Please cite this article in press as: Depken et al., Intermittent Transcription Dynamics for the Rapid Production of Long Transcripts of High Fidelity, Cell
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Cell Reports
Article
Intermittent Transcription Dynamics
for the Rapid Production
of Long Transcripts of High Fidelity
Martin Depken,1 Juan M.R. Parrondo,2,3 and Stephan W. Grill3,4,*
1Department
of Bionanoscience, Kavli Institute of Nanoscience, Delft University of Technology, Lorentzweg 1, 2628 CJ Delft, the Netherlands
de Fisica Atómica, Molecular y Nuclear and GISC, Universidad Complutense de Madrid, 28040 Madrid, Spain
3Max Planck Institute for the Physics of Complex Systems, Nöthnitzerstrasse 38, 01187 Dresden, Germany
4Max Planck Institute of Molecular Cell Biology and Genetics, Pfotenhauerstrasse 108, 01307 Dresden, Germany
*Correspondence: [email protected]
http://dx.doi.org/10.1016/j.celrep.2013.09.007
This is an open-access article distributed under the terms of the Creative Commons Attribution-NonCommercial-No Derivative Works
License, which permits non-commercial use, distribution, and reproduction in any medium, provided the original author and source are
credited.
2Departamento
SUMMARY
Normal cellular function relies on the efficient and accurate readout of the genetic code. Single-molecule
experiments show that transcription and replication
are highly intermittent processes that are frequently
interrupted by polymerases pausing and reversing
directions. Although intermittent dynamics in replication are known to result from proofreading, their
origin and significance during transcription remain
controversial. Here, we theoretically investigate transcriptional fidelity and show that the kinetic scheme
provided by the RNA-polymerase backtracking
and transcript-cleavage pathway can account for
measured error rates. Importantly, we find that intermittent dynamics provide an enormous increase in
the rate of producing long transcripts of high fidelity.
Our results imply that intermittent dynamics during
transcription may have evolved as a way to mitigate
the competing demands of speed and fidelity in the
transcription of extended sequences.
INTRODUCTION
Central to fidelity in both replication and transcription is that the
different nucleotides possess different affinities for base pairing
with template nucleotides inside the respective polymerase.
Although substantial (Blank et al., 1986), this selectivity is ultimately limited by early and immutable evolutionary choices
pertaining to nucleotide chemistry. As organisms evolved and
diversified, longer genes and bigger genomes needed to be
processed (Xu et al., 2006). With a concurrent increase in demand on fidelity, both DNA and RNA polymerases (RNAPs)
have evolved proofreading mechanisms capable of removing
errors that have already been incorporated into their growing
polymer product. Utilizing such mechanisms, replication reaches an error ratio (number of incorrect bases divided by the
number of correct bases in the final transcript) of the order
of 1/108 (Kunkel and Bebenek, 2000), whereas transcription
achieves an error ratio of at least 1/105 (Sydow and Cramer,
2009).
The theoretical underpinning of kinetic proofreading was
established by Hopfield almost 40 yeas ago (Hopfield, 1974).
However, the standard treatment assumes the bases to be
repeatedly checked before being permanently incorporated
into the growing transcript, and this preincorporation selection
(PIS) results in an ever-growing transcript. With the event of
single-molecule techniques, it is now well established that both
RNA and DNA polymerases elongate their product in a highly
intermittent manner: repeatedly pausing, moving backward,
and cleaving off bases from the growing molecule (Erie et al.,
1993; Donlin et al., 1991; Thomas et al., 1998; Orlova et al.,
1995; Wang et al., 2009; Galburt et al., 2007; Wuite et al., 2000;
Ibarra et al., 2009; Kireeva and Kashlev, 2009). In fact, postincorporation proofreading (PIP) through transcript cleavage has
long been recognized as playing a vital role in error suppression
(Erie et al., 1993; Thomas et al., 1998; Sydow and Cramer,
2009; Ibarra et al., 2009; Kunkel and Bebenek, 2000; Jeon and
Agarwal, 1996) but has received little attention at a quantitative
theoretical level (Voliotis et al., 2009, 2012).
Using stochastic modeling, we here explore the downstream
effects of PIP in transcription and elucidate the connection
among proofreading, intermittent transcription dynamics, and
overall elongation performance. Our stochastic hopping model
(Greive and von Hippel, 2005) is built using structurally wellcharacterized states, with transition rates measured in physiologically relevant settings. Importantly, the model introduces a
coupling between chain elongation and the observed transcript
shortening induced by proofreading (Erie et al., 1993; Thomas
et al., 1998)—a connection not accounted for in Hopfield’s
original development (Hopfield, 1974). In fact, the highest error
suppression calculated within the standard scheme corresponds to a pathological situation with a net shortening of the
transcript over time. This highlights the importance of performing
a detailed analysis of both fidelity and elongation dynamics.
Our analysis shows that PIP can account for an error reduction
of over two orders of magnitude under ideal conditions. It can
thus in principle account for the difference between what is
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Please cite this article in press as: Depken et al., Intermittent Transcription Dynamics for the Rapid Production of Long Transcripts of High Fidelity, Cell
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observed in fidelity experiments and what can be expected from
the relative base-pairing energies of matched and mismatched
base pairs (bp) (Sugimoto et al., 1995; Blank et al., 1986). By
considering the transcription of extended sequences, we further
suggest evolutionary arguments for why the dynamics of an
efficiently transcribing RNAP should be expected to be intermittent when adapted to transcribing long sequences at high
fidelity and speed.
RESULTS
Transcriptional Error Suppression
Much of previously published theoretical work on RNA transcription has focused on recovering the sequence-dependent
part of pausing patterns captured in transcription gels (Bai
et al., 2004; Tadigotla et al., 2006; Maoiléidigh et al., 2011) and
more recently through deep sequencing of nascent transcripts
(Churchman and Weissman, 2011). However, proofreading is
a process that should be efficient on a wide variety of genes.
To identify mechanisms that function on generic sequences,
we adopt a sequence-averaged view throughout this work.
This is not to say that there is no sequence dependence in transcriptional pausing, which is clearly evidenced by strong pause
sites (Nechaev et al., 2010), but is rather to focus on the high level
of stochastic backtracking observed throughout, for example,
highly transcribed genes (Churchman and Weissman, 2011).
To capture the effect of thermal fluctuations, we describe transcription as a stochastic hopping process between well-defined
states, with transition rates set by the intervening free energy
barriers (Risken, 1989). Although there is a wealth of biochemical
studies of transcription and transcriptional fidelity (Kellinger
et al., 2012; Thomas et al., 1998), the kinetic rates extracted
from these studies are often effective rates that depend on
implicit model assumptions. On the other hand, the more directly
interpreted single-molecule data are incomplete for any particular polymerase. Therefore, we here rely on the great structural
homology present among bacterial, eukaryotic, and archaeal
polymerases (Ebright, 2000; Hirata et al., 2008) to infer order of
magnitude estimates of transition rates between microscopic
states for an imagined generic RNAP. Although there will be
quantitative differences for any particular real polymerase, the
physical mechanisms we consider will remain applicable.
Following Hopfield (1974), we take the error suppression to
be achieved through a sequence of serially connected energyconsuming, molecular-scale, and error-correcting checkpoints.
The quality of a checkpoint i is judged by the fraction ri of errors
it lets through, and the quality of several sequential checkpoints
is given by the product of individual error fractions r1r2r3. (see
Extended Results).
In transcription, both PIS and PIP are controlled by the same
multifunctional active region inside the RNAP (Kettenberger
et al., 2003; Opalka et al., 2003). The PIS process likely involves
several steps before the incoming nucleotide is catalyzed
onto the growing RNA molecule (Sydow and Cramer, 2009).
The relative occupation of the catalysis-competent state is
dictated by the free energy cost of aligning different nucleotides
in the active site. A lower bound on the energetic penalty for
aligning a mismatch rather than a match can be estimated
2 Cell Reports 5, 1–10, October 17, 2013 ª2013 The Authors
from the free energy cost of nucleotide mismatches in RNADNA duplexes in solution: DGact z6 kB T (Sugimoto et al., 1995;
Blank et al., 1986), giving rPIS zexpðDGact =kB TÞz1=400. By
utilizing differences in base-pairing energies alone, and assuming that the polymerase operates close to the lower energetic
bound on mismatch penalties, we would therefore expect no
more than a few hundred bp to be reliably transcribed without
errors.
To correctly transcribe longer sequences, further error suppression is needed. One way of increasing fidelity beyond
what is given by base-pairing energies is through additional
discriminatory interactions in the active site. Accounting for the
full fidelity of the polymerization process in this way (Kellinger
et al., 2012) would require the total barrier to catalysis to differ
by a full ln ð105 ÞkB Tz12 kB T between the correct and incorrect
base. Although there is likely a change in the barrier to transcription as an error is incorporated, the extent of this change is
unknown. Here, we investigate the theoretical bounds on
fidelity gains offered by the experimentally established alternative to direct energetic penalties: proofreading through PIP
(Erie et al., 1993; Thomas et al., 1998; Sydow and Cramer,
2009; Ibarra et al., 2009; Kunkel and Bebenek, 2000; Jeon and
Agarwal, 1996). In the next section, we show that, by the inclusion of PIP, the total error suppression can reach physiological
levels without assuming large energy penalties beyond that
offered by base pairing alone.
Proofreading through Backtracking
PIP-mediated fidelity increases are controlled by the RNAP
entering a backtracked state followed by error removal through
transcript cleavage. The backtracked state is an off-pathway
state where the whole polymerase is displaced rearwards on
the template (Shaevitz et al., 2003; Galburt et al., 2007) and
from which the nascent transcript can be cleaved upstream
from the 30 end (see Figures 1A and 1B). Although the physiologically relevant scenario is one with multiple positions to
backtrack to and cleave from, it is instructive to first consider
the hypothetical case of a polymerase restricted to only one
backtracked state where the polymerase is displaced by a
single bp.
Single-State Backtracking
As the polymerase backtracks, the internal 8–9 bp RNA-DNA
hybrid remains in register by breaking the last-formed base
pair and reforming a previous base pair at the opposite end of
the hybrid (Shaevitz et al., 2003; Galburt et al., 2007; Wang
et al., 2009) (see Figures 1B and 1C). This exposes already
incorporated bases to the active site, blocking further elongation
but enabling cleavage of the most recently added base (catalyzed by the transcription factor IIS in eukaryotes and GreA
and GreB in prokaryotes) (Fish and Kane, 2002; Borukhov
et al., 2005; Jeon and Agarwal, 1996; Awrey et al., 1998; Opalka
et al., 2003; Kettenberger et al., 2003; Sosunov et al., 2003;
Thomas et al., 1998). If cleaved, a potential error is removed,
the active site is cleared, and elongation can resume. The cleavage process competes with the spontaneous recovery from
the backtrack (Galburt et al., 2007), by which the polymerase
returns to the elongation-competent state without removing
the potential error (see Figure 1C).
Please cite this article in press as: Depken et al., Intermittent Transcription Dynamics for the Rapid Production of Long Transcripts of High Fidelity, Cell
Reports (2013), http://dx.doi.org/10.1016/j.celrep.2013.09.007
A
D
Figure 1. Single-Step Backtracking
(A) The basic hopping model coupling one-step
backtracking to elongation is presented. The repetitive unit is highlighted, with the off-pathway
backtracked state indicated as BT. After entering a
backtrack, elongation can resume either through
cleavage out to a previous state of the chain
ðNMPÞn1 or by recovery without cleavage to the
B
entrance state ðNMPÞn .
(B) Schematic illustration shows the repeat unit
with a correct base incorporated last. The temE
plate strand, the nascent transcript, and the hybrid
region of the polymerase are shown. The poly2,000
merase can enter a backtrack with rate kbt or add a
base to the transcript with rate kcat . From the
backtracked state, recovery by cleavage occurs
with rate kclv , whereas realigning without cleavage
1,000
occurs at a rate krec .
(C) is the same as (B) but with an incorrect
C
base at the growing 30 end of the transcript.
The corresponding rates are indicated with the
superscript I.
(D) Sketch shows the free energy landscape
corresponding to (B) and (C). Solid black line
corresponds to the last base correct; dashed
red line corresponds to the last base incorrect.
-1,000
DGact refers to the free energy increase at the
active site when the last incorporated base is
wrong, whereas DGcat denotes the corresponding increase in the barrier to catalysis (cat).
Recovery without cleavage occurs at a rate kbt , which places all selectivity in the entrance step to the backtrack (see text).
(E) Three traces simulated with a Gillespie algorithm are illustrated: a generic polymerizing RNAP with (kcat = 10=s, kbt = 1=s, kclv = 0:1=s; see main text); a stalled
polymerase (kcat = 1=s, kbt = 10=9=s, kclv = 10=s); and a depolymerase (kcat = 1=s, kbt = 10=s, kclv = 10=s). Traces are black when the polymerase is elongating and
red when backtracked.
In order for cleavage from the backtracked state to lower the
error content, the net effect of backtracking and cleavage must
be to selectively remove erroneous bases rather than correct
ones. The inability of incorrectly matched bases to form proper
Watson-Crick base paring within the RNA-DNA hybrid induces
this selectivity. If an error has been catalyzed onto the 30 end
of the nascent RNA molecule, the total energy of the transcription complex is lowered if the RNAP moves into a backtrack
(see Figure 1D). Doing this, the RNAP extrudes the unmatched
bp from the hybrid and, so, returns to the low energy state of
a perfect Watson-Crick base pairing within the entire hybrid
(see Figure 1C).
Because the backtracking process needs not to equilibrate,
the total fidelity enhancements might depend on the free
energy of transition barriers as well as on the free energy of
the states themselves. Specifically, the manner in which misincorporations affect the transition state to backtracking determines if fidelity is increased through a selectively increased
entrance rate into the backtrack (no shift of transition state)
or by a decreased exit rate out of the backtrack (transition state
shifts with the hybrid energy). For the latter case to have an
appreciable proofreading capability, every single base must
be extruded from the hybrid through backtracking, or else
only a fraction of the incorporation errors will be proofread by
selectively prolonged exposure to cleavage. The required high
backtracking frequency would render the polymerization process inefficient, possibly even reverse it (see below). This is
clearly not what is observed in experiments (Galburt et al.,
2007; Abbondanzieri et al., 2005). We thus take the selectivity
to reside in the entrance step of the backtrack (see Figure 1D),
which ensures that all bases are checked, that backtracks are
predominantly induced by incorrect bases, and consequently,
that transcription can be both fast and accurate. For rates
as illustrated in Figures 1B and 1C, this corresponds to
I
I
= kbt and kbt
= kbt expðDGact =kB TÞ (rates for incorrect
krec = krec
bases are denoted with the superscript I). We will simply refer
to kbt as the backtracking rate, and we illustrate the resulting
form of the free energy landscape in Figure 1D. For our generic
RNAP, we use kcat = 10=s (Neuman et al., 2003; Tolic
Nu˛rrelykke et al., 2004) (prokaryotic) (Galburt et al., 2007)
(eukaryotic), backtracking rate kbt = 1=s (Depken et al., 2009)
(prokaryotic), and cleavage rate kclv = 0:1=s (Galburt et al.,
2007) (eukaryotic).
It is worth pointing out that there is evidence for an intermediate state between elongation and backtracking (Herbert et al.,
2010). Based on the average diffusion constant over several
backtracks (Depken et al., 2009), as well as direct observation
of backtracking in individual traces (Abbondanzieri et al.,
2005), we here assume a backtracking rate of the order one
step a second. Because this rate is close to the rates expected
for traversing the intermediate state, we simply absorb such a
possible state into the first state of the backtrack.
In a development largely parallel to the theory of kinetic proofreading through PIS (Hopfield, 1974), these rates are used to
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A
Figure 2. Multistep Backtracking
B
second
first
C
calculate the error suppression of PIP (see Extended Results;
Figure S1):
k
:
cat
(Equation 1)
rz
ðDGact + DGcat Þ
kcat + kclv exp
kB T
Here, DGcat denotes the change in barrier height for the transition to catalysis when trying to incorporate a base directly
after an error (see Figure 1D). We can get an estimate of
DGcat from published experiments that use the nucleotide
inosine to simulate the effect of a misincorporation on the addition of the next nucleotide to the nascent strand (Thomas et al.,
1998). From this, we estimate DGcat z2kB T. Assuming that
DGact is governed by the energy cost of mismatches, we estimate DGact z6 kB T (see above). For our generic polymerase,
this implies proofreading capabilities for PIP that amount to a
modest rPIP z1=30.
A comparison of the regular traces of Figure 1E with those
from single-molecule experiments (Galburt et al., 2007; Depken
et al., 2009; Ibarra et al., 2009) also demonstrates that the onestep backtracking does not adequately capture the observed
intermittent transcription dynamics (see also below). Although
much of the intermittent dynamics seen in experiments has
been attributed to structural heterogeneity through sequencespecific pauses (Herbert et al., 2006; Neuman et al., 2003;
Ibarra et al., 2009; Bai et al., 2004; Tadigotla et al., 2006;
Maoiléidigh et al., 2011), we will argue for another functional
explanation for a large subpopulation of these pauses: they
are essential for improving fidelity beyond what is allowed by
Equation 1.
4 Cell Reports 5, 1–10, October 17, 2013 ª2013 The Authors
(A) The basic repeat unit of multistate backtracking
in a nested scheme is presented. For visual clarity,
only the backtracked states in the highlighted
repeat unit are drawn.
(B) Sketch shows the free energy landscape of a
multistate backtrack. Solid black line corresponds
to the last base correct; dashed red line corresponds to the last base incorrect. Also illustrated
are the multiple backtracked states and the effect
of cleavage. See legend to Figure 1B for a
description of the rates.
(C) Three traces simulated with a Gillespie algorithm are illustrated: a generic polymerizing RNAP
with (kcat = 10=s, kbt = 1=s, kclv = 0:1=s); a stalled
complex (kcat = 10=s, kbt = 10=s, kclv = 0:1=s); and a
kbt = 10=s,
depolymerizing
one
(kcat = 1=s,
kclv = 0:1=s)—all in accordance to the theoretical
predictions derived in the Extended Results. A
section of the trace for our generic polymerase
has been magnified, showing two backtracks: one
rescued to elongation by cleavage, and one by
diffusion. Only the backtrack reentering elongation
through cleavage would have corrected an error
at the end of the transcript. Traces are black
when the polymerase is elongating and red when
backtracked.
Multistep Backtracking
It is clear from Equation 1 that, apart from increasing the
energy penalty for a mismatch, a low error ratio can be achieved
through having a high transcript-cleavage rate compared to the
elongation rate. Given their reverse arrangement (kcat = 10=s,
kclv = 0:1=s), it seems reasonable to consider the case where
the evolution of these rates has been strongly limited by external
constraints pertaining to nucleotide chemistry and the intercellular environment. To mediate these external constraints,
the polymerase would have to evolve alternative internal paths
to increase error suppression.
One such internal path could be to reduce the free energy
of the backtracked state. This would suppress spontaneous
reversal of the backtrack and increase the probability of cleavage and error removal. Because a substantial part of the free
energy relates to the energetics of base matching within the
hybrid, the energy level of the backtracked state is likely constrained by the structure of the hybrid—again presumably fixed
by early evolutionary choices. However, there exists another
possibility: an effective entropic reduction in the free energy
level of the backtracked state can be achieved by extending
the number of accessible states. RNAP is indeed able to backtrack by more than just one base and thermally move between
the different backtracking states that are available (Nudler
et al., 1997; Komissarova and Kashlev, 1997a, 1997b; Shaevitz
et al., 2003; Galburt et al., 2007) (see Figures 2A and 2B). With
N off-pathway and backtracked proofreading states, the free
energy associated with the backtracked state would in an
equilibrium setting be reduced by the entropic term kB T lnðNÞ.
This mechanism delays spontaneous recovery and raises the
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Figure 3. A Second PIP Checkpoint
The polymerase is expected to be sensitive to errors incorporated also next
to last. The magnitude of the rates is illustrated by relative thickness of the
transition arrows; bad base stackings are indicated in red. G indicates the free
energy of the complex with respect to the elongation-competent state.
chance of error removal also in our out-of-equilibrium setting
(see Extended Results).
When acting through extended backtracked states, the error
suppression of PIP can be calculated as (see Extended Results
and Figure S1)
kcat
r1:PIP z
pffiffiffiffiffiffiffiffiffiffiffiffi
ðDGact + DGcat Þ
kcat + kclv kbt exp
kB T
=
kcat
;
DG1:PIP
kcat + kbt exp
kB T
1
kbt
DG1:PIP = DGact + DGcat kB T ln
:
2
kclv
(Equation 2)
(Equation 3)
Comparing Equation 2 to Equation 1, we see that fidelity is
increased by extending the space available for backtracking:
the low cleavage rate kclv is replaced by the geometric mean
pffiffiffiffiffiffiffiffiffiffiffiffiffi
kclv kbt . This increases the fidelity by a factor of about three
for our generic polymerases and provides an error reduction of
r1:PIP z1=100.
With an extended backtracking space, it is now clear from
simulated traces (Figure 2C) that the intermittent dynamics of
our generic polymerase qualitatively match the intermittent
dynamics observed in single-molecule experiments (Herbert
et al., 2006; Neuman et al., 2003) (see below for a quantitative
assessment). It is worth pointing out that even with infinite
room for backtracking, our generic polymerase would only
backtracking steps and reach
take around kbt =kclv = 10 diffusive
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
a typical depth of around N = kbt =kclv z3 before being cleaved
off. This depth is below the lower estimates for the distance to
RNA hairpin barriers in the trailing RNA strand (Klopper et al.,
2010). We should thus be justified in assuming the available
backtracking distance to be effectively infinite even when accounting for possible barriers to backtracking (see Figures 2A
and 2B).
By comparing the experimental effects of cleavage-stimulating factors with the effect of increasing cleavage rates in
simulated traces, we provide further support of our kinetic
scheme in the Extended Results (Figure S2). We also show
that our model can capture the stalling dynamics of a polymerase as it transcribes against an increasing force (Galburt et al.,
2007; Depken et al., 2009). It is interesting to note that because
of these dependencies of backtracking dynamics on the load,
one would also expect the fidelity of transcription to generally
depend on load (Voliotis et al., 2012). Although the extension
of the backtracking space provides for an increased fidelity
already on this level, we now show that it gives additional
proofreading benefits by supplying the polymerase with further
PIP checkpoints.
Further Backtracking Checkpoints
Even when additional bases have been added to the transcript
after an erroneous incorporation, the error can in principle still
be corrected through an extended backtrack and cleavage
(Voliotis et al., 2009). For this to lead to an appreciably
increased likelihood of error removal, the RNAP must still be
biased toward entering into the backtrack. With an error at
the penultimate 30 position of the transcript, the polymerase
experiences such a bias: moving into a backtrack will eliminate a bad bp stacking within the hybrid (see Figure 3). This
is followed by another heavily biased step to completely
extrude the error from the hybrid and, so, exposing it to the
cleavage reaction. We know of no direct measurement of
the penultimate bias DG2:PIP , but because the typical stacking
energy in a nucleic acid complex is 1:5 4:5 kB T (Sugimoto
et al., 1995), we assume DG2:PIP z3 kB T. This second PIP
checkpoint provides an error ratio (see Extended Results;
Figure S3) of
kcat
:
r2:PIP z
DG2:PIP
kcat + kbt exp
kB T
(Equation 4)
For our generic polymerase r2:PIP z1=3, and the total PIPinduced error reduction is rPIP = r1:PIP r2:PIP z1=300. Combined
with the PIS error correction expected from base-pairing energies alone, the PIP error correction brings the error fraction
down to rPIS rPIP z1=400,1=300z1=105 ; thus, our scheme quantitatively accounts for the typically observed error suppression
(Rosenberger and Hilton, 1983; Blank et al., 1986; de Mercoyrol
et al., 1992).
There could in principle be additional inherent PIP checkpoints that would enable the polymerase to reach an even
lower error ratio. A free energy penalty DGn:PIP for moving the
error further into the hybrid would incur the necessary longrange bias and additional fidelity gains according to (see
Extended Results)
rPIP = r1:PIP r2:PIP /rn:PIP /
kcat
:
rn:PIP z
DGn:PIP
kcat + kbt exp
kB T
(Equation 5)
It is interesting to note that for the considered range of rates,
the error suppression for multistate backtracks depends on
the backtracking rate (Equations 4 and 5), whereas for singlestate backtracks, it did not (Equation 1). The backtracking rate
is a parameter not directly dependent on nucleotide chemistry
and the external environment. This could render the backtracking rate susceptible to selective pressures pertaining to fidelity
requirements.
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Please cite this article in press as: Depken et al., Intermittent Transcription Dynamics for the Rapid Production of Long Transcripts of High Fidelity, Cell
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Figure 4. The Effects of Proofreading
A
20,000
B
40,000
60,000
80,000
C
D
Dynamic Effects of Proofreading
Before we address the problem of how much proofreading
is appropriate, we here illustrate the consequences of the proofreading states on pause duration and frequency, as they might
be observed in single-molecule experiments. To this end, we
simulate our generic RNAP transcribing a long homogeneous
sequence and compare it to a simulation of an otherwise
identical polymerase, but which has PIP turned off ðkbt = 0=sÞ.
In Figure 4A, we show a particular stochastic realization of
incorporation errors, i.e., those errors that pass through the
PIS checkpoint and get incorporated (red), together with the
errors left after the section has been exposed to PIP (black).
The fidelity enhancements are clearly visible, but they come at
the cost of both a decreased velocity as well as an increased
intermittency. These effects are qualitatively visible already at
the level of individual traces but are quantitatively best seen in
the changes of the dwell time distribution (see Figure 4B) or
in the transition rate (inverse dwell time) distribution (see Figure 4C). In the dwell time distribution, proofreading introduces
a power law regime, throughout which the probability of a long
pause falls off with duration t as t3=2 (Galburt et al., 2007;
Depken et al., 2009), until it drops off exponentially beyond
t = 1=kclv . With no cleavage, the power law would extend to
indefinitely long times (Depken et al., 2009). In Figure 4B, we
see a clear exponential behavior of the dwell time distribution
for both processes at around t = 1=kel = 0:1 s, whereas the
proofreading polymerase also has a broad regime consistent
with the above-mentioned power law decay extending out
to t = 1=kclv = 10 s. Similarly, considering the transition rate distributions, we see a narrow but significant low-velocity peak
6 Cell Reports 5, 1–10, October 17, 2013 ª2013 The Authors
100,000
(A) On top, we show a realization of incorporation
errors according to our free energy estimates
(only PIS in red), and below, we show the errors
that survive (or, possibly, are inserted by) the
proofreading mechanisms (PIS and PIP in black).
(B) The dwell time distribution for adding one
nucleotide to the nascent transcript, for processes
with (black-filled circles) and without (red filled
squares) proofreading (p.r.), is shown. Proofreading gives rise to a power law regime, significantly increasing the fraction of long pauses.
(C) The transition rate (inverse dwell time) distribution for the same processes as in (B) is shown,
where the effects of proofreading can be seen
through a shift from a unimodal to a bimodal
distribution because many excessively slow
transitions involving backtracks start influencing
the kinetics.
(D) The pause density, or the total occupation time
plotted for a 500 bp sequence transcribed by the
same two polymerases as used in (B) and (C), is
presented. The darker the bands, the longer the
total occupation time at that position. The scales
are individually normalized to cover the range of
occupation times for each polymerase (reaching
about 1 s without proofreading, and about 100 s
with proofreading). Two incorporation errors are
indicated with red markers.
develop around the transition rate kclv = 0:1=s, diminishing the
bare elongation peak situated around the rate kcat = 10=s (see
Figure 4C; note the log scale).
The pause density, or the total time a polymerase spends at
each position along the DNA molecule, is another important
experimentally observable parameter. In Figure 4D, we show
pause density plots along a sequence of 500 bp, with darker
bands indicating longer total time spent at that position during
the transcription process. Comparing transcription with and
without PIP, it is clear that PIP leads to greater heterogeneity, exhibiting distinct regions of markedly increased occupation density even where there are no incorporation errors. Thus, our
model can partially account for both the observed intermittency
as well as the broad pause time distributions (Neuman et al.,
2003; Galburt et al., 2007)—without the need to introduce any
sequence-specific effects (Depken et al., 2009; Galburt et al.,
2007).
Having shown that external constraints can be mediated
through accessing an internal extended backtracked space—resulting in intermittent transcription dynamics—we now turn our
attention to the specific level of backtracking observed in experiments. The induced intermittency is tuned by the backtracking
rate and because increasing it would render all proofreading
checkpoints more effective (see Equation 5), one might wonder
why the backtracking rate is kept moderate and not made
much larger (Depken et al., 2009; Abbondanzieri et al., 2005).
Evolutionary Optimization
In order to elucidate a possible underlying reason for why the
backtracking rate is kept moderate, we now consider the
Please cite this article in press as: Depken et al., Intermittent Transcription Dynamics for the Rapid Production of Long Transcripts of High Fidelity, Cell
Reports (2013), http://dx.doi.org/10.1016/j.celrep.2013.09.007
Figure 5. Polymerase Performance
Proofreading efficiency hPIP (red dot-dashed line), elongation efficiency hel
(black solid line), and nucleotide efficiency hNTP (blue dashed line) as a function
of the backtracking rate, for an otherwise generic polymerase with kcat = 10=s
and kclv = 0:1=s, is illustrated. Values indicated by diamonds were obtained
numerically, through Gillespie simulations.
phenotypic space made available through extended backtracking and variations in the backtracking rate. The various quantities
used to access polymerase performance—as it varies with the
level of PIP—are calculated in the Extended Results (see also
Figure S2) using continuous-time random-walk theory (Montroll
and Lebowitz, 1987). We start with considering three instantaneous transcriptional efficiency measures pertaining to the level
of the individual bp and then move on to consider the efficiency
on extended sequences or genes.
Performance on the Base Pair Level
We are interested in quantifying how much longer it takes to transcribe with and without proofreading. Based on our estimate
of rPIS , we expect that there is only about one error passing
through the PIS checkpoint every 400 bases. Therefore, we
can ignore the effect of errors on the overall elongation
dynamics. Without proofreading, the average elongation time
is 1=kcat . In the Extended Results we calculate the average
elongation time with proofreading t el . Taking these together,
we define the elongation efficiency measure hel ,
hel =
1=kcat
ð1 kbt Þ=kcat
=
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi;
tel
1=2 + ð1=4Þ + ðkbt =kclv Þ
(Equation 6)
which describes the relative slowdown due to PIP. With no PIP
ðkbt = 0Þ, the efficiency is appropriately hel = 1, whereas it
vanishes at the transition between net polymerization and net
depolymerization kcat = kbt . At this point, elongation stops proceeding with a well-defined velocity and behaves diffusively on
large-length scales. Net depolymerization sets in for kcat <kbt .
This situation is pathological and shows that backtracking
cannot dominate the dynamics even though this would be
judged optimal in terms of fidelity. The transition to nonfunctional
polymerases can be seen directly in the experimental transcription traces presented in Figure 3D in Galburt et al. (2007), where
an opposing force was used to increase the entrance rate into
the backtrack—bringing the system to stall around 14pN. The
same stalling effect due to excessive backtracking and cleavage
can be seen in the simulated traces presented in Figure 2C
(see also Figure S2). Also note that the overall elongation rate
increases with increasing cleavage rate, as observed experi-
mentally (Herbert et al., 2010; Fish and Kane, 2002; Proshkin
et al., 2010).
We next introduce an efficiency parameter for the fidelity of
the transcription process, hPIP = 1 rPIP , which is zero (0) in
the absence of PIP and one (1) for perfect PIP. Finally, we
parameterize the nucleotide efficiency of the transcription
process by the ratio of final transcript length and the average
number of nucleotides consumed in its production. This ratio
is given by the simple expression (see Extended Results)
hNTP = 1 kbt =kcat . This measure is unity without PIP and
vanishes at stall, where transcript is continuously cleaved and
polymerized at equal overall rates. Figure 5 shows the
three efficiency measures hel , hPIP , and hNTP as functions of
the backtracking rate kbt (within the operational range
0=s%kbt %kcat = 10=s) for an otherwise generic RNAP. We see
that, whereas transcription velocity and nucleotide efficiency
correlate positively, they both correlate negatively with fidelity,
directly illustrating the cost of ensuring fidelity. This hints at an
underlying competition, which we now explore by considering
transcription of extended sequences.
Performance on the Gene Level
Here, we demonstrate that a moderate rate of backtracking is
necessary for rapidly generating transcripts with few mistakes
from extended sequences. The suitable amount of proofreading
needed varies with the length of the sequence that is to be transcribed: the longer the sequence, the harder it is to transcribe it
without errors. It is thus instructive to introduce the probability Pl
of producing a long error-free sequence. It is important to note
that this sequence length l should not necessarily be interpreted
as the complete gene length. Instead, l should be seen as the
typical error-free length l = 1=rfunc that is required when transcription needs to reach error rates rfunc to produce acceptable transcripts. For each attempt, the probability of transcribing a
sequence of length l without an error is given by
Pl ðrÞ = ð1 rÞl zexpðlrÞ, with r = rPIP rPIS representing the total
error fraction.
We define the production rate gain cel on extended sequences
by comparing the rate at which error-free transcripts are
produced with and without PIP, cel = hel Pl ðrPIS rPIP Þ=Pl ðrPIS Þ =
hel expðlrPIS hPIP Þ. Similarly, we introduce the NTP efficiency
gain on extended genes cNTP by comparing the number of
error-free transcripts produced per nucleotide used, with and
without PIP, cNTP = hNTP expðlrPIS hPIP Þ. These simple forms
justify the otherwise arbitrary-seeming local efficiency measures
for fidelity introduced above. From both these quantities, it is
clear that even moderate PIP provides enormous gains in the
rate of perfectly transcribing long ðl>1=rPIS Þ sequences.
With the two sequence-wide measures that we have introduced, it is now possible to address transcriptional efficiencies
on the level of transcription of whole genes. As an example, we
consider a sequence length comparable to that of the typical
human gene, l = 104 bp. In Figure 6A, we plot the efficiencies
cel and cNTP as a function of the backtracking rate kbt . Each
measure has a definite optimal value, and we see that the gains
in both rate of perfect transcript production and nucleotide
efficiency can be enormous, here reaching more than 13 orders
of magnitude.
Cell Reports 5, 1–10, October 17, 2013 ª2013 The Authors 7
Please cite this article in press as: Depken et al., Intermittent Transcription Dynamics for the Rapid Production of Long Transcripts of High Fidelity, Cell
Reports (2013), http://dx.doi.org/10.1016/j.celrep.2013.09.007
around 1/s are the result of an evolutionary optimization for
rapidly and efficiently producing functional transcripts from
genes in the tens of kbp range.
A
DISCUSSION
B
10,000
30,000
50,000
Figure 6. High-Fidelity Transcript Production
(A) On the left vertical axis, we mark the production rate gain on extended
sequences cel as a function of the backtracking rate (black solid line). On the
right vertical axis, we mark the NTP efficiency gain cNTP as a function of
the backtracking rate (red dashed line), all for a sequence of length l = 104 bp.
The region between the two peaks is where one might expect the optimal value
of kbt to lie.
(B) The backtracking rate that optimizes the production rate gain (black solid
line) or the energy efficiency gain (red dashed line) as a function of sequence
length is shown. The red arrow indicates the sequence length used in (A),
and the dashed horizontal line marks the backtracking rate ðkbt = 1=sÞ of
our generic RNAP. The gray area marks the sequence lengths that could
be optimized for kbt = 1=s. Inset is a magnification showing that PIP is
optimal for gene lengths between 104 and 4 3 104 bp (gray shaded region)
at kbt = 1=s.
If our generic RNAP was optimized to transcribe this particular
sequence length, then we would expect the true value of the
backtracking rate to lie somewhere in the intermediate region
between the peaks: representing a compromise between NTP
efficiency and production rate. For the intermediate value of
kbt = 1=s —coinciding with our estimate of the physiologically
relevant backtracking rate—it would take a polymerase about
1 hr to produce an error-free transcript. This should be compared
to the time needed to complete the same task without PIP, which
for our simple PIS efficiency estimate amounts to approximately
1 billion years.
Intermittency Increases with Gene Length
Finally, it is interesting to ask how the region of optimal backtracking rate changes as the transcribed sequence length
varies. Figure 6B shows the backtracking rate that optimizes
cel (black solid line) and cNTP (red dashed line) as a function
of sequence length l. The inset in Figure 6B highlights the
backtracking rate for our generic polymerase ðkbt = 1Þ and the
implied sequence lengths ð104 4,104 bpÞ for which this
backtracking rate would be optimal. A complete discussion
would need to account for relaxed fidelity constraints due to,
for example, codon redundancy (Alberts et al., 2003). Even
so, considering that the average gene length in eukaryotes
lies in the range 104–105 bp (Xu et al., 2006), it is thought
provoking that the moderately observed backtracking rates of
8 Cell Reports 5, 1–10, October 17, 2013 ª2013 The Authors
Through an analytical study of the dynamic coupling of backtracking, chain elongation, and cleavage, we have shown
that intermittent transcription dynamics are to be expected
for an efficient transcription process. Our work shows that
base-pairing energetics, together with transcriptional proofreading through backtracking and cleavage, can account for
observed error rates. This proofreading relies on a conglomerate of checkpoints, all contributing to fidelity while depending on the occurrence of extended backtracks. Through
backtracking and cleavage, an incorporated error is proofread
at least twice but could in principle be proofread as many
times as there are bases in the RNA-DNA hybrid within the
elongation complex. Investigating if there are additional proofreading checkpoints is an interesting line of future research,
potentially providing a link between the structure of the elongation complex and overall transcriptional efficiency and fidelity.
Such work might offer clues as to why the RNA-DNA hybrid
has a length of about 8–9 bp (Kent et al., 2009; Nudler et al.,
1997).
In contrast to physiological settings, where the DNA can be
covered by various DNA-binding proteins, we have in this study
considered transcription along bare DNA. Additional enhancements of the proofreading capabilities are expected for genes
crowded by proteins because the physical hindrance induced
by such proteins should bias the RNAP away from catalysis,
toward backtracking and increased proofreading.
Considering the effects of proofreading both on NTP consumption and the production rate of extended functional
transcripts, we show how the internal hopping rate in the backtracked state is not optimized for fidelity. Instead, our analysis
suggests that it is kept moderate in order to enable rapid production of extended transcripts of high quality. Importantly,
there will be many more backtracks (about one in every ten
base pairs) than there are errors to remove. This apparent
inefficiency can be understood as a direct consequence of an
enormous asymmetry in cost: undetected errors have the potential to render the whole transcript dysfunctional, whereas
removing a correct base carries only a moderate cost in energy
and time. A substantial level of paranoia is thus desirable on
part of the polymerase and could be the reason behind why
backtracking is observed in vivo at levels comparable to what
we predict (Churchman and Weissman, 2011). Although such
frequent backtracking decreases the instantaneous average
transcription rate, the observed level of backtracking—perhaps
counterintuitively—drastically increases the rate at which highfidelity transcripts are produced.
Interestingly, our work shows that the frequency of backtracks for different RNAPs should be expected to correlate
positively with the sequence length that has induced the highest
evolutionary pressures on each transcription process (see Figure 6B). For example, genomes with genes of increasing length
would be expected to be transcribed with increasingly
Please cite this article in press as: Depken et al., Intermittent Transcription Dynamics for the Rapid Production of Long Transcripts of High Fidelity, Cell
Reports (2013), http://dx.doi.org/10.1016/j.celrep.2013.09.007
intermittent dynamics in order to maintain transcriptional efficiency. Considering that, for example, in eukaryotes, Pol I, Pol
II, and Pol III transcribe drastically different sequence lengths
(Watson et al., 2013), it would be interesting to determine if
the predicted increase in backtracking rate (Galburt et al.,
2007; Depken et al., 2009)—with the concurrent increase in
the intermittency of the dynamics—could be found for polymerases optimized for increasing sequence lengths.
Although the mechanistic details are very different, the asymmetry that governs intermittency of RNAP dynamics is even
larger for DNA polymerases: whereas transcription errors affect
the production of transient proteins, errors in replication are
propagated to descendant generations. The general concept
of cost asymmetry thus applies also to replication, and it would
be interesting to extend our analysis to DNA polymerases to
see if they also remove many more bases than there are errors
incorporated into the growing product.
Understanding the evolutionary pressures that have formed
the different polymerization machines processing genomes
remains a fascinating experimental and theoretical challenge.
We hope our model can serve as a benchmark for more detailed
descriptions. Generally, our work highlights that PIP offers enormous fidelity gains and how this fundamental mechanism has
become so vital for normal cellular function.
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SUPPLEMENTAL INFORMATION
Fish, R.N., and Kane, C.M. (2002). Promoting elongation with transcript
cleavage stimulatory factors. Biochim. Biophys. Acta 1577, 287–307.
Supplemental Information includes Extended Results and four figures and
can be found with this article online at http://dx.doi.org/10.1016/j.celrep.
2013.09.007.
Galburt, E.A., Grill, S.W., Wiedmann, A., Lubkowska, L., Choy, J., Nogales, E.,
Kashlev, M., and Bustamante, C. (2007). Backtracking determines the force
sensitivity of RNAP II in a factor-dependent manner. Nature 446, 820–823.
ACKNOWLEDGMENTS
Greive, S.J., and von Hippel, P.H. (2005). Thinking quantitatively about
transcriptional regulation. Nat. Rev. Mol. Cell Biol. 6, 221–232.
We thank Eric Galburt, Justin Bois, and Abigal Klopper for fruitful discussions
and suggestions. J.M.R.P. acknowledges financial support from grants ENFASIS (FIS2011-22644, Spanish government) and MODELICO (Comunidad de
Madrid). S.W.G. acknowledges funding by the EMBO Young Investigator Program and the Paul Ehrlich Foundation. M.D. acknowledges partial support
from FOM (which is financially supported by the ‘‘Nederlandse Organisatie
voor Wetenschappelijk Onderzoek’’) as well as the hospitality of both the
Max Planck Institute for the Physics of Complex Systems in Dresden and
the Vrije Universiteit in Amsterdam, where part of this research was performed.
This research was supported in part by the National Science Foundation under
grant NSF PHY05-51164.
Received: May 16, 2012
Revised: February 1, 2013
Accepted: September 5, 2013
Published: October 10, 2013
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