Minimal model of transcriptional elongation processes with pauses

Fundamental biological processes such as transcription and translation, where a genetic sequence is sequentially read by a macromolecule, have been well described by a classical model of nonequilibrium statistical physics, the totally asymmetric exclusion principle (TASEP). This model describes particles hopping between sites of a one-dimensional lattice, with the particle current determining the transcription or translation rate. An open problem is how to analyze a TASEP where particles can pause randomly, as has been observed during transcription. In this work, we report that surprisingly, a simple mean-field model predicts well the particle current for all values of the average pause duration, using a simple description of blocking behind paused particles.

Figure 1

TASEP model with pausing. (a) Particles can transition from an active state (in white) to a paused state (in gray) and back, with respective rates $f$ and $1/\tau$. (b) Active particles can hop to the next site if it is empty (exclusion process), with unit-time probability $\epsilon$. Paused particles do not move.

Figure 2

Occurrence of traffic jams on a TASEP with long pauses. (a) Particle current $J$ as a function of the mean pause duration $\epsilon \tau$: numerical estimate in black (with error bar) compared to the mean-field value $J_1$ given by Eq. (2) (gray line). Computation is performed with 1000 particles on a lattice of $10000$ sites keeping $f\tau =0.1$ fixed. (b) Temporal evolution of the particle distribution on the lattice when $\epsilon \tau =100$. Sites occupied by an active (paused) particles are shown in green (red). (c),(d) Probability density functions of the residence time (c) and of the logarithm of residence time (d) for particles that remained active at any time (in green) and for particles that have paused at least once (in red), also for $\epsilon \tau =100$.

Figure 3

Comparison between current predicted by Eqs. (4) and (5) (solid line) and numerical estimates (crosses) over a wide parameter range. Gray bars represent the averaged distance $\langle |{\tilde{J}}_i-J_2{|\rangle }_i$ between theoretical $J_2$ and numerical estimates ${\tilde{J}}_i$.