Bayesian inference and comparison of stochastic transcription elongation models

Abstract

Transcription elongation can be modelled as a three step process, involving polymerase translocation, NTP binding, and nucleotide incorporation into the nascent mRNA. This cycle of events can be simulated at the single-molecule level as a continuous-time Markov process using parameters derived from single-molecule experiments. Previously developed models differ in the way they are parameterised, and in their incorporation of partial equilibrium approximations. We have formulated a hierarchical network comprised of 12 sequence-dependent transcription elongation models. The simplest model has two parameters and assumes that both translocation and NTP binding can be modelled as equilibrium processes. The most complex model has six parameters makes no partial equilibrium assumptions. We systematically compared the ability of these models to explain published force-velocity data, using approximate Bayesian computation. This analysis was performed using data for the RNA polymerase complexes of E. coli, S. cerevisiae and Bacteriophage T7. Our analysis indicates that the polymerases differ significantly in their translocation rates, with the rates in T7 pol being fast compared to E. coli RNAP and S. cerevisiae pol II. Different models are applicable in different cases. We also show that all three RNA polymerases have an energetic preference for the posttranslocated state over the pretranslocated state. A Bayesian inference and model selection framework, like the one presented in this publication, should be routinely applicable to the interrogation of single-molecule datasets.

Approximate Bayesian computation of transcriptional pausing mechanisms

“…where ∆G τ 1 is a term added onto the Gibbs energy of basepairing of the 241 posttranslocated state. ∆G τ 1 was found to be a necessary parameter to describe 242 elongation sufficiently for the E. coli RNAP and was estimated as ∼ −2 k B T [55] and 243 is set accordingly throughout this study (Table 1).…”

“…The first approach involves stochastic simulation of transcription at the 110 single-molecule level using the Gillespie algorithm [53,54]. This is done in a similar 111 fashion to our previous work [55], but here we have used the model to predict the dwell 112 time at each site instead of mean velocity under force.…”

“…In order for 153 RNAP to translocate from one position into the next, disruption of one hybrid basepair 154 and one gene basepair may be required. This translocation is assumed to occur through 155 a translocation transition state [55]. Four sequence-dependent methods for estimating 156 this transition state are described (Fig 2A).…”

“…The computation of translocation rates invokes transition state theory and is 216 parameterised as an extension to our previous work [55]. Translocation from state S is 217 described by the rate of backward translocation k bck (S) and the rate of forward Let T (l, t) be the translocation transition state between states S(l, t) and S(l, t + 1).…”

“…for some pre-exponential constant A, arbitrarily set here to 10 6 s −1 [55]. Two 234 energetic terms are required to compute these rates; the Gibbs energy of the 235 translocation state ∆G S(l,t) , and the Gibbs energy of the translocation transition state 236 ∆G T (l,t) .…”