PHYSICAL REVIEW E 99, 012405 (2019) Stationary RNA polymerase fluctuations during transcription elongation V. Belitsky * Instituto de Matemática e Estátistica, Universidade de São Paulo, Rua do Matão, 1010, CEP 05508-090 São Paulo, São Paulo, Brazil G. M. Schütz † Institute of Complex Systems II, Theoretical Soft Matter and Biophysics, Forschungszentrum Jülich, 52425 Jülich, Germany (Received 27 September 2018; published 7 January 2019) We study fluctuation effects of nonsteric molecular interactions between RNA polymerase (RNAP) motors that move simultaneously on the same DNA track during transcription elongation. Based on a stochastic model that allows for the exact analytical computation of the stationary distribution of RNAPs as a function of their density, interaction strength, nucleoside triphosphate concentration, and rate of pyrophosphate release we predict an almost geometric headway distribution of subsequent RNAP transcribing on the same DNA segment. The localization length which characterizes the decay of the headway distribution depends directly only the average density of RNAP and the interaction strength, but not on specific single-RNAP properties. Density correlations are predicted to decay exponentially with the distance (in units of DNA base pairs), with a correlation length that is significantly shorter than the localization length. DOI: 10.1103/PhysRevE.99.012405 I. INTRODUCTION DNA transcription is the ubiquitous process that tran- scribes the information coded in the base pair sequence of DNA into an RNA. The molecular “engine” that performs this task is RNA polymerase (RNAP), which synthesizes an RNA as determined by the base-pair sequence of the DNA [1,2]. To this end, the RNAP locally creates the so-called transcription bubble by unzipping the two DNA strands as it progresses on one of the two single DNA strands. The RNA is polymerized by the RNAP by the addition of nucleotides as the RNAP moves along the DNA, thus forming the so-called transcription elongation complex (TEC). Each translocation from one DNA base pair to the next consists of a cycle of molecular reorganizations of the TEC whose main steps are nucelotriphosphate (NTP) binding, NTP hydrolysis and release of pyrophosphate (PP i ), RNA chain elongation and forward translocation along the DNA template. Thus RNAP plays a central role in gene expression and also as therapeutic drug target [3]. The intrinsically stochastic translocation of a single RNAP has been studied in great detail from different perspectives and using different approaches, both theoretical and experimental [2,4–7]. We follow the authors of [4,8–10] and describe the kinetics of single-RNAP elongation by a biased random walk of RNAP along the DNA with a step length of one base pair for each translocation. This approach allows for describing the stochasticity of the step cycle of a single RNAP due to thermal fluctuations. In the setting studied by Wang [4], the slowest processes that mostly determine the average speed of an RNAP and thus the RNA elongation rate are the release of PP i * belitsky@ime.usp.br † g.schuetz@fz-juelich.de and the forward step of the RNAP along the DNA template by one base pair (bp). This reduced description ignores the sequence dependence of the translocation kinetics [11,12], but nevertheless accounts rather well for various experimentally established features of the kinetics of a single RNAP, and is adequate as a starting point for the purposes of the present work in which our main interest is the impact of interactions between RNAP on the fluctuations which lead to fluctuations in the overall rate of elongation, which is proportional to the stationary flux of RNAP along the DNA template. Interactions between subsequent RNAPs that move along the same DNA segment have to be taken into consideration when more than one RNAP molecule initiates from the same promoter sequence of the DNA template. Pausing RNAP may block the advancement of trailing RNAP and thus induce “traffic jams” [13–15] that slow down elongation. On the other hand, the interaction may also be cooperative: Trailing RNAP can prevent backtracking, and even “push” the leading RNAP out of pause sites [16,17]. Thus elongation is enhanced. This intriguing and seemingly paradoxical outcome of RNAP interactions has been studied intensely over the last few years using a variety of different approaches [18–25], mostly focusing on the role of specific microscopic features of the step cycle. To understand better the conditions under which jamming and pushing can arise from RNAP interactions we introduced a lattice gas model [26] that shows that indeed both phenomena arise if (in addition to pure steric hindrance on contact) RNAPs interact via a repulsive short-range in- teraction, while hard core repulsion alone can only produce jamming, see, e.g., [14,27–34] for ribosomes, RNAP, and other molecular motors. Our model is a generalization of the asymmetric simple exclusion process (ASEP) [9,35], that incorporates both the two internal states in which RNAP appears (with or with- out PP i bound to it) as in the pioneering work [14] and 2470-0045/2019/99(1)/012405(10) 012405-1 ©2019 American Physical Society