Transcription: Pausing and Backtracking:
Error Correction
Mamata Sahoo and Stefan Klumpp
Theory and Bio-systems group, Max Planck Institute of Colloids and Interfaces,
Potsdam, Germany
Transcription
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◮
Transcription is the efficient regulatory process in
cells,organisms and tissues →Control the complex form of
gene expression.
what happens?
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◮
The genetic information → stored in DNA → RNA
transcript.
How?
◮
Transcription → RNA polymerase moves along the length
of a DNA template by a single base pair per stochastic
nucleotide addition → creating a complementary RNA.
Transcriptional pausing
◮ 1 Heterogeneity
in transcription rate → Transcription is not
continuous ⇒ interrupted by pausing events.
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◮
1
2
Pauses:RNAP gets halt for times→ forms inactive
configuration.
2 Two general classes of Pauses→ most frequent.
K. Adelman et al., PNAS 99, 13538(2002)
I.Artsimovitch et al., PNAS 97, 7090(2000)
Backtracking during transcription: Backtracking pauses
◮ 3
Backtracking occurs in three phases.
◮
◮
◮
3
Phase 1: Backtracking
Phase 2: Sliding→ diffusional in nature.
Phase 3: Recovery of transcription
J.W. Shaevitz, et al., Nature 426, 684(2003)
Questions Addressed?
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What happens to the transcription → pause and
backtracking ?
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◮
◮
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Pauses have negative effect on transcription ⇒ High
transcription rate requires the pausing events to be
suppressed.
Backtracking pauses→automatically suppressed by the
trailing RNAP from behind. However, backtracking is
required for the error correction and further recovery of
transcription.
Making a pause→ creating an error, Cleaving the transcript
→ Correcting the error.
Questions??
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◮
◮
What fraction of errors are corrected??
How the efficiency of error correction limited controlled??
How the accuracy can be improved??
Model studied for transcription
D
D
D
kc
D1
D
kc
ǫ
p
α
ǫ
ǫ
′
ǫ
Transcription with pausing and backtracking
0.012
without Pausing
0.01
with pause+backtracking
0.008
J
D1=0.28, D=0.07
Kc=0.07
0.006
P=0.0
P=0.00007
P=0.0007
P=0.007
0.004
0.002
0
◮
◮
◮
◮
◮
4
0
0.02
0.04
α
0.06
0.08
0.1
Both initiation and elongation limited.
4 Low density and maximal current phase.
At high transcription intiation rate → transcription starts
limiting by elongation.
Strongly affected by pausing events → elongation limited
regime.
Suppresses⇒ with pausing and backtracking.
L.B. Shaw, et al., Phys.Rev.E 68, 021910(2003)
Single RNAP transcription: Efficiency of error
correction (fec)
D
D
D1
D
kc
ǫ
ǫ
◮
◮
◮
′
p
kc
ǫ
ǫ
Efficiency of error correction,fec =
P∞
P∞
For single RNAP transcription,fec =
m=1
m=1 Kc Pm
Kc Pm +ǫ1 Pm−1
1
ǫ1
K P
m=1 c m
1+ P∞
Kc a
Following the relation, fec = Kc a+ǫ
;
1 (1−a)
p
Kc
1
a = (1 + 2D ) − 2D (4D 2 + Kc2 + 4Kc D − 4DD1 ).
q
Kc
Kc
) − 2D
= (1 + 2D
(1 + 4D
Kc ) (for D = D1 ).
Fec with diffusive rate (D)
1
D1=0.28, D=0.007
D1=0.28, D=0.07
D1=0.28, D=0.2
D1=0.28, D=0.4
Kc=0.07
0.9
0.8
fec
0.7
0.6
0.5
0.4
0.3
0
0.025
0.05
0.075
α
0.1
0.125
0.15
0.175
0.2
◮
Fec is also both initiation and elongation limited.
◮
Increase of D affect strongly in the elongation limited
regime.
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Strong diffusivity suppresses the error correction ⇒ RNAP
spends much time in diffusive manner in any of the
backtracked sites.
Fec with backward stepping rate(D1): Single RNAP and
Multi-RNAP transcription
1
1
0.9
0.9
0.8
0.8
α=0.0
α=1.0
Kc=D/10=0.007
0.7
0.6
fec
fec
0.6
0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0
◮
◮
◮
α=0.0
α=1.0
Kc=D=0.07
0.7
0
0
0.1
0.2
0.3
D1
0.4
0.5
0.6
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
D1
Fec in multi-RNAP transcription is always reduced
comparatively with single-RNAP transcription⇒ Lack of
free spaces that restricts diffusion of backtracked RNAP.
The difference is strongly affected for higher D1 regime.
Further increase of Kc reduces the difference between both
cases ⇒ Push back effect of the trailing RNAP from behind
in the multi-RNAP transcription.
Fec with the cleavage rate(Kc ):Single-RNAP and
Multi-RNAP transcription
1
1
0.8
0.8
α=0.0
α=1.0
D=D1=0.07
fec
0.4
0.4
0.2
0.2
0
◮
◮
◮
0.6
fec
0.6
α=0.0
α=1.0
D1=0.28, D=0.07
0
0
0.1
0.2
0.3
Kc
0.4
0.5
0.6
0
0.1
0.2
0.3
Kc
0.4
0.5
0.6
Fec for single-RNAP transcription is always above the fec
for multi-RNAP transcription ⇒ Available free spaces for
error correction.
Fec for multi-RNAP transcription is always reduced ⇒
Dense traffic effect.
Error correction in multi-RNAP case is improved for higher
Kc . Further improvement is achieved with increase in D1 .
D1
Fec with both cleavage rate(Kc ) and backward
stepping rate(D1)
0.1
0.01
0.01
α=0.0
0.1
0.1
0.01
0.01
Kc
α=1.0
0.1
◮
Fec is strongly controlled both by D1 and Kc .
◮
Error correction→ Strongly improved increasing both by
backward stepping rate,D1 and cleavage rate,Kc .
Fec with distance(L) between an active RNAP and a
paused RNAP
1
0.9
0.8
Simulation
Analytical
0.7
fec
0.6
0.5
D1=D=Kc=0.07
0.4
0.3
0.2
0.1
0
0
10
20
30
40
50
60
70
80
90
100 110 120 130 140 150
L
◮
single
fec(L) = fecmax
{1 − exp(−(L/L0 ))}
◮
Approximation: L0 =
◮
L
Gap distribution, P(L) = ( αǫ )( ǫ−α
ǫ ) .
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fec increases with the distance: More free space available
for error correction.
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Larger gap size ⇒Better error correction.
ǫ
Kc .
Efficiency of error correction:Multi-RNAP transcription
1
D=D1=Kc=0.07
0.9
Simulation
Analytical
0.8
0.7
αc=0.04
fec
0.6
0.5
0.4
αc=0.08
0.3
0.2
0.1
0
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◮
0
0.025 0.05 0.075
0.1
α
0.125 0.15 0.175
0.2
0.225 0.25 0.275
Analytical results valid for low value of α ⇒ Semianalytical.
The deviation starts from the crictical value,αc = 0.04
where the density starts saturating.
Beyond αc , the error correction may depend on other
parameters.
Summary
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Transcription rate → suppressed both by pausing and
backtracking (reduced saturated density effect).
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We exactly calculate the efficiency of error correction for a
single-RNAP and multi-RNAP transcription in a
semi-analytical way.
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Error correction can be strongly improved by increasing
both the backward stepping rate and the transcript
cleavage rate.
THANK YOU