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

Abstract

Actions of molecular species, for example binding of transcription factors to chromatin, may comprise several superimposed reaction pathways. The number and the rate constants of such superimposed reactions can in principle be resolved by inverse Laplace transformation of the corresponding distribution of reaction lifetimes. However, current approaches to solve this transformation are challenged by photobleaching-prone fluorescence measurements of lifetime distributions. Here, we present a genuine rate identification method (GRID), which infers the quantity, rates and amplitudes of dissociation processes from fluorescence lifetime distributions using a dense grid of possible decay rates. In contrast to common multi-exponential analysis of lifetime distributions, GRID is able to distinguish between broad and narrow clusters of decay rates. We validate GRID by simulations and apply it to CDX2-chromatin interactions measured by live cell single molecule fluorescence microscopy. GRID reveals well-separated narrow decay rate clusters of CDX2, in part overlooked by multiexponential analysis. We discuss the amplitudes of the decay rate spectrum in terms of frequency of observed events and occupation probability of reaction states. We further demonstrate that a narrow decay rate cluster is compatible with a common model of TF sliding on DNA.The actions of biomolecules are governed by thermal fluctuations and thus are intrinsically stochastic. Accordingly, interactions such as association and dissociation events of molecular species often follow Poissonian statistics with a constant probability per time, the rate constant, to occur. In this case, the experimentally accessible lifetime of the reaction is exponentially distributed. Commonly, a biomolecule engages in several different types of interaction, with each interaction type having its own reaction rate. For example, a biomolecule might bind to different protein species, to multiple sites on DNA or RNA, or to different cellular compartments. In such a scenario, not all members of a biomolecular specie will undergo the same type of interaction at any time. Rather, each biomolecule will conduct one of the multiple possible types of interaction. If the measurement determining the reaction lifetimes cannot distinguish between the different types of interaction, the resulting lifetime distribution will be multi-exponential and include reaction rates from all superimposed Poisson processes. More precisely, the lifetime distribution is a Laplace transform of the spectrum of reaction rates inherent to the biomolecule (Fig. 1a). Retrieving the underlying spectrum of reaction rates consequently evokes an inverse Laplace transformation.The inverse Laplace transformation is an ill-posed problem for the inversion of inherently noisy, discrete distributions and numerical solutions are often unstable 1,2 . Nevertheless, algorithms treating the Laplace transform using gradient methods and appropriate regularization have been successfully developed for noisy data in NMR 3,4 and prote...

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 time-lapse 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.…”

Myosin VI moves on nuclear actin filaments and supports long-range chromatin rearrangements

“…Using interlaced time-lapse microscopy (ITM) (Reisser et al, 2018), we observed that 87% of MVI molecules were fast diffusing, whereas 13% were static, probably corresponding to chromatin bound molecules (Figure 1f and Methods). In these experiments, we defined a molecule to be bound if it was confined to a radius of 160 nm for at least 100 ms. We next identified dissociation rates of bound MVI molecules from chromatin using time-lapse microscopy (Gebhardt et al, 2013) to correct for photobleaching and genuine rate identification (GRID), which allows extracting a complete spectrum of dissociation rates from single molecule fluorescence survival time distributions (Figure 1g, Supplementary Figure 2 and Methods) (Reisser et al, 2020). (Reisser et al, 2020) using all data (magenta).…”

“…In these experiments, we defined a molecule to be bound if it was confined to a radius of 160 nm for at least 100 ms. We next identified dissociation rates of bound MVI molecules from chromatin using time-lapse microscopy (Gebhardt et al, 2013) to correct for photobleaching and genuine rate identification (GRID), which allows extracting a complete spectrum of dissociation rates from single molecule fluorescence survival time distributions (Figure 1g, Supplementary Figure 2 and Methods) (Reisser et al, 2020). (Reisser et al, 2020) using all data (magenta). Error estimation was obtained by resampling with 80% of the data (blue)(Methods).…”

“…We analyzed fluorescence survival time histograms resulting from time lapse imaging using GRID (Reisser et al, 2020). GRID is an approach for the genuine identification of decay processes contained in survival histograms.…”