A matter of time: Using dynamics and theory to uncover mechanisms of transcriptional bursting

“To gain insight into the model’s transcriptional dynamics, we use stochastic simulations based on the Gillespie Algorithm [47]; however a variety of alternative analytic and numerical approaches exist [40,41,44].”

“Although electron microscopy provided early hints of bursty transcription [1], the advent of single-molecule fluorescence in situ hybridization (smFISH) [2,3], was key to establishing its central role in transcription.”

“Live imaging and genome-wide studies have shown that RNAP pausing before initiation is common in eukaryotes [102–105] and that its half-life of up to 20 min can be consistent with transcriptional bursting [106–113].”

“These fixedtissue inferences have been confirmed with new in vivo RNA fluorescence labeling technologies such as the MS2/MCP [6] and PP7/PCP systems [7], which directly reveal stochastic bursts of transcriptional activity in living cells in culture and within animals (Figure 1AeC) [8e11].”

“Although electron microscopy provided early hints of bursty transcription [1], the advent of single-molecule fluorescence in situ hybridization (smFISH) [2, 3], was key to establishing its central role in transcription.”

“Tet system MS2 TON ≈ 6 minutes, TOFF ≈ 37 minutes [8]”

“What is the role of transcriptional bursting in cellular decision-making? One possibility is that bursty gene expression is intrinsically beneficial, helping (for instance) to coordinate gene expression or to facilitate cell-fate decision-making [12].”

“lifetimes in mammalian nuclei of 5-13 s 10 s, respectively [91–94].”

“However, recent work has cast doubt on the simple “lock and key” model of enhancer association (stable, direct contact between enhancers and promoters triggers transcription), suggesting instead that enhancers may activate cognate loci from afar and, in some cases, may activate multiple target loci simultaneously [32,…”

“1, despite qualitatively similar bursty traces from different organisms, bursts unfold across markedly distinct timescales ranging from several minutes [15, 16], to tens of minutes [17, 18], all the way to multiple hours [19].”

“ypothesis for the molecular origin of transcriptional bursting is that the OFF state between bursts is enacted by an RNAP molecule that becomes paused at the promoter, eectively creating a trac jam [102]. Live imaging and genome-wide studies have shown that RNAP pausing before initiation is common in eukaryotes [102{1…”

“Further, histone modifications may modulate nucleosomal occupancy [65, 75, 76], and the half-life as well as addition of these modifications can also span a broad range of timescales compatible with bursting, from several minutes to days [77–83].”

“rst-passage time of ˝ off, the variability in the distribution of measured rst-passage times will decrease as the number of rate-limiting steps, M on, increases following ˙ off(M on) = p ˝ off M on : (9) As predicted by Equation 9, increasing the rate-limiting step number reduces the width of the distribution for the…”

“tem Organism Experimental method Timescale Reference Nucleosomal DNA Wrapping/Unwrapping Mononucleosomes In vitro reconstitution FRET 0.1-5s [69] Mononucleosomes In vitro reconstitution FRET 10-250ms [68] Mononucleosomes In vitro reconstitution Photochemical crosslinking <1s [67] Nucleosome Turnover Histone H3.3 Dr…”

“Bicoid concentrations in the embryo in the region of hunchback expression are on the order of 10 nM ([A] ≈ 10 nM) [42], so that k ≈ 0.”

“cleosome Turnover Histone H3.3 Drosophila cell Genome-wide proling 1-1.5h [70] Histone H3 Yeast Genomic tiling arrays ˘1h [71] Histone H2B, H3, and H4 tagged with GFP Human cell FRAP several minutes [74] Histone H1 tagged with GFP Human cell FRAP several minutes [73] Histone H3 Plant cell (Alfalfa) Isotope labeling se…”

“lian cell GRO-seq ˘6.9min (average) [111] RNAP (genome-wide) Drosophila cell scRNA-seq 15-20min (at genes with low activity) [112] LacO-tagged minimal CMV promoter Human cell MS2 labeling, FRAP ˘4min [113] SMT: Single-molecule tracking FRAP: Fluorescence recovery after photobleaching FCS: Fluorescence correlation spec…”

“ing 1-1.5h [70] Histone H3 Yeast Genomic tiling arrays ˘1h [71] Histone H2B, H3, and H4 tagged with GFP Human cell FRAP several minutes [74] Histone H1 tagged with GFP Human cell FRAP several minutes [73] Histone H3 Plant cell (Alfalfa) Isotope labeling several hours [72] Histone Modication dCas9 inducible recruitment…”

“often separated by kbp to even Mbp. The mechanism by which enhancers nd their target loci from such a large distance, and how this contact triggers transcription, remain uncertain and are reviewed in [95]. In vivo measurements of enhancer-promoter separation in the Drosophila embryo have shown that this distance uctua…”

“s [86] STAT1 Mammalian cell SMT ˘0.5s [88] TFIIB In vitro reconstitution SMT ˘1.5s [89] TATA-binding protein Mammalian cell SMT 1.5-2min [90] Chromatin Protein Binding CTCF Mammalian cell SMT ˘1-2min [118] Cohesin Mammalian cell SMT ˘22min [118] Enhancer-Promoter Interaction snail shadow enhancer Drosophila embryo MS2…”

“lation half-life) [78] 19 Transcription Factor Binding Bicoid Drosophila embryo SMT ˘2s [46] Bicoid Drosophila embryo SMT ˘1s [45] Zelda Drosophila embryo SMT ˘5s [46] Sox2 Mammalian cell SMT ˘12-15s [84] p53 Mammalian cell SMT ˘3.5s [85] p53 Mammalian cell SMT, FRAP, FCS ˘1.8s [87] Glucocorticoid receptor Mammalian c…”

“Live imaging and genome-wide studies have shown that RNAP pausing before initiation is common in eukaryotes [102–105] and that its half-life of up to 20 min can be consistent with transcriptional bursting [106–113].”

“5-15 s [45, 46, 84–89].”

“multiple studies suggesting timescales of several minutes to hours [70{ 74]. Recent genome-wide studies have measured average nucleosome turnover time to be approximately 1 hour in the y and in yeast [70, 71]. Further, histone modications may modulate nucleosomal occupancy [65, 75, 76], and the half-life as well as ad…”

“lusters) [92] RNAP tagged with Dendra2 Mammalian cell tcPALM ˘8.1s [91] RNAP tagged with Dendra2 Human cell Bayesian nanoscopy several seconds [94] 20 RNAP tagged with Dendra2 Human cell tcPALM ˘5.1s [93] Mediator Cluster Dynamics Mediator tagged with Dendra2 Mammalian cell tcPALM ˘11.1s [92] Promoter-Proximal Pausing…”

“ion cycle interval) [97] snail enhancer Drosophila embryo MS2, PP7 labeling several minutes [98] endogenous even-skipped locus with homie insulator Drosophila embryo MS2, PP7 labeling several minutes [96] Transcription Initiation even-skipped stripe 2 enhancer Drosophila embryo MS2 labeling ˘3s (promoter ON) [16] HIV-…”

“While unwrapping and rewrapping are probably too fast to directly lead to long transcriptional bursts, DNA unwrapping might represent a “foothold” by which factors transiently bind DNA and enact larger-scale, sustained chromatin modifications [65].”

“The promoter stochastically switches between these states with rates kon and koff , and loads new RNA polymerase II (RNAP) molecules at a rate r when in the ON state [22, 29–31].”

“[72] Histone Modication dCas9 inducible recruitment Mammalian cell Single-cell imaging several hours to days [82] rTetR inducible recruitment Mammalian cell Single-cell imaging several hours to days [81] Chemical-mediated recruitment Mammalian cell Chromatin in vivo assay several days [83] Histone H3 Human cell Liquid…”

“The single-cell distributions of nascent RNA and cytoplasmic mRNA molecules obtained using this technology provided compelling, if indirect, evidence for the existence and ubiquity of gene expression bursts, and indicated that their dynamics were subject to regulation by transcription factors [4,5].”

“However, recent work has cast doubt on the simple “lock and key” model of enhancer association (stable, direct contact between enhancers and promoters triggers transcription), suggesting instead that enhancers may activate cognate loci from afar and, in some cases, may activate multiple target loci simultaneously [32,…”

“ics Mediator tagged with Dendra2 Mammalian cell tcPALM ˘11.1s [92] Promoter-Proximal Pausing RNAP tagged with GFP Human cell FRAP ˘40s [106] RNAP (genome-wide) Drosophila cell RNA sequencing ˘2-20min [107] RNAP (genome-wide) Drosophila cell ChIP-nexus ˘5-20min [108] RNAP (genome-wide) Drosophila cell Genome-wide footp…”

“However, recent work has cast doubt on the simple “lock and key” model of enhancer association (stable, direct contact between enhancers and promoters triggers transcription), suggesting instead that enhancers may activate cognate loci from afar and, in some cases, may activate multiple target loci simultaneously [32,…”

“Transcription factor binding recruits co-factors and general transcription factors to the promoter, triggering the biochemical cascade that ultimately initiates transcription [20].”

“5-15 s [45, 46, 84–89].”

“MS2 few minutes [11] C. elegans Notch signaling MS2 10-70 minutes [17] Human, Mouse TGF-signaling luciferase assay few hours [114] TFF-1 signaling MS2 few hours [18] HIV-1 viral gene MS2 few minutes [115] liver genes smFISH T ON ˇ 30 minutes - 2 hours [116] mammalian genes luciferase assay few hours [19] Amoeba actin…”

“o MS2 labeling ˘6s [119] RNAP Cluster Dynamics RNAP tagged with Dendra2 Mammalian cell tcPALM ˘12.9s (with small fraction of stable clusters) [92] RNAP tagged with Dendra2 Mammalian cell tcPALM ˘8.1s [91] RNAP tagged with Dendra2 Human cell Bayesian nanoscopy several seconds [94] 20 RNAP tagged with Dendra2 Human cell…”

“1, despite qualitatively similar bursty traces from different organisms, bursts unfold across markedly distinct timescales ranging from several minutes [15, 16], to tens of minutes [17, 18], all the way to multiple hours [19].”

“Further, histone modifications may modulate nucleosomal occupancy [65, 75, 76], and the half-life as well as addition of these modifications can also span a broad range of timescales compatible with bursting, from several minutes to days [77–83].”

“nwrapping Mononucleosomes In vitro reconstitution FRET 0.1-5s [69] Mononucleosomes In vitro reconstitution FRET 10-250ms [68] Mononucleosomes In vitro reconstitution Photochemical crosslinking <1s [67] Nucleosome Turnover Histone H3.3 Drosophila cell Genome-wide proling 1-1.5h [70] Histone H3 Yeast Genomic tiling a…”

“These fixedtissue inferences have been confirmed with new in vivo RNA fluorescence labeling technologies such as the MS2/MCP [6] and PP7/PCP systems [7], which directly reveal stochastic bursts of transcriptional activity in living cells in culture and within animals (Figure 1AeC) [8e11].”

“6] RNAP (genome-wide) Drosophila cell RNA sequencing ˘2-20min [107] RNAP (genome-wide) Drosophila cell ChIP-nexus ˘5-20min [108] RNAP (genome-wide) Drosophila cell Genome-wide footprinting ˘2.5-20min [109] RNAP tagged with GFP Intact Drosophila salivary glands ˘5min [110] RNAP (genome-wide) Mammalian cell GRO-seq ˘6.9…”

“liver genes smFISH TON ≈ 30 minutes - 2 hours [116]”

“even-skipped stripe 2 MS2 few minutes [11]”

“Live imaging and genome-wide studies have shown that RNAP pausing before initiation is common in eukaryotes [102–105] and that its half-life of up to 20 min can be consistent with transcriptional bursting [106–113].”

“Live imaging and genome-wide studies have shown that RNAP pausing before initiation is common in eukaryotes [102–105] and that its half-life of up to 20 min can be consistent with transcriptional bursting [106–113].”

“ethyl-SILAC labeling several hours to days (half-maximal time of methylation) [80] Targeted recruitment Yeast ChIP 5-8min (reversal of targeted deacetylation) 1.5min(reversal of targeted acetylation) [79] Histone H2a, H2b, H3, and H4 Mammalian cell Isotope labeling <15min (acetylation half-life) [77] Histone H2, H2…”

“Live imaging and genome-wide studies have shown that RNAP pausing before initiation is common in eukaryotes [102–105] and that its half-life of up to 20 min can be consistent with transcriptional bursting [106–113].”

“5 s−1 to ensure consistency with recent experimental measurements of Bicoid in [45, 46].”

“Throughout this Review, we focus on illustrative recent experimental and theoretical efforts; we therefore do not attempt to provide a comprehensive review of the current literature (see [20–25] for excellent reviews).”

“To gain insight into the model’s transcriptional dynamics, we employ stochastic simulations based on the Gillespie Algorithm [47]; however a variety of alternative analytic and numerical approaches exist [40, 41, 44].”

“actin gene family MS2 10-15 minutes [26]”

“In vivo measurements of enhancer-promoter separation in the Drosophila embryo have shown that this distance fluctuates with a timescale of tens of seconds to several minutes [96–98] —timescales strikingly similar to those of bursting.”

“Further, histone modifications may modulate nucleosomal occupancy [65, 75, 76], and the half-life as well as addition of these modifications can also span a broad range of timescales compatible with bursting, from several minutes to days [77–83].”

“TGF-β signaling luciferase assay few hours [114]”

“gap genes: hunchback, giant, Krüpple, knirps smFISH TON ≈ 3 minutes, TOFF ≈ 6 minutes [33]”

“Live imaging and genome-wide studies have shown that RNAP pausing before initiation is common in eukaryotes [102–105] and that its half-life of up to 20 min can be consistent with transcriptional bursting [106–113].”

“ylation) [79] Histone H2a, H2b, H3, and H4 Mammalian cell Isotope labeling <15min (acetylation half-life) [77] Histone H2, H2a and H2b Mammalian cell Isotope labeling ˘3min (acetylation half-life) [78] 19 Transcription Factor Binding Bicoid Drosophila embryo SMT ˘2s [46] Bicoid Drosophila embryo SMT ˘1s [45] Zelda…”

“Live imaging and genome-wide studies have shown that RNAP pausing before initiation is common in eukaryotes [102–105] and that its half-life of up to 20 min can be consistent with transcriptional bursting [106–113].”

“Other techniques, such as measuring the short-lived luminescent signal from reporters [27], have also successfully estimated first-passage times.”

“eley, Berkeley, California arXiv:2008.09225v1 [q-bio.SC] 20 Aug 2020 tional activity interspersed with periods of quiescence. Although electron microscopy provided early hints of bursty transcription [1], the advent of single-molecule uorescence in situ hybridization (smFISH) [2, 3], was key to establishing its centra…”

“The single-cell distributions of nascent RNA and cytoplasmic mRNA molecules obtained using this technology provided compelling, if indirect, evidence for the existence and ubiquity of gene expression bursts, and indicated that their dynamics were subject to regulation by transcription factors [4,5].”

“SMT ˘8.1s [85] Glucocorticoid receptor Mammalian cell SMT ˘1.45s [86] STAT1 Mammalian cell SMT ˘0.5s [88] TFIIB In vitro reconstitution SMT ˘1.5s [89] TATA-binding protein Mammalian cell SMT 1.5-2min [90] Chromatin Protein Binding CTCF Mammalian cell SMT ˘1-2min [118] Cohesin Mammalian cell SMT ˘22min [118] Enhancer-P…”

“In vivo measurements of enhancer-promoter separation in the Drosophila embryo have shown that this distance fluctuates with a timescale of tens of seconds to several minutes [96–98] —timescales strikingly similar to those of bursting.”

“1, despite qualitatively similar bursty traces from different organisms, bursts unfold across markedly distinct timescales ranging from several minutes [15, 16], to tens of minutes [17, 18], all the way to multiple hours [19].”

“A single transcriptional burst generally consists of multiple RNAP initiation events (∼10-100 at a rate of 1/6-1/3 s when the promoter is ON in Drosophila, for instance) [11, 16].”

“1-5 s [69]”

“SMT ˘3.5s [85] p53 Mammalian cell SMT, FRAP, FCS ˘1.8s [87] Glucocorticoid receptor Mammalian cell SMT ˘8.1s [85] Glucocorticoid receptor Mammalian cell SMT ˘1.45s [86] STAT1 Mammalian cell SMT ˘0.5s [88] TFIIB In vitro reconstitution SMT ˘1.5s [89] TATA-binding protein Mammalian cell SMT 1.5-2min [90] Chromatin Prote…”

“We illustrate how these kinetic models can shed light on the disconnect between the timescales of transcription factor binding and bursting using the activation of the hunchback minimal enhancer by Bicoid in the early fruit fly embryo as a case study [34, 38, 41–44].”

“FCS ˘1.8s [87] Glucocorticoid receptor Mammalian cell SMT ˘8.1s [85] Glucocorticoid receptor Mammalian cell SMT ˘1.45s [86] STAT1 Mammalian cell SMT ˘0.5s [88] TFIIB In vitro reconstitution SMT ˘1.5s [89] TATA-binding protein Mammalian cell SMT 1.5-2min [90] Chromatin Protein Binding CTCF Mammalian cell SMT ˘1-2min [1…”

“1, despite qualitatively similar bursty traces from different organisms, bursts unfold across markedly distinct timescales ranging from several minutes [15, 16], to tens of minutes [17, 18], all the way to multiple hours [19].”

“Throughout this Review, we focus on illustrative recent experimental and theoretical efforts; we therefore do not attempt to provide a comprehensive review of the current literature (see [20–25] for excellent reviews).”

“Further, histone modifications may modulate nucleosomal occupancy [65, 75, 76], and the half-life as well as addition of these modifications can also span a broad range of timescales compatible with bursting, from several minutes to days [77–83].”

“Throughout this Review, we focus on illustrative recent experimental and theoretical efforts; we therefore do not attempt to provide a comprehensive review of the current literature (see [20–25] for excellent reviews).”

“ent Yeast ChIP 5-8min (reversal of targeted deacetylation) 1.5min(reversal of targeted acetylation) [79] Histone H2a, H2b, H3, and H4 Mammalian cell Isotope labeling <15min (acetylation half-life) [77] Histone H2, H2a and H2b Mammalian cell Isotope labeling ˘3min (acetylation half-life) [78] 19 Transcription Factor…”

“lifetimes in mammalian nuclei of 5-13 s 10 s, respectively [91–94].”

“one H2B, H3, and H4 tagged with GFP Human cell FRAP several minutes [74] Histone H1 tagged with GFP Human cell FRAP several minutes [73] Histone H3 Plant cell (Alfalfa) Isotope labeling several hours [72] Histone Modication dCas9 inducible recruitment Mammalian cell Single-cell imaging several hours to days [82] rTetR…”

“facilitate important behaviors such as combinatorial regulatory logic, sensitivity to changes in transcription factor concentrations, the specificity of interactions between transcription factors and their targets, and transcriptional noise reduction [13, 14, 38–41].”

“Alternatively, bursting may not itself be functional, but might instead be a consequence of key underlying transcriptional processes, such as proofreading transcription factor identity [13, 14].”

“A discussion of this and other approaches falls beyond the scope of this work, but we direct the reader to several excellent introductions to elements of this field [61–64].”

“Alternatively, bursting may not itself be functional, but might instead be a consequence of key underlying transcriptional processes, such as proofreading transcription factor identity [13, 14].”

“control of transcriptional initiation [56] and elongation [57, 58], measure translational dynamics [59], and even count molecules [60].”

“P interaction models, the residence time of most transcription factors in mammals is typically on the order of seconds to tens of seconds, which is much shorter than the duration of a typical transcription burst of minutes to tens of minutes 77–86 .”

“9,37 Because many TFs show cooperative binding 38 and many promoters and enhancers contain multiple TF binding sites, cooperative binding and exchange of TFs may turn out to be a general kinetic mode to bridge the timescale gap between short dwell times of DNA-bound factors and longer transcription…”

“One of the outstanding questions in the field is how these transient binding events regulate transcription (14,85).”

“Thus far, we have considered regulatory networks where each gene is regulated by one TF; however, many genes are regulated by a multitude of TFs which are often shared between multiple genes 48 .”

“At the same time, the live traces reveal that the transcription in the ON cells is dynamic, in keeping with frequent fluctuations in promoter states producing ‘bursts’ ( Lammers et al., 2020 ; Meeussen and Lenstra, 2024 ).”

“It does not require specifying the molecular identity of the burst parameters (Lammers et al., 2020).”

“…is highly stochastic, occurring in episodic bursts (Bothma et al., 2014; Tantale et al., 2016; Nicolas et al., 2017; Lionnet and Wu, 2021)—periods of activity interspersed with periods of transcriptional silence—that unfold over timescales ranging from minutes to hours (Lammers et al., 2020).”

“…coordinates do not alter gene state, implying that the derivative of conditional probability, ∇ r p ( s | r ; t ), approximately equals zero partly because the time interval of downstream gene-state transition is generally longer than that of upstream chromatin motion (Lammers et al. 2020).”

“7 b shows a generalization of the leaky telegraph model to include multiple transcription factor binding sites, leading to multiple active states (102).”

“The proposed solution to these shortcomings is the use of mechanistic, stochastic models (Lammers et al. 2020; Gorin et al. 2022) as the basis of inferring gene expression dynamics.”

“(Thus, by virtue of its non-cyclic transition graph, the standard two-state random-telegraph model of gene regulation 24 implies equilibrium dynamics.)”

“Efforts to explain how such bursting arises have focussed on stochastic transitions between transcriptionally active and inactive states in a Markovian setting (Peccoud and Ycart, 1995; Lammers et al., 2020).”

“…points to an underlying mechanism controlling the burst frequency that rapidly reads and responds to changing repressor concentrations, likely within a matter of seconds — a timescale that is consistent with the fast binding and unbinding dynamics reported for eukaryotic transcription factors 64 .”

“…system have been limited to single cells in culture, tissue samples, invertebrate model organisms, such as flies and worms, and plants (Garcia et al. 2013; Lammers, Kim, et al. 2020; Wildner et al. 2023; Lee, Shin, and Kimble 2019; Corrigan et al. 2016; Alamos et al. 2021; Park et al. 2014).”

“However, it remains an unresolved question how cells make fate decisions in response to external signals through genome-wide regulation of transcriptional burst mechanisms ( Lammers et al., 2020 ; Rodriguez and Larson, 2020 ).”

“At the coarsest level of detail, this behavior is usually explained by appealing to a Markovian, two-state promoter model (Peccoud and Ycard 1995); genes that exhibit more complex transcriptional dynamics aremodeled by increasingly sophisticated Markovian (Lammers et al. 2020; Zhou and Zhang 2012; Ham et al. 2020b) as…”

“The molecular basis for these wide differences in transcription kinetics is yet unknown (Lammers et al, 2020; Meeussen and Lenstra, 2024).”

“Even small GRNs can execute involved processes such as disturbance rejection [79] and fold-change detection [80] over timescales much longer than the few seconds required for transcription initiation [16].”

“Metazoan CREs have been 46 subjected to many elegant analyses over decades, with integration of empirical data and computational 47 modeling being particularly useful (e.g. Andersson and Sandelin, 2020; Bentovim et al., 2017; Ezer et al., 48 2014; Giorgetti et al., 2010; Lammers et al., 2020; Wong and Gunawardena, 202…”

“The elevated water content may make PEDOT:sGAGh-based OECTs well-suited for mimicking the mechanical properties of tissues while enabling sensing of biomolecular signals that evolve over timescales of seconds to minutes [54].”

“…as chromatin remodeling, nucleosome clearance, transcription pausing and release, transcriptional bursting, and other important details (Fuda et al., 2009; Lammers et al., 2020; Yokoshi and Fukaya, 2019; Adelman and Lis, 2012; Gaertner and Zeitlinger, 2014; Green, 2005; Nechaev and Adelman, 2011).”

“Finally, gene timescales are very short, of the order of seconds to few minutes [73], and therefore gene species can be considered faster than both mRNA and protein species.”

“To choose cells for analysis by Monod, we identified cell barcodes which were (1) assigned to either the GABAergic or glutamatergic cell type according to annotations, (2) passed the kallisto|bustools filter and knee plot filters, and (3) did not belong to one of the excluded rare cell subtypes (Scng or L6 IT Car3).”

“…et al. 2009; Bel et al. 2010; Moffitt et al. 2010; Moffitt and Bustamante 2014; Banerjee et al. 2017; Cui and Mehta 2018; Mallory et al. 2019; Wang et al. 2021; Lammers et al. 2020; Alamos et al. 2023; Lammers et al. 2023; Dal Co et al. 2017; Ghusinga et al. 2017; Gupta et al. 2018; Ham et al. 2024).”

“E-P communication is central to gene regulation [1,2] (Figure 1a).”

“These include TF binding and unbinding, mediator dynamics, chromatin modifier and remodeller binding dynamics, nucleosome cycling and GTF binding and release amongst others [39].”

“Similarly, intracellular events are considered to be a function of a protein concentration exceeding a threshold and bursty transcription relates to the continuous movement of underlying molecules [Ghusinga et al., 2017, Lammers et al., 2020].”

“However, neither the stable nor the transient version of the looping model can explain the following observations: (1) Transcription factors remain bound to their motif for a few seconds at most,[47] while transcription bursts can last minutes.[48,49] This is incompatible”

“In this context, we note that our τ E − P - estimate matches the residence time of many transcription factors and components of the general transcriptional machinery, which is also on the order of seconds to tens of seconds ( 88–96 ).”

“The timescale of transcriptional and translational dynamics is on the order of tens of minutes [78], which would constrain accurate self-organized patterning to be on the order of hundreds of minutes, which is indeed a typical patterning timescale.”

“…us to track single molecules of Dorsal binding to DNA for the first time, finding that Dorsal spends only a few seconds bound to the DNA, an observation consistent with the binding times of several other transcription factor in the fruit fly and beyond ( Lammers et al., 2020b ; Lu and Lionnet, 2021 ).”

“…minutes of promoter activation by recruiting RNA pol-II and its phosphorylation at the Ser5 of C-terminal domain (CTD) (RNA pol-II Ser5Ph), 43–45 followed by promoter-proximal pausing within minutes stabilized by Negative Elongation Factor (NELF), 46–48 where RNA pol-II remains stalled for…”

“This model seems however unlikely given the short residency time of most TFs, temporal disconnection with the dynamics of chromatin opening (47), and the slower kinetics of 3D loop formation (48, 49).”

“The CRN representation of a promoter model generally is more versatile, as it may describe not only the number of bound transcription factors but also different DNA conformations in a possible multistep transcriptional activation.”

“In general, chromatin states can be stable for hours or even days [64] and the antisense-transcription associated H3K36me3 mark has a lifespan for ~ 1 h in yeast [65].”

“In Drosophila melanogaster, transcriptional bursts often last approximately 5 min and occur about every 5 min at room temperature, which is around 25°C (Lammers et al. (2020a)).”

“52 Canonical bursts are stochastic, 13,48 at odds with the notion of regular oscillations.”

“…occurs within minutes of activation by recruiting RNA pol-II and its phosphorylation at Ser5 of the C-terminal domain (CTD) (RNA pol-II Ser5Ph) 46 – 48 , followed by promoter-proximal pausing within minutes stabilized by Negative Elongation Factor (NELF) 49 – 51 , where RNA pol-II remains stalled…”

“For example, ‘ ON ’ times are typically minutes to hours (and even days), and this creates variability and noise (Lammers et al., 2020) – but polymerases and transcription factors bind to DNA in seconds.”

“In all organisms examined so far, transcription appears stochastic, marked by active periods (bursts of mRNA production) interspersed by inactive periods of various timescales (Lammers et al., 2020b).”

“…to order single cells of scRNA-seq data based on transcriptomic divergence (Peccoud and Ycart 1995, Paulsson and Ehrenberg 2000, Dar et al. 2012, Corrigan et al. 2016, Tantale et al. 2016, Nicolas et al. 2017, Lammers et al. 2020, Tunnacliffe and Chubb 2020, Pimmett et al. 2021, Chen et al. 2024).”

“We found that the intrinsic noise supplemented with transcriptional bursts, which are well documented in yeast [18], suffice to”

“Quasi-steady state analysis reveals that PER2 protein promotes Per2AS transcription Wenextperformedquasi-steadystateanalysistosimplifytheequationsand reducethenumberofindependentvariables,giventhatthetimescaleof 30,31 .”

“Experiments have shown that holding times in different gene states play a significant role in various cellular processes, such as transcriptional regulation [19], cell differentiation [20], epigenetic modifications [21], and response to environmental changes [22, 23].”

“…limits and features of the general problem of concentration sensing have been studied for individual receptors at [17] and far from equilibrium [18, 19], under time [20] and physical constraints [21, 22], in changing environments [23, 24], and in the context of information transmission [25,…”

“Whereas Pol II engages genes in stochastic bursts lasting minutes to hours 121,122 , TF–DNA binding typically occurs on sub-second to second timescales 123 .”

“While in the ON state, RNA polymerase initiates transcription at a consistent rate γ (mRNA min − 1 or h − 1 ); in the OFF state, transcription initiation does not occur [18,19].”

“…of transcriptional regulation, where it is well-known that different regulatory steps—such as chromatin remodelling, transcription initiation, and RNA polymerase pausing—operate on distinct timescales (reviewed in [41]), and TFs may selectively regulate a subset of these processes [27,46,47].”

“…model Peccoud and Ycart (1995) treats the promoter as switching between a single active (ON) and inactive (OFF) state, while more elaborate multistate models Neuert et al. (2013); Rodriguez et al. (2019); Lammers et al. (2020) introduce intermediate OFF states to capture complex regulatory steps.”

“Such separations of timescales have been widely recognised in the setting of gene regulation, where changes in chromatin state are typically measured to proceed on slower timescales than TF binding and the reactions that comprise the polymerase cycle [33,39–41].”

“The molecular basis for these wide differences in transcription kinetics is yet unknown (15, 16).”

“Episodic bursting of expression is a prevalent phenomenon in eukaryotic cells (Lammers et al. 2020) compared to prokaryotic cells, which reflects their relative complexity and hierarchical nature of transcriptional regulation.”