Transcriptional Bursts in a Nonequilibrium Model for Gene Regulation by Supercoiling.

We analyze transcriptional bursting within a stochastic nonequilibrium 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 behavior 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.

Emergence of effective temperatures in an out-of-equilibrium model of biopolymer folding.

We investigate the possibility of extending the notion of temperature in a stochastic model for the RNA or protein folding driven out of equilibrium. We simulate the dynamics of a small RNA hairpin subject to an external pulling force, which is time-dependent. First, we consider a fluctuation-dissipation relation (FDR) whereby we verify that various effective temperatures can be obtained for different observables, only when the slowest intrinsic relaxation timescale of the system regulates the dynamics of the system. Then, we introduce a different nonequilibrium temperature, which is defined from the rate of heat exchanged with a weakly interacting thermal bath. Notably, this "kinetic" temperature can be defined for any frequency of the external switching force. We also discuss and compare the behavior of these two emerging parameters, by discriminating the time-delayed nature of the FDR temperature from the instantaneous character of the kinetic temperature. The validity of our numerics are corroborated by a simple four-state Markov model which describes the long-time behavior of the RNA molecule.