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We analyse transcriptional bursting within a stochastic non-equilibrium model which accounts for the coupling between the dynamics of DNA supercoiling and gene transcription. We find a clear signature of bursty transcription when there is a separation between the timescales of transcription initiation and supercoiling dissipation - the latter may either be diffusive or mediated by topological enzymes, such as type I or type II topoisomerases. In multigenic DNA domains we observe either bursty transcription, or transcription waves; the type of behaviour can be selected for by controlling gene activity and orientation. In the bursty phase, the statistics of supercoiling fluctuations at the promoter are markedly non-Gaussian.
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There is increasing evidence that protein binding to specific sites along DNA can activate the reading out of genetic information without coming into direct physical contact with the gene. There also is evidence that these distant but interacting sites are embedded in a liquid droplet of proteins which condenses out of the surrounding solution. We argue that droplet-mediated interactions can account for crucial features of gene regulation only if the droplet is poised at a non-generic point in its phase diagram. We explore a minimal model that embodies this idea, show that this model has a natural mechanism for self-tuning, and suggest direct experimental tests.
We study the effect of transcription on the kinetics of DNA supercoiling in 3D by means of Brownian dynamics simulations of a single nucleotide resolution coarse-grained model for double stranded DNA. By accounting for the action of a transcribing RNA polymerase (RNAP), we characterise the geometry and non equilibrium dynamics of the twin supercoiling domains forming on each side of the RNAP. Textbook pictures depict such domains as symmetric, with plectonemes (writhed DNA) appearing close to the RNAP. On the contrary, we find that the twist generated by transcription results in asymmetric domains, with plectonemes formed far from the RNAP. We show that this translates into an action-at-a-distance on DNA-binding proteins: for instance, positive supercoils downstream of an elongating RNAP destabilise nucleosomes long before the transcriptional machinery reaches the histone octamer. To understand these observations we use our framework to quantitatively analyse the relaxation dynamics of supercoiled DNA. We find a striking separation of timescales between twist diffusion, which is a simple and fast process, and writhe relaxation, which is slow and entails multiple steps.
We propose a stochastic model for gene transcription coupled to DNA supercoiling, where we incorporate the experimental observation that polymerases create supercoiling as they unwind the DNA helix, and that these enzymes bind more favourably to regions where the genome is unwound. Within this model, we show that when the transcriptionally induced flux of supercoiling increases, there is a sharp crossover from a regime where torsional stresses relax quickly and gene transcription is random, to one where gene expression is highly correlated and tightly regulated by supercoiling. In the latter regime, the model displays transcriptional bursts, waves of supercoiling, and up-regulation of divergent or bidirectional genes. It also predicts that topological enzymes which relax twist and writhe should provide a pathway to down-regulate transcription. This article has been published in Physical Review Letters, May 2016.
Current models for the folding of the human genome see a hierarchy stretching down from chromosome territories, through A/B compartments and TADs (topologically-associating domains), to contact domains stabilized by cohesin and CTCF. However, molecular mechanisms underlying this folding, and the way folding affects transcriptional activity, remain obscure. Here we review physical principles driving proteins bound to long polymers into clusters surrounded by loops, and present a parsimonious yet comprehensive model for the way the organization determines function. We argue that clusters of active RNA polymerases and their transcription factors are major architectural features; then, contact domains, TADs, and compartments just reflect one or more loops and clusters. We suggest tethering a gene close to a cluster containing appropriate factors -- a transcription factory -- increases the firing frequency, and offer solutions to many current puzzles concerning the actions of enhancers, super-enhancers, boundaries, and eQTLs (expression quantitative trait loci). As a result, the activity of any gene is directly influenced by the activity of other transcription units around it in 3D space, and this is supported by Brownian-dynamics simulations of transcription factors binding to cognate sites on long polymers.
The effects of carrying capacity of environment $K$ for degradation (the $K$ effect for short) on the constitutive gene expression and a simple genetic regulation system, are investigated by employing a stochastic Langevin equation combined with the corresponding Fokker-Planck equation for the two stochastic systems subjected to internal and external noises. This $K$ effect characterizes the limited degradation ability of the environment for RNA or proteins, such as insufficient catabolic enzymes. The $K$ effect could significantly change the distribution of mRNA copy-number in constitutive gene expression, and interestingly, it leads to the Fano factor slightly larger than 1 if only the internal noise exists. Therefore, that the recent experimental measurements suggests the Fano factor deviates from 1 slightly (Science {bf 346} (2014) 1533), probably originates from the $K$ effect. The $K$ effects on the steady and transient properties of genetic regulation system, have been investigated in detail. It could enhance the mean first passage time significantly especially when the noises are weak and reduce the signal-to-noise ratio in stochastic resonance substantially.
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