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

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 multi-exponential 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.