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Individual cells exhibit substantial heterogeneity in protein abundance and activity, which is frequently reflected in broad distributions of fluorescently labeled reporters. Since all cellular components are intrinsically fluorescent to some extent, the observed distributions contain background noise that masks the natural heterogeneity of cellular populations. This limits our ability to characterize cell-fate decision processes that are key for development, immune response, tissue homeostasis, and many other biological functions. It is therefore important to separate the contributions from signal and noise in single-cell measurements. Addressing this issue rigorously requires deconvolving the noise distribution from the signal, but approaches in that direction are still limited. Here we present a non-parametric Bayesian formalism that performs such a deconvolution efficiently on multidimensional measurements, in a way that allows estimating confidence intervals precisely. We use the approach to study the expression of the mesodermal transcription factor Brachyury in mouse embryonic stem cells undergoing differentiation.