RealTrace: Uncovering biological dynamics hidden under measurement noise in time-lapse microscopy data

Abstract

One of the most powerful approaches for identifying the mechanisms underlying complex biological phenomena is not just to measure bulk populations, or even take single-cell snapshots, but to directly track the behaviors of single cells in time. Indeed, in recent years there has been a steep rise in the use of time-lapse microscopy with fluorescent reporters to quantify single-cell time dynamics in many different biological systems. However, there is a major challenge with the analysis of such data. Since biological changes are inherently small on short time scales, much of the true biological dynamics is hidden under unavoidable measurement noise, but we do not know what functional form the time dynamics may take, and smoothing over neighboring time points simply replaces the true dynamics with a time average. Here, we present RealTrace, a Bayesian method that rigorously solves this challenge using only the assumption that, while true biological fluctuations are correlated on short time scales, measurement errors are uncorrelated. We show that this assumption can be formalized in a Bayesian model using maximum entropy process priors and that this model can be accurately solved by recursively approximating the non-linear dynamics over short time intervals. Given raw input cell size and fluorescence measurements, RealTrace calculates the estimated true sizes, total GFP contents, instantaneous growth rates, and volumic GFP production rates across all cells and time, together with rigorous error bars on all these quantities. We demonstrate the broad applicability of RealTrace by analyzing time-lapse microscopy datasets from E. coli bacteria, mouse embryonic stem cells, and entire C. elegans embryos. To exemplify the subtle dynamical features RealTrace can uncover, we perform an in-depth study of E. coli cells carrying fluorescent reporters for constitutive and ribosomal promoters, across multiple growth conditions. We find growth rates of single cells substantially fluctuate in time and, as the average growth rate decreases, these fluctuations systematically increase in amplitude and duration. Both growth rate and gene expression vary systematically across the cell cycle, but while the pattern of growth rate variation is condition-independent, the systematic variation in gene expression across the cell cycle is both condition and promoter-dependent. Finally, under a sudden change in nutrients, single cells exhibit highly consistent transient changes in growth rate and gene expression. While gene expression rates settle into a new steady-state surprisingly rapidly, the growth rate shows a dramatic drop followed by an overshoot that takes several cell cycles to settle down. All these observations give fundamental new insights into the single-cell physiology of bacteria. RealTrace is a highly versatile method that accurately removes measurement noise from any fluorescence time-lapse microscopy data, enabling the identification and quantification of subtle features in the biological dynamics that would otherwise be hidden under measurement noise.