Cells respond to environmental perturbations with changes in their gene expression that are coordinated in magnitude and time. Timing in- formation about individual genes, rather than clusters, provides a refined way to view and analyze responses, but is hard to estimate accurately. To analyze response timing of individual genes, we developed a para- metric model that captures the typical temporal responses: an abrupt early response followed by a second transition to a steady state. This im- pulse model explicitly represents natural temporal properties such as the onset and the offset time, and can be estimated robustly, as demonstrated by its superior ability to impute missing values in gene expression data. Using response time of individual genes, we identify relations between gene function and their response timing, showing, for example, how cy- tosolic ribosomal genes are only repressed after mitochondrial ribosom is activated. We further demonstrate a strong relation between the binding affinity of a transcription factor and the activation timing of its targets, suggesting that graded binding affinities could be a widely used mecha- nism for controlling expression timing.
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