elife00971.xml

<?xml version="1.0" encoding="UTF-8"?><!DOCTYPE article PUBLIC "-//NLM//DTD JATS (Z39.96) Journal Archiving and Interchange DTD v1.1d1 20130915//EN"  "JATS-archivearticle1.dtd"><article article-type="research-article" dtd-version="1.1d1" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><front><journal-meta><journal-id journal-id-type="nlm-ta">elife</journal-id><journal-id journal-id-type="hwp">eLife</journal-id><journal-id journal-id-type="publisher-id">eLife</journal-id><journal-title-group><journal-title>eLife</journal-title></journal-title-group><issn publication-format="electronic">2050-084X</issn><publisher><publisher-name>eLife Sciences Publications, Ltd</publisher-name></publisher></journal-meta><article-meta><article-id pub-id-type="publisher-id">00971</article-id><article-id pub-id-type="doi">10.7554/eLife.00971</article-id><article-categories><subj-group subj-group-type="display-channel"><subject>Research article</subject></subj-group><subj-group subj-group-type="heading"><subject>Biophysics and structural biology</subject></subj-group></article-categories><title-group><article-title>Complete dissection of transcription elongation reveals slow translocation of RNA polymerase II in a linear ratchet mechanism</article-title></title-group><contrib-group><contrib contrib-type="author" equal-contrib="yes" id="author-5561"><name><surname>Dangkulwanich</surname><given-names>Manchuta</given-names></name><xref ref-type="aff" rid="aff1"/><xref ref-type="aff" rid="aff2"/><xref ref-type="fn" rid="equal-contrib">†</xref><xref ref-type="fn" rid="con1"/><xref ref-type="fn" rid="conf1"/></contrib><contrib contrib-type="author" equal-contrib="yes" id="author-5562"><name><surname>Ishibashi</surname><given-names>Toyotaka</given-names></name><xref ref-type="aff" rid="aff1"/><xref ref-type="aff" rid="aff3"/><xref ref-type="fn" rid="equal-contrib">†</xref><xref ref-type="fn" rid="con2"/><xref ref-type="fn" rid="conf1"/></contrib><contrib contrib-type="author" equal-contrib="yes" id="author-5563"><name><surname>Liu</surname><given-names>Shixin</given-names></name><xref ref-type="aff" rid="aff1"/><xref ref-type="aff" rid="aff4"/><xref ref-type="fn" rid="equal-contrib">†</xref><xref ref-type="fn" rid="con3"/><xref ref-type="fn" rid="conf1"/></contrib><contrib contrib-type="author" id="author-5564"><name><surname>Kireeva</surname><given-names>Maria L</given-names></name><xref ref-type="aff" rid="aff5"/><xref ref-type="fn" rid="con5"/><xref ref-type="fn" rid="conf1"/></contrib><contrib contrib-type="author" id="author-5565"><name><surname>Lubkowska</surname><given-names>Lucyna</given-names></name><xref ref-type="aff" rid="aff5"/><xref ref-type="fn" rid="con7"/><xref ref-type="fn" rid="conf1"/></contrib><contrib contrib-type="author" id="author-5566"><name><surname>Kashlev</surname><given-names>Mikhail</given-names></name><xref ref-type="aff" rid="aff5"/><xref ref-type="fn" rid="con6"/><xref ref-type="fn" rid="conf1"/></contrib><contrib contrib-type="author" corresp="yes" id="author-3861"><name><surname>Bustamante</surname><given-names>Carlos J</given-names></name><xref ref-type="aff" rid="aff1"/><xref ref-type="aff" rid="aff2"/><xref ref-type="aff" rid="aff3"/><xref ref-type="aff" rid="aff4"/><xref ref-type="aff" rid="aff6"/><xref ref-type="aff" rid="aff7"/><xref ref-type="corresp" rid="cor1">*</xref><xref ref-type="other" rid="par-1"/><xref ref-type="other" rid="par-2"/><xref ref-type="other" rid="par-3"/><xref ref-type="fn" rid="con4"/><xref ref-type="fn" rid="conf1"/></contrib><aff id="aff1"><institution content-type="dept">Jason L Choy Laboratory of Single-Molecule Biophysics</institution>, <institution>University of California, Berkeley</institution>, <addr-line><named-content content-type="city">Berkeley</named-content></addr-line>, <country>United States</country></aff><aff id="aff2"><institution content-type="dept">Department of Chemistry</institution>, <institution>University of California, Berkeley</institution>, <addr-line><named-content content-type="city">Berkeley</named-content></addr-line>, <country>United States</country></aff><aff id="aff3"><institution content-type="dept">California Institute for Quantitative Biosciences</institution>, <institution>University of California, Berkeley</institution>, <addr-line><named-content content-type="city">Berkeley</named-content></addr-line>, <country>United States</country></aff><aff id="aff4"><institution content-type="dept">Department of Physics</institution>, <institution>Howard Hughes Medical Institute, University of California, Berkeley</institution>, <addr-line><named-content content-type="city">Berkeley</named-content></addr-line>, <country>United States</country></aff><aff id="aff5"><institution content-type="dept">Gene Regulation and Chromosome Biology Laboratory</institution>, <institution>Center for Cancer Research–National Cancer Institute</institution>, <addr-line><named-content content-type="city">Frederick</named-content></addr-line>, <country>United States</country></aff><aff id="aff6"><institution content-type="dept">Department of Molecular and Cell Biology</institution>, <institution>University of California, Berkeley</institution>, <addr-line><named-content content-type="city">Berkeley</named-content></addr-line>, <country>United States</country></aff><aff id="aff7"><institution content-type="dept">Physical Biosciences Division</institution>, <institution>Lawrence Berkeley National Laboratory</institution>, <addr-line><named-content content-type="city">Berkeley</named-content></addr-line>, <country>United States</country></aff></contrib-group><contrib-group content-type="section"><contrib contrib-type="editor"><name><surname>Zhuang</surname><given-names>Xiaowei</given-names></name><role>Reviewing editor</role><aff><institution>Harvard University</institution>, <country>United States</country></aff></contrib></contrib-group><author-notes><corresp id="cor1"><label>*</label>For correspondence: <email>carlos@alice.berkeley.edu</email></corresp><fn fn-type="con" id="equal-contrib"><label>†</label><p>These authors contributed equally to this work</p></fn></author-notes><pub-date date-type="pub" publication-format="electronic"><day>24</day><month>09</month><year>2013</year></pub-date><pub-date pub-type="collection"><year>2013</year></pub-date><volume>2</volume><elocation-id>e00971</elocation-id><history><date date-type="received"><day>20</day><month>05</month><year>2013</year></date><date date-type="accepted"><day>13</day><month>08</month><year>2013</year></date></history><permissions><license xlink:href="http://creativecommons.org/publicdomain/zero/1.0/"><license-p>This is an open-access article, free of all copyright, and may be freely reproduced, distributed, transmitted, modified, built upon, or otherwise used by anyone for any lawful purpose. The work is made available under the <ext-link ext-link-type="uri" xlink:href="http://creativecommons.org/publicdomain/zero/1.0/">Creative Commons CC0 public domain dedication</ext-link>.</license-p></license></permissions><self-uri content-type="pdf" xlink:href="elife00971.pdf"/><related-article ext-link-type="doi" id="ra1" related-article-type="commentary" xlink:href="10.7554/eLife.01414"/><abstract><object-id pub-id-type="doi">10.7554/eLife.00971.001</object-id><p>During transcription elongation, RNA polymerase has been assumed to attain equilibrium between pre- and post-translocated states rapidly relative to the subsequent catalysis. Under this assumption, recent single-molecule studies proposed a branched Brownian ratchet mechanism that necessitates a putative secondary nucleotide binding site on the enzyme. By challenging individual yeast RNA polymerase II with a nucleosomal barrier, we separately measured the forward and reverse translocation rates. Surprisingly, we found that the forward translocation rate is comparable to the catalysis rate. This finding reveals a linear, non-branched ratchet mechanism for the nucleotide addition cycle in which translocation is one of the rate-limiting steps. We further determined all the major on- and off-pathway kinetic parameters in the elongation cycle. The resulting translocation energy landscape shows that the off-pathway states are favored thermodynamically but not kinetically over the on-pathway states, conferring the enzyme its propensity to pause and furnishing the physical basis for transcriptional regulation.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.00971.001">http://dx.doi.org/10.7554/eLife.00971.001</ext-link></p></abstract><abstract abstract-type="executive-summary"><object-id pub-id-type="doi">10.7554/eLife.00971.002</object-id><title>eLife digest</title><p>The production of a protein inside a cell starts with a region of the DNA inside the cell nucleus being transcribed to form a molecule of messenger RNA. This process involves an enzyme called RNA polymerase that moves along the DNA, reading the bases and making a complementary strand of messenger RNA from molecules called nucleoside triphosphates (NTPs). Just as there are four different bases in DNA, there are four different natural NTPs. In addition to supplying the correct bases for the messenger RNA molecule, these NTPs also provide the energy needed to drive the transcription process.</p><p>In many species the RNA polymerase oscillates between two neighbouring positions on the DNA, with this back-and-forth motion–which is powered by thermal energy–being converted into forward movement of the enzyme along the DNA when a new NTP binds to the growing messenger RNA molecule. It has long been assumed that the back-and-forth motion occurs much faster than the overall reaction of adding one NTP to the messenger RNA. This assumption has now been tested by using a single-molecule assay to monitor transcription in real time.</p><p>Dangkulwanich et al. measured the elongation velocities of yeast RNA polymerase II (Pol II) on bare DNA and on DNA in which a nucleosome–a structure that consists of a segment of DNA wrapped around histone proteins–had been placed as a “road block” in front of the enzyme. Surprisingly, the rate of the back-and-forth motion was found to be comparable in magnitude to the rate for adding one molecule of NTP. Dangkulwanich et al. also measured the rates associated with a process called backtracking in which the polymerase moves away from the transcription site to “pause” the process. These measurements show that there is a delicate balance between elongation and pausing during transcription.</p><p>Overall, by revealing the energy landscape associated with transcription, the work of Dangkulwanich et al. will bring us closer to the goal of creating a molecular movie of this extremely important–and complex–process.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.00971.002">http://dx.doi.org/10.7554/eLife.00971.002</ext-link></p></abstract><kwd-group kwd-group-type="author-keywords"><title>Author keywords</title><kwd>RNA polymerase II</kwd><kwd>transcription elongation</kwd><kwd>Brownian ratchet</kwd><kwd>translocation</kwd><kwd>backtracking</kwd><kwd>optical tweezers</kwd></kwd-group><kwd-group kwd-group-type="research-organism"><title>Research organism</title><kwd><italic>S. cerevisiae</italic></kwd></kwd-group><funding-group><award-group id="par-1"><funding-source><institution-wrap><institution>National Institutes of Health</institution></institution-wrap></funding-source><award-id>R01-GM032543</award-id><principal-award-recipient><name><surname>Bustamante</surname><given-names>Carlos J</given-names></name></principal-award-recipient></award-group><award-group id="par-2"><funding-source><institution-wrap><institution>Department of Energy</institution></institution-wrap></funding-source><award-id>DE-AC02-05CH11231</award-id><principal-award-recipient><name><surname>Bustamante</surname><given-names>Carlos J</given-names></name></principal-award-recipient></award-group><award-group id="par-3"><funding-source><institution-wrap><institution>Howard Hughes Medical Institute</institution></institution-wrap></funding-source><principal-award-recipient><name><surname>Bustamante</surname><given-names>Carlos J</given-names></name></principal-award-recipient></award-group><funding-statement>The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.</funding-statement></funding-group><custom-meta-group><custom-meta><meta-name>elife-xml-version</meta-name><meta-value>2</meta-value></custom-meta><custom-meta specific-use="meta-only"><meta-name>Author impact statement</meta-name><meta-value>Quantification of all the major on- and off-pathway kinetic parameters in the transcription elongation cycle reveals that RNA polymerase II translocates slowly in a linear, non-branched Brownian ratchet mechanism.</meta-value></custom-meta></custom-meta-group></article-meta></front><body><sec id="s1" sec-type="intro"><title>Introduction</title><p>Transcription constitutes the first and a central regulatory step for gene expression (<xref ref-type="bibr" rid="bib21">Greive and von Hippel, 2005</xref>; <xref ref-type="bibr" rid="bib14">Coulon et al., 2013</xref>). During the process of RNA synthesis, RNA polymerase (RNAP) converts the energy from chemical catalysis of the nucleoside triphosphate (NTP) into mechanical translocation along the DNA template. Two classes of mechanisms have been offered to describe the mechanochemical coupling of transcription elongation. The first class, known as the ‘power stroke’ mechanism, suggests that the forward translocation of RNAP is directly driven by a chemical step such as the release of the pyrophosphate (PP<sub>i</sub>) (<xref ref-type="bibr" rid="bib69">Yin and Steitz, 2004</xref>). The second class, known as the ‘Brownian ratchet’ mechanism, postulates that the polymerase oscillates back and forth on the DNA template between a pre- and a post-translocated state at the beginning of each nucleotide addition cycle, and that such thermally-driven motions are rectified to the post-translocated state by the incorporation of the incoming NTP (<xref ref-type="bibr" rid="bib22">Guajardo and Sousa, 1997</xref>). After extensive structural and biochemical investigations, it is now generally thought that multi-subunit RNAPs, including bacterial and eukaryotic enzymes, function through the Brownian ratchet mechanism (<xref ref-type="bibr" rid="bib35">Komissarova and Kashlev, 1997a</xref>; <xref ref-type="bibr" rid="bib4">Bai et al., 2004</xref>; <xref ref-type="bibr" rid="bib5">Bar-Nahum et al., 2005</xref>; <xref ref-type="bibr" rid="bib9">Brueckner and Cramer, 2008</xref>). This mechanism received further support from single-molecule studies, which followed the dynamics of individual transcription elongation complexes (TECs) (<xref ref-type="bibr" rid="bib1">Abbondanzieri et al., 2005</xref>; <xref ref-type="bibr" rid="bib3">Bai et al., 2007</xref>; <xref ref-type="bibr" rid="bib39">Larson et al., 2012</xref>). Nonetheless, in order to explain the relationship between the elongation velocity and the external force applied to RNAP obtained from single-molecule experiments, the classical linear ratchet mechanism (<xref ref-type="fig" rid="fig1">Figure 1</xref>) had to be modified such that the incoming NTP must also bind to the pre-translocated TEC (<xref ref-type="fig" rid="fig1s1">Figure 1—figure supplement 1</xref>) (<xref ref-type="bibr" rid="bib1">Abbondanzieri et al., 2005</xref>; <xref ref-type="bibr" rid="bib39">Larson et al., 2012</xref>). In the pre-translocated TEC, the primary nucleotide binding site is occupied by the 3′-end of the nascent transcript. Thus, the branched Brownian ratchet scheme necessarily requires a secondary NTP binding site on the enzyme. However, the precise location of this secondary site and the mechanism by which the NTP is transferred to the primary site remain poorly defined.<fig-group><fig id="fig1" position="float"><object-id pub-id-type="doi">10.7554/eLife.00971.003</object-id><label>Figure 1.</label><caption><title>Nucleotide addition cycle and off-pathway pausing of transcription elongation.</title><p>The nucleotide addition phase and the pausing phase are colored in green and blue, respectively. At the beginning of a nucleotide addition cycle, the transcription elongation complex (TEC) with a transcript length of <italic>n</italic> thermally fluctuates between the pre-translocated state (TEC<sub>n,0</sub>) and the post-translocated state (TEC<sub>n,1</sub>) with a forward rate constant <italic>k</italic><sub>1</sub> and a reverse rate constant <italic>k</italic><sub>−1</sub>. After translocation, the incoming NTP binds to the active site with a binding rate constant <italic>k</italic><sub>2</sub> and a dissociation rate constant <italic>k</italic><sub>−2</sub>. NTP binding is followed by NTP sequestration, bond formation, and PP<sub>i</sub> release, which are collectively described by a single catalysis rate constant <italic>k</italic><sub>3</sub> in our study. Upon the release of the PP<sub>i</sub>, TEC is reset to the pre-translocated state (TEC<sub>n+1,0</sub>) and ready for the next nucleotide addition cycle. From the pre-translocated state, the polymerase can also enter the off-pathway pausing phase by backtracking. The pausing kinetics are determined by the backward stepping rate constants <italic>k</italic><sub>bn</sub> and forward stepping rate constants <italic>k</italic><sub>fn</sub>. The inset shows cartoon configurations of the TEC in a pre-translocated and a post-translocated state.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.00971.003">http://dx.doi.org/10.7554/eLife.00971.003</ext-link></p></caption><graphic xlink:href="elife00971f001"/></fig><fig id="fig1s1" position="float" specific-use="child-fig"><object-id pub-id-type="doi">10.7554/eLife.00971.004</object-id><label>Figure 1—figure supplement 1.</label><caption><title>A branched Brownian ratchet model for the nucleotide addition cycle.</title><p>This kinetic model, proposed by Larson et al. (<xref ref-type="bibr" rid="bib39">Larson et al., 2012</xref>), allows NTP to bind to the TEC both before and after translocation, postulating a secondary nucleotide binding site for NTP binding to the pre-translocated TEC (TEC<sub>n,0</sub>). Additionally, the model assumes rapid forward and reverse translocation of the polymerase and hence describes the translocation step simply with an equilibrium constant <italic>K</italic><sub>δ</sub>.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.00971.004">http://dx.doi.org/10.7554/eLife.00971.004</ext-link></p></caption><graphic xlink:href="elife00971fs001"/></fig></fig-group></p><p>Pausing is an off-pathway process that plays crucial roles in the regulation of transcription elongation (<xref ref-type="bibr" rid="bib38">Landick, 2006</xref>; <xref ref-type="bibr" rid="bib48">Nudler, 2012</xref>). In one view of the mechanisms of transcriptional pausing, RNAP first enters an elemental pause state (<xref ref-type="bibr" rid="bib24">Herbert et al., 2006</xref>; <xref ref-type="bibr" rid="bib57">Toulokhonov et al., 2007</xref>; <xref ref-type="bibr" rid="bib52">Sydow et al., 2009</xref>), whose structural evidence was recently presented in bacterial RNAP (<xref ref-type="bibr" rid="bib64">Weixlbaumer et al., 2013</xref>). However, similar evidence is lacking for eukaryotic polymerases. These elemental pauses can be subsequently stabilized into longer-lived pauses by the formation of a hairpin structure in the nascent RNA transcript or by RNAP backtracking (<xref ref-type="bibr" rid="bib2">Artsimovitch and Landick, 2000</xref>; <xref ref-type="bibr" rid="bib23">Herbert et al., 2008</xref>). The backtracking process is caused by upstream movements of the polymerase, displacing the 3′-end of the nascent RNA away from the active site into the secondary channel of the enzyme (<xref ref-type="bibr" rid="bib49">Nudler et al., 1997</xref>; <xref ref-type="bibr" rid="bib36">Komissarova and Kashlev, 1997b</xref>). An alternative view poses that most pauses are attributed to backtracking, which can be described as a one-dimensional random walk of the enzyme along the DNA template (<xref ref-type="bibr" rid="bib19">Galburt et al., 2007</xref>; <xref ref-type="bibr" rid="bib45">Mejia et al., 2008</xref>; <xref ref-type="bibr" rid="bib16">Depken et al., 2009</xref>; <xref ref-type="bibr" rid="bib25">Hodges et al., 2009</xref>). RNA synthesis resumes when the polymerase diffusively realigns its active site with the 3′-end of the transcript.</p><p>Both the nucleotide addition phase and the pausing phase are closely regulated by conserved structural motifs near the active center of the polymerase, namely the bridge helix and the trigger loop (TL) (<xref ref-type="bibr" rid="bib5">Bar-Nahum et al., 2005</xref>; <xref ref-type="bibr" rid="bib63">Wang et al., 2006</xref>; <xref ref-type="bibr" rid="bib58">Vassylyev et al., 2007</xref>; <xref ref-type="bibr" rid="bib9">Brueckner and Cramer, 2008</xref>; <xref ref-type="bibr" rid="bib29">Kaplan et al., 2008</xref>; <xref ref-type="bibr" rid="bib54">Tan et al., 2008</xref>). In order to understand the mechanism of transcription and its regulation, it is important to achieve a detailed description of both on- and off-pathway kinetics of the elongation reaction. Previous efforts to dissect the kinetic scheme of transcription elongation have assumed that the forward and reverse translocation steps of the Brownian ratchet occur in rapid equilibrium relative to the chemical steps in the nucleotide addition cycle (<xref ref-type="bibr" rid="bib22">Guajardo and Sousa, 1997</xref>; <xref ref-type="bibr" rid="bib4">Bai et al., 2004</xref>; <xref ref-type="bibr" rid="bib1">Abbondanzieri et al., 2005</xref>; <xref ref-type="bibr" rid="bib53">Tadigotla et al., 2006</xref>). However, the assumption of fast translocation equilibrium has never been experimentally validated. In fact, recent studies suggested that the translocation step may be partially rate-limiting for the nucleotide addition cycle, which gives rise to the heterogeneous elongation rates at different template positions (<xref ref-type="bibr" rid="bib46">Nedialkov et al., 2003</xref>; <xref ref-type="bibr" rid="bib31">Kireeva et al., 2010</xref>; <xref ref-type="bibr" rid="bib44">Maoiléidigh et al., 2011</xref>; <xref ref-type="bibr" rid="bib43">Malinen et al., 2012</xref>; <xref ref-type="bibr" rid="bib47">Nedialkov et al., 2012</xref>; <xref ref-type="bibr" rid="bib27">Imashimizu et al., 2013</xref>).</p><p>In this work, we sought to achieve a comprehensive kinetic characterization of transcription elongation without making any assumption about the rate-limiting mechanism of the reaction. We used an optical tweezers assay to follow the transcription trajectories of single yeast RNA polymerase II (Pol II) molecules under a variety of conditions, including varying NTP concentrations, assisting and opposing applied forces, and different tracks (bare and nucleosomal DNA). In vivo, eukaryotic DNA is organized around histone octamers to form nucleosomes, which impose physical barriers to transcription elongation. We have previously demonstrated that a transcribing Pol II cannot actively unravel a wrapped nucleosome. Instead, the polymerase pauses and waits until the local nucleosomal DNA spontaneously unwraps and permits Pol II to advance (<xref ref-type="bibr" rid="bib25">Hodges et al., 2009</xref>; <xref ref-type="bibr" rid="bib6">Bintu et al., 2012</xref>). Here we used the nucleosomal barrier as a tool to specifically perturb forward translocation of a transcribing Pol II and separately measured the forward and reverse translocation rates. Surprisingly, we found that the forward translocation rate is of the same order of magnitude as the catalysis rate, in contradiction to previous assumptions of fast translocation. This finding reveals that translocation and catalysis together constitute the rate-limiting steps in the nucleotide addition cycle. As a consequence, we were able to rationalize the observed force–velocity relationship of the enzyme with a linear Brownian ratchet scheme in which the incoming NTP only binds to the post-translocated TEC, thus reconciling bulk and single-molecule data and arriving at a unifying view of the transcription elongation process. We further obtained all the major kinetic parameters in the nucleotide addition phase and the pausing phase of the elongation cycle. The energy landscape for transcription elongation derived from these parameters shows that: (i) the enzyme thermodynamically favors the pre-translocated state to the post-translocated state; (ii) entry into the 1-basepair (bp) backtracked state is easier than into further backtracked states; and (iii) from the pre-translocated state, the enzyme thermodynamically favors the backtracked states, but kinetically favors forward translocation. We also applied this analysis to a TL mutant Pol II, Rpb1-<italic>E1103G</italic> (<xref ref-type="bibr" rid="bib42">Malagon et al., 2006</xref>), to quantitatively elucidate the roles of the TL in transcription elongation. Our results indicate that the conformational transitions of the TL control enzyme translocation, catalysis, and pausing, rendering it a vital target element for transcriptional regulation.</p></sec><sec id="s2" sec-type="results"><title>Results</title><sec id="s2-1"><title>NTP concentration dependence of elongation velocity and pausing frequency</title><p>The Brownian ratchet kinetic scheme for the nucleotide addition cycle of transcription elongation (<xref ref-type="fig" rid="fig1">Figure 1</xref>) can be simplified to: <disp-formula id="equ1"><mml:math id="m1"><mml:mrow><mml:msub><mml:mrow><mml:mtext>TEC</mml:mtext></mml:mrow><mml:mrow><mml:mtext>n</mml:mtext><mml:mo>,</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:munderover><mml:mo>⇄</mml:mo><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow></mml:munderover><mml:msub><mml:mrow><mml:mtext>TEC</mml:mtext></mml:mrow><mml:mrow><mml:mtext>n</mml:mtext><mml:mo>,</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:munderover><mml:mo>⇄</mml:mo><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mrow><mml:mo>[</mml:mo><mml:mtext>NTP</mml:mtext><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:munderover><mml:msub><mml:mrow><mml:mtext>TEC</mml:mtext></mml:mrow><mml:mrow><mml:mtext>n</mml:mtext><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo>⋅</mml:mo><mml:mtext>NTP</mml:mtext></mml:mrow></mml:msub><mml:mrow><mml:mover accent="true"><mml:mo>→</mml:mo><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:mover></mml:mrow><mml:msub><mml:mrow><mml:mtext>TEC</mml:mtext></mml:mrow><mml:mrow><mml:mtext>n</mml:mtext><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mtext>0</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:math></disp-formula>where <italic>k</italic><sub>1</sub> and <italic>k</italic><sub>−1</sub> are the forward and reverse translocation rate constants, <italic>k</italic><sub>2</sub> and <italic>k</italic><sub>−2</sub> are the NTP binding and dissociation rate constants, and <italic>k</italic><sub>3</sub> is the combined catalysis rate constant that includes NTP sequestration, bond formation, and PP<sub>i</sub> release. Because of the large equilibrium constant of transcription elongation and the very low PP<sub>i</sub> concentration (1 μM) in the buffer, <italic>k</italic><sub>3</sub> was considered essentially irreversible (<xref ref-type="bibr" rid="bib16a">Erie et al., 1992</xref>). Using the concept of net rate constants (<xref ref-type="bibr" rid="bib13">Cleland, 1975</xref>), we can replace the reversible rate constants between two adjacent states with a single net rate constant and re-write the above scheme as:<disp-formula id="equ2"><mml:math id="m2"><mml:mrow><mml:msub><mml:mrow><mml:mtext>TEC</mml:mtext></mml:mrow><mml:mrow><mml:mtext>n</mml:mtext><mml:mo>,</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mover accent="true"><mml:mo>→</mml:mo><mml:mrow><mml:msubsup><mml:mi>k</mml:mi><mml:mn>1</mml:mn><mml:mtext>net</mml:mtext></mml:msubsup></mml:mrow></mml:mover></mml:mrow><mml:msub><mml:mrow><mml:mtext>TEC</mml:mtext></mml:mrow><mml:mrow><mml:mtext>n</mml:mtext><mml:mo>,</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mover accent="true"><mml:mo>→</mml:mo><mml:mrow><mml:msubsup><mml:mi>k</mml:mi><mml:mn>2</mml:mn><mml:mtext>net</mml:mtext></mml:msubsup></mml:mrow></mml:mover></mml:mrow><mml:msub><mml:mrow><mml:mtext>TEC</mml:mtext></mml:mrow><mml:mrow><mml:mtext>n</mml:mtext><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo>⋅</mml:mo><mml:mtext>NTP</mml:mtext></mml:mrow></mml:msub><mml:mrow><mml:mover accent="true"><mml:mo>→</mml:mo><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:mover></mml:mrow><mml:msub><mml:mrow><mml:mtext>TEC</mml:mtext></mml:mrow><mml:mrow><mml:mtext>n</mml:mtext><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>,</mml:mo><mml:mtext>0</mml:mtext></mml:mrow></mml:msub></mml:mrow></mml:math></disp-formula><inline-formula><mml:math id="inf1"><mml:mrow><mml:msubsup><mml:mi>k</mml:mi><mml:mn>1</mml:mn><mml:mrow><mml:mtext>net</mml:mtext></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula> and <inline-formula><mml:math id="inf2"><mml:mrow><mml:msubsup><mml:mi>k</mml:mi><mml:mn>2</mml:mn><mml:mrow><mml:mtext>net</mml:mtext></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula> are the net rate constants for translocation and NTP binding, respectively, which are given by:<disp-formula id="equ3"><label>(1)</label><mml:math id="m3"><mml:mrow><mml:msubsup><mml:mi>k</mml:mi><mml:mn>2</mml:mn><mml:mtext>net</mml:mtext></mml:msubsup><mml:mo>=</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:mrow><mml:mo>[</mml:mo><mml:mi mathvariant="italic">NTP</mml:mi><mml:mo>]</mml:mo></mml:mrow><mml:mo>⋅</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:mfrac></mml:mrow></mml:math></disp-formula><disp-formula id="equ4"><label>(2)</label><mml:math id="m4"><mml:mrow><mml:msubsup><mml:mi>k</mml:mi><mml:mn>1</mml:mn><mml:mtext>net</mml:mtext></mml:msubsup><mml:mo>=</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>⋅</mml:mo><mml:mfrac><mml:mrow><mml:msubsup><mml:mi>k</mml:mi><mml:mn>2</mml:mn><mml:mtext>net</mml:mtext></mml:msubsup></mml:mrow><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msubsup><mml:mi>k</mml:mi><mml:mn>2</mml:mn><mml:mtext>net</mml:mtext></mml:msubsup></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:msub><mml:mi>k</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>k</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:mrow><mml:mo>[</mml:mo><mml:mi mathvariant="italic">NTP</mml:mi><mml:mo>]</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>k</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:mrow><mml:mo>[</mml:mo><mml:mi mathvariant="italic">NTP</mml:mi><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:mfrac></mml:mrow></mml:math></disp-formula></p><p>The time the enzyme takes to finish one nucleotide addition cycle (<italic>τ</italic>) equals the step size of the polymerase (<italic>d</italic> = 1 nt) divided by the pause-free velocity (<italic>v</italic>), and also equals the sum of the inverse of each net rate:<disp-formula id="equ5"><label>(3)</label><mml:math id="m5"><mml:mrow><mml:mi>τ</mml:mi><mml:mo>=</mml:mo><mml:mfrac><mml:mi>d</mml:mi><mml:mi>v</mml:mi></mml:mfrac><mml:mo>=</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:msubsup><mml:mi>k</mml:mi><mml:mn>1</mml:mn><mml:mtext>net</mml:mtext></mml:msubsup></mml:mrow></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:msubsup><mml:mi>k</mml:mi><mml:mn>2</mml:mn><mml:mtext>net</mml:mtext></mml:msubsup></mml:mrow></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:mfrac></mml:mrow></mml:math></disp-formula></p><p>Plugging <xref ref-type="disp-formula" rid="equ3">Equations 1</xref> and <xref ref-type="disp-formula" rid="equ4">2</xref> into <xref ref-type="disp-formula" rid="equ5">Equation 3</xref> yields the following expression for the pause-free velocity:<disp-formula id="equ6"><label>(4)</label><mml:math id="m6"><mml:mrow><mml:mi>v</mml:mi><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:msub><mml:mi>k</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:mfrac><mml:mo>⋅</mml:mo><mml:mfrac><mml:mrow><mml:mrow><mml:mo>[</mml:mo><mml:mi mathvariant="italic">NTP</mml:mi><mml:mo>]</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mfrac><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>⋅</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>⋅</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:mfrac><mml:mo>+</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:mi mathvariant="italic">NTP</mml:mi><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:mfrac><mml:mo>⋅</mml:mo><mml:mi>d</mml:mi></mml:mrow></mml:math></disp-formula></p><p>We note that this expression is more general than those shown in previous studies (<xref ref-type="bibr" rid="bib1">Abbondanzieri et al., 2005</xref>; <xref ref-type="bibr" rid="bib3">Bai et al., 2007</xref>), as it is derived without assuming local equilibration of translocation and NTP binding. In particular, we describe the kinetics of the translocation step with <italic>k</italic><sub>1</sub> and <italic>k</italic><sub>−1</sub>, instead of a single equilibrium constant <italic>K</italic><sub>δ</sub> = <italic>k</italic><sub>−1</sub>/<italic>k</italic><sub>1</sub>. Such treatment is a prerequisite to explicitly determine the forward and reverse translocation rates. <xref ref-type="disp-formula" rid="equ6">Equation 4</xref> can be simplified to the Michaelis–Menten equation form:<disp-formula id="equ7"><label>(5)</label><mml:math id="m7"><mml:mrow><mml:mi>v</mml:mi><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mi>max</mml:mi></mml:msub><mml:mrow><mml:mo>[</mml:mo><mml:mi mathvariant="italic">NTP</mml:mi><mml:mo>]</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mtext>M</mml:mtext></mml:msub><mml:mo>+</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:mi mathvariant="italic">NTP</mml:mi><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:mfrac></mml:mrow></mml:math></disp-formula>where <inline-formula><mml:math id="inf3"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mi>max</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:msub><mml:mi>k</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:mfrac><mml:mo>⋅</mml:mo><mml:mi>d</mml:mi></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="inf4"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mtext>M</mml:mtext></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:mfrac><mml:mo>⋅</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:mfrac></mml:mrow></mml:math></inline-formula>.</p><p>We followed the transcriptional dynamics of individual Pol II molecules with a dual-trap optical tweezers instrument. One laser trap holds a polystyrene bead attached to a stalled Pol II molecule, while the other trap holds another bead attached to the upstream DNA template (assisting force geometry; <xref ref-type="fig" rid="fig2">Figure 2A</xref>) or to the downstream template (opposing force geometry, not shown). Upon addition of NTP, transcription restarts, resulting in a change of the DNA tether length and thereby a variation of the force applied to Pol II. Single-molecule transcription trajectories were collected at a range of NTP concentrations (35 μM–2 mM) (<xref ref-type="fig" rid="fig2">Figure 2B,C</xref>). The relationship between pause-free velocity (<italic>v</italic>) and [NTP] for the wild-type enzyme fits well to <xref ref-type="disp-formula" rid="equ7">Equation 5</xref>, with <italic>V</italic><sub>max</sub> <italic>=</italic> 25 ± 3 nt/s and <italic>K</italic><sub>M</sub> = 39 ± 12 μM (errors are SEM) (<xref ref-type="fig" rid="fig2">Figure 2D</xref>, gray line). We also examined the dynamics of the E1103G mutant Pol II, which is known to transcribe DNA at a faster overall velocity than the wild-type (<xref ref-type="fig" rid="fig2">Figure 2B,C</xref>) (<xref ref-type="bibr" rid="bib42">Malagon et al., 2006</xref>; <xref ref-type="bibr" rid="bib34">Kireeva et al., 2008</xref>). We found that the maximum pause-free velocity of the mutant is ∼1.5-fold higher than that of the wild-type, with <italic>V</italic><sub>max</sub> = 38 ± 5 nt/s and <italic>K</italic><sub>M</sub> = 62 ± 15 μM (<xref ref-type="fig" rid="fig2">Figure 2D</xref>, blue line).<fig-group><fig id="fig2" position="float"><object-id pub-id-type="doi">10.7554/eLife.00971.005</object-id><label>Figure 2.</label><caption><title>Single-molecule transcription assay.</title><p>(<bold>A</bold>) Experimental setup for the single-molecule transcription assay. Each of the two optical traps holds a 2.1-μm polystyrene bead. Biotinylated Pol II is attached to the streptavidin (SA) bead. The upstream DNA is attached to the antibody (AD) bead via the digoxigenin–antidigoxigenin linkage. The black arrow indicates the direction of transcription. A nucleosome can be loaded on the downstream DNA as shown. (<bold>B</bold>) Example transcription trajectories of the wild-type Pol II at 50 μM NTP on bare DNA, 1 mM NTP on bare DNA, and 1 mM NTP in the presence of a nucleosome. The nucleosome positioning sequence (NPS) is represented by the yellow shaded region. (<bold>C</bold>) Example transcription trajectories of the E1103G mutant Pol II under various conditions. (<bold>D</bold>) Pause-free velocities of the wild-type (black) and mutant Pol II (blue) at various NTP concentrations. Dashed lines are fits to the Michaelis–Menten equation (<xref ref-type="disp-formula" rid="equ5">Equation 3</xref>; R<sup>2</sup> = 0.80 for the wild-type; R<sup>2</sup> = 0.85 for mutant). (<bold>E</bold>) The apparent pause densities (<italic>ρ</italic><sub>pause</sub>) of the wild-type Pol II at different NTP concentrations are plotted against the corresponding pause-free velocities (<italic>v</italic>). (<bold>F</bold>) <italic>ρ</italic><sub>pause</sub>–<italic>v</italic> relationship for the mutant enzyme. Error bars represent standard error of the mean (SEM).</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.00971.005">http://dx.doi.org/10.7554/eLife.00971.005</ext-link></p></caption><graphic xlink:href="elife00971f002"/></fig><fig id="fig2s1" position="float" specific-use="child-fig"><object-id pub-id-type="doi">10.7554/eLife.00971.006</object-id><label>Figure 2—figure supplement 1.</label><caption><title>Cumulative distribution of the pause durations for the wild-type Pol II on bare DNA (black solid line) and nucleosomal DNA (red solid line).</title><p>Dashed lines are theoretical fits of the experimental data to the one-dimensional diffusion model for backtracking (<xref ref-type="disp-formula" rid="equ10">Equation 8</xref>).</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.00971.006">http://dx.doi.org/10.7554/eLife.00971.006</ext-link></p></caption><graphic xlink:href="elife00971fs002"/></fig><fig id="fig2s2" position="float" specific-use="child-fig"><object-id pub-id-type="doi">10.7554/eLife.00971.007</object-id><label>Figure 2—figure supplement 2.</label><caption><title>A gel-based time-coursed transcription assay of the wild-type Pol II on bare and nucleosomal DNA.</title><p>The transcription reactions were carried out in 40 mM KCl and quenched with EDTA after 1, 2, 5, and 20 min incubation with 1 mM NTPs.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.00971.007">http://dx.doi.org/10.7554/eLife.00971.007</ext-link></p></caption><graphic xlink:href="elife00971fs003"/></fig><fig id="fig2s3" position="float" specific-use="child-fig"><object-id pub-id-type="doi">10.7554/eLife.00971.008</object-id><label>Figure 2—figure supplement 3.</label><caption><title>A gel-based transcription assay of the wild-type Pol II and the E1103G mutant Pol II in various KCl concentrations.</title><p>The experiment was carried out in 40, 150, 300, 450 mM of KCl. The transcription reactions were quenched with EDTA after 10 min incubation with 1 mM NTPs. The run-off length is 612 nt. The nucleosomal dyad is located at nucleotide position 407. The arrows indicate the salt condition used in the single-molecule experiments (300 mM KCl).</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.00971.008">http://dx.doi.org/10.7554/eLife.00971.008</ext-link></p></caption><graphic xlink:href="elife00971fs004"/></fig><fig id="fig2s4" position="float" specific-use="child-fig"><object-id pub-id-type="doi">10.7554/eLife.00971.009</object-id><label>Figure 2—figure supplement 4.</label><caption><title>Mean dwell times of the wild-type Pol II at different nucleotide positions.</title><p>The experiments were conducted at 1 mM NTP concentration. The yellow shade indicates the extended NPS region (−115 bp to +85 bp relative to the dyad). The arrow on the top axis marks the position of the dyad. The same DNA sequence was used in the bulk and single-molecule assays. Both assays show the most predominant pausing about 20 bp before the dyad, consistent with previous results (<xref ref-type="bibr" rid="bib8">Bondarenko et al., 2006</xref>).</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.00971.009">http://dx.doi.org/10.7554/eLife.00971.009</ext-link></p></caption><graphic xlink:href="elife00971fs005"/></fig><fig id="fig2s5" position="float" specific-use="child-fig"><object-id pub-id-type="doi">10.7554/eLife.00971.010</object-id><label>Figure 2—figure supplement 5.</label><caption><title>Mean dwell times of the mutant Pol II at different nucleotide positions.</title><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.00971.010">http://dx.doi.org/10.7554/eLife.00971.010</ext-link></p></caption><graphic xlink:href="elife00971fs006"/></fig></fig-group></p><p>As shown in the example trajectories (<xref ref-type="fig" rid="fig2">Figure 2B,C</xref>), transcription elongation is punctuated by pauses of various durations. Pause density, <italic>ρ</italic><sub>pause</sub>, is defined as the average number of pauses per bp of template transcribed. As the concentration of NTP goes up, the pause-free velocity increases and the apparent <italic>ρ</italic><sub>pause</sub>, which counts pauses lasting longer than 1 s, decreases (<xref ref-type="fig" rid="fig2">Figure 2E</xref>). The same trend was also observed for the mutant Pol II (<xref ref-type="fig" rid="fig2">Figure 2F</xref>). The inverse relationship between <italic>v</italic> and <italic>ρ</italic><sub>pause</sub> indicates that elongation and pausing are in kinetic competition and that pausing occurs prior to NTP binding (<xref ref-type="bibr" rid="bib2">Artsimovitch and Landick, 2000</xref>; <xref ref-type="bibr" rid="bib15">Davenport et al., 2000</xref>; <xref ref-type="bibr" rid="bib17">Forde et al., 2002</xref>; <xref ref-type="bibr" rid="bib38">Landick, 2006</xref>; <xref ref-type="bibr" rid="bib45">Mejia et al., 2008</xref>). Note that pausing has also been observed to occur after NTP binding at certain sequences for <italic>Escherichia coli</italic> RNAP; however, yeast Pol II does not seem to employ such mechanism (<xref ref-type="bibr" rid="bib33">Kireeva and Kashlev, 2009</xref>). The pause-free velocities and apparent pause densities at various NTP concentrations are summarized in <xref ref-type="table" rid="tbl1">Table 1</xref>.<table-wrap id="tbl1" position="float"><object-id pub-id-type="doi">10.7554/eLife.00971.011</object-id><label>Table 1.</label><caption><p>Summary of pause-free velocities and apparent pause densities measured at various NTP concentrations</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.00971.011">http://dx.doi.org/10.7554/eLife.00971.011</ext-link></p></caption><table frame="hsides" rules="groups"><thead><tr><th>Pol II</th><th>[NTP] (μM)</th><th><italic>N</italic></th><th>Pause-free velocity (nt/s)</th><th>Apparent pause density (bp<sup>−1</sup>)</th></tr></thead><tbody><tr><td rowspan="7">wild-type</td><td align="char" char=".">35</td><td align="char" char=".">10</td><td align="char" char="plusmn">12.4 ± 0.7</td><td align="char" char="plusmn">0.0721 ± 0.0099</td></tr><tr><td align="char" char=".">50</td><td align="char" char=".">11</td><td align="char" char="plusmn">11.6 ± 1.1</td><td align="char" char="plusmn">0.0526 ± 0.0086</td></tr><tr><td align="char" char=".">75</td><td align="char" char=".">9</td><td align="char" char="plusmn">17.8 ± 1.2</td><td align="char" char="plusmn">0.0358 ± 0.0079</td></tr><tr><td align="char" char=".">100</td><td align="char" char=".">13</td><td align="char" char="plusmn">15.7 ± 1.4</td><td align="char" char="plusmn">0.0326 ± 0.0077</td></tr><tr><td align="char" char=".">200</td><td align="char" char=".">17</td><td align="char" char="plusmn">21.0 ± 2.4</td><td align="char" char="plusmn">0.0184 ± 0.0046</td></tr><tr><td align="char" char=".">1000</td><td align="char" char=".">44</td><td align="char" char="plusmn">24.7 ± 1.8</td><td align="char" char="plusmn">0.0156 ± 0.0031</td></tr><tr><td align="char" char=".">2000</td><td align="char" char=".">9</td><td align="char" char="plusmn">26.7 ± 4.3</td><td align="char" char="plusmn">0.0188 ± 0.0076</td></tr><tr><td rowspan="8">E1103G</td><td align="char" char=".">35</td><td align="char" char=".">10</td><td align="char" char="plusmn">16.1 ± 0.9</td><td align="char" char="plusmn">0.0374 ± 0.0055</td></tr><tr><td align="char" char=".">50</td><td align="char" char=".">13</td><td align="char" char="plusmn">15.2 ± 1.0</td><td align="char" char="plusmn">0.0266 ± 0.0055</td></tr><tr><td align="char" char=".">75</td><td align="char" char=".">13</td><td align="char" char="plusmn">18.9 ± 1.5</td><td align="char" char="plusmn">0.0290 ± 0.0069</td></tr><tr><td align="char" char=".">100</td><td align="char" char=".">13</td><td align="char" char="plusmn">24.2 ± 1.7</td><td align="char" char="plusmn">0.0106 ± 0.0036</td></tr><tr><td align="char" char=".">200</td><td align="char" char=".">13</td><td align="char" char="plusmn">27.4 ± 3.9</td><td align="char" char="plusmn">0.0100 ± 0.0027</td></tr><tr><td align="char" char=".">400</td><td align="char" char=".">10</td><td align="char" char="plusmn">35.6 ± 1.9</td><td align="char" char="plusmn">0.0094 ± 0.0062</td></tr><tr><td align="char" char=".">1000</td><td align="char" char=".">96</td><td align="char" char="plusmn">37.6 ± 4.9</td><td align="char" char="plusmn">0.0051 ± 0.0008</td></tr><tr><td align="char" char=".">2000</td><td align="char" char=".">15</td><td align="char" char="plusmn">42.1 ± 4.9</td><td align="char" char="plusmn">0.0083 ± 0.0011</td></tr></tbody></table><table-wrap-foot><fn><p>Data are shown as mean ± SEM. The apparent pause densities are determined by counting pauses that last between 1 s and 120 s. <italic>N</italic> is the number of single-molecule transcription trajectories at each condition.</p></fn></table-wrap-foot></table-wrap></p></sec><sec id="s2-2"><title>Determine the stepping rates during a backtracked pause</title><p>Backtracking is a major mechanism for transcriptional pauses. We have previously modeled backtracking as a one-dimensional random walk of the enzyme along the DNA template (<xref ref-type="bibr" rid="bib25">Hodges et al., 2009</xref>). In this model, Pol II diffuses back and forth on DNA with a forward stepping rate constant <italic>k</italic><sub>f</sub> and a backward stepping rate constant <italic>k</italic><sub>b</sub> during a backtracked pause. These rate constants are dependent on the applied force (<italic>F</italic>, which is positive for assisting forces and negative for opposing forces) according to:<disp-formula id="equ8"><label>(6)</label><mml:math id="m8"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mtext>f</mml:mtext></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mi>F</mml:mi><mml:mo>⋅</mml:mo><mml:mi>Δ</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mi>B</mml:mi></mml:msub><mml:mi>T</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math></disp-formula><disp-formula id="equ9"><label>(7)</label><mml:math id="m9"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mtext>b</mml:mtext></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mi>F</mml:mi><mml:mo>⋅</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mi>Δ</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>/</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mi>B</mml:mi></mml:msub><mml:mi>T</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math></disp-formula>where <italic>k</italic><sub>0</sub> is the intrinsic zero-force stepping rate constant of Pol II diffusing along DNA during backtracking, <italic>Δ</italic> is the distance to the transition state for each step (taken to be 0.5 bp, or 0.17 nm), <italic>k</italic><sub><italic>B</italic></sub> is the Boltzmann constant, and <italic>T</italic> is the temperature (<italic>k</italic><sub><italic>B</italic></sub><italic>T</italic> = 4.11 pN·nm at 25ºC). The probability density of pause durations, <italic>ψ</italic>(<italic>t</italic>), is equivalent to the distribution of first-passage times for a particle diffusing on a one-dimensional lattice to return to the origin (<xref ref-type="bibr" rid="bib16">Depken et al., 2009</xref>), and is given by:<disp-formula id="equ10"><label>(8)</label><mml:math id="m10"><mml:mrow><mml:mi>ψ</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msqrt><mml:mrow><mml:mfrac><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mtext>f</mml:mtext></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mtext>b</mml:mtext></mml:msub></mml:mrow></mml:mfrac></mml:mrow></mml:msqrt><mml:mfrac><mml:mrow><mml:mi>exp</mml:mi><mml:mrow><mml:mo>[</mml:mo><mml:mo>−</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mtext>f</mml:mtext></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mtext>b</mml:mtext></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mi>t</mml:mi><mml:mo>]</mml:mo></mml:mrow></mml:mrow><mml:mi>t</mml:mi></mml:mfrac><mml:msub><mml:mi>I</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mn>2</mml:mn><mml:mi>t</mml:mi><mml:msqrt><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mtext>f</mml:mtext></mml:msub><mml:msub><mml:mi>k</mml:mi><mml:mtext>b</mml:mtext></mml:msub></mml:mrow></mml:msqrt></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></disp-formula>where <italic>I</italic><sub>1</sub> is the modified Bessel function of the first kind. We fit the distribution of pause durations for the wild-type enzyme on bare DNA to this model and extracted a characteristic <italic>k</italic><sub>0</sub> of 1.3 ± 0.3 s<sup>−1</sup> (<xref ref-type="fig" rid="fig2s1">Figure 2—figure supplement 1</xref>, gray dashed line). Using the values of <italic>k</italic><sub>0</sub> and the applied force in our experiment (6.5 pN), we calculated <italic>k</italic><sub>f</sub> and <italic>k</italic><sub>b</sub> to be 1.7 ± 0.4 s<sup>−1</sup> and 1.0 ± 0.3 s<sup>−1</sup>, respectively (<xref ref-type="disp-formula" rid="equ8">Equations 6</xref> and <xref ref-type="disp-formula" rid="equ9">7</xref>).</p></sec><sec id="s2-3"><title>Pausing properties on nucleosomal DNA</title><p>Next, we investigated the transcriptional dynamics of Pol II through the nucleosome by loading a histone octamer on the 601 nucleosome positioning sequence (NPS) (<xref ref-type="bibr" rid="bib41">Lowary and Widom, 1998</xref>) (<xref ref-type="fig" rid="fig2">Figure 2B,C</xref>, <xref ref-type="fig" rid="fig2s1 fig2s2 fig2s3 fig2s4 fig2s5">Figure 2—figure supplements 2–5</xref>). The wild-type enzyme displays a two-fold increase in the apparent pause density upon encountering the nucleosome (<xref ref-type="table" rid="tbl2">Table 2</xref>). The mean pause duration on nucleosomal DNA is significantly longer than that on bare DNA (<xref ref-type="table" rid="tbl2">Table 2</xref>; <xref ref-type="fig" rid="fig2s1">Figure 2—figure supplement 1</xref>). Similarly, the mutant Pol II displays higher pause density and longer pause duration in the presence of a nucleosome (<xref ref-type="table" rid="tbl2">Table 2</xref>).<table-wrap id="tbl2" position="float"><object-id pub-id-type="doi">10.7554/eLife.00971.012</object-id><label>Table 2.</label><caption><p>Apparent pause densities and mean pause durations on bare DNA and nucleosomal DNA in the extended NPS region</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.00971.012">http://dx.doi.org/10.7554/eLife.00971.012</ext-link></p></caption><table frame="hsides" rules="groups"><thead><tr><th>Pol II</th><th>DNA template</th><th><italic>N</italic></th><th>Apparent pause density (bp<sup>−1</sup>)</th><th>Mean pause duration (s)</th></tr></thead><tbody><tr><td rowspan="2">wild-type</td><td>Bare</td><td align="char" char=".">38</td><td align="char" char="plusmn">0.0153 ± 0.0041</td><td align="char" char="plusmn">3.9 ± 0.6</td></tr><tr><td>Nucleosomal</td><td align="char" char=".">94</td><td align="char" char="plusmn">0.0280 ± 0.0036</td><td align="char" char="plusmn">9.4 ± 0.8</td></tr><tr><td rowspan="2">E1103G</td><td>Bare</td><td align="char" char=".">85</td><td align="char" char="plusmn">0.0046 ± 0.0015</td><td align="char" char="plusmn">3.9 ± 0.5</td></tr><tr><td>Nucleosomal</td><td align="char" char=".">64</td><td align="char" char="plusmn">0.0202 ± 0.0050</td><td align="char" char="plusmn">7.6 ± 1.0</td></tr></tbody></table><table-wrap-foot><fn><p>Data are shown as mean ± SEM. The extended NPS region spans −115 nt to+85 nt relative to the nucleosomal dyad.</p></fn></table-wrap-foot></table-wrap></p><p>It has been shown that the nucleosomal DNA can spontaneously unwrap and rewrap around the histones (<xref ref-type="bibr" rid="bib40">Li et al., 2005</xref>; <xref ref-type="bibr" rid="bib37">Koopmans et al., 2008</xref>; <xref ref-type="bibr" rid="bib59">Voltz et al., 2012</xref>). The increased pause duration of Pol II on nucleosomal DNA can be explained by rewrapping of the DNA downstream of a backtracked Pol II, which prevents the polymerase from diffusing back to the 3′-end of the nascent RNA to resume transcription (<xref ref-type="bibr" rid="bib25">Hodges et al., 2009</xref>; <xref ref-type="bibr" rid="bib6">Bintu et al., 2012</xref>). Because one bp of nucleosomal DNA fluctuates much faster (&gt;1000 s<sup>−1</sup>; see ‘Materials and methods’ for the derivation) than Pol II stepping (∼1 s<sup>−1</sup>), the nucleosomal DNA in front of the polymerase reaches wrapping/unwrapping equilibrium between each backtracking step. It follows that the pause durations on nucleosomal DNA can be drawn from the same distribution as on bare DNA, except that the effective forward stepping rate is reduced by a factor, <italic>γ</italic><sub>u</sub>, corresponding to the fraction of time the local nucleosomal DNA is unwrapped (<xref ref-type="bibr" rid="bib25">Hodges et al., 2009</xref>), that is <inline-formula><mml:math id="inf5"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mtext>f</mml:mtext><mml:mrow><mml:mo>(</mml:mo><mml:mi mathvariant="italic">nucl</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:msub><mml:mi>γ</mml:mi><mml:mtext>u</mml:mtext></mml:msub><mml:mo>⋅</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mtext>f</mml:mtext></mml:msub></mml:mrow></mml:math></inline-formula>. The backward stepping rate <italic>k</italic><sub>b</sub> is not affected by the nucleosome, because little histone transfer occurs in our experimental geometry where the DNA template is under tension (<xref ref-type="bibr" rid="bib25">Hodges et al., 2009</xref>; <xref ref-type="bibr" rid="bib7">Bintu et al., 2011</xref>) and therefore the polymerase does not encounter any roadblock when it diffuses backward. The distribution of pause durations for wild-type Pol II on nucleosomal DNA can be correctly fit by this model with a <italic>γ</italic><sub>u</sub> value of 0.6 ± 0.2 (<xref ref-type="fig" rid="fig2s1">Figure 2—figure supplement 1</xref>, red dashed line).</p></sec><sec id="s2-4"><title>Determine the rates of forward translocation and catalysis by comparing pause-free velocities on nucleosomal DNA and bare DNA</title><p>Having understood the effect of the nucleosomal barrier on the pausing dynamics, we then turned our attention to its effect on the on-pathway elongation kinetics. Interestingly, we found that the nucleosome also delays the transcribing enzyme by modulating its pause-free velocity. As the wild-type Pol II transcribes through nucleosomal DNA at saturating [NTP], its mean pause-free velocity decreases by 14% from 26.9 ± 0.8 nt/s to 23.2 ± 0.6 nt/s (<xref ref-type="fig" rid="fig3">Figure 3A</xref>). The mutant Pol II is even more dramatically slowed down by the nucleosome, with its mean pause-free velocity reduced by 35% from 39.8 ± 0.6 nt/s to 26.0 ± 0.7 nt/s (<xref ref-type="fig" rid="fig3">Figure 3B</xref>).<fig id="fig3" position="float"><object-id pub-id-type="doi">10.7554/eLife.00971.013</object-id><label>Figure 3.</label><caption><title>Comparison of pause-free velocities on bare DNA and nucleosomal DNA.</title><p>(<bold>A</bold>) Pause-free velocities of the wild-type Pol II on bare DNA (black) and nucleosomal DNA (red) are plotted as a function of the transcript length. The nucleosomal dyad position corresponds to a transcript length of 407 nt. The extended NPS region (−115 nt to +85 nt relative to the nucleosomal dyad) is highlighted in yellow. The arrow on the top axis marks the position of the dyad. (<bold>B</bold>) Pause-free velocities of the E1103G mutant Pol II on bare DNA (blue) and nucleosomal DNA (green) are plotted as a function of the transcript length. These experiments were conducted at 1 mM NTP. Note that after the polymerase exits the nucleosome, the velocity does not return to the same level of that on bare DNA. This observation could be rationalized if the nucleosome rolls along the DNA and remains ahead of the transcribing polymerase in a fraction of the traces. Error bars are SEM.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.00971.013">http://dx.doi.org/10.7554/eLife.00971.013</ext-link></p></caption><graphic xlink:href="elife00971f003"/></fig></p><p>We have previously shown that a transcribing Pol II cannot actively open a wrapped nucleosome; instead, the enzyme passively waits for the DNA immediately in front of it to spontaneously unwrap and then translocates forward through a locally unwrapped nucleosome (<xref ref-type="bibr" rid="bib25">Hodges et al., 2009</xref>). Since the fluctuations of local nucleosomal DNA occur orders of magnitude faster than the translocations of Pol II during backtracking, we assume that they are also much faster than the on-pathway translocation steps of Pol II. Under this assumption, local DNA reaches wrapping/unwrapping equilibrium before Pol II makes a translocation step and the forward translocation rate (<italic>k</italic><sub>1</sub>) is effectively reduced by the fraction of time the local nucleosomal DNA is unwrapped (<italic>γ</italic><sub>u</sub>). The reverse translocation rate (<italic>k</italic><sub>−1</sub>) is unlikely to be affected, again due to the lack of a roadblock against reverse translocation. Thus, according to <xref ref-type="disp-formula" rid="equ7">Equation 5</xref>, the maximum pause-free velocity for nucleosomal DNA transcription is: <disp-formula id="equ11"><label>(9)</label><mml:math id="m11"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mi>max</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi mathvariant="italic">nucl</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>γ</mml:mi><mml:mtext>u</mml:mtext></mml:msub><mml:mo>⋅</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>⋅</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>γ</mml:mi><mml:mtext>u</mml:mtext></mml:msub><mml:mo>⋅</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:mfrac><mml:mo>⋅</mml:mo><mml:mi>d</mml:mi></mml:mrow></mml:math></disp-formula></p><p>In comparison, the maximum pause-free velocity for bare DNA transcription is:<disp-formula id="equ12"><label>(10)</label><mml:math id="m12"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mi>max</mml:mi></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:msub><mml:mi>k</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:mfrac><mml:mo>⋅</mml:mo><mml:mi>d</mml:mi></mml:mrow></mml:math></disp-formula></p><p>Using an optimal <italic>γ</italic><sub>u</sub> value of 0.6, we solved <xref ref-type="disp-formula" rid="equ11">Equations 9</xref> and <xref ref-type="disp-formula" rid="equ12">10</xref> and obtained <italic>k</italic><sub>1</sub> = 112 ± 30 s<sup>−1</sup> (indeed much slower than local DNA wrapping/unwrapping) and <italic>k</italic><sub>3</sub> = 35 ± 3 s<sup>−1</sup> for the wild-type. Importantly, these values show that the forward translocation rate is only three times faster than the catalysis rate and, therefore, has a significant contribution to the overall elongation velocity. For the mutant Pol II, translocation becomes even slower than catalysis (<italic>k</italic><sub>1</sub> = 50 ± 4 s<sup>−1</sup> and <italic>k</italic><sub>3</sub> = 195 ± 65 s<sup>−1</sup>). The mutant’s higher <italic>k</italic><sub>3</sub> compensates for its lower <italic>k</italic><sub>1</sub>, rendering its overall velocity faster than that of the wild type. We note that these numbers were extracted by using the average values of the pause-free velocity and <italic>γ</italic><sub>u</sub> over the whole nucleosomal region. Such a simplifying treatment is based on the observations that both the pause-free velocity (<xref ref-type="fig" rid="fig3">Figure 3</xref>) and the local DNA wrapping equilibrium (<xref ref-type="bibr" rid="bib6">Bintu et al., 2012</xref>) do not change substantially along the NPS.</p></sec><sec id="s2-5"><title>The first backtracking step is distinct from subsequent steps</title><p>The pause density, <italic>ρ</italic><sub>pause</sub>, is governed by the kinetic competition between pause entry and elongation. Previously, an overall elongation rate, which includes translocation, NTP binding, and catalysis, was used in the expression for <italic>ρ</italic><sub>pause</sub> (<xref ref-type="bibr" rid="bib24">Herbert et al., 2006</xref>; <xref ref-type="bibr" rid="bib25">Hodges et al., 2009</xref>; <xref ref-type="bibr" rid="bib72">Zhou et al., 2011</xref>). A more accurate treatment is to use the elementary rate constant in the elongation pathway directly connected to pausing, which is the net rate constant for forward translocation, <inline-formula><mml:math id="inf6"><mml:mrow><mml:msubsup><mml:mi>k</mml:mi><mml:mn>1</mml:mn><mml:mrow><mml:mtext>net</mml:mtext></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula> (<xref ref-type="fig" rid="fig1">Figure 1</xref>; <xref ref-type="disp-formula" rid="equ4">Equation 2</xref>):<disp-formula id="equ13"><label>(11)</label><mml:math id="m13"><mml:mrow><mml:msub><mml:mi>ρ</mml:mi><mml:mtext>pause</mml:mtext></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mtext>b</mml:mtext><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mtext>b</mml:mtext><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msubsup><mml:mi>k</mml:mi><mml:mn>1</mml:mn><mml:mtext>net</mml:mtext></mml:msubsup></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mtext>b</mml:mtext><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mtext>b</mml:mtext><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:mo>[</mml:mo><mml:mi mathvariant="italic">NTP</mml:mi><mml:mo>]</mml:mo></mml:mrow><mml:mrow><mml:mfrac><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mn>3</mml:mn></mml:msub><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn>2</mml:mn></mml:msub><mml:msub><mml:mi>k</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:mfrac><mml:mo>+</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:mi mathvariant="italic">NTP</mml:mi><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:mfrac><mml:mo>⋅</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow></mml:mfrac></mml:mrow></mml:math></disp-formula>where <italic>k</italic><sub>b1</sub> is the rate constant of entering the 1-bp backtracked pausing state. At saturating NTP concentrations ([NTP]&gt;&gt;<italic>k</italic><sub>−1</sub>(<italic>k</italic><sub>−2</sub>+<italic>k</italic><sub>3</sub>)/(<italic>k</italic><sub>2</sub><italic>k</italic><sub>3</sub>)), <inline-formula><mml:math id="inf7"><mml:mrow><mml:msubsup><mml:mi>k</mml:mi><mml:mn>1</mml:mn><mml:mrow><mml:mtext>net</mml:mtext></mml:mrow></mml:msubsup></mml:mrow></mml:math></inline-formula> becomes equivalent to <italic>k</italic><sub>1</sub>. Hence<disp-formula id="equ14"><label>(12)</label><mml:math id="m14"><mml:mrow><mml:msub><mml:mi>ρ</mml:mi><mml:mrow><mml:mtext>pause</mml:mtext><mml:mo>(</mml:mo><mml:mi mathvariant="italic">sat</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mtext>b</mml:mtext><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mtext>b</mml:mtext><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow></mml:mfrac></mml:mrow></mml:math></disp-formula>where <italic>ρ</italic><sub>pause(sat)</sub> is the pause density at saturating NTP concentration. In order to obtain a true pause density, the apparent <italic>ρ</italic><sub>pause</sub> needs to be corrected to include pauses shorter than 1 s that are missed by our pause detection algorithm. After such a correction (‘Materials and methods’), the total <italic>ρ</italic><sub>pause(sat)</sub> is 0.045 ± 0.012 bp<sup>−1</sup>. Solving <xref ref-type="disp-formula" rid="equ14">Equation 12</xref> yields <italic>k</italic><sub>b1</sub> = 5.3 ± 2.0 s<sup>−1</sup>. This value is approximately five times larger than subsequent backward stepping rates, which are force-biased stepping rates obtained from <xref ref-type="disp-formula" rid="equ9">Equation 7</xref> (<italic>k</italic><sub>bn</sub> = 1.0 ± 0.3 s<sup>−1</sup>, n≥2). The difference between <italic>k</italic><sub>b1</sub> and <italic>k</italic><sub>bn</sub> indicates that the first backtracking transition is easier to make than subsequent backtracking transitions. Using this value of <italic>k</italic><sub>b1</sub>, along with the value of <italic>γ</italic><sub>u</sub> obtained above, we can predict a nucleosomal pause density of 0.035 ± 0.015 bp<sup>−1</sup> for pauses longer than 1 s, which agrees with the experimental measurement (<xref ref-type="table" rid="tbl2">Table 2</xref>).</p><p>We then compared the pausing kinetics between the wild-type and the mutant enzymes. Interestingly, on bare DNA, the mutation only affects the distribution of pauses that are shorter than 2 s (<xref ref-type="fig" rid="fig4">Figure 4A</xref>, p=0.003, Kolmogorov-Smirnov test). In contrast, the distributions of longer pauses are indistinguishable between the mutant and the wild-type Pol II (<xref ref-type="fig" rid="fig4s1">Figure 4—figure supplement 1</xref>, p=0.9). It is possible to rationalize this observation if the mutation selectively influences the kinetics of the first backtracking step (<italic>k</italic><sub>b1</sub> and/or <italic>k</italic><sub>f1</sub>) without affecting subsequent backtracking steps, given that pauses of short durations involve small backtracking excursions and that entering the 1-bp backtracked state is distinct from entering longer backtracked ones (<italic>k</italic><sub>b1</sub> is different from <italic>k</italic><sub>bn</sub>, n≥2). The first backward stepping rate (<italic>k</italic><sub>b1</sub>) only influences the pause density but not the pause duration, while the first forward stepping rate (<italic>k</italic><sub>f1</sub>) does affect the pause duration. Specifically, the increase in short pauses can be explained if the mutation increases <italic>k</italic><sub>f1</sub> and accelerates the return from a pause to active elongation. Indeed, Monte Carlo kinetic simulations show that setting <italic>k</italic><sub>f1</sub> to be larger than 4 s<sup>−1</sup>—2.4-fold higher than the wild-type value (1.7 ± 0.4 s<sup>−1</sup>; <xref ref-type="disp-formula" rid="equ8">Equation 6</xref>)—can reproduce the experimentally observed pause duration distributions for the mutant Pol II on bare DNA (<xref ref-type="fig" rid="fig4">Figure 4A</xref>, blue dashed line) and nucleosomal DNA (<xref ref-type="fig" rid="fig4">Figure 4B</xref>, green dashed line, and <xref ref-type="fig" rid="fig4s2">Figure 4—figure supplement 2</xref>). Moreover, by comparing the experimentally measured and simulated pause densities using different <italic>k</italic><sub>b1</sub> values, we can set a lower bound for the mutant’s <italic>k</italic><sub>b1</sub> to be 2.8 s<sup>−1</sup>.<fig-group><fig id="fig4" position="float"><object-id pub-id-type="doi">10.7554/eLife.00971.014</object-id><label>Figure 4.</label><caption><title>Pause durations on bare DNA and nucleosomal DNA.</title><p>(<bold>A</bold>) Cumulative distributions of the pause durations on bare DNA for the wild-type Pol II (black solid line) and the mutant enzyme (blue solid line). The wild-type curve is fit to the one-dimensional random walk model for backtracked pausing (gray dashed line). The blue dashed line represents the simulated pause duration distribution for the mutant enzyme, using a <italic>k</italic><sub>f1</sub> value of 4 s<sup>−1</sup>. (<bold>B</bold>) Cumulative distributions of the pause durations in the nucleosome region for the wild-type enzyme (red solid line) and the mutant enzyme (green solid line). The wild-type curve is fit to the one-dimensional diffusion model for backtracked pausing, using a <italic>γ</italic><sub>u</sub> value of 0.6 (red dashed line). The green dashed line is the simulated pause duration distribution for nucleosomal DNA transcription by the mutant enzyme, using a <italic>k</italic><sub>f1</sub> value of 4 s<sup>−1</sup>.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.00971.014">http://dx.doi.org/10.7554/eLife.00971.014</ext-link></p></caption><graphic xlink:href="elife00971f004"/></fig><fig id="fig4s1" position="float" specific-use="child-fig"><object-id pub-id-type="doi">10.7554/eLife.00971.015</object-id><label>Figure 4—figure supplement 1.</label><caption><title>Cumulative pause duration distributions of pauses longer than 3 s.</title><p>The curves for the wild-type and the E1103G mutant Pol II are statistically indistinguishable (<italic>P</italic> = 0.9, Kolmogorov-Smirnov test).</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.00971.015">http://dx.doi.org/10.7554/eLife.00971.015</ext-link></p></caption><graphic xlink:href="elife00971fs007"/></fig><fig id="fig4s2" position="float" specific-use="child-fig"><object-id pub-id-type="doi">10.7554/eLife.00971.016</object-id><label>Figure 4—figure supplement 2.</label><caption><title>Comparison between the experimentally obtained distribution of pause durations and the simulated distribution for the nucleosomal DNA transcription by the mutant Pol II.</title><p>The square of the difference between the experimental and simulated data is plotted as a function of <italic>k</italic><sub>f1</sub> used in the simulation.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.00971.016">http://dx.doi.org/10.7554/eLife.00971.016</ext-link></p></caption><graphic xlink:href="elife00971fs008"/></fig></fig-group></p><p>Taken together, we have shown that the rate of entering the 1-bp backtracked state is higher than those of entering further backtracked states, and that the E1103G mutation modulates the transition kinetics between the 1-bp backtracked state and the pre-translocated state. Until now, <italic>k</italic><sub>f1</sub> and <italic>k</italic><sub>b1</sub> have been assumed to be identical with the other stepping rates during backtracking (<italic>k</italic><sub>fn</sub> and <italic>k</italic><sub>bn</sub>, n≥2) (<xref ref-type="bibr" rid="bib19">Galburt et al., 2007</xref>; <xref ref-type="bibr" rid="bib25">Hodges et al., 2009</xref>; <xref ref-type="bibr" rid="bib6">Bintu et al., 2012</xref>). Our data here suggest that the first backtracking step should be treated differently, consistent with published structural data (<xref ref-type="bibr" rid="bib62">Wang et al., 2009</xref>; <xref ref-type="bibr" rid="bib11">Cheung and Cramer, 2011</xref>) (see ‘Discussion’).</p></sec><sec id="s2-6"><title>Determine the rate of reverse translocation</title><p>We have determined the rates of forward translocation (<italic>k</italic><sub>1</sub>) and catalysis (<italic>k</italic><sub>3</sub>) in the nucleotide addition cycle and shown that they are comparable. What remains unknown is the reverse translocation rate <italic>k</italic><sub>−1</sub>, which may also affect the elongation velocity under sub-saturating NTP conditions (<xref ref-type="disp-formula" rid="equ6">Equation 4</xref>). To determine <italic>k</italic><sub>−1</sub>, we examined the pause densities measured at various NTP concentrations. <xref ref-type="disp-formula" rid="equ13">Equation 11</xref> can be re-written as:<disp-formula id="equ15"><label>(13)</label><mml:math id="m15"><mml:mrow><mml:msub><mml:mi>ρ</mml:mi><mml:mtext>pause</mml:mtext></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mtext>b</mml:mtext><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mtext>b</mml:mtext><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:mfrac><mml:mrow><mml:mo>[</mml:mo><mml:mi mathvariant="italic">NTP</mml:mi><mml:mo>]</mml:mo></mml:mrow><mml:mrow><mml:mfrac><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:mfrac><mml:mo>+</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:mi mathvariant="italic">NTP</mml:mi><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:mfrac><mml:mo>⋅</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mn>1</mml:mn></mml:msub></mml:mrow></mml:mfrac></mml:mrow></mml:math></disp-formula>where <italic>K</italic> = (<italic>k</italic><sub>−2</sub>+<italic>k</italic><sub>3</sub>)/<italic>k</italic><sub>2</sub>. The total <italic>ρ</italic><sub>pause</sub> as a function of [NTP] fits well to <xref ref-type="disp-formula" rid="equ15">Equation 13</xref> (<xref ref-type="fig" rid="fig5">Figure 5A,B</xref>). Using the values of <italic>k</italic><sub>1</sub>, <italic>k</italic><sub>3</sub>, and <italic>k</italic><sub>b1</sub> determined above, we obtained <italic>k</italic><sub>−1</sub><italic>K</italic> equal to (4.7 ± 0.5) × 10<sup>3</sup> µM·s<sup>−1</sup> and (2.5 ± 0.4) × 10<sup>4</sup> µM·s<sup>−1</sup> for the wild-type and the mutant enzymes, respectively.<fig-group><fig id="fig5" position="float"><object-id pub-id-type="doi">10.7554/eLife.00971.017</object-id><label>Figure 5.</label><caption><title>Relationship between pause density and NTP concentration.</title><p>(<bold>A</bold>) The total pause density for the wild-type Pol II (black circles) is plotted against the NTP concentration. The gray dashed line is the fit to <xref ref-type="disp-formula" rid="equ15">Equation 13</xref> (R<sup>2</sup> = 0.93). (<bold>B</bold>) <italic>ρ</italic><sub>pause</sub>–[NTP] relationship (blue squares) for the mutant Pol II is fit to <xref ref-type="disp-formula" rid="equ15">Equation 13</xref> (blue dashed line, R<sup>2</sup> = 0.89).</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.00971.017">http://dx.doi.org/10.7554/eLife.00971.017</ext-link></p></caption><graphic xlink:href="elife00971f005"/></fig><fig id="fig5s1" position="float" specific-use="child-fig"><object-id pub-id-type="doi">10.7554/eLife.00971.018</object-id><label>Figure 5—figure supplement 1.</label><caption><title>Constraining the value of <italic>K</italic> for the mutant Pol II.</title><p>The apparent pause densities obtained experimentally for the E1103G Pol II are plotted against the NTP concentration (blue squares). Simulated pause densities using a <italic>K</italic> value of 1, 20, 40, 100, and 200 μM are shown in blue, purple, red, orange, and green dashed lines, respectively. The simulated curve starts to deviate from the experimental data once <italic>K</italic> exceeds 100 μM.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.00971.018">http://dx.doi.org/10.7554/eLife.00971.018</ext-link></p></caption><graphic xlink:href="elife00971fs009"/></fig></fig-group></p><p>We then revisited the relationship between the pause-free velocity and [NTP] (<xref ref-type="fig" rid="fig2">Figure 2D</xref>), which follows Michaelis–Menten kinetics. According to <xref ref-type="disp-formula" rid="equ7">Equation 5</xref>, the Michaelis constant <italic>K</italic><sub>M</sub> is expressed as:<disp-formula id="equ16"><label>(14)</label><mml:math id="m16"><mml:mrow><mml:msub><mml:mi>K</mml:mi><mml:mtext>M</mml:mtext></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:mfrac><mml:mo>⋅</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn>2</mml:mn></mml:msub></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mo>+</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:mfrac><mml:mo>⋅</mml:mo><mml:mi>K</mml:mi></mml:mrow></mml:math></disp-formula></p><p>Plugging the values of <italic>K</italic><sub>M</sub>, <italic>k</italic><sub>1</sub>, <italic>k</italic><sub>3</sub>, and <italic>k</italic><sub>−1</sub><italic>K</italic> into <xref ref-type="disp-formula" rid="equ16">Equation 14</xref> yields the values of <italic>K</italic> and <italic>k</italic><sub>−1</sub> for the wild-type Pol II: <italic>K</italic> = 9.2 µM and <italic>k</italic><sub>−1</sub> = 510 s<sup>−1</sup>. We could further calculate the translocation equilibrium constant, <italic>K</italic><sub>δ</sub> = [pre-translocated]/[post-translocated] = <italic>k</italic><sub>−1</sub>/<italic>k</italic><sub>1</sub> = 4.6. This result indicates that the enzyme favors the pre-translocated state to the post-translocated one, in agreement with most previous reports (<xref ref-type="bibr" rid="bib5">Bar-Nahum et al., 2005</xref>; <xref ref-type="bibr" rid="bib3">Bai et al., 2007</xref>; <xref ref-type="bibr" rid="bib34">Kireeva et al., 2008</xref>; <xref ref-type="bibr" rid="bib44">Maoileidigh et al., 2011</xref>). For the mutant enzyme, we could set an upper bound of <italic>K</italic> to be 100 µM and a lower bound of <italic>k</italic><sub>−1</sub> to be 210 s<sup>−1</sup> (<xref ref-type="fig" rid="fig5s1">Figure 5—figure supplement 1</xref>). Assuming that the mutant shares a similar <italic>K</italic> value with the wild-type, we calculated <italic>k</italic><sub>−1</sub> to be ∼2700 s<sup>−1</sup> and <italic>K</italic><sub>δ</sub> to be ∼54 for the mutant Pol II (see ‘Materials and methods’ for a discussion of this assumption).</p></sec><sec id="s2-7"><title>Force–velocity relationship</title><p>A central piece of evidence previously used to favor a branched kinetic scheme (<xref ref-type="fig" rid="fig1s1">Figure 1—figure supplement 1</xref>) over a simpler linear scheme (<xref ref-type="fig" rid="fig1">Figure 1</xref>) for the nucleotide addition cycle is the relationship between the pause-free velocity (<italic>v</italic>) and the applied force (<italic>F</italic>) (<xref ref-type="bibr" rid="bib1">Abbondanzieri et al., 2005</xref>; <xref ref-type="bibr" rid="bib39">Larson et al., 2012</xref>). However, in those studies, translocation was assumed to be in rapid equilibrium relative to catalysis. Having explicitly determined the translocation rates (<italic>k</italic><sub>±1</sub>) and found that the forward translocation rate (<italic>k</italic><sub>1</sub>) is comparable to the catalysis rate (<italic>k</italic><sub>3</sub>), we went on to examine whether a linear kinetic scheme (<xref ref-type="fig" rid="fig1">Figure 1</xref>) is sufficient to explain the <italic>F</italic>–<italic>v</italic> relationship, which for such scheme can be expressed as:<disp-formula id="equ17"><label>(15)</label><mml:math id="m17"><mml:mrow><mml:mi>v</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>F</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>F</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>⋅</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>F</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:mfrac><mml:mo>⋅</mml:mo><mml:mfrac><mml:mrow><mml:mo>[</mml:mo><mml:mi mathvariant="italic">NTP</mml:mi><mml:mo>]</mml:mo></mml:mrow><mml:mrow><mml:mfrac><mml:mrow><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>F</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>F</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow><mml:mo>⋅</mml:mo><mml:mi>K</mml:mi></mml:mrow><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>F</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:mfrac><mml:mo>+</mml:mo><mml:mrow><mml:mo>[</mml:mo><mml:mi mathvariant="italic">NTP</mml:mi><mml:mo>]</mml:mo></mml:mrow></mml:mrow></mml:mfrac><mml:mo>⋅</mml:mo><mml:mi>d</mml:mi></mml:mrow></mml:math></disp-formula></p><p>We assume that only the translocation transitions in the nucleotide addition cycle are force-sensitive and that the translocation rates depend on force according to the Boltzmann-type equation: <inline-formula><mml:math id="inf8"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>F</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mn>0</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:mo>⋅</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mi>F</mml:mi><mml:mi>δ</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mi>B</mml:mi></mml:msub><mml:mi>T</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, and <inline-formula><mml:math id="inf9"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>F</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mn>0</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:mo>⋅</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mo>−</mml:mo><mml:mi>F</mml:mi><mml:mo>⋅</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mi>δ</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>/</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mi>B</mml:mi></mml:msub><mml:mi>T</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>, where <italic>δ</italic> is the distance to the transition state for forward translocation, the only unknown variable left in <xref ref-type="disp-formula" rid="equ17">Equation 15</xref>. We measured the pause-free velocity at different applied forces for both wild-type and mutant enzymes and obtained values in good agreement with previously published single-molecule data (<xref ref-type="bibr" rid="bib39">Larson et al., 2012</xref>) (<xref ref-type="fig" rid="fig6">Figure 6A,B</xref>). The velocity of the wild-type enzyme shows a weak but detectable dependence on force, while the velocity of the mutant displays a much stronger force dependence. The <italic>F</italic>–<italic>v</italic> plots can be fit well to <xref ref-type="disp-formula" rid="equ17">Equation 15</xref> with <italic>δ</italic> of 0.46 ± 0.09 bp for the wild-type (<xref ref-type="fig" rid="fig6">Figure 6A</xref>) and 0.24 ± 0.05 bp for the mutant (<xref ref-type="fig" rid="fig6">Figure 6B</xref>). Therefore, it is indeed possible to explain the observed force–velocity relationship of transcription elongation with a classic, non-branched Brownian ratchet mechanism, in which NTP binding occurs after translocation.<fig id="fig6" position="float"><object-id pub-id-type="doi">10.7554/eLife.00971.019</object-id><label>Figure 6.</label><caption><title>Relationship between transcription velocity and applied force.</title><p>(<bold>A</bold>) The pause-free velocity of the wild-type Pol II is plotted against the applied force. Experimental data in the present study are shown in solid squares (error bars indicate SEM). Open triangles represent data from a previously published single-molecule study (<xref ref-type="bibr" rid="bib39">Larson et al., 2012</xref>). The combined data are fit to the force-velocity relationship predicted by a linear Brownian ratchet model (dashed line), yielding a characteristic distance to the transition state δ = 0.46 ± 0.09 bp (error is SEM, R<sup>2</sup> = 0.88). Positive and negative force values indicate assisting and opposing forces, respectively. (<bold>B</bold>) The force-velocity relationship for the mutant Pol II. δ = 0.24 ± 0.05 bp for the mutant (R<sup>2</sup> = 0.85).</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.00971.019">http://dx.doi.org/10.7554/eLife.00971.019</ext-link></p></caption><graphic xlink:href="elife00971f006"/></fig></p></sec></sec><sec id="s3" sec-type="discussion"><title>Discussion</title><sec id="s3-1"><title>Rate-limiting steps in the Brownian ratchet mechanism</title><p>RNAP transcribes DNA through a multi-step kinetic pathway. The rate-limiting nature of the various steps in the nucleotide addition cycle has so far remained largely conjectural. Almost all the existing kinetic studies of transcription elongation relied on the major assumption that translocation and NTP binding follow rapid equilibrium kinetics. As a result, the catalytic step occurring after NTP binding has been assigned to be rate-limiting of the overall elongation reaction.</p><p>The linear Brownian ratchet mechanism that assumes fast translocation equilibrium predicts that, as the NTP concentration increases, the force-sensitivity of the elongation velocity decreases and eventually vanishes, because the enzyme spends less time in the load-sensitive translocation steps. However, the <italic>F</italic>–<italic>v</italic> relationships of the enzyme obtained from optical tweezers studies have shown significant dependence of elongation velocity on external force even at saturating NTP concentrations (<xref ref-type="bibr" rid="bib1">Abbondanzieri et al., 2005</xref>; <xref ref-type="bibr" rid="bib3">Bai et al., 2007</xref>; <xref ref-type="bibr" rid="bib39">Larson et al., 2012</xref>), in contradiction to the above prediction. To account for this discrepancy, a modified, branched ratchet model was proposed in which the NTP must also bind to a secondary site on the polymerase in the pre-translocated configuration. Although the existence of such additional binding site may be rationalized by the downstream allosteric site (<xref ref-type="bibr" rid="bib26">Holmes and Erie, 2003</xref>; <xref ref-type="bibr" rid="bib20">Gong et al., 2005</xref>), the ‘E’ site or pre-insertion site (<xref ref-type="bibr" rid="bib65">Westover et al., 2004</xref>; <xref ref-type="bibr" rid="bib55">Temiakov et al., 2005</xref>), or the tilted hybrid structure (<xref ref-type="bibr" rid="bib12">Cheung et al., 2011</xref>), whether it constitutes a significant pathway in the elongation reaction and how it is related to the primary nucleotide binding pathway remain obscure. More importantly, the branched model neglects the possibility that the translocation steps may not be as fast as assumed.</p><p>In this study, we tested this possibility of slow translocation by placing a nucleosome in the path of the transcribing polymerase and directly determining the rates of forward and reverse translocation. Our analyses show that the forward translocation rate is in fact within the same order of magnitude as the catalysis rate. For the wild-type Pol II, <italic>k</italic><sub>1</sub> is only 2.5 times higher than <italic>k</italic><sub>3</sub> (<xref ref-type="fig" rid="fig7">Figure 7A</xref>; <xref ref-type="table" rid="tbl3">Table 3</xref>). For the E1103G mutant, <italic>k</italic><sub>1</sub> even becomes the slowest step in the nucleotide addition cycle (<xref ref-type="table" rid="tbl3">Table 3</xref>). Hence, the translocation step is one of the rate-limiting transitions during transcription elongation. Translocation and catalysis together control the overall elongation velocity. These findings naturally explain the observed <italic>F</italic>–<italic>v</italic> relationship: because the enzyme always spends a considerable amount of time in the force-sensitive pre-translocated state even at high [NTP], we should always expect a force-dependence of the velocity. Moreover, a lower <italic>k</italic><sub>1</sub> renders the velocity more sensitive to force, consistent with the experimental observation that the mutant Pol II shows a steeper <italic>F</italic>–<italic>v</italic> curve than the wild-type (<xref ref-type="fig" rid="fig6">Figure 6A,B</xref>). Therefore, our results demonstrate that a linear ratchet model can explain the transcriptional kinetics of Pol II and that it is not necessary to invoke a conceptually more complicated branched model, as long as the constraint of fast translocation equilibrium is relieved. Note that although our data argue against rapid oscillation of the ratchet, they still support the notion that the enzyme is able to spontaneously diffuse along the DNA between the pre- and post-translocated states, as suggested by the Brownian ratchet mechanism.<fig-group><fig id="fig7" position="float"><object-id pub-id-type="doi">10.7554/eLife.00971.020</object-id><label>Figure 7.</label><caption><title>A quantitative kinetic model for transcription elongation.</title><p>(<bold>A</bold>) A comprehensive kinetic characterization of the nucleotide addition phase (highlighted in green) and the pausing phase (highlighted in blue) for transcription by the wild-type Pol II. Inside the yellow box are the transitions affected by the nucleosomal barrier. (<bold>B</bold>) The schematic translocation free energy landscape at a given RNA length for the wild-type Pol II (solid black) and the E1103G Pol II (dashed cyan). The on-pathway elongation is highlighted in green and the off-pathway pausing is highlighted in blue.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.00971.020">http://dx.doi.org/10.7554/eLife.00971.020</ext-link></p></caption><graphic xlink:href="elife00971f007"/></fig><fig id="fig7s1" position="float" specific-use="child-fig"><object-id pub-id-type="doi">10.7554/eLife.00971.021</object-id><label>Figure 7—figure supplement 1.</label><caption><title>The schematic three-dimensional free energy landscape for transcription elongation by the wild-type Pol II at 1 mM NTP and zero force.</title><p>The ribbons represent the minimal energy paths of the nucleotide addition cycle (green) and the off-pathway processes (blue). The nomenclature for the TECs (e.g., n,1) is the same as that used in <xref ref-type="fig" rid="fig7">Figure 7</xref>. Chemical and mechanical transitions are shown in two orthogonal axes. Mechanical perturbations, such as force, affect the mechanical transitions of the enzyme by tilting the landscape around the chemical axis to a first approximation, while chemical perturbations, such as [NTP] and [PP<sub>i</sub>], rotate the landscape around the mechanical axis, again to a first approximation. Two-dimensional projections on the grids highlight the relative free energy of each state.</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.00971.021">http://dx.doi.org/10.7554/eLife.00971.021</ext-link></p></caption><graphic xlink:href="elife00971fs010"/></fig></fig-group><table-wrap id="tbl3" position="float"><object-id pub-id-type="doi">10.7554/eLife.00971.022</object-id><label>Table 3.</label><caption><p>Summary of kinetic parameters measured in this study</p><p><bold>DOI:</bold> <ext-link ext-link-type="doi" xlink:href="10.7554/eLife.00971.022">http://dx.doi.org/10.7554/eLife.00971.022</ext-link></p></caption><table frame="hsides" rules="groups"><thead><tr><th>Parameters</th><th>Wild-type Pol II</th><th>E1103G Pol II</th></tr></thead><tbody><tr><td><italic>k</italic><sub>1</sub> (s<sup>−1</sup>)</td><td>88 ± 23</td><td><italic>44 ± 4</italic></td></tr><tr><td><italic>k</italic><sub>−1</sub> (s<sup>−1</sup>)</td><td>∼680</td><td><italic>∼4.1 × 10</italic><sup><italic>3</italic></sup></td></tr><tr><td><italic>K</italic><sub><italic>δ</italic></sub> <italic>= k</italic><sub>−1</sub><italic>/k</italic><sub>1</sub></td><td>∼7.7</td><td><italic>∼92</italic></td></tr><tr><td><italic>K</italic> = (<italic>k</italic><sub>−2</sub>+<italic>k</italic><sub>3</sub>)/<italic>k</italic><sub>2</sub> (μM)</td><td>∼9.2</td><td>∼9.2</td></tr><tr><td><italic>k</italic><sub>3</sub> (s<sup>−1</sup>)</td><td>35 ± 3</td><td><italic>195 ± 65</italic></td></tr><tr><td><italic>k</italic><sub>b1</sub> (s<sup>−1</sup>)</td><td>6.9 ± 2.6</td><td><italic>∼3.7*</italic></td></tr><tr><td><italic>k</italic><sub>f1</sub> (s<sup>−1</sup>)</td><td>1.3 ± 0.3</td><td><italic>∼3.1*</italic></td></tr><tr><td><italic>k</italic><sub>bn</sub> (s<sup>−1</sup>), n ≥ 2</td><td>1.3 ± 0.3</td><td>1.3 ± 0.3</td></tr><tr><td><italic>k</italic><sub>fn</sub> (s<sup>−1</sup>), n ≥ 2</td><td>1.3 ± 0.3</td><td>1.3 ± 0.3</td></tr></tbody></table><table-wrap-foot><fn><p>The values reported in the text were measured at 6.5 pN of applied assisting force and are normalized to zero force here. The italicized numbers indicate the parameters that are altered by the E1103G mutation. The asterisks indicate lower bounds of the corresponding values.</p></fn></table-wrap-foot></table-wrap></p><p>We extracted the values of <italic>k</italic><sub>1</sub> and <italic>k</italic><sub>3</sub> by comparing the maximum pause-free velocities on bare DNA and nucleosomal DNA (<xref ref-type="disp-formula" rid="equ11">Equations 9</xref> and <xref ref-type="disp-formula" rid="equ12">10</xref>). In principle, <italic>k</italic><sub>1</sub> and <italic>k</italic><sub>3</sub> can also be determined by examining <italic>V</italic><sub>max</sub> as a function of applied force:<disp-formula id="equ18"><label>(16)</label><mml:math id="m18"><mml:mrow><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mi>max</mml:mi></mml:mrow></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>F</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>F</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>⋅</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>F</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>+</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mn>3</mml:mn></mml:msub></mml:mrow></mml:mfrac><mml:mo>⋅</mml:mo><mml:mi>d</mml:mi></mml:mrow></mml:math></disp-formula>where <inline-formula><mml:math id="inf10"><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>F</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mo>=</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mn>1</mml:mn></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mn>0</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:mo>⋅</mml:mo><mml:msup><mml:mi>e</mml:mi><mml:mrow><mml:mi>F</mml:mi><mml:mi>δ</mml:mi><mml:mo>/</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mi>B</mml:mi></mml:msub><mml:mi>T</mml:mi></mml:mrow></mml:msup></mml:mrow></mml:math></inline-formula>. Using our data and the previously published data (<xref ref-type="bibr" rid="bib39">Larson et al., 2012</xref>) collected at saturating [NTP] (1 mM) and various forces (<xref ref-type="fig" rid="fig6">Figure 6</xref>), we fit the <italic>V</italic><sub>max</sub>–<italic>F</italic> dependence to <xref ref-type="disp-formula" rid="equ18">Equation 16</xref> and obtained the values of <italic>k</italic><sub>1</sub> = 87 ± 61 s<sup>−1</sup>, <italic>k</italic><sub>3</sub> = 33 ± 8 s<sup>−1</sup>, and <italic>δ</italic> = 0.64 ± 0.58 bp for the wild-type Pol II, and <italic>k</italic><sub>1</sub> = 65 ± 37 s<sup>−1</sup>, <italic>k</italic><sub>3</sub> = 62 ± 32 s<sup>−1</sup>, and <italic>δ</italic> = 0.64 ± 0.50 bp for the mutant Pol II. Thus, the same qualitative conclusion that both translocation and catalysis are rate-limiting for the elongation reaction can be drawn from this alternative approach. Compared to the approach of using the nucleosomal barrier as a tool to determine <italic>k</italic><sub>1</sub> and <italic>k</italic><sub>3</sub>, fitting the <italic>V</italic><sub>max</sub>–<italic>F</italic> relationship involves one additional free parameter (<italic>δ</italic>) and the values are less constrained (larger errors). In the future, it is worthwhile to use either of these two approaches or both to test whether prokaryotic transcription also employs a linear ratchet mechanism.</p></sec><sec id="s3-2"><title>The energy landscape for transcription elongation</title><p>With the same transcript length, RNAP is able to move back and forth on the DNA template, forming different TEC configurations (<xref ref-type="fig" rid="fig7">Figure 7A,B</xref>). Each translocation state corresponds to a local energy minimum (<xref ref-type="bibr" rid="bib68">Yager and von Hippel, 1991</xref>; <xref ref-type="bibr" rid="bib4">Bai et al., 2004</xref>; <xref ref-type="bibr" rid="bib53">Tadigotla et al., 2006</xref>). Transitions between the pre- and post-translocated states, together with NTP binding and catalysis, constitute the active elongation pathway (<xref ref-type="fig" rid="fig7s1">Figure 7—figure supplement 1</xref>, green). The enzyme can also enter the pausing pathway by transiting from the pre-translocated state to the backtracked states (<xref ref-type="fig" rid="fig7s1">Figure 7—figure supplement 1</xref>, blue). The hyper-translocated states, in which the enzyme undergoes further forward translocation beyond 1 bp, are energetically unfavorable. The rate constants extracted from our single-molecule experiments translate into a free energy landscape for Pol II’s mechanical translocations and chemical transitions (<xref ref-type="fig" rid="fig7">Figure 7B</xref>, <xref ref-type="fig" rid="fig7s1">Figure 7—figure supplement 1</xref>; ‘Materials and methods’), which reveals many detailed features of the kinetics of Pol II transcription.</p><p>First, the staircase shape formed by the energy minima of post-translocated, pre-translocated, and 1-bp backtracked states shows that the off-pathway backtracked states are thermodynamically more stable than the on-pathway states (<xref ref-type="fig" rid="fig7">Figure 7B</xref>). This feature confers the enzyme its propensity to enter the pausing pathway, which is the central mechanism for various types of transcriptional control, such as arrest, proofreading, co-transcriptional RNA folding, and recruitment of regulators.</p><p>Second, the energy barrier from the pre-translocated to the 1-bp backtracked state is 2.5 <italic>k</italic><sub>B</sub>T higher than the barrier from the pre-translocated to the post-translocated state, causing <italic>k</italic><sub>1</sub> to be more than 10 times faster than <italic>k</italic><sub>b1</sub>. Thus, at the beginning of each nucleotide addition cycle, the pre-translocated TEC favors the catalysis-competent post-translocated state kinetically over the 1-bp backtracked state, even though it is thermodynamically more favorable to move in the opposite direction. This property ensures that pausing only occurs sporadically so that the transcript can be synthesized within a reasonable amount of time. In addition, the barriers between neighboring backtracked states are also relatively high, preventing the enzyme from backtracking too far, which could lead to transcriptional arrest.</p><p>Third, the first backtracking step appears to be unique from further backtracking steps in two aspects. Kinetically, entering the 1-bp backtracked state is easier than entering subsequent backtracked states, as reflected by the difference between <italic>k</italic><sub>b1</sub> and <italic>k</italic><sub>bn</sub> (n≥2). Such a difference is supported by structural data: the structure of an arrested Pol II complex suggests that backtracking beyond 1 bp is disfavored as it is sterically hindered by a ‘gating’ tyrosine (Rpb2-<italic>Y769</italic>) (<xref ref-type="bibr" rid="bib11">Cheung and Cramer, 2011</xref>). Thermodynamically, transiting from the pre-translocated state to the 1-bp backtracked state is favorable, while backtracking for more steps yields no additional energetic benefit. This result can also find structural support: the first backtracked nucleotide is stabilized by a binding pocket formed by several Pol II residues, whereas the second or third backtracked nucleotide makes no additional contact to the enzyme (<xref ref-type="bibr" rid="bib62">Wang et al., 2009</xref>).</p><p>Thus, our model depicts an enzyme with a delicate balance between active elongation and inactive pausing (<xref ref-type="bibr" rid="bib60">von Hippel and Pasman, 2002</xref>). This model can serve as a framework to study the effects of DNA sequence and nascent RNA structure on transcriptional dynamics (<xref ref-type="bibr" rid="bib4">Bai et al., 2004</xref>; <xref ref-type="bibr" rid="bib53">Tadigotla et al., 2006</xref>; <xref ref-type="bibr" rid="bib70">Zamft et al., 2012</xref>). Moreover, this model may improve our understanding of the control of transcription fidelity. The 1-bp backtracked state is closely associated with the proofreading process of Pol II, as the enzyme in this location preferentially cleaves the 3′ dinucleotide of the RNA containing the mismatched base, empting the active site for NTP binding (<xref ref-type="bibr" rid="bib62">Wang et al., 2009</xref>). It is possible that nucleotide misincorporation slows down forward translocation, thereby promoting the entry to the pausing pathway and the removal of the dinucleotide.</p><p>It is worth noting that we cannot definitively rule out the alternative scenario in which the first unique pausing state corresponds to a non-backtracked intermediate. Nonetheless, no evidence has been found for the universal occurrence of such an intermediate in Pol II transcription. The interpretation that most pauses in Pol II transcription are caused by enzyme backtracking is more parsimonious, especially given the corroborating structural data mentioned above.</p></sec><sec id="s3-3"><title>Roles of the TL element in transcriptional regulation</title><p>The kinetic characterization of the E1103G mutant Pol II reveals that this TL mutation results in many modifications to the enzyme dynamics (<xref ref-type="table" rid="tbl3">Table 3</xref>). Between the pre-translocated state and the post-translocated state, the mutant is significantly more biased toward the former than the wild type (<xref ref-type="fig" rid="fig7">Figure 7B</xref>). This property, together with its lower forward translocation rate, renders the mutant’s elongation velocity more sensitive to perturbations of its forward translocation, such as an externally applied force (<xref ref-type="fig" rid="fig6">Figure 6B</xref>) or the presence of a nucleosomal barrier (<xref ref-type="fig" rid="fig3">Figure 3B</xref>). It has been shown that the inter-conversion between pre- and post-translocated states involves the transitions of the TL between an open conformation and a wedged conformation (<xref ref-type="bibr" rid="bib9">Brueckner and Cramer, 2008</xref>). It is plausible that the mutation modulates the enzyme’s translocation kinetics by altering the rates of transition between these two conformations.</p><p>Furthermore, our analyses lead to the conclusion that the faster overall elongation velocity of the mutant is due to its much greater catalysis rate despite a slower translocation step. The increase of the catalysis rate is most likely due to a faster NTP sequestration step induced by the closure of the TL (<xref ref-type="bibr" rid="bib34">Kireeva et al., 2008</xref>). The lack of hydrogen bonding between T1095 and the mutated E1103 residue may destabilize the open state of the TL and speed up its closure (<xref ref-type="bibr" rid="bib61">Walmacq et al., 2012</xref>).</p><p>The E1103G mutation also affects the pausing kinetics. Specifically, a decrease in the activation energy required to return from the first backtracked state to the pre-translocated state accelerates the recovery from a pause (<xref ref-type="fig" rid="fig7">Figure 7B</xref>). Consequently, the mutant populates the 1-bp backtracked state less than the wild-type. This property might affect the overall fidelity of transcription. It has been previously shown that E1103G mutation strongly promotes incorporation of non-cognate NMP and mismatch extension (<xref ref-type="bibr" rid="bib29">Kaplan et al., 2008</xref>; <xref ref-type="bibr" rid="bib34">Kireeva et al., 2008</xref>). The destabilization of the 1-bp backtracked state relative to the pre-translocated state in the E1103G mutant, established in this work, is consistent with its efficient mismatch extension and suggests that this mutation might also confer a defect in proofreading activity.</p><p>Together, our results suggest that the dynamics of TL are involved in multiple phases of transcription elongation, including translocation, catalysis, and pausing. In vivo, various transcription factors and small molecules can directly manipulate the TL dynamics and regulate transcription elongation. For example, transcription factor IIS (TFIIS) stimulates the endonuclease activity of Pol II by replacing the TL with its zinc finger domain, and thus, rescues transcription elongation by creating a new 3′-end of the transcript at Pol II’s active site (<xref ref-type="bibr" rid="bib30">Kettenberger et al., 2003</xref>). In fact, the viability of yeast cells expressing only the E1103G mutant Pol II is strictly dependent on TFIIS (<xref ref-type="bibr" rid="bib42">Malagon et al., 2006</xref>). It is interesting to investigate how these trans-acting factors modify the rate-limiting mechanism and detailed kinetics of the elongation reaction. Finally, the elementary rate constants extracted from our analyses should provide a reference frame for future computational studies aiming to fully describe the molecular trajectory of a transcribing polymerase.</p></sec></sec><sec id="s4" sec-type="materials|methods"><title>Materials and methods</title><sec id="s4-1"><title>Proteins and DNA preparation</title><p>Biotinylated wild-type and E1103G <italic>S. cerevisae</italic> Pol II (unphosphorylated C-terminal domain) were purified as previously described (<xref ref-type="bibr" rid="bib32">Kireeva et al., 2005</xref>). The 3-kb DNA handle was prepared by PCR from Lambda DNA (NEB, Ipswich, MA) using a digoxigenin-labeled primer. The 574-bp DNA template was prepared by PCR from a modified pUC19 plasmid (<xref ref-type="bibr" rid="bib71">Zhang et al., 2006</xref>) containing the 601 nucleosome positioning sequence (NPS) (<xref ref-type="bibr" rid="bib41">Lowary and Widom, 1998</xref>). Each histone protein was recombinantly expressed and purified from <italic>E. coli</italic>, reconstituted to octamers (<xref ref-type="bibr" rid="bib66">Wittmeyer et al., 2004</xref>), and loaded on the NPS-containing DNA using salt gradient dialysis (<xref ref-type="bibr" rid="bib56">Thåström et al., 2004</xref>).</p></sec><sec id="s4-2"><title>Assembly of transcription elongation complexes</title><p>The transcription elongation complexes (TECs) were assembled by annealing a 9-nt RNA primer (IDT, Coralville, IA) to a 93-nt template DNA, incubating the hybrid with a biotinylated Pol II, and subsequently annealing a 96-nt complementary DNA using previously published sequences and procedures (<xref ref-type="bibr" rid="bib25">Hodges et al., 2009</xref>). The TEC was walked to a stall site by addition of ATP, CTP and GTP. In the assisting force geometry, the downstream end of the stalled TEC was ligated to the 574-bp DNA containing the 601 NPS (with or without a preloaded nucleosome), while its upstream end was ligated to the 3-kb DNA handle. In the opposing force geometry, the downstream end of the TEC was ligated to a 4-kb DNA amplified from Lambda DNA (<xref ref-type="bibr" rid="bib70">Zamft et al., 2012</xref>). The complexes were incubated with 2.1-μm streptavidin-coated beads (Spherotech, Lake Forest, IL), and DNA tethers were formed in a dual-trap optical tweezers instrument by attaching the digoxigenin-labeled DNA handle to a 2.1-μm anti-digoxigenin IgG-coated bead. In the assisting force geometry, Pol II and its upstream DNA were under tension, while no external force was applied to the downstream nucleosome (<xref ref-type="fig" rid="fig2">Figure 2A</xref>). The tension in the upstream DNA prevented intra-nucleosomal loop transfer and thus ensured that the nucleosome was always ahead of the transcribing polymerase. Transcription was restarted in optical tweezers by addition of NTPs (Thermo Fisher Scientific, Waltham, MA). The transcription buffer contains 20 mM Tris-HCl (pH 7.9), 5 mM MgCl<sub>2</sub>, 10 μM ZnCl<sub>2</sub>, 1 mM β-mercaptoethanol, 1 μM pyrophosphate, 300 mM KCl, and NTPs ranging from 35 μM to 2 mM each.</p></sec><sec id="s4-3"><title>Data collection and analysis</title><p>Position data were recorded at 2 kHz, averaged and decimated to 50 Hz, and filtered using a second-order Savitzky-Golay filter with a time constant of 1 s. The contour length of the DNA was calculated from the extension and force using the worm-like-chain formula of DNA elasticity (<xref ref-type="bibr" rid="bib10">Bustamante et al., 1994</xref>) with a persistent length of 30 nm. This value of persistent length was obtained from pulling 3-kb DNA in our transcription buffer (data not shown). To alleviate calibration error and improve positional accuracy, single-molecule transcription traces that passed 85% of the template were aligned using both the stall site and the expected run-off length (<xref ref-type="bibr" rid="bib6">Bintu et al., 2012</xref>). Shorter traces were also proportionally extended based on the average error from the run-off traces. To identify pauses, we computed the dwell time of Pol II at each nucleotide position. Pauses were identified from dwell times that were longer the average dwell time by at least a factor of two. Due to the limited spatial resolution, we joined pauses that were separated by 3 bp or fewer into a single continuous pause. Pauses longer than 1 s are most likely caused by backtracking (<xref ref-type="bibr" rid="bib44">Maoileidigh et al., 2011</xref>) and were counted. Pause-free velocities were calculated from time derivatives of the filtered position data, with a threshold of 2 nt/s to remove pauses. All curve fittings were performed by non-linear regression of the means weighted by the inverse of the variance.</p></sec><sec id="s4-4"><title>Monte Carlo simulation</title><p>From an elongation-competent state, Pol II can either elongate by 1 nt with the net forward translocation rate <inline-formula><mml:math id="inf11"><mml:mrow><mml:msubsup><mml:mi>k</mml:mi><mml:mn>1</mml:mn><mml:mtext>net</mml:mtext></mml:msubsup></mml:mrow></mml:math></inline-formula> and incorporate an NMP to the RNA transcript, or enter a backtracked pause by 1 nt. During a pause, Pol II diffuses forward and backward with force-biased rate constants <italic>k</italic><sub>f</sub> and <italic>k</italic><sub>b</sub>, respectively. For each condition, we simulated 100 trajectories and extracted the pause durations and densities to compare with the experimentally measured values.</p></sec><sec id="s4-5"><title>Estimation of the timescale of local nucleosomal DNA fluctuations</title><p>Fluorescence correlation spectroscopy and fluorescence resonance energy transfer experiments showed that the first 20–30 bp of DNA at the nucleosome ends spontaneously unwrap and rewrap on the histone surface every 10–250 ms (<xref ref-type="bibr" rid="bib40">Li et al., 2005</xref>; <xref ref-type="bibr" rid="bib37">Koopmans et al., 2008</xref>). The timescale of the 1-bp DNA fluctuations has not been directly reported but can be estimated from the experimental results above for longer DNA fluctuations. Assuming the wrapping/unwrapping kinetics is uniform along the DNA, we can model the unwrapping of a 25-bp DNA segment as:<disp-formula id="equ19"><mml:math id="m19"><mml:mrow><mml:mn>0</mml:mn><mml:munderover><mml:mo>⇄</mml:mo><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mtext>w</mml:mtext></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mtext>u</mml:mtext></mml:msub></mml:mrow></mml:munderover><mml:mn>1</mml:mn><mml:munderover><mml:mo>⇄</mml:mo><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mtext>w</mml:mtext></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mtext>u</mml:mtext></mml:msub></mml:mrow></mml:munderover><mml:mn>2</mml:mn><mml:munderover><mml:mo>⇄</mml:mo><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mtext>w</mml:mtext></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mtext>u</mml:mtext></mml:msub></mml:mrow></mml:munderover><mml:mn>3</mml:mn><mml:mo>…</mml:mo><mml:munderover><mml:mo>⇄</mml:mo><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mtext>w</mml:mtext></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mtext>u</mml:mtext></mml:msub></mml:mrow></mml:munderover><mml:mn>24</mml:mn><mml:mrow><mml:mover accent="true"><mml:mo>→</mml:mo><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mtext>u</mml:mtext></mml:msub></mml:mrow></mml:mover></mml:mrow><mml:mn>25</mml:mn></mml:mrow></mml:math></disp-formula>where <italic>k</italic><sub>u</sub> and <italic>k</italic><sub>w</sub> are the local unwrapping and wrapping rate constants of each basepair, respectively. Since the local wrapping equilibrium constant has been shown to be close to 1 (<xref ref-type="bibr" rid="bib25">Hodges et al., 2009</xref>; <xref ref-type="bibr" rid="bib6">Bintu et al., 2012</xref>), we further approximate <italic>k</italic><sub>u</sub> and <italic>k</italic><sub>w</sub> with a single value <italic>k</italic>:<disp-formula id="equ20"><mml:math id="m20"><mml:mrow><mml:mn>0</mml:mn><mml:munderover><mml:mo>⇄</mml:mo><mml:mi>k</mml:mi><mml:mi>k</mml:mi></mml:munderover><mml:mn>1</mml:mn><mml:munderover><mml:mo>⇄</mml:mo><mml:mi>k</mml:mi><mml:mi>k</mml:mi></mml:munderover><mml:mn>2</mml:mn><mml:munderover><mml:mo>⇄</mml:mo><mml:mi>k</mml:mi><mml:mi>k</mml:mi></mml:munderover><mml:mn>3</mml:mn><mml:mo>…</mml:mo><mml:munderover><mml:mo>⇄</mml:mo><mml:mi>k</mml:mi><mml:mi>k</mml:mi></mml:munderover><mml:mn>24</mml:mn><mml:mrow><mml:mover accent="true"><mml:mo>→</mml:mo><mml:mi>k</mml:mi></mml:mover></mml:mrow><mml:mn>25</mml:mn></mml:mrow></mml:math></disp-formula></p><p>A net rate constant can substitute for each pair of forward and reverse rate constants (<xref ref-type="bibr" rid="bib13">Cleland, 1975</xref>):<disp-formula id="equ21"><mml:math id="m21"><mml:mrow><mml:mn>0</mml:mn><mml:mrow><mml:mover accent="true"><mml:mo>→</mml:mo><mml:mrow><mml:msubsup><mml:mi>k</mml:mi><mml:mrow><mml:mn>0</mml:mn><mml:mo>→</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mtext>net</mml:mtext></mml:msubsup></mml:mrow></mml:mover></mml:mrow><mml:mn>1</mml:mn><mml:mrow><mml:mover accent="true"><mml:mo>→</mml:mo><mml:mrow><mml:msubsup><mml:mi>k</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>→</mml:mo><mml:mn>2</mml:mn></mml:mrow><mml:mtext>net</mml:mtext></mml:msubsup></mml:mrow></mml:mover></mml:mrow><mml:mn>2</mml:mn><mml:mrow><mml:mover accent="true"><mml:mo>→</mml:mo><mml:mrow><mml:msubsup><mml:mi>k</mml:mi><mml:mrow><mml:mn>2</mml:mn><mml:mo>→</mml:mo><mml:mn>3</mml:mn></mml:mrow><mml:mtext>net</mml:mtext></mml:msubsup></mml:mrow></mml:mover></mml:mrow><mml:mn>3</mml:mn><mml:mo>…</mml:mo><mml:mrow><mml:mover accent="true"><mml:mo>→</mml:mo><mml:mrow><mml:msubsup><mml:mi>k</mml:mi><mml:mrow><mml:mn>23</mml:mn><mml:mo>→</mml:mo><mml:mn>24</mml:mn></mml:mrow><mml:mtext>net</mml:mtext></mml:msubsup></mml:mrow></mml:mover></mml:mrow><mml:mn>24</mml:mn><mml:mrow><mml:mover accent="true"><mml:mo>→</mml:mo><mml:mrow><mml:msubsup><mml:mi>k</mml:mi><mml:mrow><mml:mn>24</mml:mn><mml:mo>→</mml:mo><mml:mn>25</mml:mn></mml:mrow><mml:mtext>net</mml:mtext></mml:msubsup></mml:mrow></mml:mover></mml:mrow><mml:mn>25</mml:mn></mml:mrow></mml:math></disp-formula></p><p>The net rate constants are given by:<disp-formula id="equ22"><mml:math id="m22"><mml:mtable columnalign="left"><mml:mtr><mml:mtd><mml:msubsup><mml:mi>k</mml:mi><mml:mrow><mml:mn>24</mml:mn><mml:mo>→</mml:mo><mml:mn>25</mml:mn></mml:mrow><mml:mtext>net</mml:mtext></mml:msubsup><mml:mo>=</mml:mo><mml:mi>k</mml:mi></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:msubsup><mml:mi>k</mml:mi><mml:mrow><mml:mn>23</mml:mn><mml:mo>→</mml:mo><mml:mn>24</mml:mn></mml:mrow><mml:mtext>net</mml:mtext></mml:msubsup><mml:mo>=</mml:mo><mml:mi>k</mml:mi><mml:mo>⋅</mml:mo><mml:mfrac><mml:mrow><mml:msubsup><mml:mi>k</mml:mi><mml:mrow><mml:mn>24</mml:mn><mml:mo>→</mml:mo><mml:mn>25</mml:mn></mml:mrow><mml:mtext>net</mml:mtext></mml:msubsup></mml:mrow><mml:mrow><mml:msubsup><mml:mi>k</mml:mi><mml:mrow><mml:mn>24</mml:mn><mml:mo>→</mml:mo><mml:mn>25</mml:mn></mml:mrow><mml:mtext>net</mml:mtext></mml:msubsup><mml:mo>+</mml:mo><mml:mi>k</mml:mi></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mfrac><mml:mi>k</mml:mi><mml:mn>2</mml:mn></mml:mfrac></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:msubsup><mml:mi>k</mml:mi><mml:mrow><mml:mn>22</mml:mn><mml:mo>→</mml:mo><mml:mn>23</mml:mn></mml:mrow><mml:mtext>net</mml:mtext></mml:msubsup><mml:mo>=</mml:mo><mml:mi>k</mml:mi><mml:mo>⋅</mml:mo><mml:mfrac><mml:mrow><mml:msubsup><mml:mi>k</mml:mi><mml:mrow><mml:mn>23</mml:mn><mml:mo>→</mml:mo><mml:mn>24</mml:mn></mml:mrow><mml:mtext>net</mml:mtext></mml:msubsup></mml:mrow><mml:mrow><mml:msubsup><mml:mi>k</mml:mi><mml:mrow><mml:mn>23</mml:mn><mml:mo>→</mml:mo><mml:mn>24</mml:mn></mml:mrow><mml:mtext>net</mml:mtext></mml:msubsup><mml:mo>+</mml:mo><mml:mi>k</mml:mi></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mfrac><mml:mi>k</mml:mi><mml:mn>3</mml:mn></mml:mfrac></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula><disp-formula id="equ23"><mml:math id="m23"><mml:mo>⋮</mml:mo></mml:math></disp-formula><disp-formula id="equ24"><mml:math id="m24"><mml:mtable columnalign="left"><mml:mtr><mml:mtd><mml:msubsup><mml:mi>k</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>→</mml:mo><mml:mn>2</mml:mn></mml:mrow><mml:mtext>net</mml:mtext></mml:msubsup><mml:mo>=</mml:mo><mml:mi>k</mml:mi><mml:mo>⋅</mml:mo><mml:mfrac><mml:mrow><mml:msubsup><mml:mi>k</mml:mi><mml:mrow><mml:mn>2</mml:mn><mml:mo>→</mml:mo><mml:mn>3</mml:mn></mml:mrow><mml:mtext>net</mml:mtext></mml:msubsup></mml:mrow><mml:mrow><mml:msubsup><mml:mi>k</mml:mi><mml:mrow><mml:mn>2</mml:mn><mml:mo>→</mml:mo><mml:mn>3</mml:mn></mml:mrow><mml:mtext>net</mml:mtext></mml:msubsup><mml:mo>+</mml:mo><mml:mi>k</mml:mi></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mfrac><mml:mi>k</mml:mi><mml:mrow><mml:mn>24</mml:mn></mml:mrow></mml:mfrac></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:msubsup><mml:mi>k</mml:mi><mml:mrow><mml:mn>0</mml:mn><mml:mo>→</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mtext>net</mml:mtext></mml:msubsup><mml:mo>=</mml:mo><mml:mi>k</mml:mi><mml:mo>⋅</mml:mo><mml:mfrac><mml:mrow><mml:msubsup><mml:mi>k</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>→</mml:mo><mml:mn>2</mml:mn></mml:mrow><mml:mtext>net</mml:mtext></mml:msubsup></mml:mrow><mml:mrow><mml:msubsup><mml:mi>k</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>→</mml:mo><mml:mn>2</mml:mn></mml:mrow><mml:mtext>net</mml:mtext></mml:msubsup><mml:mo>+</mml:mo><mml:mi>k</mml:mi></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mfrac><mml:mi>k</mml:mi><mml:mrow><mml:mn>25</mml:mn></mml:mrow></mml:mfrac></mml:mtd></mml:mtr></mml:mtable></mml:math></disp-formula></p><p>The time required for unwrapping 25 bp of DNA equals the total time of unwrapping each bp of DNA:<disp-formula id="equ25"><mml:math id="m25"><mml:mrow><mml:msub><mml:mi>τ</mml:mi><mml:mrow><mml:mn>0</mml:mn><mml:mo>→</mml:mo><mml:mn>25</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:msubsup><mml:mi>k</mml:mi><mml:mrow><mml:mn>0</mml:mn><mml:mo>→</mml:mo><mml:mn>1</mml:mn></mml:mrow><mml:mtext>net</mml:mtext></mml:msubsup></mml:mrow></mml:mfrac><mml:mo>+</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:msubsup><mml:mi>k</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>→</mml:mo><mml:mn>2</mml:mn></mml:mrow><mml:mtext>net</mml:mtext></mml:msubsup></mml:mrow></mml:mfrac><mml:mo>+</mml:mo><mml:mo>…</mml:mo><mml:mo>+</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mrow><mml:msubsup><mml:mi>k</mml:mi><mml:mrow><mml:mn>24</mml:mn><mml:mo>→</mml:mo><mml:mn>25</mml:mn></mml:mrow><mml:mtext>net</mml:mtext></mml:msubsup></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:mn>325</mml:mn></mml:mrow><mml:mi>k</mml:mi></mml:mfrac><mml:mo>≈</mml:mo><mml:mrow><mml:mo>(</mml:mo><mml:mn>10</mml:mn><mml:mo>−</mml:mo><mml:mn>250</mml:mn><mml:mo>)</mml:mo></mml:mrow><mml:mi>m</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:math></disp-formula></p><p>Thus, the time for 1-bp DNA to unwrap from the nucleosome is expected to be less than 1 ms:<disp-formula id="equ26"><mml:math id="m26"><mml:mrow><mml:msub><mml:mi>τ</mml:mi><mml:mrow><mml:mn>0</mml:mn><mml:mo>→</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mn>1</mml:mn><mml:mi>k</mml:mi></mml:mfrac><mml:mo>&lt;</mml:mo><mml:mn>1</mml:mn><mml:mi>m</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:math></disp-formula></p><p>In the same way, we can also show that the 1-bp DNA rewrapping occurs on a similar timescale (<italic>τ</italic><sub>1→0</sub> &lt; 1 ms). In addition, molecular dynamics simulations also suggested that the local nucleosomal DNA fluctuates very fast (ns–µs timescale) (<xref ref-type="bibr" rid="bib59">Voltz et al., 2012</xref>). Therefore, we assume that the 1 bp of DNA in front of the polymerase unwraps and rewraps much faster than the translocation of the enzyme.</p></sec><sec id="s4-6"><title>Correction for undercounted short pauses</title><p>Experimentally we only counted pauses with lifetimes between 1 s and 120 s. The total pause density <italic>ρ</italic><sub>pause, total</sub> is given by:<disp-formula id="equ27"><mml:math id="m27"><mml:mrow><mml:msub><mml:mi>ρ</mml:mi><mml:mrow><mml:mtext>pause</mml:mtext><mml:mo>,</mml:mo><mml:mtext>total</mml:mtext></mml:mrow></mml:msub><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mtext>b</mml:mtext></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mtext>b</mml:mtext></mml:msub><mml:mo>+</mml:mo><mml:msubsup><mml:mi>k</mml:mi><mml:mn>1</mml:mn><mml:mtext>net</mml:mtext></mml:msubsup></mml:mrow></mml:mfrac><mml:mo>=</mml:mo><mml:mfrac><mml:mrow><mml:msub><mml:mi>ρ</mml:mi><mml:mrow><mml:mtext>pause</mml:mtext><mml:mo>,</mml:mo><mml:mn>1</mml:mn><mml:mo>&lt;</mml:mo><mml:mi>t</mml:mi><mml:mo>&lt;</mml:mo><mml:mn>120</mml:mn></mml:mrow></mml:msub></mml:mrow><mml:mrow><mml:mstyle displaystyle="true"><mml:mrow><mml:munderover><mml:mo>∫</mml:mo><mml:mn>1</mml:mn><mml:mrow><mml:mn>120</mml:mn></mml:mrow></mml:munderover><mml:mrow><mml:mi>ψ</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>t</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:mi>d</mml:mi><mml:mi>t</mml:mi></mml:mrow></mml:mrow></mml:mstyle></mml:mrow></mml:mfrac></mml:mrow></mml:math></disp-formula></p><p>The correction factor can be solved analytically to be 2.9 for the wild-type Pol II. For the mutant enzyme, the values of <italic>k</italic><sub>f1</sub> and <italic>k</italic><sub>b1</sub> are different from those for the wild-type (<xref ref-type="table" rid="tbl3">Table 3</xref>). We simulated transcriptional pauses using the lower bounds of <italic>k</italic><sub>f1</sub> and <italic>k</italic><sub>b1</sub> and obtained a correction factor of ∼7 for the mutant Pol II.</p></sec><sec id="s4-7"><title>Estimation of the value of <italic>K</italic> for the mutant Pol II</title><p>The value of <italic>K</italic> for the mutant Pol II (<italic>K</italic><sub>mutant</sub>) cannot be constrained by <xref ref-type="disp-formula" rid="equ16">Equation 14</xref> due to the relatively large experimental error. We took a different approach to constrain <italic>K</italic><sub>mutant</sub> by simulating the <italic>ρ</italic><sub>pause</sub>–[NTP] relationship with varying <italic>K</italic><sub>mutant</sub> values and then comparing it to the experimental data (<xref ref-type="fig" rid="fig5s1">Figure 5—figure supplement 1</xref>). We found that the simulated curve substantially deviates from the experimental curve when <italic>K</italic><sub>mutant</sub> becomes larger than 100 µM. Hence, we set the upper bound of <italic>K</italic><sub>mutant</sub> to be 100 µM. Using the <italic>k</italic><sub>−1</sub><italic>K</italic> value of (2.5 ± 0.4) × 10<sup>4</sup> µM·s<sup>−1</sup> obtained from <xref ref-type="disp-formula" rid="equ15">Equation 13</xref>, we set the lower bound of <italic>k</italic><sub>−1</sub> for the mutant to be 210 s<sup>−1</sup>. The notion that the NTP dissociation rate is much faster than the catalysis rate (<italic>k</italic><sub>−2</sub> &gt;&gt; <italic>k</italic><sub>3</sub>) has been widely used in the kinetic studies of RNA and DNA polymerases, and is supported by biochemical evidence (<xref ref-type="bibr" rid="bib50">Rhodes and Chamberlin, 1974</xref>; <xref ref-type="bibr" rid="bib28">Johnson, 1993</xref>; <xref ref-type="bibr" rid="bib18">Foster et al., 2001</xref>; <xref ref-type="bibr" rid="bib4">Bai et al., 2004</xref>; <xref ref-type="bibr" rid="bib44">Maoiléidigh et al., 2011</xref>). It follows from this notion that <italic>K</italic> = (<italic>k</italic><sub>−2</sub>+<italic>k</italic><sub>3</sub>)/<italic>k</italic><sub>2</sub> ≈ <italic>k</italic><sub>−2</sub>/<italic>k</italic><sub>2</sub>. Thus, <italic>K</italic> becomes virtually identical to <italic>K</italic><sub>D</sub>, the NTP dissociation constant. Because the mutated residue (Glu1103) is located distal from the NTP-interacting part of TL (<xref ref-type="bibr" rid="bib63">Wang et al., 2006</xref>) and the E1103G mutation affects TL closure and NTP sequestration after the initial docking step (<xref ref-type="bibr" rid="bib34">Kireeva et al., 2008</xref>), the NTP binding/dissociation kinetics are unlikely to be markedly affected by the mutation. Therefore, it is reasonable to assume that the wild-type and the mutant enzymes share similar <italic>K</italic><sub>D</sub> values (∼9.2 µM). Under this assumption, we could estimate the <italic>k</italic><sub>−1</sub> value for the mutant to be ∼2700 s<sup>−1</sup>.</p></sec><sec id="s4-8"><title>Construction of the energy landscape</title><p>The free energy difference (ΔΔ<italic>G</italic>) between two neighboring translocation states was computed using the forward and reverse rate constants between these states (<italic>k</italic><sub>+</sub> and <italic>k</italic><sub>−</sub>):<disp-formula id="equ28"><mml:math id="m28"><mml:mrow><mml:mi>Δ</mml:mi><mml:mi>Δ</mml:mi><mml:mi>G</mml:mi><mml:mo>=</mml:mo><mml:mo>−</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mi>B</mml:mi></mml:msub><mml:mi>T</mml:mi><mml:mo>⋅</mml:mo><mml:mi>ln</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mfrac><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mo>−</mml:mo></mml:msub></mml:mrow><mml:mrow><mml:msub><mml:mi>k</mml:mi><mml:mo>+</mml:mo></mml:msub></mml:mrow></mml:mfrac></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></disp-formula></p><p>The height of the activation energy barrier (Δ<italic>G</italic><sup>†</sup>) was calculated according to the Arrhenius equation:<disp-formula id="equ29"><mml:math id="m29"><mml:mrow><mml:mi>k</mml:mi><mml:mo>=</mml:mo><mml:mi>A</mml:mi><mml:mo>⋅</mml:mo><mml:mi>exp</mml:mi><mml:mrow><mml:mrow><mml:mo>(</mml:mo><mml:mrow><mml:mo>−</mml:mo><mml:mi>Δ</mml:mi><mml:msup><mml:mi>G</mml:mi><mml:mi mathvariant="normal">†</mml:mi></mml:msup><mml:mo>/</mml:mo><mml:msub><mml:mi>k</mml:mi><mml:mtext>B</mml:mtext></mml:msub><mml:mi>T</mml:mi></mml:mrow><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:mrow></mml:math></disp-formula>where <italic>k</italic> is the corresponding rate constant and <italic>A</italic> is the pre-exponential factor. In this study, for illustration purposes, we made a simplifying assumption that all reaction steps share the same pre-exponential factor. <italic>A</italic> was calculated using the stepping rate constant during backtracking <italic>k</italic><sub>0</sub> = 1.3 s<sup>−1</sup> and the barrier height between neighboring backtracked states Δ<italic>G</italic><sub>b</sub><sup>†</sup>. We assumed that one DNA–RNA hybrid basepair and one DNA–DNA basepair in the transcription bubble must be broken before any other bonds are formed and that no other interactions contribute to the barrier (<xref ref-type="bibr" rid="bib53">Tadigotla et al., 2006</xref>). Using the available free energy data for basepairing (<xref ref-type="bibr" rid="bib51">Sugimoto et al., 1996</xref>; <xref ref-type="bibr" rid="bib67">Wu et al., 2002</xref>), we estimated Δ<italic>G</italic><sub>b</sub><sup>†</sup> to be ∼8.5 <italic>k</italic><sub>B</sub>T, which translates to an Arrhenius pre-factor of ∼6.4 × 10<sup>3</sup> s<sup>−1</sup>. The catalysis step is essentially irreversible in our experimental condition. The free energy drop after each nucleotide addition cycle is arbitrarily set to be 10 <italic>k</italic><sub>B</sub>T.</p></sec></sec></body><back><ack id="ack"><title>Acknowledgements</title><p>We thank Lacramioara Bintu, Gheorghe Chistol, Yves Coello, Craig L Hetherington, Masahiko Imashimizu, Troy A Lionberger, Ninning Liu, Yara X Mejia, and Maya Sen for critical readings of the manuscript, and W Gregory Alvord for help with statistical analyses. We would like to dedicate this work to the memory of W Wallace Cleland whose pioneering studies on enzyme kinetics provide the foundation for this work.</p></ack><sec sec-type="additional-information"><title>Additional information</title><fn-group content-type="competing-interest"><title>Competing interests</title><fn fn-type="conflict" id="conf1"><p>The authors declare that no competing interests exist.</p></fn></fn-group><fn-group content-type="author-contribution"><title>Author contributions</title><fn fn-type="con" id="con1"><p>MD, Conception and design, Acquisition of data, Analysis and interpretation of data, Drafting or revising the article</p></fn><fn fn-type="con" id="con2"><p>TI, Conception and design, Acquisition of data, Analysis and interpretation of data, Drafting or revising the article</p></fn><fn fn-type="con" id="con3"><p>SL, Conception and design, Analysis and interpretation of data, Drafting or revising the article</p></fn><fn fn-type="con" id="con4"><p>CJB, Conception and design, Analysis and interpretation of data, Drafting or revising the article</p></fn><fn fn-type="con" id="con5"><p>MLK, Analysis and interpretation of data, Drafting or revising the article, Contributed unpublished essential data or reagents</p></fn><fn fn-type="con" id="con6"><p>MK, Analysis and interpretation of data, Drafting or revising the article, Contributed unpublished essential data or reagents</p></fn><fn fn-type="con" id="con7"><p>LL, Drafting or revising the article, Contributed unpublished essential data or reagents</p></fn></fn-group></sec><ref-list><title>References</title><ref id="bib1"><element-citation publication-type="journal"><person-group 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States</country></aff></contrib></contrib-group></front-stub><body><boxed-text><p>eLife posts the editorial decision letter and author response on a selection of the published articles (subject to the approval of the authors). An edited version of the letter sent to the authors after peer review is shown, indicating the substantive concerns or comments; minor concerns are not usually shown. Reviewers have the opportunity to discuss the decision before the letter is sent (see <ext-link ext-link-type="uri" xlink:href="http://elife.elifesciences.org/review-process">review process</ext-link>). Similarly, the author response typically shows only responses to the major concerns raised by the reviewers.</p></boxed-text><p>Thank you for sending your work entitled “Complete dissection of transcription elongation reveals slow translocation of Pol II in a linear ratchet mechanism” for consideration at <italic>eLife</italic>. Your article has been favorably evaluated by a Senior editor and 3 reviewers, one of whom is a member of our Board of Reviewing Editors.</p><p>The Reviewing editor and the other reviewers discussed their comments before we reached this decision, and the Reviewing editor has assembled the following comments to help you prepare a revised submission.</p><p>All three reviewers find your work of significant interest and high quality. By measuring the transcription kinetics on bare and nucleosomal DNA, this single-molecule force study dissected the transcription elongation pathway, determined each individual rate constant on the pathway, and mapped out the energy landscape for transcription elongation and backtracking. Instead of assuming that the reversible transition between pre- and post-translocated states of the nucleotide addition cycle occurs much faster than the subsequent catalysis steps, this study found that the forward translocation rate is comparable to the catalysis rate. The results suggest that a linear Brownian Ratchet Model can explain the measured behavior of transcription elongation kinetics. The reviewers feel that the findings in this work are important, the experimental design is elegant, and that the data are of high quality.</p><p>The reviewers have the following concerns regarding the use of the nucleosome barrier as a tool to separately measure the forward and reverse translocation rates. Pol II interactions with a nucleosome are rather complex and hence could complicate the interpretation of data here. One of the key assumptions is that the local nucleosomal DNA fluctuations (wrapping and unwrapping) are faster than Pol II forward translocation. Is this assumption valid for the present study, which uses nucleosomes with the 601 sequence and involves predominant transcriptional pauses close to the nucleosomal dyad? What is the evidence that wrapping/unwrapping kinetics near the dyad of the 601 nucleosome is faster than Pol II translocation? How do the different interaction strengths at different sites of the nucleosome affect the results in this work? Is it possible to obtain the same conclusion using a simpler system without involving nucleosomes? For example, the application of force can also perturb the energy landscape. <italic>k</italic><sub>1</sub>, <italic>k</italic><sub>3</sub>, and δ may be obtained by examining <italic>V</italic><sub>max</sub> as a function of force. This approach removes the need for <xref ref-type="disp-formula" rid="equ6">Equation 4</xref> and may potentially remove the need for using nucleosomes. Given the importance of the nucleosome barrier as an experimental tool in the work, the advantages and requirements of using this system should be more clearly explained and justified in the main text.</p><p>The reviewers also feel that the manuscript is written in a very concise and dense manner. It is not easy to follow, especially for non-experts. Give that <italic>eLife</italic> has a broad audience, we suggest that you expand the manuscript to make it easier to read and understand. In particular, the derivations of various kinetic rate constants from experimentally measured quantities are nontrivial and the manuscript often relied on citations of previous papers rather than explaining clearly the rationale of how these rate constants are derived. The manuscript should be made more self-sufficient.</p></body></sub-article><sub-article article-type="reply" id="SA2"><front-stub><article-id pub-id-type="doi">10.7554/eLife.00971.024</article-id><title-group><article-title>Author response</article-title></title-group></front-stub><body><p><italic>The reviewers have the following concerns regarding the use of the nucleosome barrier as a tool to separately measure the forward and reverse translocation rates. Pol II interactions with a nucleosome are rather complex and hence could complicate the interpretation of data here. One of the key assumptions is that the local nucleosomal DNA fluctuations (wrapping and unwrapping) are faster than Pol II forward translocation. Is this assumption valid for the present study, which uses nucleosomes with the 601 sequence and involves predominant transcriptional pauses close to the nucleosomal dyad? What is the evidence that wrapping/unwrapping kinetics near the dyad of the 601 nucleosome is faster than Pol II translocation? How do the different interaction strengths at different sites of the nucleosome affect the results in this work? Is it possible to obtain the same conclusion using a simpler system without involving nucleosomes? For example, the application of force can also perturb the energy landscape.</italic> k<sub><italic>1</italic></sub><italic>,</italic> k<sub><italic>3</italic></sub><italic>, and δ may be obtained by examining</italic> V<sub><italic>max</italic></sub> <italic>as a function of force. This approach removes the need for</italic> <xref ref-type="disp-formula" rid="equ6"><italic>Equation 4</italic></xref> <italic>and may potentially remove the need for using nucleosomes. Given the importance of the nucleosome barrier as an experimental tool in the work, the advantages and requirements of using this system should be more clearly explained and justified in the main text</italic>.</p><p>The reviewers correctly pointed out that the derivation of <italic>k</italic><sub>1</sub> and <italic>k</italic><sub>3</sub> relies on the assumption that nucleosomal DNA fluctuations are much faster than Pol II forward translocation. The timescale of DNA fluctuations at the nucleosome ends has been studied. Fluorescence correlation spectroscopy and fluorescence resonance energy transfer experiments showed that the first 20–30 bp of nucleosomal DNA spontaneously unwrap and rewrap every 10–250 ms (Li et al., NSMB 2005; Koopmans et al., Chemphyschem. 2008). Since the polymerase moves 1 bp per step, the timescale of Pol II translocation (10 ms–1 s) should be compared to that of one-bp DNA fluctuation, which has not been directly reported but can be estimated from the above experimental results. The average time for 1-bp DNA to open or close on the histone surface is expected to be less than 1 ms (a derivation is shown in the Materials and methods section). In addition, coarse-grained molecular dynamics simulations showed that the first 9-bp DNA segment fluctuates very fast (ns–µs timescale) (Voltz et al., Biophys. J. 2012). Therefore, the local DNA in front of the polymerase most likely fluctuates much faster than the translocation of the polymerase. The timescale of DNA fluctuations near the nucleosomal dyad has not been directly studied. Nonetheless, we have previously compared the local wrapping/unwrapping equilibrium constants between the entry and the central regions of the nucleosome and found that they are very similar (Bintu et al., Cell 2012). It is difficult to envision a scenario in which both wrapping and unwrapping rates would slow down by the exact same amount in the central region compared to the entry region of the nucleosome. A much more likely scenario is that the wrapping/unwrapping kinetics of DNA in front of a transcribing polymerase is relatively uniform across the whole nucleosome region. Therefore, we think that the assumption of fast DNA fluctuation compared to Pol II translocation is a reasonable one.</p><p>Regarding the predominant pauses observed near the nucleosomal dyad with the 601 sequence, we have shown that they are due to the lack of secondary structures formed in the nascent transcript behind the transcribing enzyme in this region that induces extensive Pol II backtracking, rather than due to particularly strong histone-DNA interactions (Bintu et al., Cell 2012). Moreover, the pauses were also observed on bare DNA with the same sequence, although to a lesser degree (<xref ref-type="fig" rid="fig2s4">Figure 2—Figure supplement 4</xref>). In addition, gel-based assays showed a lack of 5-bp or 10-bp pausing periodicity within the nucleosome region for yeast Pol II (Kireeva et al., Mol. Cell 2005; Bondarenko et al., Mol. Cell 2006). Such periodicity would be expected if the strength of the histone-DNA interactions were the major determinant for Pol II pausing (Luger et al., Nature 1997; Hall et al., NSMB 2009). Therefore, we do not think that the strong pauses near the dyad drastically affect the on-pathway kinetic parameters of Pol II (i.e., <italic>k</italic><sub>1</sub> and <italic>k</italic><sub>3</sub>), which were derived from the pause-free velocity. To further rule out the possibility that the different behavior of Pol II near the dyad may bias the values of these kinetic rates, we reanalyzed the pause-free velocity data without a 40-nt span (−35 to +5 relative to the dyad) in the central region of the nucleosome and obtained <italic>k</italic><sub>1</sub> = 158±43 s<sup>-1</sup> and <italic>k</italic><sub>3</sub>= 33±2 s<sup>-1</sup> for the wild-type Pol II, and <italic>k</italic><sub>1</sub> = 59±4 s<sup>-1</sup> and <italic>k</italic><sub>3</sub> = 120±13 s<sup>-1</sup> for the mutant Pol II at 6.5 pN of applied aiding force. These values are close to those obtained with all the pause-free velocity data and lead to the same conclusion that <italic>k</italic><sub>1</sub> and <italic>k</italic><sub>3</sub> are of the same order of magnitude.</p><p>Nonetheless, it is true that the interaction between Pol II and the nucleosome is rather complex and their interaction may vary at different sites. We simplified the problem by using the averaged values of the pause-free velocity and the fraction of time the local nucleosomal DNA is unwrapped (γ<sub>u</sub>) over the whole nucleosome region to extract the intrinsic kinetic properties of Pol II. This point was probably not stressed enough in the original manuscript. It is now clearly stated in the revised manuscript.</p><p>The reviewers also made an excellent suggestion that <italic>k</italic><sub>1</sub>, <italic>k</italic><sub>3</sub>, and <italic>δ</italic> may be extracted by examining <italic>V</italic><sub>max</sub> as a function of force. This is indeed possible: <italic>V</italic><sub>max</sub>(<italic>F</italic>) = <italic>k</italic><sub>1</sub>(<italic>F</italic>)<italic>k</italic><sub>3</sub>/(<italic>k</italic><sub>1</sub>(<italic>F</italic>)+<italic>k</italic><sub>3</sub>)*<italic>d</italic>, where <italic>k</italic><sub>1</sub>(<italic>F</italic>) = <italic>k</italic><sub>1</sub>(0)<italic>e</italic><sup><italic>Fδ/k<sub>B</sub></italic></sup><sup><italic>T</italic></sup>. Using our data and the published data from Larson et al. (Larson et al., PNAS 2012) collected at saturating [NTP] (1 mM) and various forces (<xref ref-type="fig" rid="fig6">Figures 6A and 6B</xref>), we fit the <italic>V</italic><sub>max</sub>-<italic>F</italic> dependence to the above equation and obtained <italic>k</italic><sub>1</sub>= 87±61 s<sup>-1</sup>, <italic>k</italic><sub>3</sub>= 33±8 s<sup>-1</sup>, and <italic>δ</italic> = 0.64±0.58 bp for the wild-type Pol II, and <italic>k</italic><sub>1</sub>= 65±37 s<sup>-1</sup>, <italic>k</italic><sub>3</sub>= 62±32 s<sup>-1</sup>, and <italic>δ</italic> = 0.64±0.50 bp for the mutant Pol II. Thus, the same qualitative conclusion, i.e., <italic>k</italic><sub>1</sub> and <italic>k</italic><sub>3</sub> are comparable and translocation is one of the rate-limiting steps, can be drawn from this analysis. Compared to the approach in which the nucleosomal barrier is used to specifically perturb forward translocation, fitting the <italic>V</italic><sub>max</sub>-<italic>F</italic> dependence involves one additional free parameter (<italic>δ</italic>) and the values are less constrained. If we fix <italic>δ</italic> at 0.5 bp and only fit for <italic>k</italic><sub>1</sub> and <italic>k</italic><sub>3</sub> using the <italic>V</italic><sub>max</sub>-<italic>F</italic> dependence, the values are better bound (<italic>k</italic><sub>1</sub>= 72±13 s<sup>-1</sup> and <italic>k</italic><sub>3</sub>= 35±3 s<sup>-1</sup> for the wild-type; <italic>k</italic><sub>1</sub>= 55±10 s<sup>-1</sup> and <italic>k</italic><sub>3</sub>= 75±13 s<sup>-1</sup> for the mutant). However, this analysis involves one additional assumption (<italic>δ</italic> = 0.5 bp), which may not always be valid as is the case for the mutant Pol II (<italic>δ</italic> = 0.24±0.05 bp). One reason for this relatively poor fitting is that force has a relatively small effect on <italic>k</italic><sub>1</sub>, given the small step size of the polymerase (1 bp or 0.34 nm). The nucleosomal barrier effectively decreases <italic>k</italic><sub>1</sub> by 40%. The same amount of reduction would require 13 pN of opposing force, which is not feasible because the operational stall force for Pol II is only ∼8 pN due to backtracking (Galburt et al., Nature 2007). In the revised Discussion section, we have added a comparison between the two approaches of using force or nucleosome to extract the kinetic parameters of Pol II transcription.</p><p><italic>The reviewers also feel that the manuscript is written in a very concise and dense manner. It is not easy to follow, especially for non-experts. Give that</italic> eLife <italic>has a broad audience, we suggest that you expand the manuscript to make it easier to read and understand. In particular, the derivations of various kinetic rate constants from experimentally measured quantities are nontrivial and the manuscript often relied on citations of previous papers rather than explaining clearly the rationale of how these rate constants are derived. The manuscript should be made more self-sufficient</italic>.</p><p>In the revised Results section, we have included the derivations of various rate constants as well as the corresponding rationales. We have also expanded the text considerably to more clearly explain the results and their implications.</p></body></sub-article></article>