Abstract
Recently, a novel approach has been developed to study gene expression in single cells with high time resolution using RNA Fluorescent In Situ Hybridization (FISH). The technique allows individual mRNAs to be counted with high accuracy in wild-type cells, but requires cells to be fixed; thus, each cell provides only a “snapshot” of gene expression. Here we show how and when RNA FISH data on pairs of genes can be used to reconstruct real-time dynamics from a collection of such snapshots. Using maximum-likelihood parameter estimation on synthetically generated, noisy FISH data, we show that dynamical programs of gene expression, such as cycles (e.g., the cell cycle) or switches between discrete states, can be accurately reconstructed. In the limit that mRNAs are produced in short-lived bursts, binary thresholding of the FISH data provides a robust way of reconstructing dynamics. In this regime, prior knowledge of the type of dynamics – cycle versus switch – is generally required and additional constraints, e.g., from triplet FISH measurements, may also be needed to fully constrain all parameters. As a demonstration, we apply the thresholding method to RNA FISH data obtained from single, unsynchronized cells of Saccharomyces cerevisiae. Our results support the existence of metabolic cycles and provide an estimate of global gene-expression noise. The approach to FISH data presented here can be applied in general to reconstruct dynamics from snapshots of pairs of correlated quantities including, for example, protein concentrations obtained from immunofluorescence assays.
Highlights
Cells are well known to respond to external conditions by altering their gene expression
We suggest that the two-step approach of thresholding followed by Maximum Likelihood Estimation (MLE) or Principal Component Analysis (PCA) is likely to prove the best practical approach to reconstructing gene-expression dynamics for most real Fluorescent In Situ Hybridization (FISH) data sets, and we demonstrate this approach using the data set of Silverman et al [14]
Optimal treatment of the intermediate regime requires a more detailed and/or empirical noise model, but the thresholding method we develop for the bursty regime can be usefully applied in the intermediate case, as demonstrated by our analysis of FISH data for metabolic cycles in yeast [14]
Summary
Cells are well known to respond to external conditions by altering their gene expression. Many examples of altered gene expression programs have been revealed by population level studies, including microarray studies of yeast, mammalian, and bacterial cells. Many cells are known to alter gene expression is ways that are heterogeneous across a cell population. Heterogeneous changes in gene expression in response to homogeneous external cues may be purely stochastic as in the switch to competence in B. subtilis [1,2,8], or may depend on pre-existing non-genetic differences such as the phase of the cell cycle in budding yeast [6,7]. Since population level studies are not well suited to reveal heterogenous behavior, how can heterogeneous changes in gene expression be studied and quantified? Construction of fluorescent reporters can be laborious and impractical for studies of large-scale transcriptional responses
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