The data published by Ma et. al. is presented (red dots) as well as the curve fit to the data (black).

<p>The values that we choose based on biological information for very high and very low torque values are shown also (green dots). (A) shows the velocity as a function of torque, while pause frequency and pause duration as a function of torque are given by (B) and (C) respectively. The equation for each curve can be found in Eqs <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005069#pcbi.1005069.e039" target="_blank">(19)</a>–<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005069#pcbi.1005069.e041" target="_blank">(21)</a>, respectively.</p

As a function of the initiation rate <i>α</i> ⋅ <i>β</i>, we present the average transcription time (A) and the average total delay per RNAP (B).

<p>The ETAM model (blue triangles) and TASEP model (magenta) are both plotted for comparison. The dashed lines represent baseline simulations with no pauses. The error bars for the transcription time represent the standard deviation, with the standard deviation on the ETAM model decreasing as <i>α</i> increases.</p

A flowchart for our simulation of the elongation process.

<p>RNAPs that translocate follow the chart from elongation and continue in order depending on if that RNAP experiences a collision or a pause. If a neighboring RNAP translocates, updates for torque, velocity, and pause frequency are calculated for the affected RNAPs starting with that block of the flowchart.</p

Polymerases <i>P</i>_{<i>i</i> − 1}, <i>P</i>_<i>i</i>, and <i>P</i>_<i>i</i>+1 in order on the DNA strand.

<p>When <i>P</i>_<i>i</i> translocates, the DNA between <i>P</i>_{<i>i</i> − 1} and <i>P</i>_<i>i</i> will over-twist and the DNA between <i>P</i>_<i>i</i> and <i>P</i>_<i>i</i>+1 will under-twist, increasing the elongation velocity of <i>P</i>_{<i>i</i> − 1} and <i>P</i>_<i>i</i>+1.</p

A Mechanistic Model for Cooperative Behavior of Co-transcribing RNA Polymerases - Fig 5

<p>As a function of increasing initiation rates determined by <i>α</i>, the coefficient of variation (A), and the variance to mean ratio (B), are given for the transcription time. Both ETAM and TASEP models are presented as well as their baseline results (no pauses). The variance of the pause duration (C), and collision duration (D), are presented for the ETAM model (blue triangles) and the TASEP model (magenta).</p

This figure depicts the four different cases of RNAP <i>P</i>_{<i>i</i> − 1}, <i>P</i>_<i>i</i>, and <i>P</i>_<i>i</i>+1.

<p>Fig 7A shows the three RNAPs with the original distances between them. Then there are four different configurations; Fig 7B, <i>L</i>_0,<i>i</i> > <i>L</i>_<i>i</i> and <i>L</i>_0,<i>i</i>+1 > <i>L</i>_<i>i</i>+1, Fig 7C, <i>L</i>_0,<i>i</i> > <i>L</i>_<i>i</i> and <i>L</i>_0,<i>i</i>+1 < <i>L</i>_<i>i</i>+1, Fig 7D, <i>L</i>_0,<i>i</i> < <i>L</i>_<i>i</i> and <i>L</i>_0,<i>i</i>+1 > <i>L</i>_<i>i</i>+1, and Fig 7E, <i>L</i>_0,<i>i</i> < <i>L</i>_<i>i</i> and <i>L</i>_0,<i>i</i>+1 < <i>L</i>_<i>i</i>+1.</p

In addition to the nonlinear fit (blue triangles) and the piecewise linear fit (green dots), we also present our results for average transcription time (A) and average total delay (B) per RANP for a piecewise linear fit except for the pause duration on the interval [-10, 5], “Nonlinear Left” (red stars), or on the interval [5, 10], “Nonlinear Right” (black stars).

<p>In addition to the nonlinear fit (blue triangles) and the piecewise linear fit (green dots), we also present our results for average transcription time (A) and average total delay (B) per RANP for a piecewise linear fit except for the pause duration on the interval [-10, 5], “Nonlinear Left” (red stars), or on the interval [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005069#pcbi.1005069.ref005" target="_blank">5</a>, <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005069#pcbi.1005069.ref010" target="_blank">10</a>], “Nonlinear Right” (black stars).</p

For the range of initiation rates <i>α</i> ⋅ <i>β</i>, these results show average transcription time (A) and average total delay (B) over different fits of the pause frequency function.

<p>The legend labels the pause frequency at the highest torque value.</p

Linear fit for the average number of collisions experienced per RNAP.

<p>The collisions in the results for TASEP (magenta) and compared to the linear fit (magenta stars) and similarly for the ETAM results (blue and blue stars).</p

The differences in the pause duration for the piecewise linear fit (green) and the nonlinear fit (blue) at low torque values is highlighted here.

<p>This difference accounts for the very different results in average transcription time and average total delay depicted in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005069#pcbi.1005069.g012" target="_blank">Fig 12</a>.</p