Interacting RNA polymerase motors on DNA track: effects of traffic congestion and intrinsic noise on RNA synthesis

RNA polymerase (RNAP) is an enzyme that synthesizes a messenger RNA (mRNA) strand which is complementary to a single-stranded DNA template. From the perspective of physicists, an RNAP is a molecular motor that utilizes chemical energy input to move along the track formed by a DNA. In many circumstances, which are described in this paper, a large number of RNAPs move simultaneously along the same track; we refer to such collective movements of the RNAPs as RNAP traffic. Here we develop a theoretical model for RNAP traffic by incorporating the steric interactions between RNAPs as well as the mechano-chemical cycle of individual RNAPs during the elongation of the mRNA. By a combination of analytical and numerical techniques, we calculate the rates of mRNA synthesis and the average density profile of the RNAPs on the DNA track. We also introduce, and compute, two new measures of fluctuations in the synthesis of RNA. Analyzing these fluctuations, we show how the level of {\it intrinsic noise} in mRNA synthesis depends on the concentrations of the RNAPs as well as on those of some of the reactants and the products of the enzymatic reactions catalyzed by RNAP. We suggest appropriate experimental systems and techniques for testing our theoretical predictions.

💡 Research Summary

The paper addresses the collective dynamics of many RNA polymerases (RNAPs) moving simultaneously along a single DNA template, a phenomenon the authors term “RNAP traffic.” Treating RNAPs as molecular motors, the authors construct a theoretical framework that couples steric exclusion between RNAPs with the mechano‑chemical cycle governing each enzyme’s elongation step. The DNA is modeled as a one‑dimensional lattice; each RNAP occupies two adjacent sites to enforce volume exclusion, thereby preventing overtaking. The individual enzymatic cycle is reduced to two kinetic states—“forward” (translocation) and “pause” (waiting)—with transition rates that depend on the concentration of nucleoside‑triphosphates (NTPs) and on intrinsic catalytic parameters (k_cat, K_M). Boundary conditions are introduced via an entry rate α (RNAP loading at the promoter) and an exit rate β (termination and release at the terminator).

Using the master equation for the stochastic process, the authors first apply a mean‑field approximation to derive analytical expressions for the stationary density ρ and the particle current J (the transcription rate). The resulting current–density relation, J = ρ(1 − ρ) v_eff, mirrors the well‑known TASEP (totally asymmetric simple exclusion process) but with an effective velocity v_eff that incorporates the NTP‑dependent forward stepping rate. Depending on α, β, and v_eff, the system falls into three distinct phases: low‑density (LD), high‑density (HD), and maximal‑current (MC). In the LD phase the entry rate limits transcription; in the HD phase the exit rate is the bottleneck; in the MC phase the bulk dynamics dominate and the current reaches its theoretical maximum.

To test the analytical predictions, the authors perform Gillespie‑type kinetic Monte‑Carlo simulations of the full stochastic model across a wide parameter space. The simulations reproduce the phase diagram, confirming that the mean‑field theory captures the average behavior. Moreover, the authors compute spatial density profiles of RNAPs along the DNA, revealing characteristic shock‑like structures at phase boundaries and flat profiles in the MC regime.

A central contribution of the work is the quantitative analysis of transcriptional fluctuations. Two novel noise metrics are introduced: (i) the Fano factor F = σ²/μ of the mRNA count, and (ii) the coefficient of variation CV = σ/μ of the inter‑event times between successive transcription completions. In the LD regime both F and CV approach unity, indicating Poissonian statistics typical of independent events. As traffic congestion increases (HD and MC regimes), both metrics rise sharply above one, evidencing super‑Poissonian noise generated by RNAP queuing and steric hindrance. The authors further explore how varying NTP concentration modulates these fluctuations. At low NTP levels the forward stepping rate is rate‑limiting, leading to a linear increase of the mean transcription rate with NTP concentration while noise remains modest. Beyond a threshold NTP concentration, the stepping rate saturates, but the increased influx of RNAPs amplifies crowding, causing a non‑linear surge in both F and CV. This counter‑intuitive result suggests that cells may tune NTP pools not only for speed but also to control transcriptional noise.

Finally, the paper proposes experimental strategies to validate the model. In vitro transcription assays with defined DNA templates of varying length, combined with fluorescently labeled RNAPs and single‑molecule imaging, could directly measure RNAP density profiles and inter‑completion intervals. Systematic variation of RNAP concentration, NTP levels, and the use of transcription inhibitors (e.g., α‑amanitin) would allow testing of the predicted phase transitions and noise behavior.

In summary, the study provides a comprehensive physical description of RNAP traffic, linking steric interactions, enzymatic kinetics, and stochastic fluctuations to the overall efficiency and fidelity of gene expression. By integrating analytical theory with stochastic simulations and proposing concrete experimental tests, it offers a robust framework for understanding how collective motor dynamics shape transcriptional regulation and intrinsic noise in living cells.