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: hw@bio.vu.nl 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. 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