Vol. 20 no. 16 2004, pages 2719–2725
doi:10.1093/bioinformatics/bth317
BIOINFORMATICS
Transcription/replication collisions cause
bacterial transcription units to be longer on
the leading strand of replication
Nicolas Omont and François Képès∗
ATGC, CNRS UMR 8071/genopole® , 523 Terrasses de l’Agora, 91000 Evry, France
Received on January 11, 2004; revised on April 19, 2004; accepted on April 26, 2004
Advance Access publication May 14, 2004
ABSTRACT
Motivation: The costs of head-on versus codirectional collisions between the replication complex and the much slower
transcription complex on the circular bacterial chromosomes
are much debated. Although it is established that the number
of genes on the leading strand is higher than on the lagging
strand of replication, the consequences of collisions on the
length of transcription units are unknown.
Results: Here, we show that transcription units are generally longer on the leading strand, in rough proportion to the
bias in number of units between the two strands. We propose a statistical physics model, based on the assumption
that the proportion of interrupted transcripts for each unit is the
major factor contributing to these biases. Its main prediction is
that a large replication/transcription speed ratio implies a low
leading/lagging bias for transcription unit length and number.
This model is validated by an analysis of proven and predicted
units in Escherichia coli and Bacillus subtilis. The results are
consistent with an equal cost of head-on versus codirectional
collisions.
Contact: [email protected]
1
INTRODUCTION
In Escherichia coli, the replication forks progress along the
two parts of the single circular chromosome, from the oriC
locus (Hirose et al., 1983; Campbell and Kleckner, 1990) to
the dif locus (Tecklenburg et al., 1995) in the ter region (Hill,
1992), thus defining two replichores. A similar organization
is observed in Bacillus subtilis (Lemon et al., 2002; Duggin
and Wake, 2002), although the two replichores are of unequal
length. In E.coli, the ratio of replication to transcription speeds
is estimated to be between 14 and 24 [transcription speed
is 42 bp/s (Gotta et al., 1991), replication speed is ∼600–
1000 bp/s (Mok and Marians, 1987)].
Collisions between the replication complex and the much
slower transcription complex have been observed in different organisms. The two types of collisions, i.e. head-on and
∗ To
whom correspondence should be addressed.
Bioinformatics vol. 20 issue 16 © Oxford University Press 2004; all rights reserved.
Trans. complex:
colliding
not colliding
oriC
Rep. complex.:
Direction of:
replication
transcription
Transcription unit:
start
end
ter
Fig. 1. Illustration of head-on (upper unit) and codirectional (lower
unit) collisions between replication and transcription complexes. At
the time shown, the upper replication complex has already collided
with all transcription complexes that were on the upper unit when it
was near the end of this unit. It will now collide with grey transcription complexes that started meanwhile. Consequently, if solving a
collision takes longer than the time between two transcription initiations, the replication could be blocked. On the contrary, the other
replication complex is at the start of the lower unit and will not collide with all transcription complexes that are on the unit as the black
ones will reach the end of the unit before being caught up by the replication complex. As a consequence, long units tend to be translated
codirectionally and short units are favoured over long ones, as they
led to fewer interrupted transcripts.
codirectional, are illustrated in Figure 1. Experiments give
varying results, suggesting significant differences between
organisms. In E.coli, the replication complex is slowed only
by head-on transcribed units and no transcription activity is
detected just behind the replication fork (French, 1992). We
interpreted that transcription complexes are dislodged near
the replication fork. In vitro, with the bacteriophage T4 DNA
replication apparatus and stalled or moving E.coli RNA polymerase, head-on collisions take 1.7 s to be resolved, twice
longer than codirectional ones (Liu et al., 1994; Liu and
Alberts, 1995). The transcription complex seems to collide
with the helicase, a protein of the replication fork. Contrary to
the experiments with E.coli replication apparatus, we suggest
2719
N.Omont and F.Képès
a mechanism that solves all collisions and avoids transcription
abortion. In vitro, with B.subtilis phage 29, stalled transcription complexes block replication. Codirectionally progressing
transcription complexes slow down replication much more
than head-on progressing ones. Because replication initiates
at either end of the phage linear chromosome, a mechanism
exists to solving replication fork collisions (Elias-Arnanz and
Salas, 1997, 1999). We suggest that head-on collisions are
resolved by this mechanism whereas codirectional ones are
resolved as transcription ends.
French’s (1992) experiments are most relevant for analysis
of the relationship between transcription and replication in
live bacteria. They led to the assumption that collisions are
resolved by disruption of transcription. Although they suggest that head-on collisions are more difficult to solve than
codirectional ones because they slow down more replication,
our analysis is based on the assumption that all collisions
have equal cost to the cell and that all asymmetries come
from differences in the number of collisions. Indeed, in case
of a very active unit, many more collisions occur if it is transcribed head-on. A simple head-on collision model explains
this effect: given a head-on transcribed unit of length L, if
one assumes that a collision needs the time tc to be solved
and that the time between two transcription initiations is fixed
and equal to tr , the time T spent by the replication complex progressing on the unit and the number of collisions
N solved during this time can be computed through the following equations where S = L/T is the mean speed of the
replication complex progressing on the unit and R the speed
of a replication complex progressing without collisions:
T = L/R + N tc .
N = T /tr .
(1)
Therefore
S/R = 1 − tc /tr .
(2)
If tc /tr 1, replication progresses at normal speed, conversely if tc /tr ∼ 1, i.e. if the unit is actively transcribed,
replication is nearly stopped. As all experiments used very
actively transcribed units, it suggests that head-on collisions
slow down more replication than codirectional ones because
they happen much more often on actively transcribed units
than on other units, making plausible the hypothesis of an
equal collision cost. However, under the hypothesis that collisions involve polymerases themselves and not other proteins
of the replication fork, the fact that both strands are replicated
by the same polymerase in E.coli and by different polymerases
in B.subtilis (Dervyn et al., 2001; Rocha, 2002) introduces a
new asymmetry for the latter bacterium, and consequently
potentially different collision costs.
Brewer’s (1988) review on collisions in E.coli suggests
that ribosomal proteins are transcribed codirectionally and
that large chromosomal inversions are often lethal. Moreover,
complete genome analysis shows that there are more open
2720
reading frames (ORFs) on the leading strand than on the lagging strand (55% in E.coli, 74% in B.subtilis). Therefore,
we hypothesis that evolutionary pressure drives this bias is
still valid. However, it is not known whether the evolutionary advantage comes from an improved resilience towards
collisions of either replication or transcription. The hypothesis of replication resilience is supported by Equation (2)
and experiments on chromosomal inversions because they
suggest that replication fails if one of the few very active
units is transcribed head-on. However, it has also been shown
that the leading factor to explain gene strand bias in E.coli
and B.subtilis is essentiality more than activity (Rocha and
Danchin, 2003). This supports the hypothesis of transcription
resilience because proteins translated from truncated transcripts are more often toxic to the cells when they are encoded
by essential genes. As our analysis considers all genes and not
only the most transcribed ones, it is based on this hypothesis
of transcription resilience.
In summary, consistent with the hypothesis of equal collision cost and of transcription resilience, more transcription
units are transcribed codirectionally, but essentiality and not
transcription level is the leading factor for the vast majority of
transcription units. Moreover, the following prediction can be
made: this bias is expected to increase with transcription unit
length because length is proportional to collision probability.
2
SYSTEMS AND METHODS
To construct a quantitative model, we propose to use tools
derived from statistical physics, although other approaches are
possible. The system is analogous to a steady-state because
it satisfies four prerequisites. First, the pool of transcription
units is large enough for statistics to be valid. Second, ‘states’
are described by different parameters, such as unit position
and orientation on chromosome. Third, recombination and
units merging/splitting allow a good approximation of this
steady-state on an evolutionary timescale. Indeed, physical
interaction of the products and not only functional relationship is required for gene order conservation (Huynen and
Bork, 1998). Therefore, besides coregulation, decreasing collision effects may be an evolutionary advantage to explain
transcription unit length distribution. Fourth, the strength of
the evolutionary pressure could be compared with the ‘temperature’ of the system, therefore evolutionary cost can be
considered as the ‘energy’ of the transcription unit. However,
unless experiments on the same organism submitted to different pressures are carried out, this ‘temperature’ and the
base energy level associated are unquantifiable. Consequently,
measures of evolutionary cost remain related to this energy
level and thus are dimensionless. Incidentally, comparisons
of costs between organisms require the assumption that they
are subjected to the same evolutionary pressure.
In our analysis, the only parameters of a transcription unit
are its orientation with respect to replication s ∈ {+, −}
Transcription/replication collisions on bacterial chromosomes
(codirectional and head-on, respectively), its replichore h ∈
{1, 2} (convention to be defined for each organism) and its
length L, defined as the distance between the end of the last
gene and the start of the first gene in the transcription unit.
For a unit in a given state (s, h, L), the assumption is made
that evolutionary cost Es,h (L) is proportional to the collision
int
probability Ps,h
(L) of an initiated transcription, i.e. to the proportion of transcripts truncated for this unit, consistent with
the hypothesis of transcription resilience. According to the
equal cost hypothesis, the dimensionless collision cost Ch
does not depend on the orientation of collision:
int
Es,h (L) = Ch Ps,h
(L).
(3)
Given the probability ps,h (L) of presence in a given
state
+∞ and the normalization constant Z such that
s,h ps,h (L)dL = 1, the steady-state hypothesis leads
0
to the following mathematical formulation:
ps,h (L) = Z −1 exp[−Es,h (L)].
(4)
Other parameters deemed to be independent, like activity
level or essentiality, could be modelled as additional terms to
Es,h (L). Therefore, thanks to the properties of multivariable
exponential distribution, they could be studied independently.
Moreover, the collision probability can be determined from
the replication to transcription speed ratio γh and from the
length Ltot
h of the replichore. Head-on collision probability is
higher than the codirectional one because the speed of replication complex with respect to the transcription complex is
greater when moving towards each other (i.e. head-on) than
when moving away from each other (i.e. codirectionally), as
illustrated in Figure 1:
int
P+,h
(L) = (γh − 1)L/Ltot
h .
int
P−,h
(L) = (γh + 1)L/Ltot
h .
(5)
Due to Equations (3)– (5), probability of presence is expected to decrease exponentially with the length L. Besides,
the parameter of an exponential distribution is also its mean.
Therefore, if Ns,h is the number of units transcribed in orientation s on replichore h and θs,h is their mean length, the
model has the following important internal constraint:
θ+,h
N+,h
=
.
θ−,h
N−,h
(6)
The model also gives the following relationship, meaning that
a high speed ratio is correlated with a low mean length bias:
θ+,h
γh + 1
=
.
θ−,h
γh − 1
3
75% of all operons known from the literature. In B.subtilis,
transcription units are predicted based on ORF transcriptional
orientation and transcription terminators (d’Aubenton Carafa
et al., 1990; Vermat et al., 2002; Thermes, C., Personal
communication). Length distributions have identical shapes
for E.coli and B.subtilis. The longest B.subtilis replichore is
labelled 1. The other one is labelled 2. The E.coli replichores
are not labelled because they are not statistically different.
Estimation of probability of presence is averaged over a
300 bp sliding window. To compute confidence intervals, each
variable is written as a function of a binomial variable, which is
itself approximated with its asymptotic Gaussian (δ-method).
Estimation of speed ratios and collision costs uses bias in
mean length and not bias in number because the latter may
be influenced by other factors than the increase in collision
probability with operon length. For instance, the length independent effect described in (Equation 2) increases only the
bias in number.
(7)
DATA
In E.coli K-12, 2328 transcription units are predicted (Salgado
et al., 2000), covering ∼ 77% of all ORFs. This set comprises
4
RESULTS
Model estimators for B.subtilis and E.coli are presented in
Table 1. As mentioned in the Introduction section, more units
are transcribed codirectionally than head-on. Consistent with
the model, units transcribed codirectionally are longer than
units transcribed head-on [Equation (5)], and biases in number
are equal to the biases in mean-length [Equation (6)] except
for B.subtilis replichore 1.
Figure 2A–C display probabilities of presence for B.subtilis
and E.coli. The model predicts exponentially decreasing probabilities of presence (broken lines). Probabilities are estimated
for head-on and codirectionally transcribed units (light and
dark grey, respectively). In Figure 2D–F, quantile–quantile
plots of experimental probabilities of presence are plotted for
head-on and codirectionally transcribed units (light and dark
grey, respectively). They are useful to assess whether distribution tails are exponential, while plots of probability of
presence are useful to assess whether the left part of distributions are exponential. Finally, Figure 2G–I show the ratio
of codirectionally to head-on transcribed unit probability of
presence. The model predicts that the ratio increases exponentially with length [Equation (5)]. Therefore, on this semi-log
plot, straight lines are expected (broken lines). According to
the fact that number/mean length bias is greater than 1 for
B.subtilis replichore 1, probability of presence ratio is larger
than that expected for this replichore (Figure 2G). Indeed, the
experimental line has an average on the same slope as the
predicted line but is shifted upwards.
5
DISCUSSION
The hypothesis that the evolutionary cost of collisions is
proportional to the probability of transcription interruption
[Equation (3)] is consistent with the observations. Figure 2A–
C show that distributions have a peak that does not fit the
2721
N.Omont and F.Képès
Table 1. Model estimators for E.coli and B.subtilis
Replichore (h)
B.subtilis 1
Value
Min–Max
B.subtilis 2
Value
Min–Max
E.coli 1+2
Value
Min–Max
Replichore length (Ltot
h )
Codirectionally transcribed units (N+,h )
Head-on transcribed units (N−,h )
Bias in number (N+,h /N−,h )
Codirectionally transcribed units mean length (θ+,h )
Head-on transcribed units meanlength (θ−,h)
2 191 525
923
410
2.25
1624
1198
906–940
393–427
2.19–2.31
1570–1677
1138–1257
2 023 105
705
398
1.77
1996
1123
689–720
382–414
1.72–1.82
1921–2072
1067–1180
2 319 610
1174
1109
1.06
1355
1264
1150–1198
1085–1132
1.04–1.08
1316–1395
1226–1302
Number/mean length bias ratio
1.66
1.49–1.85
1.00
0.88–1.12
0.99
0.91–1.07
6.62
240
6.03–9.01
174–309
3.57
394
3.97–4.18
331–460
29.0
61.8
16.0–190
9.34–114
N+,h θ+,h
N−,h / θ−,h
Replication/transcription speed ratio (γh )
Collision cost (Ch )
Replichores start from origin of replication and end in termination region. B.subtilis longest replichore (2 023 105–4 214 630 bp) is labelled 1. The data for E.coli replichores are
merged because they are statistically identical. Confidence between min and max is 84% per variable. The model expects biases in number to be greater than 1 and number/mean
length bias ratios equal to 1. Lengths are in bp.
expected exponential distributions, whereas Figure 2D–F
show that distribution tails are well approximated by exponentials. Indeed, functional constraints like minimum gene
length are predominant for short unit length. In contrast, it is
plausible that collision avoidance is the leading factor for long
units. Further development of the model may require introduction of a cost for very short transcription units. However,
as analysis focuses on the estimators of Table 1, exponential
approximation is considered satisfactory, thus validating the
formulation of the evolutionary cost [Equation (3)].
Functional constraints might also prevent bacteria from
reducing unit length to compensate for higher collision probabilities. Indeed, when replication/transcription speed ratio
increases, the evolutionary cost of collisions can be kept constant by decreasing either the collision cost or the unit length
[Equations (3) and (5)]. Observations show that collision cost
decreases when speed ratio increases (Table 1) and that headon transcribed unit mean lengths are nearly the same for
all replichores. These observations suggest that evolutionary
cost is kept constant by decreasing collision cost Ch and not
unit mean length. Finally, this issue of functional constraints
implies that essentiality would not be a good parameter to
study, as essentiality cannot be changed independently from
gene function.
The equal cost hypothesis is consistent with the results. Indeed, speed ratio γh can be independently estimated
from the literature. For E.coli, the speed ratio is 14–24
(Gotta et al., 1991; Mok and Marians, 1987), consistent
with our value of 29. For B.subtilis, chromosome duplication time is ∼55 min (Sharpe et al., 1998) whereas it is
only 40 min for E.coli (Helmstetter, 1968). This slower
replication in B.subtilis is in keeping with the observed
lower speed ratio (Table 1). Moreover, for B.subtilis, the
speed ratio is higher for the longest replichore than for
the shortest (Table 1), suggesting that replication may
be slower on the shortest replichore. On the other hand,
2722
the fact that different polymerases replicate leading and
lagging strands in B.subtilis and not in E.coli (Dervyn
et al., 2001; Rocha, 2002) hints that collision costs may
be unequal in B.subtilis unlike in E.coli. This could be
confirmed by measuring more precisely the speed of the
transcription complex. In case these measures prove the
equal cost hypothesis wrong, the model can be easily adapted. Introducing different costs, C−,h and C+,h , for headon and codirectional collisions, respectively led to replace
Equation (7) by:
θ+,h
γh + 1 C−,h
=
.
θ−,h
γh − 1 C+,h
(8)
As a result, on a given replichore, for which the left
term is constant, the higher the speed ratio, the lower the
cost ratio. For instance, if the speed ratios were 10 in
B.subtilis, the head-on cost would be larger than the codirectional cost (cost ratios would be 1.11 for replichore 1
and 1.45 for replichore 2). Finally, it is noteworthy that
unequal costs would not explain the fact that the number/
mean length ratio is larger than 1 on B.subtilis replichore 1
(Table 1).
In fact, such differences between B.subtilis replichores were
unexpected. In addition to the difference in number/mean
length ratio, speed ratio is higher for replichore 1, which
hosts more units, whereas codirectionally transcribed unit
mean length is much larger for replichore 2. Thus, it might
be that the replichores are specialized. Units very sensitive
to truncations like long and essential units would be hosted by replichore 2. Indeed, all ribosomal protein genes are
codirectionally transcribed and 27 out of 30 are hosted on
this replichore (http://genolist.pasteur.fr/SubtiList/). On the
contrary, the majority of units is hosted on replichore 1,
on which replication is faster, would be less sensitive to
truncations.
Transcription/replication collisions on bacterial chromosomes
Fig. 2. (A)–(C) Upper and lower estimation of probabilities of presence as a function of length for head-on and codirectionally transcribed
units (light and dark grey, respectively). Probabilities of presence are estimated by averaging over a 300 bp sliding window. Confidence
interval between estimations is 84%. E.coli replichores are merged because they are not statistically different. The model predicts exponential
distributions (broken lines). (D)–(F) Quantile–quantile plots (QQ-plots) of probabilities of presence function of the exponential distribution
of parameter 1 for head-on and codirectionally transcribed units (light and dark grey, respectively). The model predicts a linear relationship
(broken lines). The quantile is defined in the following way: the probability that the variable X is lower than the quantile of level α, noted
Q(α), is α, i.e. p[X < Q(α)] = α. In general, a QQ-plot is a plot of a quantile Q(α) (on the y-axis) as a function of a reference quantile
Qref (α) (on the x-axis). Here, the reference is the exponential distribution of parameter 1 because the model predicts exponential probabilities
of presence. Indeed, QQ-plots of probabilities of presence predicted by the model are straight lines of slope θs,h (broken lines) because the
QQ-plot of an exponential distribution of parameter λ against the exponential distribution of parameter 1 is a straight line of slope λ. (H)–(J)
Upper and lower estimation of the ratio of codirectionally to head-on transcribed unit probability of presence (semi-log scale) as a function
of length. Confidence interval between estimations is 84% per variable, here 71% for two variables. The model predicts a linear relationship
(broken lines). All confidence intervals are computed through asymptotic Gaussian approximation.
2723
N.Omont and F.Képès
The transcription resilience hypothesis is also consistent
with the observations. Indeed, if replication resilience was
more important than transcription resilience, the evolutionary
cost would be related to the absolute number of transcripts
truncated for each unit, which is roughly in proportion with
the slow down of the replication fork, and not to the proportion of truncated transcripts that are linked to their toxicity.
Therefore, as the absolute number of truncated transcripts are
directly proportional to the unit transcription level, the evolutionary cost would be proportional to the unit transcription
level too. As our study does not use transcription level data
and thanks to parameter independence in the evolutionary cost
[Equation (4)], transcription levels could be approximated
by the global mean transcription level, noted T . Therefore,
Equation (3) would be replaced by:
int
Es,h (L) = Ch T Ps,h
(L).
(9)
In this equation, Ch T is a constant, so that it still means that the
evolutionary cost Es,h (L) is proportional to the interruption
int
(L), therefore the two models are mathematprobability Ps,h
ically equivalent, except in the determination of the collision
cost Ch . In constrast, B.subtilis replichore 1 has a number bias
which is larger than what is expected from the bias in mean
length (Table 1). This unexplained bias does not depend on
unit length (Fig. 2G), hinting that it might not come from transcription but rather from replication resilience improvement.
Indeed, if mean transcription level is higher on replichore 1,
the bias towards codirectional transcription will be increased.
Moreover, if the quality of transcription level data allowed
quantitative study, the model, once validated on this new dataset, could bring new estimations of collision costs in order to
test the equal cost hypothesis.
In both cases, the discontinuous synthesis of the lagging
strand of DNA might increase resilience for units of a given
length. Indeed, a periodicity of about 1000 bp (E.coli) to
1200 bp (B.subtilis) is visible on presence density ratio plots
(Fig. 2G–I). This period is longer than the mean length of
genes (E.coli, 950 bp; B.subtilis, 883 bp) but is reminiscent of
the peak length of Okazaki fragments (Chastain et al., 2000).
ACKNOWLEDGEMENTS
We thank Alessandra Carbone and Eduardo Rocha for
helpful discussions and for critically reading this paper,
Claude Thermes for transcription terminator identification
in B.subtilis, Pierre Nicolas for sharing his knowledge of
B.subtilis.
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