Inferring quantity and qualities of superimposed reaction rates in single molecule survival time distributions

Abstract

Actions of molecular species, for example binding of transcription factors to chromatin, are intrinsically stochastic and may comprise several mutually exclusive pathways. Inverse Laplace transformation in principle resolves the rate constants and frequencies of superimposed reaction processes, however current approaches are challenged by single molecule fluorescence time series prone to photobleaching. Here, we present a genuine rate identification method (GRID) that infers the quantity, rates and frequencies of dissociation processes from single molecule fluorescence survival time distributions using a dense grid of possible decay rates. In particular, GRID is able to resolve broad clusters of rate constants not accessible to common models of one to three exponential decay rates. We validate GRID by simulations and apply it to the problem of in-vivo TF-DNA dissociation, which recently gained interest due to novel single molecule imaging technologies. We consider dissociation of the transcription factor CDX2 from chromatin. GRID resolves distinct, decay rates and identifies residence time classes overlooked by other methods. We confirm that such sparsely distributed decay rates are compatible with common models of TF sliding on DNA.

Transcription factor residence time dominates over concentration in transcription activation

“…We then accumulated the binding times of each time-lapse condition in survival time distributions ( Figure 2B and Figure S4). Next, we extracted the dissociation rate spectra of TALE-TFs using genuine rate identification (GRID) ( Figure 2B, 2C and S4) 53 . GRID yields the dissociation rate spectrum by inverse Laplace transformation of survival time distributions and enables correcting for photobleaching by global consideration of all timelapse conditions.…”

“…We determined the dissociation rate spectrum of bound TALE-TF by analysing the fluorescence survival time distributions obtained from time-lapse imaging with GRID 53 . In brief, GRID performs an inverse Laplace transformation of a fluorescence survival time distribution to reveal the underlying dissociation rate spectrum.…”

Single molecule tracking and analysis framework including theory-predicted parameter settings

“…Lifetimes of immobile molecules, imaged at different time-lapse conditions to allow for photobleaching correction 25 , are collected in survival time distributions 23 . From these, the complete spectrum of dissociation rates is extracted by inverse Laplace transformation using GRID 26 . Also, the fractions of bound molecules can be assessed using interlaced time-lapse microscopy 32 .…”

“…We tracked the molecules by specifying a loss probability and using the suggested tracking parameters for each time-lapse condition in the nearest neighbour algorithm. Subsequently, we used GRID to extract the spectrum of dissociation rates 26 . To determine to which extend tracking errors influenced the result we varied the loss probability over two orders of magnitude.…”

“…Using this formalism, we calculate optimal parameter settings for tracking and subsequent residence time analysis. We apply the theorysuggested parameter set to extract residence times of the transcription factor CDX2 in the cell nucleus from a single molecule experiment 26 .…”