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The standard model of transcription — the totally asymmetric simple exclusion process (TASEP) — predicts the existence of a gene-independent limit on the maximal rate of transcription as a result of polymerase “traffic jams” in the bulk of the gene at sufficiently high polymerase concentrations. Recent experiments in living Drosophila embryos provide quantitative access to the transcription-al dynamics of genes in the high polymerase concentration limit. Our analysis suggests uniformity of the maximal rate of transcription in the genes hunchback, snail, and knirps, and their modified constructs. Intriguingly, the observed maximal rate of transcription is only about 40 % of the one predicted by the TASEP model. We propose that the appearance of a gene-independent maxi-mum rate of transcription indeed hints at fundamental physical constraints on the process due to traffic jams, but the observed reduction in the maximal rate reflects jamming in the promoter region, where the polymerase elongation rate is lower due to cycles of abortive initiation. This implies that the transcription bottleneck is not in the bulk of the gene, but rather in its pro-moter region, and we suggest experiments to test this hypoth-esis. This provides an alternative transcription rate reduction mechanism compared to earlier promoter dynamics studies.
Alexander S. Serov1,2, Alexander J. Levine3, Madhav Mani4
E-mail: [email protected] Department of Chemistry & Biochemistry, University of California, Los An-
geles, CA 90095, USA2 Decision and Bayesian Computation Group, Institut Pasteur, 25 Rue du
Docteur Roux, Paris, 75015, France3 Department of Chemistry & Biochemistry, Department of Physics & Astron-
omy, and Department of Biomathematics, University of California, Los An-geles, CA 90095, USA
4 Engineering Sciences and Applied Mathematics, Northwestern University, 2145 Sheridan Road, Evans ton, IL 60208, USA
ABORTIVE INITIATION AS A BOTTLENECK FOR TRANSCRIPTION IN THE EARLY DROSOPHILA EMBRYO
Abstract
Motivation
• How fast can devel-oping cells produce new material in early embryonic stages?
• Are there fundamen-tal physical limits? Ph
oto
cre
dit:
Nin
a
Polymerase injection rates in nuclear cycles 13 and 14 for the Hb gene:
Complete entry rule k β=k
Particle of length ℓ
Without steric hindrance particles jump 1 site at a time with rate k
Incremental exit with no steric hindrance
Jump suppressed if next site is occupied
αMacDonald et al. (Biopolymers, 1968, 1969)
Problems:
• Maximal transcription rate and polymerase density do not depend on specific gene, construct or nuclear cycle;
• The experimental measurements correspond to ~ 40 % of the predicted limits;
• Considering the abortive initiation effect is enough to ac-count for this discrepancy.
Our approximate formulas are validated by numerical simulations:
Reduced steady-state polymerase number:
Steady-state active polymerase number in nu-clear cycles 13 and 14 for the Hb gene:
The decrease in the injection rate is due to abor-tive injection.
This effect can be modeled by making polymerases pause at the first site for a random amount of time.
The four distributions exhibit average values ~ 40 % of the values predicted by the standard TASEP model in the maximal current regime.
Normalized poly-merase recruitement rate on the Hb gene does not depend on AP, nc or enhancer construct!
1. MacDonald et al., Biopolymers 6, 1 (1968)2. MacDonald and Gibbs, Biopolymers 7, 707 (1969)3. Revyakin et al., Science, 314 (5802), 1139 (2006)
Original ℓ-TASEP model
0 10 20 30Initial injection rate s, pol/min
0
0.02
0.04
0.06
0.08
0.1
nc 13
0 50 100Max. polymerase number N ss
0
0.01
0.02
0.03
nc 13
0 10 20 30Initial injection rate s, pol/min
0
0.02
0.04
0.06
0.08
0.1
nc 14
0 50 100Max. polymerase number N ss
0
0.005
0.01
0.015
0.02
0.025
nc 14
Hypothesis
The Abortive Model
New Predictions
Comparison to Data
References
Conclusions
Complete entry rule k β=k
Particle of length ℓ
Without steric hindrance particles jump 1 site at a time with rate k
Incremental exit with no steric hindrance
Jump suppressed if next site is occupied
Abortive transcription initiation makes particles remain on the �rst site for an average time τ
α
Data
Independent of anterior-posterior (AP) position
0.2 0.3 0.4 0.5AP position
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
s/s m
ax
Hb
nc 13, bacnc 13, no prnc 13, no shnc 14, bacnc 14, no prnc 14, no sh
Pattern formation
0
Anteriorend
Drosophila melanogaster
Posteriorend
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Pho
to c
red
it: N
ina
Interestingly, the model predicts less noise than seen in experiment:
The predictions are in line with the experimental data:
One can estimate τ in the in vivo experiments:
0 5 10 15Time since the start of a nuc. cyc. (min)
0
10
20
30
40
50
60
N
Mean evolution of the active polymerase number in a nuclear cycle for the hunchback (blue), snail (yellow) and knirps (red) genes:
Number of analyzed fluores-cence traces for different genes and constructs:
0 2 4 6t (min)
s max
Nss
0
20
40
60
80 = 1.0 s = 3.0 s = 4.0 s = 5.0 s = 7.0 s = 9.0 s = 10.0 s
2 4 6 8 10 (s)
0.2
0.3
0.4
0.5
0.6
0.7
2 4 6 8 10 (s)
0.2
0.3
0.4
0.5
0.6
0.7
0.8
arXiv: 1701.06079
The abortive initiation proceeds through a scrunching mecha-nism [3].
flexible element in DNA(”scrunching”)
-35 -10 +1
-35 -10 +1
-35 -10 +1 -35 -10 +1
-35 -10 +1
-35 -10 +1
(NTP)n (PPi)n
abortive RNA
abortive RNA
abortive RNA
(NTP)n (PPi)n
(NTP)n (PPi)n
flexible element in RNAP(”inchworming”)
forward-reverse translocations(”transient excursions”)
Re
vya
kin
et
al.
(Sc
ien
ce
, 200
6)
Tscrunch= 5±1 s
Inte
grat
ed p
roba
bilit
y, P(
t > T
)
scrunches withTscrunch < 1 s
time (T, s)5 10 15
10-1
10-2
100
0
Re
vya
kin
et
al.
(Sc
ien
ce
, 200
6)
In vitro experiments show that the wait-ing time is exponen-tially distributed with the mean pause time τ = 5 ± 1 s.
Reduced injection rate:
Pho
to c
red
it: A
nd
ré K
arw
ath
• the observed steady-state poly-merase (particle) density is ~ 40 % of the model prediction in the maximal current regime [2].
• the observed injection rate is ~ 40 % of the model prediction in the maxi-mal current regime [2],
2 4 6 8 100
0.02
0.04
0.06
0.08
0.1
0.12
SimulationData nc 13Data nc 14
2 4 6 8 100
0.05
0.1
0.15
0.2
SimulationData nc 13Data nc 14
