Temporally correlated zero-range process with open boundaries: Steady state and fluctuations

Large Deviation Full Counting Statistics in Adiabatic Open Quantum Dynamics

The state of an open quantum system undergoing an adiabatic process evolves by following the instantaneous stationary state of its time-dependent generator. This observation allows one to characterize, for a generic adiabatic evolution, the average dynamics of the open system. However, information about fluctuations of dynamical observables, such as the number of photons emitted or the time-integrated stochastic entropy production in single experimental runs, requires controlling the whole spectrum of the generator and not only the stationary state. Here, we show how such information can be obtained in adiabatic open quantum dynamics by exploiting tools from large deviation theory. We prove an adiabatic theorem for deformed generators, which allows us to encode, in a biased quantum state, the full counting statistics of generic time-integrated dynamical observables. We further compute the probability associated with an arbitrary "rare" time history of the observable and derive a dynamics which realizes it in its typical behavior. Our results provide a way to characterize and engineer adiabatic open quantum dynamics and to control their fluctuations.

3 '-5 ' crosstalk contributes to transcriptional bursting

BACKGROUND

Transcription in mammalian cells is a complex stochastic process involving shuttling of polymerase between genes and phase-separated liquid condensates. It occurs in bursts, which results in vastly different numbers of an mRNA species in isogenic cell populations. Several factors contributing to transcriptional bursting have been identified, usually classified as intrinsic, in other words local to single genes, or extrinsic, relating to the macroscopic state of the cell. However, some possible contributors have not been explored yet. Here, we focus on processes at the 3 ' and 5 ' ends of a gene that enable reinitiation of transcription upon termination.

RESULTS

Using Bayesian methodology, we measure the transcriptional bursting in inducible transgenes, showing that perturbation of polymerase shuttling typically reduces burst size, increases burst frequency, and thus limits transcriptional noise. Analysis based on paired-end tag sequencing (PolII ChIA-PET) suggests that this effect is genome wide. The observed noise patterns are also reproduced by a generative model that captures major characteristics of the polymerase flux between the ends of a gene and a phase-separated compartment.

CONCLUSIONS

Interactions between the 3 ' and 5 ' ends of a gene, which facilitate polymerase recycling, are major contributors to transcriptional noise.

Blockage-induced condensation controlled by a local reaction

We consider the setup of stationary zero range models and discuss the onset of condensation induced by a local blockage on the lattice. We show that the introduction of a local feedback on the hopping rates allows us to control the particle fraction in the condensed phase. This phenomenon results in a current versus blockage parameter curve characterized by two nonanalyticity points.