Báo cáo Y học: DNA supercoiling in Escherichia coli is under tight and subtle homeostatic control, involving gene-expression and metabolic regulation of both topoisomerase I and DNA gyrase docx

DNA supercoiling in
Escherichia coli
is under tight and subtle
homeostatic control, involving gene-expression and metabolic
regulation of both topoisomerase I and DNA gyrase
Jacky L. Snoep
1,2
, Coen C. van der Weijden
1
, Heidi W. Andersen
2,3
, Hans V. Westerhoff
1,4
and Peter Ruhdal Jensen
3
1
Departments of Molecular Cell Physiology and Mathematical Biochemistry, BioCentrum Amsterdam, Free University, Amsterdam,
the Netherlands;
2
Department of Biochemistry, University of Stellenbosch, South Africa;
3
Section of Molecular Microbiology,
Biocentrum, Technical University of Denmark, Lyngby, Denmark;
4
Stellenbosch Institute for Advanced Study, South Africa
DNA of prokaryotes is in a nonequilibrium structural
state, characterized as ÔactiveÕ DNA supercoiling. Altera-
tions in this state aect many life processes and a
homeostatic control of DNA supercoiling has been sug-
gested [Menzel, R. & Gellert, M. ( 1983) Ce ll 34, 105±113].
We here report on a new method for quantifying home-

ostatic control of the high-energy state of in vivo DNA.
The method involves making small perturbation in the
expression of topoisomerase I, and m easuring the e ect
on DNA supercoiling of a reporter plasmid and on the
expression of DNA gyrase. In a separate set of experi-
ments the expression of DNA g yrase w as man ipulated
and the control on DNA supercoiling and topoisom-
erase I expression was measured [part of these latter
experiments has been published in Jensen, P.R., van der
Weijden, C.C., Jensen, L.B., Westerho, H.V. & Snoep,
J.L. (1999) E ur. J. Bio chem. 266, 865±877]. Of t he two
regulatory mechanisms via which homeostasis is conferred,
regulation of enzyme activity or regulation of enzyme
expression, we quanti®ed the ®rst to be res ponsible for
72% and the latter for 28%. The gene expression regu-
lation could be dissected to DNA gyrase (21%) and to
topoisomerase I (7%). On a scale from 0 (no homeostatic
control) to 1 (full homeostatic control) we quanti®ed the
homeostatic control o f DNA supercoiling at 0.87. A 10%
manipulation o f either topoisomerase I or DNA gyrase
activity results in a 1.3% change of DNA supercoiling
only. We conclude that the homeostatic regulation of the
nonequilibrium DNA structure in wild-type Escherichia
coli is almost complete and subtle (i.e. i nvolving at least
three regulatory mechanisms).
Keywords: metabolic control analysis (MCA); hierarchical
control a nalysis (HCA); homeostasis coecient.
DNA in the bacterial nucleoid i s negatively supercoiled and
it has been estimated that roughly 50% of the supercoiling is
constrained by proteins binding to the DNA [1]. This

constraint does not depend on the c ontinuous expenditure
of ATP. The r emaining supercoils are maintained actively at
the cost of ATP hydrolysis, via topoisomerase activities.
Four topoisomerases h ave been identi®ed in Escherichia coli
(reviewed in [2]). Topoisomerase I [3,4] and DNA gyrase
(topoisomerase II) are mostly held responsible for main-
taining the supercoiled state of the DNA while topoisom-
erase I II and IV manage the decatenation reactions.
A recent publication suggested that topoisomerase IV may
also be important for the relaxation of DNA supercoiling
[5].
The importance of DNA gyrase and topoisomerase I for
supercoiling has been shown in studies involving mutants
with ac tivities differing greatly from the wild-t ype ac tivity.
Such studies cannot be used to assess the homeostasis of
supercoiling in the physiological situation, where the
response to smaller challenges is important. When chal-
lenged suf®ciently, all systems will respond in drastic
manners, or fail. It may well be that a system is robust
with respect to small challenge s, whilst i t fails to deal with
the same but larger challenges, or vice versa.
DNA gyrase activity is known to be controlled home-
ostatically [6], but the extent o f this control a nd its
implications for the h omeostatic control of s upercoiling
itself, have not been quanti®ed. In general, homeostasis can
be conferred via changes in enzyme activity (e.g. due to
sensitivities for substrate, product or allosteric effectors) or
via c hanges in enzyme concentration transferred through
gene expression regulation. T he activities of both DNA
gyrase and topoisomerase I depend on the level of

supercoiling. In vitro, topoisomerase I has been shown to
be more active on more negatively supercoiled DNA, and
it does not completely relax DNA [7]. In contrast, DNA
gyrase is more active in vitro on relaxed DNA as compared
to negatively supercoiled DNA [8]. Expression of the
topoisomerase I [9] and DNA gyrase [6] also depends on
DNA supercoiling as has been determined using gene
fusion studies or ( for DNA gyra se) via direct measur e-
ments of the expression (e.g [10]).
Correspondence to H. V. Westerho, Free University, De Boelelaan
1087, NL-1081 HV Amsterdam, the Netherlands.
Fax: + 31 20 4447229, Tel.: + 31 20 4447230,
E-mail:
Abbreviations:IPTG,isopropylthio-b-
D
-galactosidase;
aLk, active linking number.
(Received 1 6 October 2001, revised 17 December 2001, accepted
22 January 2002)
Eur. J. Biochem. 269, 1662±1669 (2002) Ó FEBS 2002
Recently we used metabolic and h ierarchical control
analysis to determine the control of DNA gyrase on DNA
supercoiling [11]. We have now used a similar strategy to
determine the control of topoisomerase I. In addition we
have now been able to determine the strength of the
homeostasis and the relative importance of the regulatory
loops. To our knowledge this is the ®rst time that the relative
contributions of gene expression and enzyme activity to
homeostasis have been quanti®ed.
MATERIALS AND METHODS

Bacterial strains
The cloning work was performed in the strain DH5a or
JM105 [12,13]. Chromosome integration was performed in
strain MC1000 [14].
Growth of cultures
In th e t opoisomerase I and DNA gyrase modulation
experiments cells were pregrown in Mops (40 m
M
,
pH 7.4) minimal salts medium [15] containing 0.5% w/v
glucose, tricine ( 4 m
M
), valine, le ucine a nd isoleu cine
(40 lgámL
)1
each), thiamine (10 lgámL
)1
) and ampicillin
as antibiotic marker for pBR322 (100 lgámL
)1
)atthe
relevant isopropyl thio-b-
D
-galactosidase (IPTG) concen-
tration. After over night growth, the cells were diluted in the
same medium to an D
540
of 0.005 and growth was followed
for at least ®ve generations before sampling. All samples
were withdrawn between D

540
 0.2 and 0.4.
Enzymes
Restriction enzymes, T 4 DNA ligase, and T4 DNA
polymerase were obtained from and used as recommended
by New England Biolabs and Boehringer Mannheim.
Plasmid and ATP, ADP extraction
Aliquots (0.8 mL) were removed f rom cell cultures a nd
placed into an equal v olume of 80 °C phenol. After
centrifugation and chloroform extraction, ATP/ADP was
measured in a sample from the water phase and DNA was
extracted u sing standard isopropanol precipitation. This
method has been described m ore extensively previously [16].
ATP/ADP assay
Intracellular concentrations o f ATP and ADP were meas-
ured using a l uciferin±luciferase ATP monitoring kit (LKB),
essentially according to the manufacturer's recommenda-
tions. This method has been described previously [17].
Supercoiling assay
DNA supercoiling was assessed in t erms of the linking
number of intracellular plasmid pBR322 [18]. DNA super-
coiling was expressed as t he ac tive linking number, aLk ,
which is the difference in linking number of p BR322 in th e
respective s ample and of pBR322 isolated from cells
incubatedfor30minwith0.1mgámL
)1
of coumermycin
and 0.2 mgámL
)1
rifampicin.

Topoisomerase concentration
The t opoisomerase I and DNA gyrase content of the cells
was estimated by quantitative W estern blotting using a n
antibody against topoisomerase I and GyrA subunit,
respectively. P uri®ed topoisomerase I and gyrase were
subjected to SDS/PAGE. After subsequent blotting to
nitrocellulose and Ponceau staining [Ponceau-S, 0.2% in
3% trichlororacetic acid (Serva)] the topoisomerase I and
gyrase A bands were cut out and ground. Polyclonal
antibodies were raised by Eurogentec by immunizing
rabbits with the ground fragments.
Construction of the plasmid used for the integration
at the
topA
locus pHA2
A 1549-bp PCR fragment c ontaining the DNA region
upstream of topA,thetopA promoter and the N-terminal
part of topA was ampli®ed using primers ECTOPA,
accession number X04475, bp322± 342, i.e. 5¢-CGAA
GAAGGGCGGGGAGAAAT-3¢ +bp1870±1850, i.e. 5¢-
TCCATAGCAGCGGCGAAACCA-3¢ and chromosomal
DNA from strain LM1237 [17] as a template. The PCR
fragment was subsequently digested with the enzymes DraI
and EcoRV and a 842-bp fragment containing the DNA
region upstream of topA and the topA promoter was
isolated and inserted into pUC19 (New England Biolabs)
digested with SmaI, resulting in the plasmid pHA2.
PHA5
The 1549-bp PCR f ragment described above w as digested
with EcoRV and SspI and a 572-bp fragment containing the

N-terminal part of the topA gene was isolated and inserted
into pUC19 digested with SmaI, re sulting in th e plasmid
pHA5.
PTOPA2
TS
pGYRAB
TS
was c onstructed previously for site s peci®c
integration of a lac-type promoter in the gyrA locus [11].
Important features of this plasmid are that the r eplication is
temperature sensitive, and that the pA1lacO-1 promoter
and the lacI
q1
gene are surrounded by a DNA fragment
originating from upstream the gyrA gene and a fragment
containing the N-terminal part of the gyrA gene. To create a
plasmid for integration of the lac-type promoter at the topA
locus, it is necessary to replace the two r egions containing
DNA from the gy rA locus o n pGYRAB
TS
with DNA
fragments taken from upstream t he topA gene and a
fragment containing the N-terminal part of the topA ge ne.
pGYRAB
TS
was ® rst digested with KpnIandBamHI to
excise the gyrA upstream region, treated with T4 DNA
polymerase to create blunt ends. Subsequently, a 811-bp
HincII fragment from pHA2 containing the DNA region
upstream of topA and t he topA promoter was inserted into

the blunted Kpn I±BamHI sites, resulting in t he plasmid
pTOPA2
TS
.
PTOPA2A5
TS
pTOPA2
TS
was digested ®rst with PstI and then with EcoRI
(partial digest), which removes the N-terminal part of the
Ó FEBS 2002 Control of DNA supercoiling by topoisomerase I (Eur. J. Biochem. 269) 1663
gyrA gene. Subsequently a 625-bp EcoRI±PstIfragment
from pHA5 containing the N -terminal part of topA was
inserted. T his resulted i n the plasmid pTOPA2A5
TS
,in
which the pA1lacO-1 promoter a nd the lacI
q1
gene are
surrounded by a DNA fragment originating from upstream
the topA gene and a fragment containing the N-terminal
part of the topA gene.
Replacement of the chromosomal
topA
promoter
with an inducible
lac
-type promoter and a
lacI
q1

gene
Plasmid pTOPA2A5
TS
was integrated in the chromosome
of E. coli strain MC1000. Clones in which a second cross
over has taken place were selected on basis of chloram-
phenicol sensitivity. Such clones were found at a frequency
of 2.7 ´ 10
)3
. The second cross over will either re-establish
the wild-type g ene con®guration in t he topA locus, or it will
leave the IPTG re gulatory elements upstream of topA.The
latter clones should still respond to the presence of IPTG,
and s uch c lones were indeed found at a frequency of 22% of
the second cross over event. Southern blot analysis and
DNA s equencing of one of these clones in the topA locus,
i.e. strain HWA36, con®rmed that t he pA1lacO-1 promoter
and the lacI
q1
gene had indeed been inserted upstream of
the topA gene.
RESULTS
Modulation of the expression of topoisomerase I by IPTG
To determine how readily changes in topoisomerase I
activity compromises DNA structure, we set up a system
where we could modulate the enzyme around its physio-
logical concentration. We substituted an IPTG driven
promoter for the natural promoter of the chromosomal
topA gene. I n E. coli strain HWA36 topoisomerase I
expression was indeed dependent on IPTG concentration

as is shown in Fig. 1. I n the absence of IPTG the expression
was very low (2±5% of wild-type). Precise modulation of
expression around the wild-type level (at % 40 l
M
IPTG),
but also over-expression up to 20 times w ild-type was
possible. At any given IPTG concentration no signi®cant
dependence of topoisomerase concentration on cell density
was detected, in the range of cell concentrations represented
by D
540
 0.2±0.4, indicating a constant expression level of
the enzyme ( data not shown; cf [19]). Under these conditions
we should be able t o ask how readily DNA supe rcoiling is
perturbed by changes in topoisomerase I activity.
Is DNA supercoiling readily compromised
by topoisomerase I?
From t he p lot of aLk vs. the topoisomerase I c oncentration
(Fig. 2 ), it can be deduced that supercoiling is not very
sensitive for changes in topoisomerase I activity. Over a
thousand-fold range of expression of topoisomerase I the
aLk varied by no more than six linking numbers, i.e.
between )3 and +3 linking numbers relative to the )13
active links of the same plasmid in wild-type cells. Figure 2A
shows that at very low activities of topoisomerase I the
DNA supercoiling d epended even more weakly, if at all, on
the enzyme. At wild-type expression levels, the dependence
appeared to be stronger.
Fig. 1. IPTG induction of topoisomerase I expression. E. coli strain
HWA36 was inc ub ated with I PTG a t c oncentrations ranging fro m 0 to

0.5 m
M
. Topoisomerase I concentrations in cellular extracts were
measured by Western analysis using polyclonal topoisomerase I anti-
bodies. Topoisome rase I conc entration w as expressed a s amoun ts per
gram protein and then normalized to the amount found in wild-type
cells. Results from ® ve independent experiments are shown using dif-
ferent symbols for each. Each d ata p oint is the average of three
measurement s (samples take n at D
540
 0.2, 0.3 and 0.4). The e rror
bars den ote the standard error of the mean. Precise gro wth conditions
are given in Materials and methods.
Fig. 2. Dependence of DNA supercoiling on topoisomerase I expression.
(A) HWA36 was incubated with IPTG concentrations ranging from
0to0.5m
M
. Results of ®ve independent experiment s a re shown using
dierent symbols for each. Each data p oint is the average of th re e
measurements. The error bars d enote the stand ard error o f the mean.
Wild-type is s hown as a c losed circle. The f ollowing equations were
®tted through the data points: solid line, aLk  a 
b
1 
topoisomera se I
c

d
with a  )16.1886, b  7.1069, c  1.4141, d  )1.0819,
short dash, aLk  a 

b
1  e
Àtopoisomerase IÀc
d
with a  )173.219,
b  163.529, c  ) 5.2409, d  1.6430, long dash, aLk 
a  cÁlntopoisomerase I
1  bÁlntopoisomerase IdÁlntopoisomerase I
2
with a  )13.460, b  )0.0125,
c  1.3983, d  0.0072. (B) Shown a s an insert is the c ontrol of
topoisomerase I on DNA supercoiling. Inherent control c oecients
are calculated by multiplying the derivative of the ®tted c urves in
(A) at each point of the graph with the quotient of the respective
x/y coordinates. Thus the control coecient de®ned as
c
aLk
topoisomerase I

daLk
dtopoisomerase I
Á
topoisomerase I
aLk
is obtained. A t w ild-type
topoisomerase concentration an inherent control coecient of )0.14
was c alculated. `topoi somerase I ' refers to the concentration of
topoisomerase I relative to the wild-type.
1664 J. L. Snoep et al. (Eur. J. Biochem. 269) Ó FEBS 2002
How strong or weak the effect of topoisomerase I on

supercoiling actually was, can be quanti®ed in terms of the
control coef®cient of m etabolic control analysis [20,21].
With respect to the control of DNA supercoiling by
topoisomerase I this coef®cient (c
supercoiling
topoisomerase I
) corresponds
to the percentage change in aLk upon a 1% change in
topoisomerase I activity. Because it depends o n the ratio of
small differences, this coef®cient is subject to substantial
experimental error and this required us to be c areful in its
estimation. Three t ypes of curve were therefore ®tted to the
data points o f Fig. 2A. The types of curve were selected such
that they should p rovide bounds for the true dependence of
aLk on topoisomerase concentration at the wild-type level
(see ®gure legend for details on the curves used). The slopes
of these curves w ere then c alculated at e ach point and
normalized by the ratio of aLk to the t opoisomerase activity
of that point. In this m anner an upper ()0.09) and a lower
()0.16) boundary for the control coef®cient at wild-type
concentration was obtained. The same procedure gave
estimates for the control coef®cient a t all other topoisom-
erase I concentrations (cf. Figure 2B).
At the physiological level of expression the control of
DNA supercoiling b y t opoisomerase I amounted to no
more than )0.14 ( 0.03), i.e. for a 1 0% increase in
topoisomerase I activity, supercoiling decreased by only
1.4%. The negative sign of the coef®cient expresses that the
aLk decreased with increasing topoisomerase activity, as
expected. T hroughout th e vast range of expression levels

tested, topoisomerase I never had a high control on DNA
supercoiling. Also when the DNA became quite relaxed , its
control remained well below 0.2: DNA supercoiling is not
readily compromised by extra topoisomerase I.
Homeostasis of growth rate
Under t he conditions tested the s peci®c growth rate of
E. coli strain MC1000 was 0.93 h
)1
( 0.03) and was
observed to be almost in sensitive to a modulation of
topoisomerase I around its wild-type expression level. Only
at very low and very high expression levels was the growth
rate reduced by at most 25% (data not shown). The
dependence o f g rowth r ate on topoisomerase activity
around the physiological state was estimated as precisely
as possible: the c orresponding control c oef®cient w as as low
as 0.03, re¯ecting that a doubling of t he topoisomerase
activity decreased growth rate by a mere 3%.
Homeostasis through supercoiling dependent DNA
gyrase expression
The e xpression of the DNA gyra se g enes is alte red b y
mutations th at strongly affect DNA supercoiling [6,9]. If in
our experiments the concentration of DNA gyrase changed
in proportion to the change in concentration o f topoisom-
erase I, one should expect supercoiling t o be virtually
unaffected by the modulation o f topoisomerase expression
levels; i ndeed such a compensation mechanism could
explain the observed homeostasis. Accordingly we meas-
ured the cellular concentration of DNA gyrase at the
various expression levels of topoisomerase I.

However, over the thousand-fold range of e xpression
levels of topoisomerase I the DNA gyrase concentration
changed b y a factor of 2 only (data not shown), i.e. much
less than the factor o f perhaps 500 required t o counteract
the effect of topoisomerase I and explain that supercoiling
only varied by 50% (Fig. 2). This lack of response of gyrase
expression to the modulation of the topoisomerase I activity
implies that, notwithstanding the indications [6] that strong
interference with DNA sup ercoiling induces gyrase e xpres-
sion, in the physiological state topoisomerase I has little
control over gyrase gene expression.
The purported mechanism for such a control of gyrase
gene expression is the effect that topoisomerase I has on
DNA superc oiling in connection with the dependence of
gyrase gene expression on DNA supercoiling. This promp-
ted us to ask whether t his lack of control by topoisomerase I
on DNA gyrase expression was due to a l ow sensitivity of
the gyrase p romoters to supercoiling. The variation of the
expression level of DNA gyrase with DNA supercoiling
when modulating topoisomerase I is shown in Fig. 3. There
was a weak dependence of gyrase expression on DNA
supercoiling, which was evaluated in terms of the elasticity
coef®cient of metabolic control analysis. The derivative o f
the plot in Fig. 3 was taken and normalized to the ratio of
expression to supercoiling. In this way t he overall [11,22]
elasticity of gyrase expression with respect to supercoiling
was estimated, i.e. the percentage change in expression rate
of gyrase upon a 1% change in aLk.AttheaLk observed in
the wild-type strain, i.e. )12.7  0.3, a n elasticity of )1.6
was calculated. Accordingly, the absolute magnitude of this

elasticity coef®cient suggests that gyrase gene expression was
suf®ciently sensitive to DNA supercoiling to respond to
signi®cant changes in supercoiling (cf. below). Therefore,
the lack of control of topoisomerase I on gyrase expression
must again have been due to, rather than caused by, the
small effect the former had on DNA supercoiling. Clearly
Fig. 3. DNA gyrase expression as a function of aLk. T he concentration
of D NA gyrase is plotted at dierent aLk values obtained by incu-
bation of strain HWA36 with dierent concentrations of IPTG. Data
from ®ve independent experiments are shown using dierent symbols
for each. Data points are averages of three me asurements. The
error bars denote the standa rd error of the mean. Wild-type is
shown as a closed circle. The elasticity coecient de®ned as
e
kt
gyrase
supercoiling

dkt
gyrase
daLk
Á
aLk
kt
gyrase
was calculated by multiplying the derivative
of the ®tted curve at each point of the graph with the quotient of the
respective x/y coordinates. At wild-type level of supercoiling a n elasti-
city coecient of )1.6 was calculated.
Ó FEBS 2002 Control of DNA supercoiling by topoisomerase I (Eur. J. Biochem. 269) 1665

the supercoiling-dependence of gyrase expression was
not the dominant homeostatic mechanism for DNA
supercoiling.
Homeostasis through supercoiling dependent
topoisomerase-I expression?
In strain HWA36 the expression of topoisomerase I is
controlled by the IPTG concentration in the medium and
does not re¯ect the normal supercoiling sensitivity. Having
determined the o verall elasticity of DNA gyrase gene-
expression to supercoiling, we became interested in quan-
tifying the extent to which topoisomerase I gene expression
normally depends on DNA structure. Perhaps this depend-
ence could contribute signi®cantly to homeostasis of DNA
structure in wild-typ e cells. A strain in which DNA gyrase
expression can be modulated by IPTG, and in which the
topoisomerase I gene is und er control of its normal
promoter, was used to address this question (E. coli
PJ4273 [11]). Through gyrase modulation, DNA supercoil-
ing of t he pBR322 probe plasmid c ould be directed to
anywhere between )15 and )6 aLks [11]. Only at highly
negative supercoiling was an e ffect on topoisomerase I
expression detected (Fig. 4). The elasticity of the topoisom-
erase expression re¯ects this dependency. At wild-type aLk
()12.7  0.3) an elasticity of 0.56 was estimated. These
results suggest that in the wild-type cells supercoiling
dependent expression of topoisomerase I is not a dominant
mechanism either for the homeostasis of DNA structure.
What we are left with is the possibility that there is a third
dominant homeostatic mechanism, or that various mecha-
nisms contribute, such than none is dominant. In the

Discussion we shall address these possibilities in detail.
DISCUSSION
Homeostatic control of DNA supercoiling in prokaryotes
has been proposed previously [6]: the enzyme that causes
negative supercoiling, i.e. DNA gyrase, was repre ssed b y
highly negative supercoiling. This observation showed
homeostatic control of DNA gyrase expression but not of
DNA supercoiling itself, as the implications for DNA
supercoiling were not determined. In addition the strength
of the homeostatic control and whether it also occurred i n
and around the physiological state, had not yet been
addressed.
DNA gyrase and topoisomerase I are considered to be
the m ost important en zymes in c ontrolling t he level of
supercoiling in E. coli [23]. This suggests two mechanisms of
homeostasis [6,9]. One is that decreased supercoiling may
enhance the expression level of DNA gyrase that then leads
to an increase of supercoiling. The second is that the
decreased supercoiling diminishes the expression level of
topoisomerase I, which leads to enhanced supercoiling.
There should be two additional, more direct mechanisms.
One consists of the phenomenon that the rate at which
DNA gyrase supercoils DNA may decrease with the extent
to which that DNA is supercoiled, with zero activity at t he
static head situation [24]. The other relies on a more than
proportional dependence of the catalytic rate of topoisom-
erase I on the extent of DNA supercoiling. Homeostasis of
DNA supercoiling could be called ÔsubtleÕ if all four of these
mechanisms were involved. It could be called ÔsimpleÕ if only
one mechanism was operative. In our analysis we focus on

topoisomerase I and DNA gyrase as the main topoisom-
erases controlling DNA supercoiling in wild-type E. coli.
Recently it was found that also topoisomerase IV plays a
role in controlling DNA supercoiling m ost importantly in
DNA that is less negatively supercoiled [5]. Our analysis
method can be extended t o also includ e topoisomerase IV
but this would make it u nnecessarily c omplicated (see later).
We have here quanti®ed experimentally the c ontrol o f
topoisomerase I on DNA supercoiling. In combination
with the results published recently on DNA gyrase [11] these
results can be used to q uantify the strengths of these
homeostatic mechanisms, in terms of the strengths of the
corresponding regulatory lo ops. I n metabolic contr ol ana-
lysis the extent to which a parameter controls a variable is
quanti®ed by a control c oef®cient. For instance for the
control of aLk by topoisomerase I this ( ÔintrinsicÕ,seebelow
and [11]) control coef®cient is de®ned as:
c
supercoiling
topoisomerase I

dlnjaLkj
dlnV
topoisomeras e I

system at st eady state
1
where V
topoisomerase I
represents the V

max
of the topoisom-
erase I reaction. Note that the lower case c is used for this
type of control coef®cient. The v alue of the c ontrol
coef®cient is equal to the percentage change that is observed
in the aLk upon a percentage change in the activity of
topoisomerase I.
In addition gyrase activity will in¯uence DNA supercoil-
ing. The sensitivities (de®ned as elasticity coef®cients by
metabolic control analysis) of both enzymes to changes in
supercoiling will determine the magnitude of the control
coef®cients. Using the concentration summation and
connectivity theorems (cf. [22]). th e intrinsic control by
Fig. 4. Topoisomerase I expression as a function of aL k. The concen-
tration o f topoisomerase I is plotted at dierent aLk values ob tain ed
by incubation of strain PJ4273 [11] with dierent concentrations
of IPTG. Data from two in depen dent experiments are s hown using
dierent symbols f or each. Data p oints are averages of three
measurements. The error bars denote the standard error of the mean.
Wild-type is sho wn as a closed circle. The ela sticity coe cient d e®ned
as e
kt
topoisomerase I
supercoiling

dkt
topoisomerase I
daLk
Á
aLk

kt
topoisomerase I
was calculated by multiplying
the derivative of t he ®tte d curve at each point of the graph with the
quotient of the respective x/y co ordinates. A wild-type level of super-
coiling an elasticity coecient of 0.56 was calculated.
1666 J. L. Snoep et al. (Eur. J. Biochem. 269) Ó FEBS 2002
topoisomerase I and gyrase can be expressed in terms of
elasticities:
c
supercoiling
gyrase

1
e
v
topoisomerase I
supercoiling
À e
v
gyrase
supercoiling
Àc
supercoiling
topoisomerase I
2
Not only the activity but also the expression level of DNA
gyrase and topoisomerase I depend on supercoiling. In the
analysis this is expressed in two additional elasticities, as was
deduced previously [25]; e

kt
topoisomerase I
supercoiling
and e
kt
gyrase
supercoiling
, re¯ecting
the s ensitivity of transcription of topoisomerase I and DNA
gyrase for D NA superco iling. Certain sim pli®cations were
made in [25], i.e. grouping of transcription and translation,
assuming that transcription/translation i s product insensit-
ive a nd mRNA and p rotein degradation follow ®rst order
kinetics (for a more general treatment, see [26]). Expressing
the control coef®cients in terms of elasticities in such a
system leads to the following expression for the ÔglobalÕ
control (hence the capital Cs) by the topoisomerases on
supercoiling:
C
supercoiling
gyrase

1
e
v
topoisomerase I
supercoiling
e
kt
topoisomerase I

supercoilin g
Àe
v
gyrase
supercoiling
Àe
kt
gyrase
supercoiling
ÀC
supercoiling
topoisomerase I
3
In this paper we have shown that homeostasis o f DNA
supercoiling is strong; a thousand-fold variation of the
topoisomerase I activity has relatively little effect o n DNA
supercoiling, as indicated by an inherent control coef®-
cients of only )0.14. We attribute this s mall effect to
intracellular mechanisms that work t o maintain the DNA
supercoiling at its physiological magnitude. Amassing these
mechanisms under the single title of Ôhomeostatic mech-
anismsÕ, we aimed at identifying some of them and at
determining their relative importance. Especially for the
latter issue, we required a quantitative measure of the
extent of homeostatic control. We therefore introduce
the so-called homeostasis coef®cient H, which quanti®es
the extent to which homeostatic processes annul DNA
relaxation activity. It is de®ned a s the percentage change in
aLk that is prevented by the homeostatic processes. In
exact terms this becomes:

H  1À
dlnaLk
dlnv
topoisomerase I

system at steady state
 1 ÀC
supercoiling
topoisomer ase I
With this de®nition, when a 10% increase in relaxation
activity leads to a 10% decrease in linking number, no
relaxation is prevented and H becomes equal to 0; there is no
homeostasis. When there is no decrease in linking number,
H equals 1, i.e. there is complete homeostasis. The utility of
the d e®nition is that we can now evaluate intermediary cases
between no and complete homeostasis. Homeostasis of
DNA supercoiling in E. coli is such an intermediary case: in
terms of t his de®nition, it is quanti®ed as 1 ) 0.13  0.87,
i.e. 87% of complete homeostasis. This shows that home-
ostasis of DNA supercoiling is quite strong.
From Eqn (3) and the de®nition of H, it follows that this
coef®cient is independent of whether topoisomerase I is
activated or DNA gyrase i s inhibited to compromise DNA,
and equal to:
H
supercoiling

e
v
topoisomerase I

supercoiling
 e
kt
topoisomerase I
supercoiling
À e
v
gyrase
supercoiling
À e
kt
gyrase
supercoiling
À 1
e
v
topoisomerase I
supercoiling
 e
kt
topoisomerase I
supercoiling
À e
v
gyrase
supercoiling
À e
kt
gyrase
supercoiling

4
The elasticities o f gyrase a ctivity and gyrase expre ssion for
supercoiling are ne gative (i.e. the activity and expression of
DNA gyrase i s inhibited not stimulated by higher levels of
supercoiling) and those of topoisomerase I positive. Con-
sequently all four of these elasticities c an contribute
positively to the homeostatic control of supercoiling. The
equation suggests that the subtlety of the homeostatic
control in the above sense can be determined by inspecting
whether all four elasticities are of signi®cant magnitudes.
In the strain used to manipulate the topoisomerase I
concentration, expression of topoisomerase I is controlled
by IPTG and the elasticity with respect to supercoiling is
zero. The transcription rate of topoisomerase I was modu-
lated and the effect on topoisomerase I concentration and
supercoiling measured, leading to a measured value for the
inherent control coef®cient of topoisomerase I with r espect
to DNA supercoiling (in metabolic control analysis terms, a
coresponse coef®cient):
t
topoisomerase I
O
supercoiling
e
topoisomerase I

C
supercoiling
t
topoisomerase I

C
e
topoisomerase I
t
topoisomerase I

1
e
v
topoisomerase I
supercoiling
Àe
kt
gyrase
supercoilin g
Àe
v
gyrase
supercoiling
5
For the corresponding inherent control by gyrase one ®nds:
t
gyrase
O
supercoiling
e
gyrase

C
supercoiling

t
gyrase
C
e
gyrase
t
gyrase

1
e
v
topoisomerase I
supercoiling
e
kt
topoisomerase I
supercoilin g
Àe
v
gyrase
supercoiling
6
For topoisomerase I an inherent control of )0.14 ( 0.03)
was determined experimentally while for DNA gyrase an
inherent control of 0.17 ( 0.01) was measured [11]. Global
control coef®cients (Eqn 3) can be calculated from the
inherent control coef®cients by adding the elasticities of
expression of DNA gyrase and topoisomerase I (i.e. )1.6
and +0.56, respectively) for supercoiling in Eqns (6) a nd (5),
respectively. In this manner a global control of supercoiling

by activity of 0.13 (absolute value) is obtained both for
DNA gyrase and topoisomerase I. The sum of these two
control coef®cients had to be zero, providing a consistency
check of the calculations. Also the inherent (ÔmetabolicÕ)
control c oef®cients (Eqn 2) can be calculated: for topoiso-
merase I and DNA gyrase a value of 0.18 was calculated
(positive for DNA gyrase, negative for topoisomerase I).
The consistency (i.e. both the inherent and the global control
coef®cients of t opoisomerase I and DNA gyrase must add
up to zero) indicates that the assumption made in the
analysis (i.e. that topoisomerase I and DNA gyrase are the
main contributors to the steady state wild-type level of
supercoiling) is correct within the error of measurement.
Via the elasticity coef®cients the contribution of the two
regulatory loops, i.e. via enzyme activity or via gene
expression regulation, to this homeostasis can be quanti®ed.
Ó FEBS 2002 Control of DNA supercoiling by topoisomerase I (Eur. J. Biochem. 269) 1667
The su m of elasticities of the gene expression loops equal 2.2
(i.e. 1.6 + 0.56). The sum of the kinetic elasticity coef®-
cients can be calculated from Eqn (5):
e
v
topoisomerase I
supercoiling
À e
v
gyrase
supercoiling
 e
kt

gyrase
supercoiling
À
1
t
topoisomerase I
O
supercoiling
e
topoisomerase I
À1X6  7X2  5X6
And from Eqn (6):
e
v
topoisomerase I
supercoiling
À e
v
gyrase
supercoiling
Àe
kt
topoisomerase I
supercoiling

1
t
topoisomerase I
O
supercoiling

e
topoisomerase I
À0X56  6X1  5X5
The two independent determinations of the sum of the
kinetic elasticity coef®cients (i.e. 5.6 and 5.5) are in good
agreement with each other. Thus, 72% (5.6 of 7.8) of the
homeostasis of DNA supercoiling in the wild-type cells is
due to regulation at the activity level and 28% (2.2 of 7.8) is
due to regulation at the gene expression level. Of the l atter
28%, 7% is accounted for by regulation through topo-
isomerase I expression levels and 21% through gyrase
expression levels. Clearly, homeostasis of DNA supercoiling
is regulated in a subtle manner involving at least three
different regulatory routes, with the direct effect of super-
coiling on enzyme rates being the strongest, although not
dominant, homeostatic mechanism.
Several of the ®ndings of this paper are c onsistent with
existing information. Here we determined the concentra-
tions of gyrase a nd topoisomerase I to calculate the
sensitivity of the transcription/translation level fo r changes
in DNA supercoiling. In an previous study [11] we used a
lacZ fusion to the gyrB promoter to measure t his sensitivity
for DNA gyrase. The elasticity of gyrase e xpression
measured with the lacZ fusion e
DNAgyrase expression
supercoiling
À1X7
in that paper i s in good agreement with t he elasticity
determined via gyrase concentration measurements here, i.e.
)1.6. In other studies in which the sensitivity of expression

of DNA gyrase or topoisomerase I was measured using
promoter fusion, always large perturbations in DNA
supercoiling were made [9,27]. As can been seen from
Figs 3 and 4 the sensitivity of gene expre ssion to s upercoil-
ing does depend on th e level of supercoiling, especially for
the topoisomerase I, which is almost insensitive at wild-type
levels of supercoiling and much more sensitive at h igh levels
of supercoiling. One can compare the results of these earlier
studies with ours by extrapolating our results to larger
changes in supercoiling. Fusion of the gyrB promoter to the
galactokinase gene showed a two to three f old increase upon
inhibition of gyrase with coumermycin [27]. Our results are
in good agreement with this: Extrapolation of our ®ts i n
Fig. 3 to an aLk of 0 (corresponding to coumermycin
inhibition) indicates a 2.8-fold induction. Fusion of the topA
promoters to the galactokinase gene showed a twofold to
fourfold inhibition of expression upon addition of gyrase
inhibitors [9]. With our DNA gyrase modulatable strain we
did not observe a strong effect upon decreasing the level of
supercoiling below the wild-type level. Rather at higher
levels of supercoiling an i nduction of topoisomerase I was
observed. Perhaps t opoisomerase I expression becomes
more sensitive for supercoiling when the DNA relaxes
more than was tested in our strains. In the e arlier studies the
promoter fusions were plasmid c onstructs while in the
present study we looked at the native chromosomal
promoter activities. The location of the promoter might
very well have an effect on its sensitivity for supercoiling.
We have shown that for the speci®c case of DNA
supercoiling, homeostatic control resides predominantly

(72%) in the metabolic (enzyme activity) le vel and to a l esser
extent (28%) in the gene-expression level of the cellular
control hierarchy. Although the speci®c distribution over
these regulatory levels will depend on the system under
study, the methods we have used to delineate our system
(metabolic and hierarchical control analysis) are generally
applicable. Such quantitative analysis t ools are essential to
understand the working of the multilayered cell. Recent
advances i n th e X-omics and bioinformatics ®elds make it
possible to study the regulation of cell function both
comprehensively a nd fairly quantitatively. Yet it is of crucial
importance to evaluate how much of a given regulation is
effected at the level of gene expression and how much by
metabolic regulation. Although this argument has been
clear in principle, it has never been demonstrated experi-
mentally to be relevant. One important general aspect of this
paper m ay be that it does furnish this experimental
demonstration. That calculations were necessary to s how
this should not detract f rom the point that the proof comes
from our experimental results; the calculations were just a
tool for the interpretation of the data; no modelling was
involved.
ACKNOWLEDGEMENTS
We wish to thank Jan Schouten (MRC, Holland) f or supplying us with
puri®ed topoisomerase I for the preparation of antibodies. This study
was supported by the Netherlands Organization for Scienti®c Research
(NWO), the Association of Netherlands Biotechnological Research
Schools (ABON), the Danish Natural Research Council (SNF) a nd the
Danish Centre for M icrobiology (CM).
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