Isogenic cells sharing a common environment present a large degree of heterogeneity in gene expression, and stochasticity inherent to transcription substantially participates in this cell-to-cell variability. Notably, a majority of mammalian genes are transcribed during short periods termed transcription bursts followed by longer periods of transcriptional inactivity. Interestingly, genes display variability in the frequencies and sizes of their bursts, implying that different regulatory mechanisms actively participate in shaping gene-specific bursting signatures. However, the nature of these molecular mechanisms and their precise contribution to transcriptional bursting remains elusive. In this work, we used a short-lived luciferase reporter under the control of a Bmal1 circadian promoter stably inserted into the genome of NIH-3T3 cultured fibroblasts to quantify its transcriptional bursting along the circadian cycle and at three different reporter integration sites. By recording dynamic variations of the luminescence signal at the single-cell level and counting individual transcripts using smRNA-FISH at specific time-points, we could infer the transcriptional bursting parameters characteristic of these conditions using a telegraph (on-off) model of gene expression. We observed that while the integration site-specific differences in expression levels mainly arose from burst size dissimilarities, the burst frequency predominantly modulated the temporal variations in expression of Bmal1 over the circadian cycle. Thus, both parameters are uncoupled and can be independently modulated to regulate expression levels. By focusing on the molecular origins of bursting, we found that the rhythmic circadian modulation of burst frequencies depended on the presence of ROR responsive elements (ROREs) on Bmal1 promoter. These DNA motifs recruit the REV-ERBs repressors involved in the rhythmic regulation of the histone acetylation state at target promoters. Indeed, the H3K27ac profile in the Bmal1 promoter corresponded to that of its burst frequency. More generally, higher histone acetylation levels were observed during Bmal1 circadian peaks of expression, while H3K27ac signal did not vary between clones harboring different reporter integration sites. Similar properties were observed on other rhythmically expressed genes: despite variability in promoter motifs and expression phases, endogenous circadian genes displaying rhythmic variations in their promoter acetylation state also modulated their burst frequencies over the circadian period. By inferring the transcriptional bursting parameters of non-circadian genes using smRNA-FISH datasets, we also observed significant correlations between histone acetylation signal around promoters and the burst frequency. In conclusion, this study identified an association between the burst frequency and the histone acetylation state of promoters. While the molecular mechanisms behind this association remain elusive, it could be related to the facilitated binding of transcription regulators upon histone acetylation-mediated chromatin loosening. In this thesis we clarified how transcription of circadian genes is rhythmically modulated, and we further elucidated the link between molecular events and transcriptional bursting, with particular focus on histone acetylation.