a kinetic model of transcription initiation by rna polymerase

doi:10.1016/j.jmb.2008.03.008 J. Mol. Biol. (2008) 378, 520–529

Available online at www.sciencedirect.com

A Kinetic Model of Transcription Initiation byRNA Polymerase

Xiao-chuan Xue1⁎, Fei Liu1 and Zhong-can Ou-Yang1,2

1Center for Advanced Study,Tsinghua University, Beijing100084, China2Institute of Theoretical Physics,The Chinese Academy ofSciences, P.O. Box 2735, Beijing100080, China

Received 19 September 2007;received in revised form23 January 2008;accepted 5 March 2008Available online12 March 2008

*Corresponding author. E-mail [email protected] used: RNAP, RNA

initial transcribing complex; NTP, ntriphosphate; MSAT, maximum sizetranscript; APR, abortive/productivcomplex; UTP, uridine triphosphatetriphosphate; CTP, cytidine triphosp

0022-2836/$ - see front matter © 2008 E

We establish a sequence-dependent kinetic model for the later stage oftranscription initiation by RNA polymerase. We suggest that there are threereaction pathways, the abortive pathway, the scrunching pathway and theescape pathway, competitive with each other at each site during thetranscription initiation. Using this three-pathway model, we mainlycalculate the maximum sizes of the abortive transcripts, the abortiveprobabilities and the abortive/productive ratios for different promoters byMonte Carlo simulation and analytical methods. These results arequantitatively comparable with the experimental observations. In particu-lar, our model can account for the unproductive initial transcribing complexand the nucleoside triphosphate concentration dependence of the transcrip-tion initiation, which have been found in the experiments and were hardlyunderstood by the previous two-pathway kinetic competition model.

© 2008 Elsevier Ltd. All rights reserved.

Keywords: RNA polymerase; transcription initiation; abortive; scrunching;escape
Edited by R. Ebright
Introduction

Transcription is the first step in the Central Dogma.Gene regulation mainly takes place in this step.Transcription is also a complicated process and isusually divided into three phases: initiation, elonga-tion and termination. A considerable number ofexperiments, including sophisticated single-mole-cule methods, have investigated these phases ingreat detail.1–7 Unlike double-stranded DNA repli-cation, initiation of transcription does not needprimers to start. Instead, a process called abortiveinitiation is involved. In this process many pieces ofsmall RNAs (2–15 nt) are synthesized and releasedbefore RNA polymerase (RNAP) leaves thepromoter.6–8 In particular, the latest single-moleculeexperiments found that transcription initiation pro-ceeds through a novel scrunching mechanism in

ess:

polymerase; ITC,ucleosideof the abortivee ratio; EC, elongation; GTP, guanosine 5′-hate.

lsevier Ltd. All rights reserve

which RNAP remains fixed on the promoter andpulls the downstream DNA into itself and past itsactive center.9,10 Because these two features are notinvolved in the elongation phase, RNA synthesisprocess in the initiation phase could be different fromthat in the elongation phase.11,12 On the other hand,initiation also shows some similarities with elonga-tion, namely, both of them are sequence-dependent:the thermodynamic and kinetic behaviors of RNAPare distinct for different promoters.13–15

To the best of our knowledge, there are fewquantitative models about transcription initiationexisting in the literature. However, several theoreticalmodels have been proposed to elucidate sequence-dependent elongation processes.11,12 They can pre-dict the pause positions in the transcriptionelongation phase by treating the backtracked andforward-tracked translocation as the competitivepathways for RNA polymerization reaction. Witha similar competitive idea, a two-pathway modelhas been proposed to understand transcriptioninitiation. This model treats initiation as the firstfew steps of the elongation process accompaniedby abortive pathways that are competitive withthe elongation process.13 Although this model issimple and intuitional, it cannot account for twoimportant experimental observations: the unpro-ductive initial transcribing complex (ITC) and the

d.

mailto:[email protected]

521Transcription Initiation by RNAP

nucleoside triphosphate (NTP) concentrationdependence of the abortive process.13–15 Motivatedby the specificity of the initiation phase and limitedsuccess of the two-pathway model, in this work weconstruct a quantitative kinetic model to describepromoter-specific initiation process. This model isprimarily based on a series of experiments.9,13–15 Wepropose that there are three competitive reactionpathways taking part in the initiation process,abortive pathway, scrunching pathway and escapepathway.We calculatemaximum sizes of the abortivetranscripts (MSAT), abortive probabilities and abor-tive/productive ratios (APR). All of them arecomparable with the experimental data. Particularly,this model can account for the two abnormal proper-ties that we mentioned above.This article is organized as follows. In the next

section, we first introduce the three reaction path-ways and their features. Then we detail the methodfor the calculation of sequence-dependent stateenergies. Using the state energies and the reactionkinetics, we deduce the expressions of the reactionrates of the three reaction pathways. In Results andDiscussion, after introducing promoters and para-meters, we calculate the MASTs, the abortiveprobabilities and the APRs by using Monte Carlosimulation and analytical methods. Then we analyzethe cause of the unproductive ITC and the effects ofadding the product RNA in solution on the abortiveprocess. The analysis of the role of NTP concentra-tion in transcription initiation is also carried outtherein. The last section concludes the paper.

Model and Method

Our model focuses on the latter processes oftranscription initiation after the formation of RNAP–promoter open complex. The earlier processes,including RNAP searching for and binding topromoter and the formation of RNAP–promoterclosed complex are not studied here.

Reaction pathways in the transcription initiation

Figure 1a is a schematic representation of thereaction pathways of the transcription initiation. Inthese pathways, RNAP, the promoter and the nascentRNA transcript form an RNAP–promoter ITC orelongation complex (EC). These complexes are uni-formly denoted as Pm(M, N, n), where m denotes thepathway on which RNAP stays, which will beexplained shortly, M represents the length of thetranscription bubble, N represents the length of thenascent RNA, and n is the base-pair number of theRNA–DNAhybrid,which is always less than or equalto 9 inside the ITC or EC.16–18 Upon the formation ofthe RNAP–promoter open complex P0(14, 0, 0),19

RNAP catalyzes the formation of the first phospho-diester bond by using the first two complementarynucleotides. Then the complex changes its configura-tions through a series of different reactions, whichinclude polymerization, RNA–RNAP dissociation or

RNA releasing, scrunching, unscrunching and escapereactions. According to their reaction consequences,we conveniently classify these reactions into threepathways: the scrunching, the abortive and the escapepathways.20 We describe them below.The scrunching pathway is the main pathway in the

initiation phase, which invokes two types of reac-tions (see Fig. 1a). One is the scrunching reaction, inwhich RNAP unwinds a base pair of the down-stream DNA and scrunches the DNA into itself andpast its active site. Remarkably, in this processRNAP remains fixed on the promoter and thescrunched DNA is accumulated as single-strandedbulges in the RNAP–promoter ITC (the DNA bubblelength changing fromM toM+1).9,10 The other typeof reaction is the irreversible polymerization reac-tion, which occurs rapidly upon the completion ofthe scrunching reaction (the nascent RNA lengthchanging from N to N+1). We denote the RNAP–promoter ITC states on the scrunching pathwaywith m=0.The abortive pathway is one of the pathways

competitive with the scrunching pathway,13–15

through which the RNAP–promoter ITC releasesthe nascent RNA, ejects the scrunchedDNA from thedownstream, and reforms the RNAP–promoter ITC,P0(14, 2, 2) in the figure.7,9 Compared with thescrunching pathway, existing knowledge is not yetsufficient to establish a detailed reaction processabout the abortive pathway.6,9 In this work we haveto resort to several assumptions. For the nascentRNA longer than 3 nt, this pathway involves a seriesof reversible “unscrunching” reactions (R. H.Ebright, personal communication) followed by anirreversible NTP-assisted RNA releasing. At eachunscrunching reaction, the length of theDNAbubbledecreases 1 bp, and the number of the DNA–RNAhybrid is still 9 bp (more than 9-nt RNA upstream ofthe RNAP active site) or decreases 1 bp (fewer than 9-nt RNA upstream of the RNAP active site). At thesame time, the 3′ end of the nascent RNA is extrudedthrough the RNAP secondary channel. Uponunscrunching, arriving at a state whose RNA–DNAhybrid length is 2 bp, with the help of the first twocomplementary NTPs the last two DNA–RNAhybrids are opened and the nascent RNA isirreversibly released from RNAP. Then RNAPquickly catalyzes the formation of the 2-nt nascentRNA (Fig. 1b). In contrast, the releasing of the 2-ntRNA is reversible (Fig. 1b).6,7,9 Itmay be attributed tothe smaller size of 2-nt RNA thatmakes it freely enteror leave the secondary channel. The experiments alsofound that 2-nt RNA could be used as a primer fortranscription by directly hybridizingwithDNA7 (seeFig. 1a). The RNAP–promoter ITC states on theseabortive pathways are denoted with m=−1.The escape pathway is the last pathway in the

transcription initiation.21–23 In this process, RNAPescapes from the promoter, releases the contractedDNA from the upstream, and only leaves a 12-bp-long bubble inside itself. Additionally, RNAP alsotranslocates 1 bp ahead to the downstream DNA,which makes the active site empty for another

522 Transcription Initiation by RNAP

polymerization reaction. Hence, if the length of theRNA–DNA hybrid was 9 bp, this translocationwould make the most upstream base pair of thehybrid open and leave 8 bp there.3 This newcomplex is the EC. The formation of the EC indicatesthat the transcription formally enters into theelongation phase. The RNAP–promoter EC stateson this pathway are denoted with m=+1.These three pathways together compose the

transcription initiation phase. Before RNAP entersinto the escape pathway to start the elongationphase, the abortive pathway and scrunching path-way keep cycling repetitively.

Fig. 1. (a) Scheme of the transcription initiation reaction pRNAP–promoter ITC or EC. The single arrows in the figuredenote the reversible reactions. (b) A possible reaction schemeby us. The releasing of the nascent RNA longer than 3 nt is irre“A” and “B” in the figure correspond to the first and second cSequences of the three promoters used in this study. The sequefrom site −11 to +20. The numbers above the sequences denotetranscripts observed in the experiments is 15 nt long and thesequences are only shown from site −11 to +20; they aretranscription initiation.

State energy

The state energy ΔGmM,N,n of the RNAP–promoter

ITC or EC is a measurement of its stability. It iscalculated from the standard free energy of formationof the complex from its isolated components2,11,12:

DGmM;N;n; ¼ DGbubbleM;N;n; þ DGhybridM;N;n; þ DGbindingm : ð1Þ

The first and second terms are the free-energychanges related to the formation of the DNA bubbleand RNA–DNA hybrid, respectively. Both aresequence-dependent. We calculate them using the

athways. Each Pm(M, N, n) represents a different state ofdenote the irreversible reactions, and the double arrowsof the NTP-assisted RNA-releasing assumption proposedversible, while the releasing of the 2-nt RNA is reversible.omplementary NTP to the template DNA, respectively. (c)nces of the nontemplate promoter DNA strands are shownthe sequence site. Since the maximum size of the abortive

transcribing bubble is usually opened from site −11, theseenough for the analysis of the abortive process in the


nearest-neighbor model with energy values at 37 °C,and ionic effect is also considered.24,25 The third termin Eq. (1) is the binding energy of the RNAP–DNAinteraction and only depends on the pathway onwhich RNAP stays. Because RNAP binding topromoter is specific and binding to nonpromoterarea is nonspecific,26–28 we simply think that thebinding energies of the scrunching and abortivepathways, in which RNAP remains stationary on thepromoter, are the same, and the binding energy of theescape pathway, in which RNAP has translocatedalong the DNA and left the promoter, has a differentvalue. This difference substantially affects the possi-bility of RNAP entering into the escape pathway.Although there are other possible energy contribu-tions, such as σ factor steric hindrance energy, RNAsecondary-structure energy, etc., we ignore them inthis work.

The reaction rates of the three pathways

In order to study the transcription initiation in aquantitative way, we need to calculate the reactionrates in the three pathways.First, consider the reaction rates from the RNAP–

promoter ITC state P0(M, N, n) to the next state P0(M+1, N+1, n+1) in the scrunching pathway. Wecall these rates scrunching rates for convenience. Inthe previous section, we have pointed out thatthere are two reactions involved in this pathway:one is the scrunching reaction, the other is the RNApolymerization reaction. We describe them asMichaelis–Menten enzyme kinetics in the presenceof competitive inhibitors.11,12 Before applying thisdescription, we must emphasize that besides P0(M,N, n), the other RNAP–promoter ITC states, hereincluding P0(M+1, N, n) and all P−1(M′, N′, n′)(14≤M′≤M, 0≤n′≤n) on the abortive pathway,also contribute to the enzyme kinetics as inhibitionstates. Considering that the unscrunching reactionsare similar with the backtracking reactions in theelongation phase, we follow Tadigotla et al. whoused rapid equilibrium kinetics to describe theunscrunching reactions.12 Although there are sig-nificant debates about this assumption in theelongation phase,11,12 we believe it might beplausible in the transcription initiation due to thefollowing reasons. First, in the abortive process,because the releasing of the DNA bubble issimultaneous with the opening of the RNA–DNAhybrid, most of the energy differences between theadjacent unscrunching states are lower than 1.5kBT(data not shown). Second, the reaction rates of eachunscrunching step should be comparable with thescrunching rates, while the latter are fast inexperiments. Third, the nascent RNA in theinitiation phase is usually short, and no secondarystructures will form to inhibit the unscrunchingsteps. Finally, the rapid equilibrium kinetics wouldlead to a prediction of substantial amounts ofabortive products, which was indeed observedexperimentally.13 Hence, we obtain the scrunchingrate of a nascent RNA of length N to the next

nascent RNA of length N+1 (the scrunching rate atDNA site N):

kN0 ¼ k1CCþ KN

d1ð2Þ

with an effective equilibrium dissociation constant:

KNd1 ¼ KCf1þXN�1

i¼2e�bDG�1

iþ12;N;minði;9Þ�DG0Nþ13;N;minðN;9Þ

þ e�b DG0

Nþ12;N;minðN;9Þ�DG0Nþ13;N;minðN;9Þ

h ig;where β−1=kBT with kB the Boltzmann's constantand T the absolute temperature, C is the concen-tration of the complementary NTP, k1 is themaximum rate for the irreversible step of thepolymerization, and KC is the equilibrium dissocia-tion constant for the complementary NTP.Based on the same rapid equilibrium kinetics, we

can also calculate the overall reaction rate from theRNAP state P0(M, N, n) to the state P0(14, 2, 2) in theabortive pathway. The full calculation method is thesame as that for calculating the scrunching ratesexcept that the abortive pathway contains a two-substrate enzymatic reaction.6 Then the abortiverate of a nascent RNA of length N (the abortive rateat DNA site N) is:

kN�1 ¼k2AB

ABþ KBAþ KBKNd2

ð3Þ

with an effective equilibrium dissociation constantfor the first complementary NTP:

KNd2 ¼ KAfe�b½DG0

Nþ13;N;minðN;9Þ�DG014;N;2�

þXN�1

i¼2e�bDG�1

iþ12;N;minði;9Þ�DG014;N;2

þ e�b½DG0Nþ12;N;minðN;9Þ�DG0

14;N;2�g;where A and B are the concentrations of the first andsecond NTPs needed for the polymerization, k2 is themaximum rate of the irreversible step of thepolymerization, and KA and KB are the equilibriumdissociation constants for the first and secondcomplementary NTPs, respectively.Different from the calculations of the scrunching

and abortive rates, a Michaelis–Mentenmechanism isnot needed for the escape pathway because nopolymerization reaction is involved there. We simplytreat it as an irreversible reaction29 and calculate therate from theRNAP stateP0(M,N, n) to the elongationcomplex by Arrhenius kinetics. We call it escape ratein this work. Using the rapid equilibrium kinetics, weobtain the escape ratewith a nascent RNAof lengthN(the escape rate at DNA site N):

kNþ1 ¼ UN=VN;

UN ¼ k3e�bDGþ1

12;N;minðN;9Þ ;

VN ¼ e�bDG0Nþ12;N;minðN;9Þ þ e�bDG0

Nþ13;N;minðN;9Þ

þXN�1

i¼2e�bDG�1

iþ12;N;minði;9Þ ;

ð4Þ

where k3 is a prefactor constant. Eqs. (2)–(4) are thebases of our calculation in practice.


Results and Discussion

In addition to the energy parameters of theDNA bubble and RNA–DNA hybrid, we stillneed seven extra parameters. These parametersare the energy difference between the bindingenergies of the RNAP–DNA interaction on thescrunching (abortive) and escape pathways, i.e.,ΔΔGbinding =ΔG+1

binding−ΔG0binding, the maximum

RNA polymerization rates k1 and k2, the equili-brium dissociation constants KA, KB and KC and theprefactor k3. ΔΔGbinding is known to depend on thepromoter sequence and its value is between 1 and7 kcal/mol.26–28 We always choose an intermediatevalue, 3.5 kcal/mol, except when we discuss theeffect of the binding energy. The remaining para-meters are k1=k2=24.7 s−1,11 KA=1800 μM, KB=31μM,6 KC=15.6 μM,11 and k3≈0.8 s−1,9; they areeither from previous theoretical studies or fromexperimental measurements or estimation. We donot further optimize these parameters because ourmodel with these parameters has already providedmuch insight about the transcription initiation.The current theoretical study mainly concentrates

on a series of biochemical experiments of transcrip-tion initiation in vitro carried out by Hsu et al.13 andVo et al.14,15 As in the experiments, we study RNAPkinetic properties on three promoters, T7A1, T5N25and T5N25anti (see Fig. 1c). The calculationmethodsare Monte Carlo simulation and analytical methods.

Abortive probability, MSAT and APR

Following the experimental studies,13 we firstcalculate three specific parameters of the transcrip-

Fig. 2. (a) Abortive probabilities for the three promotersReaction rates of the three promoters: the abortive rate k−sub 1(△). The latter two rates have quite different values at differe

tion initiation, the abortive probabilities, MSATs andAPRs for different promoters. According to thedefinition, the abortive probability reflects the possi-bility that the abortive process occurs at a certainDNA site. We calculate it by the following equation:

Pi ¼ Xi

T �Pi�1j¼2ðXj þ YjÞ

; ð5Þ

where Pi is the abortive probability at DNA site i,T=∑i=2

∞ (Xi+Yi) is the total times that RNAP leavesthe scrunching pathway, Xj and Yj represent thenumbers of the abortive RNA (getting into theabortive pathway and released) and the productiveRNA (getting into the escape pathway and full-length transcribed) at DNA site j in simulation. TheMSAT simply corresponds to the maximum site thathas nonzero abortive probability. The APR isobtained by calculating the ratio of the total abortiveRNA number to the total productive RNA numberfor the promoter. In our simulation, it is indeedthe average number of the abortive products persuccessful escape event. Figure 2a and Table 1summarize the three parameters obtained from theexperiment and our simulation at 100 μM NTPs. Wesee that the agreement is satisfactory in quantitativeand qualitative ways, especially for theMSATs. Thus,our model has captured some essence of the trans-cription initiation.In order to understand the good prediction of the

MSATs in our model, we list all of the reaction ratesat each DNA site for the three promoters in Fig. 2b.We immediately see that the abortive rates arealmost invariant along the DNA sequences. This isnot unexpected according to Eq. (3), because thestate energy of the RNAP–promoter complex P(14,

at different sites. Insets are the experimental results. (b)(×), the scrunching rate k0 (○), and the escape rate k+sub 1nt sites. The NTP concentration is 100 μM.

Table 1. The MSATs and APRs at 100 μM NTPs obtainedby the experiment13 and our simulations at 100 μM NTPs

Sequence

MSAT (nt) APR

Experiment This study Experiment This study

T5N25 10 10 31±5 31T5N25anti 15 12 174±27 102T7A1 8 8 7±2 12


N, 2) is lower than those of all other RNAP–promoter complexes (data not shown). The invar-iant abortive rates also remind us that the quanti-tative characteristics of the transcription initiationshould be determined by the scrunching and escaperates. For instance, if the escape rate k+1

N at DNA siteN is much larger than the other two rates, or thescrunching rate k0

N− 1 at the upstream siteN−1 is toosmall to make RNA synthesis extend to site N, theabortive process would rarely occur at DNA site Nand the MSAT would be N−1. We apply the sameanalysis to the real promoters. Figure 2b shows thatfor T5N25 the escape rates are larger than theabortive rates after site 11, and the scrunching ratesbecome very small relative to the other two ratesafter site 10. For T5N25anti, although the abortiveand escape rates are comparable at all higher sites,the scrunching rates become much smaller than theother two rates after site 12. Finally, for T7A1 thescrunching rates are not small until site 13, but theescape rates become much larger than the other tworates after site 8. Hence, the MSATs should be 10 ntfor T5N25, 12 nt for T5N25anti, and 8 nt for T7A1.All of them are consistent with those obtained by thesimulations. From the discussion above we can seethe scrunching and escape rates are the twodeterminate factors for the MSAT. Additionally, wealso analyze other promoters' MSATs (7 nt for PL,7 nt for PR).

15 The difference between our predic-tions and the experimental data is no more than 1 nt.The discrepancies between our calculations and

the experimental data on the abortive probability,MSAT and APR may be induced by two possiblereasons. First is that the current transcriptioninitiation model uses nonoptimal parameters. Sec-ond is the significant fluctuations of the abortiveprobabilities at higher sites, especially for T5N25and T5N25anti; see the error bars in Fig. 2a. Thisuncertainty is attributed to the very low scrunchingrates; only small amounts of the abortive andproductive transcripts are produced at those sites.

Unproductive ITC

The experiment found an unusual class of ITCs,which synthesizes mostly abortive transcripts of 2–3 nt and escapes from the promoters extremelyslowly, if at all.14 These ITCs were called unproduc-tive ITCs. Based on the experimental measurementthat the RNAP activities of these unproductive ITCswere very similar with the activities of the produc-tive ITCs, Vo et al. suggested that the conformationof the unproductive ITC was distinct from the

conformation of the productive one.14 A possibleconsequence of the conformational difference of theITCs is that they have different binding energies.30

To test this hypothesis, we increase the bindingenergy differenceΔΔGbinding to 4.5 kcal/mol and dothe simulation again. We see that, although theMSATs are the same as before, the APRs of the threepromoters change dramatically: 155 for T5N25, 256for T5N25anti and 17 for T7A1. It means that RNAPsspend much more time in abortive cycles and hardlyenter into the elongation phase.This observation is expected according to Eq. (4):

increasing of the binding energy decreases the escaperate or lowers the probability of RNAP escaping frompromoter.On the experimental side, it has been knownthat the variation of the specific binding energy ofRNAP on promoter is about 2 kcal/mol.9 Hence, theITC conformational changes that decrease the specificbinding energy could be a possible reason for thepresence of the unproductive ITCs. A similar explana-tion was also mentioned by experimenters.31

Addition of 2-nt product RNA

In contrast to longer RNA chains, 2-nt RNA canfreely enter intoRNAP through the secondary channelwithout steric constraints.6,7 Particularly, the additionof the 2-nt product RNA makes the 2-nt RNA-releasing step reversible (Fig. 1b).Under this situation,the abortive rate at site 2 has the following expression:

k2�1 ¼k2AB

ABþ RkRðABþ KBAþ KBKA þ KAKBe

�bðDG015;2;2�DG

014;2;2ÞÞ

;

ð6Þ

whereKR is the dissociation constant for the 2-nt RNAand R denotes the concentrations of the 2-nt RNA insolution.If R is larger than KR, this abortive rate at site 2 is

smaller than that given by Eq. (3). This means thatadding the 2-nt product RNA in solution shouldinhibit the release of the nascent 2-nt RNA. We carryout simulations to confirm this inhibition effect. Asan illustration, we set R/KR=10. The simulationshows that the abortive probability at site 2 reducesfrom 17.5% to 2.5%, and the abortive probabilities atother sites have no visible changes. This confirmsour simple inference. The experiment also showed asimilar effect.7

NTP-concentration dependence of thetranscription initiation

NTP concentration plays important roles in thetranscription initiation. Surprisingly, the experi-ments found that the influence of NTP concentrationis more complicated than the sole influence topolymerization reactions.13,14 For instance, theexperiment showed that as NTP concentrationsincreased, there was an increase in the amounts ofboth the abortive and the productive transcripts, incontrast to the prediction given by the two-pathway

Fig. 3. Quantitative characteristics for T5N25 at different NTP concentrations. Squares are the results with the NTP-assisted RNA releasing assumption and triangles are the results without that assumption. (a) Average productive rates atdifferent NTP concentrations. (b) Average abortive rates at different NTP concentrations. (c) Abortive/productive ratiosat different NTP concentrations. (d) Abortive probabilities at different NTP concentrations and sites. Insets in (a), (b) and(c) are the experimental data. Their labels are the same as those in the main figures.


kinetic competition model.13 Moreover, NTP con-centrations are even capable of modulating the par-tition of the productive and unproductive ITCs.14

Hence, understanding the influence of NTP concen-tration to initiation is one of the biggest challenges toour model.

Effects of varying all NTP concentrations

We first change the concentrations of all four NTPsfrom 100 to 600 μM and repeat the previoussimulation for T5N25. Through the simulation, wecan get the dependence of the abortive rates, theAPRs and the abortive probabilities on the NTPconcentrations directly. The dependence of theproductive rates kp (the rate of obtaining the full-length transcripts) on the NTP concentrations iscalculated by the following equation:

kp ¼ 1Ti þ Te

; ð7Þ

where Ti and Te are the time spent in the initiationand elongation phases, respectively. We calculate Teby the transcript length dividing the elongation rate[Eq. (3) in Ref. 11]; an average state energy differenceis used here. The results are shown in Fig. 3. We seethat there is a positive dependence of both theproductive rates and the abortive rates (Fig. 3a andb). We also note that these concentration dependen-

cies are significantly different. Increase of the pro-ductive rates is limited, while the abortive ratesincrease linearly and a plateau is still not reachedeven at 600 μM. In addition, the APRs exhibit alinear dependence on the NTP concentrations (Fig.3c), and the abortive probabilities change little whenthe NTP concentrations are above 100 μM (Fig. 3d).All of the observations are qualitatively consistentwith those of the experiment13 (insets in Fig. 3).These interesting observations can be qualitatively

understood in our model. First, let us see the NTP-concentration dependence of the productive andabortive rates. Unlike the two-pathway kineticscompetition model13 in which the NTPs are notinvolved in the abortive process, in our model,based on the NTP-assisted RNA-releasing assump-tion, the abortive, scrunching and elongation ratesare all NTP dependent; see Eqs. (2) and (3) and Refs.11,12. Obviously, these equations ensure that boththe productive and the abortive rates are positivelydependent on the NTP concentration. On the otherhand, their dependence has a fine difference. For thescrunching and the elongation rates, the dissociationconstants of the complementary NTPs are 15.6 μM.The elongation rate then reaches the maximumearlier at 600 μM NTPs.11,12 Considering that theelongation phase is time-limited in the productiveprocesses (Te∼10Ti in simulations), the increase inthe productive rate is therefore limited. In contrast,for the abortive rate, the dissociation constant KA

Fig. 4. Effect of varying individual NTP concentrations on the abortive pattern. (a) Abortive probabilities after varyingATP, UTP and GTP concentrations for T5N25. (b) Abortive probabilities after varying ATP, CTP and GTP concentrationsfor T7A1.


of the first complementary NTP is 1800 μM. Theabortive rate is still not saturated at 600 μM NTPs(Fig. 3a and b).Based on the above discussion, we can then

understand the reason why the APRs exhibit alinear dependence on the NTP concentrations (Fig.3c): the APR is proportional to the abortive rates,while the abortive rates increase linearly with theincrease in the NTP concentrations. Finally, con-sidering that the amount of the abortive RNAs ismuch larger than that of the full-length transcripts athigh NTP concentrations, the contribution of thelatter to the abortive probabilities is negligible.Because the numbers of the abortive RNAs at eachsite are proportional to the abortive rates at thosesites, and these rates have similar dependence on theNTP concentrations, the abortive probabilities areinsensitive to the NTP concentrations as they arehigh enough (Fig. 3d).

Effects of varying individual NTP concentrations

Next we vary individual NTP concentrations tosimulate their effects on the transcription initiationfor T5N25 and T7A1. The results are shown inFig. 4. For T5N25 nothing unusual happens whenthe ATP and uridine triphosphate (UTP) concentra-tions are varied independently. But when we inc-rease the guanosine 5′-triphosphate (GTP) concen-tration, the abortive probability at site 8 decreasesprominently as observed in the experiment.13 ForT7A1 there are also some unusual sites while vary-ing the cytidine triphosphate (CTP) and the GTPconcentrations.

The observations in the simulation and the expe-riment could be explained by our model. Weattribute them to the NTP dependence of theabortive rates. The polymerization reactions in thescrunching pathway need all kinds of NTPs, whilethe polymerization reactions in the abortive path-ways only need two kinds of NTPs that arecomplementary to the first two nucleotides of theDNA template. They are ATP and UTP for T5N25and T7A1, respectively. If the concentrations of thesetwo NTPs are increased, the scrunching andabortive rates at the sites that need ATP and UTPfor polymerization would increase simultaneously.In contrast, if the concentrations of the other twoNTPs are increased, the scrunching rate wouldincrease at the sites that need GTP or CTP forpolymerization, while the abortive rate would notchange. Hence, at these sites the possibility that thescrunching reaction occurs increases, while theabortive possibilities decrease with the increase inthe GTP or CTP concentration. For T5N25, the firstsite that is not A or U is G9 and the next is G11.According to our analysis above, at sites U8 andA10, GTP is only needed by the RNA polymeriza-tion reaction in the scrunching pathway; thus, theabortive probabilities at those sites should decreasewhen the GTP concentration is increased. This effectat site U8 has been confirmed by our simulation (seeFig. 4a), but at site A10, this effect is not significantdue to the large fluctuation. For T7A1, we predictthat the abortive probability at site U2 woulddecrease if we increased CTP concentration, andthe abortive probabilities at sites C3, A5 and A7would decrease with increasing GTP concentration.


All of them except site A7 are confirmed by oursimulation (Fig. 4b). No prominent effect at site A7 isdue to the small abortive probability at this site.All these results show that NTP-assisted RNA

releasing assumption (Fig. 1b) can well account forthe influence of the NTP concentration on theabortive process. We also carry out the simulationwithout this assumption, which was assumed in thetwo-pathway model. The calculation results areshown in Fig. 3a–c (triangles). We see that they arenot comparable to the experimental data.

Conclusion

In this work we establish a three-pathway modelto account for the sequence-dependent features ofthe transcription initiation. Our model shows thatdifferent promoters have different abortive prob-abilities, MSATs and APRs. These calculations agreewith the experimental data well. By including theNTP-assisted RNA-releasing assumption, ourmodel can account for the effects of the NTPconcentrations on the transcription initiation. Wealso present a possible explanation for the unpro-ductive initiation transcribing complex observed inthe experiments, namely, it could be induced by thelarge energy gap between the specific and non-specific RNAP–DNA bindings. All of these resultsare based on our assumed pattern of the abortivepathway. We believe they would not be changedmuch if other possible pathway patterns were used,because the most important states in the initiationtranscription should be always P0(14, N, 2), P0(M,N,n) and P0(M+1, N, n).Nonetheless, some discrepancies remain between

our calculations and the experimental data. Furtherdevelopment of the three-pathway transcriptioninitiation model is necessary. One possible way isto improve the prediction ability of our model byusing optimized parameters or considering the NTPdependence of the maximum RNA polymerizationrates and the equilibrium dissociation constants.32

In addition, combining new knowledge abouttranscription initiation into the current three-path-way model is another possible way. The latterwould become more important when new experi-mental techniques, e.g., single-molecule fluores-cence spectroscopy,10 are applied in the studies oftranscription initiation. We hope that such animproved model would come in the near future.

Acknowledgements

We are very grateful to Prof. R. H. Ebright forgenerously sharing his idea about transcriptioninitiation. We also thank Dr. Li Ming, Gong Linchenand Shuching Ou for their helpful discussion aboutthis work. This work is funded in part by TsinghuaBasic Research Foundation and by the National

Science Foundation of China under Grant No.10704045.

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a kinetic model of transcription initiation by rna polymerase

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