between states become comparable to or greater than "# , there is a large probability that the s of a signal trajectory will contain one or more transitions, and that, consequently, many of the signal values of the signal trajectory will exhibit this time averaging. Given such a scenario, analysis methods in which individual s are assigned to particular states (e.g., the widely used strategy of idealizing signal trajectories using signal thresholds (13), or hidden Markov models (HMMs) (14,15)) will introduce significant errors into the calculated rate constants for transitions between states and into the signal values assigned to those states (2).…”

“…Much like learning the point spread function describing the fluorescence signal from a single fluorophore in a superresolution imaging experiment enables the spatial position of the fluorophore to be inferred beyond the spatial resolution of the experiment, learning the model describing the kinetic behavior of a single molecule in a timeresolved single-molecule experiment using BIASD enables the kinetic behavior of the single molecule to be inferred beyond the temporal resolution of the experiment. By using Bayesian inference, BIASD can also integrate information from other experiments to further enhance its resolving power, while also employing a natural framework with which to describe the precision that the amount of data collected during the singlemolecule experiment will lend to the determination of the parameters governing the single-molecule kinetics (2,6,7). It is worth noting that, in a close parallel to the approach we describe here, Bayesian inference has been previously employed to improve the time resolution of the time-dependent free induction decay in NMR spectroscopy experiments, resulting in an orders-of-magnitude improvement in spectral resolution (7,8).…”