If in our experiments the concentration of DNA gyrase changed in proportion to the change in concentration of topoisom-erase I, one should expect supercoiling to be virtually unaffected
Trang 1DNA 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 Snoep1,2, Coen C van der Weijden1, Heidi W Andersen2,3, Hans V Westerhoff1,4
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 aect many life processes and a
homeostatic control of DNA supercoiling has been
sug-gested [Menzel, R & Gellert, M (1983) Cell 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 measuring the eect
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 gyrase was manipulated
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) Eur J Biochem 266, 865±877] Of the two
regulatory mechanisms via which homeostasis is conferred, regulation of enzyme activity or regulation of enzyme expression, we quanti®ed the ®rst to be responsible 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 of DNA supercoiling at 0.87 A 10% manipulation of 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 involving at least three regulatory mechanisms)
Keywords: metabolic control analysis (MCA); hierarchical control analysis (HCA); homeostasis coecient
DNA in the bacterial nucleoid is 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 continuous expenditure
of ATP The remaining supercoils are maintained actively at
the cost of ATP hydrolysis, via topoisomerase activities
Four topoisomerases have 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 III 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 activities differing greatly from the wild-type activity 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 challenges, whilst it 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 of this control and its implications for the homeostatic control of supercoiling 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 changes in enzyme concentration transferred through gene expression regulation The 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 gyrase) via direct measure-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: hw@bio.vu.nl
Abbreviations: IPTG, isopropyl thio-b- D -galactosidase;
aLk, active linking number.
(Received 16 October 2001, revised 17 December 2001, accepted
22 January 2002)
Trang 2Recently we used metabolic and hierarchical 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
M A T E R I A L S A N D M E T H O D S
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 the topoisomerase I and DNA gyrase modulation
pH 7.4) minimal salts medium [15] containing 0.5% w/v
glucose, tricine (4 mM), valine, leucine and isoleucine
(40 lgámL)1each), thiamine (10 lgámL)1) and ampicillin
as antibiotic marker for pBR322 (100 lgámL)1) at the
relevant isopropyl thio-b-D-galactosidase (IPTG)
concen-tration After over night growth, the cells were diluted in the
same medium to an D540of 0.005 and growth was followed
for at least ®ve generations before sampling All samples
were withdrawn between D540 0.2 and 0.4
Enzymes
Restriction enzymes, T4 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 from cell cultures and
placed into an equal volume of 80 °C phenol After
centrifugation and chloroform extraction, ATP/ADP was
measured in a sample from the water phase and DNA was
extracted using standard isopropanol precipitation This
method has been described more extensively previously [16]
ATP/ADP assay
Intracellular concentrations of ATP and ADP were
meas-ured using a luciferin±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 terms of the linking
number of intracellular plasmid pBR322 [18] DNA
super-coiling was expressed as the active linking number, aLk,
which is the difference in linking number of pBR322 in the
respective sample and of pBR322 isolated from cells
incubated for 30 min with 0.1 mgámL)1 of coumermycin
and 0.2 mgámL)1rifampicin
Topoisomerase concentration The topoisomerase I and DNA gyrase content of the cells was estimated by quantitative Western blotting using an antibody against topoisomerase I and GyrA subunit, respectively Puri®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
A 1549-bp PCR fragment containing the DNA region upstream of topA, the topA 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 fragment described above was 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, resulting in the plasmid pHA5
PTOPA2TS
pGYRABTS was constructed previously for site speci®c integration of a lac-type promoter in the gyrA locus [11] Important features of this plasmid are that the replication is temperature sensitive, and that the pA1lacO-1 promoter and the lacIq1gene 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 regions containing
fragments taken from upstream the topA gene and a fragment containing the N-terminal part of the topA gene
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 the topA promoter was inserted into the blunted KpnI±BamHI sites, resulting in the plasmid pTOPA2TS
pTOPA2TSwas digested ®rst with PstI and then with EcoRI (partial digest), which removes the N-terminal part of the
Trang 3gyrA gene Subsequently a 625-bp EcoRI±PstI fragment
from pHA5 containing the N-terminal part of topA was
inserted This resulted in the plasmid pTOPA2A5TS, in
which the pA1lacO-1 promoter and the lacIq1 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
with an induciblelac-type promoter and a lacIq1gene
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 gene con®guration in the topA locus, or it will
leave the IPTG regulatory elements upstream of topA The
latter clones should still respond to the presence of IPTG,
and such clones were indeed found at a frequency of 22% of
the second cross over event Southern blot analysis and
DNA sequencing of one of these clones in the topA locus,
i.e strain HWA36, con®rmed that the pA1lacO-1 promoter
and the lacIq1gene had indeed been inserted upstream of
the topA gene
R E S U L T S
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 In E coli strain HWA36 topoisomerase I
expression was indeed dependent on IPTG concentration
as is shown in Fig 1 In 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 lM IPTG),
but also over-expression up to 20 times wild-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 D540 0.2±0.4, indicating a constant expression level of
the enzyme (data not shown; cf [19]) Under these conditions
we should be able to ask how readily DNA supercoiling is
perturbed by changes in topoisomerase I activity
Is DNA supercoiling readily compromised
by topoisomerase I?
From the plot of aLk vs the topoisomerase I concentration
(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 depended 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 incubated with IPTG at concentrations ranging from 0 to 0.5 m M Topoisomerase I concentrations in cellular extracts were measured by Western analysis using polyclonal topoisomerase I anti-bodies Topoisomerase I concentration was expressed as amounts 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 data point is the average of three measurements (samples taken at D 540 0.2, 0.3 and 0.4) The error bars denote the standard error of the mean Precise growth 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
0 to 0.5 m M Results of ®ve independent experiments are shown using dierent symbols for each Each data point is the average of three measurements The error bars denote the standard error of the mean Wild-type is shown as a closed circle The following equations were
1 topoisomerase I
c d
1 eÿ topoisomerase Iÿcd with a )173.219,
b 163.529, c ) 5.2409, d 1.6430, long dash, aLk
a cln topoisomerase I
1 bln topoisomerase I d ln topoisomerase I 2 with a )13.460, b )0.0125,
c 1.3983, d 0.0072 (B) Shown as an insert is the control of topoisomerase I on DNA supercoiling Inherent control coecients are calculated by multiplying the derivative of the ®tted curves in (A) at each point of the graph with the quotient of the respective x/y coordinates Thus the control coecient de®ned as
c aLk
d topoisomerase I topoisomerase I
topoisomerase concentration an inherent control coecient of )0.14 was calculated `topoisomerase I' refers to the concentration of topoisomerase I relative to the wild-type.
Trang 4How strong or weak the effect of topoisomerase I on
supercoiling actually was, can be quanti®ed in terms of the
control coef®cient of metabolic control analysis [20,21]
With respect to the control of DNA supercoiling by
topoisomerase I this coef®cient (csupercoilingtopoisomerase I) corresponds
to the percentage change in aLk upon a 1% change in
topoisomerase I activity Because it depends on the ratio of
small differences, this coef®cient is subject to substantial
experimental error and this required us to be careful in its
estimation Three types of curve were therefore ®tted to the
data points of Fig 2A The types of curve were selected such
that they should provide 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 were then calculated at each point and
normalized by the ratio of aLk to the topoisomerase activity
of that point In this manner 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 at all other
topoisom-erase I concentrations (cf Figure 2B)
At the physiological level of expression the control of
DNA supercoiling by topoisomerase I amounted to no
more than )0.14 ( 0.03), i.e for a 10% 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 Throughout the 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 the conditions tested the speci®c growth rate of
E coli strain MC1000 was 0.93 h)1 ( 0.03) and was
observed to be almost insensitive 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 of growth rate on topoisomerase activity
around the physiological state was estimated as precisely
as possible: the corresponding control coef®cient was as low
as 0.03, re¯ecting that a doubling of the topoisomerase
activity decreased growth rate by a mere 3%
Homeostasis through supercoiling dependent DNA
gyrase expression
The expression of the DNA gyrase genes is altered by
mutations that strongly affect DNA supercoiling [6,9] If in
our experiments the concentration of DNA gyrase changed
in proportion to the change in concentration of
topoisom-erase I, one should expect supercoiling to be virtually
unaffected by the modulation of topoisomerase expression
levels; indeed 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 expression
levels of topoisomerase I the DNA gyrase concentration
changed by a factor of 2 only (data not shown), i.e much
less than the factor of perhaps 500 required to 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 supercoiling induces gyrase expres-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 supercoiling in connection with the dependence of gyrase gene expression on DNA supercoiling This promp-ted us to ask whether this lack of control by topoisomerase I
on DNA gyrase expression was due to a low sensitivity of the gyrase promoters 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 of the plot in Fig 3 was taken and normalized to the ratio of expression to supercoiling In this way the 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 At the aLk observed in the wild-type strain, i.e )12.7 0.3, an 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 The concentration
of DNA gyrase is plotted at dierent aLk values obtained by incu-bation of strain HWA36 with dierent concentrations of IPTG Data from ®ve independent experiments are shown using dierent symbols for each Data points are averages of three measurements The error bars denote the standard error of the mean Wild-type is shown as a closed circle The elasticity coecient de®ned as
ektgyrase
supercoiling dktgyrase
daLk 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 an elasti-city coecient of )1.6 was calculated.
Trang 5the 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 overall 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-type cells A strain in which DNA gyrase
expression can be modulated by IPTG, and in which the
topoisomerase I gene is under control of its normal
promoter, was used to address this question (E coli
PJ4273 [11]) Through gyrase modulation, DNA
supercoil-ing of the pBR322 probe plasmid could be directed to
anywhere between )15 and )6 aLks [11] Only at highly
negative supercoiling was an effect 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
D I S C U S S I O N
Homeostatic control of DNA supercoiling in prokaryotes has been proposed previously [6]: the enzyme that causes negative supercoiling, i.e DNA gyrase, was repressed by 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 in and around the physiological state, had not yet been addressed
DNA gyrase and topoisomerase I are considered to be the most important enzymes in controlling the 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 the 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 most importantly in DNA that is less negatively supercoiled [5] Our analysis method can be extended to also include topoisomerase IV but this would make it unnecessarily complicated (see later)
We have here quanti®ed experimentally the control of topoisomerase I on DNA supercoiling In combination with the results published recently on DNA gyrase [11] these results can be used to quantify the strengths of these homeostatic mechanisms, in terms of the strengths of the corresponding regulatory loops In metabolic control ana-lysis the extent to which a parameter controls a variable is quanti®ed by a control coef®cient For instance for the control of aLk by topoisomerase I this (ÔintrinsicÕ, see below and [11]) control coef®cient is de®ned as:
csupercoilingtopoisomerase I dlnVdlnjaLkj
topoisomerase I
system at steady state 1 where Vtopoisomerase Irepresents the Vmaxof the topoisom-erase I reaction Note that the lower case c is used for this type of control coef®cient The value of the control 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]) the intrinsic control by
Fig 4 Topoisomerase I expression as a function of aLk The
concen-tration of topoisomerase I is plotted at dierent aLk values obtained
by incubation of strain PJ4273 [11] with dierent concentrations
of IPTG Data from two independent experiments are shown using
dierent symbols for each Data points are averages of three
measurements The error bars denote the standard error of the mean.
Wild-type is shown as a closed circle The elasticity coecient de®ned
as ekttopoisomerase I
supercoiling dkttopoisomerase I
kt topoisomerase I 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 A wild-type level of
super-coiling an elasticity coecient of 0.56 was calculated.
Trang 6topoisomerase I and gyrase can be expressed in terms of
elasticities:
csupercoiling
evtopoisomerase I
supercoilingÿ evgyrase
supercoiling
ÿcsupercoilingtopoisomerase 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]; ekttopoisomerase I
supercoiling and ektgyrase
supercoiling, re¯ecting the sensitivity of transcription of topoisomerase I and DNA
gyrase for DNA supercoiling Certain simpli®cations were
made in [25], i.e grouping of transcription and translation,
assuming that transcription/translation is product
insensit-ive and mRNA and protein 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:
Csupercoiling
evtopoisomerase I
supercoilingekttopoisomerase I
supercoiling ÿevgyrase
supercoilingÿektgyrase
supercoiling
ÿCtopoisomerase Isupercoiling 3
In this paper we have shown that homeostasis of DNA
supercoiling is strong; a thousand-fold variation of the
topoisomerase I activity has relatively little effect on DNA
supercoiling, as indicated by an inherent control
coef®-cients of only )0.14 We attribute this small effect to
intracellular mechanisms that work to 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 as the percentage change in
aLk that is prevented by the homeostatic processes In
exact terms this becomes:
topoisomerase I
system at steady state
1ÿCsupercoilingtopoisomerase 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 de®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 this 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 is inhibited to compromise DNA,
and equal to:
Hsupercoiling
v topoisomerase I
supercoiling ekttopoisomerase I
supercoiling ÿ evgyrase
supercoilingÿ ektgyrase
supercoilingÿ 1
evtopoisomerase I
supercoiling ekttopoisomerase I
supercoiling ÿ evgyrase
supercoilingÿ ektgyrase
supercoiling
4 The elasticities of gyrase activity and gyrase expression for supercoiling are negative (i.e the activity and expression of DNA gyrase is inhibited not stimulated by higher levels of supercoiling) and those of topoisomerase I positive Con-sequently all four of these elasticities can 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 respect
to DNA supercoiling (in metabolic control analysis terms, a coresponse coef®cient):
t topoisomerase IOsupercoiling
e topoisomerase IC
supercoiling
ttopoisomerase I
Cetopoisomerase I
t topoisomerase I
evtopoisomerase I
supercoilingÿektgyrase
supercoilingÿevgyrase
supercoiling
5 For the corresponding inherent control by gyrase one ®nds:
t gyraseOsupercoiling
e gyrase
supercoiling
t gyrase
Cegyrase
t gyrase
evtopoisomerase I
supercoilingekttopoisomerase I
supercoiling ÿevgyrase
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) and (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 coef®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 topoisomerase 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
Trang 7The sum 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):
evtopoisomerase I
supercoilingÿ evgyrase
supercoiling ektgyrase
supercoilingÿt 1
topoisomerase IOsupercoiling
etopoisomerase I
ÿ1:6 7:2 5:6 And from Eqn (6):
evtopoisomerase I
supercoilingÿ evgyrase
supercoiling ÿekttopoisomerase I
supercoiling t 1
topoisomerase IOsupercoiling
etopoisomerase I
ÿ0:56 6:1 5:5 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 latter
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 consistent with
existing information Here we determined the
concentra-tions of gyrase and topoisomerase I to calculate the
sensitivity of the transcription/translation level for changes
in DNA supercoiling In an previous study [11] we used a
lacZ fusion to the gyrB promoter to measure this sensitivity
for DNA gyrase The elasticity of gyrase expression
measured with the lacZ fusion eDNAgyrase expressionsupercoiling ÿ1:7
in that paper is in good agreement with the 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 expression to
supercoil-ing does depend on the level of supercoilsupercoil-ing, especially for
the topoisomerase I, which is almost insensitive at wild-type
levels of supercoiling and much more sensitive at high 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 fold increase upon
inhibition of gyrase with coumermycin [27] Our results are
in good agreement with this: Extrapolation of our ®ts in
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 induction of topoisomerase I was
observed Perhaps topoisomerase I expression becomes
more sensitive for supercoiling when the DNA relaxes
more than was tested in our strains In the earlier studies the
promoter fusions were plasmid constructs 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) level and to a lesser 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 tools are essential to understand the working of the multilayered cell Recent advances in the X-omics and bioinformatics ®elds make it possible to study the regulation of cell function both comprehensively and 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 may be that it does furnish this experimental demonstration That calculations were necessary to show this should not detract from 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
A C K N O W L E D G E M E N T S
We wish to thank Jan Schouten (MRC, Holland) for 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) and the Danish Centre for Microbiology (CM).
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