Density- and elongation speed-dependent error correction in RNA polymerization.

Backtracking of RNA polymerase (RNAP) is an important pausing mechanism during DNA transcription that is part of the error correction process that enhances transcription fidelity. We model the backtracking mechanism of RNAP, which usually happens when the polymerase tries to incorporate a noncognate or 'mismatched' nucleotide triphosphate. Previous models have made simplifying assumptions such as neglecting the trailing polymerase behind the backtracking polymerase or assuming that the trailing polymerase is stationary. We derive exact analytic solutions of a stochastic model that includes locally interacting RNAPs by explicitly showing how a trailing RNAP influences the probability that an error is corrected or incorporated by the leading backtracking RNAP. We also provide two related methods for computing the mean times for error correction and incorporation given an initial local RNAP configuration. Using these results, we propose an effective interacting-RNAP lattice that can be readily simulated.

Models of continuous-time networks with tie decay, diffusion, and convection.

The study of temporal networks in discrete time has yielded numerous insights into time-dependent networked systems in a wide variety of applications. However, for many complex systems, it is useful to develop continuous-time models of networks and to compare them to associated discrete models. In this paper, we study several continuous-time network models and examine discrete approximations of them both numerically and analytically. To consider continuous-time networks, we associate each edge in a graph with a time-dependent tie strength that can take continuous non-negative values and decays in time after the most recent interaction. We investigate how the moments of the tie strength evolve with time in several models, and we explore-both numerically and analytically-criteria for the emergence of a giant connected component in some of these models. We also briefly examine the effects of the interaction patterns of continuous-time networks on the contagion dynamics of a susceptible-infected-recovered model of an infectious disease.