CORE Metadata, citation and similar papers at core.ac.uk Provided by Elsevier - Publisher Connector Biophysical Journal Volume 70 January 1996 135-145 135 Hypothesis: Hypersensitive Plasmid Copy Number Control for ColEI MAns Ehrenberg Department of Molecular Biology, Uppsala University, S-75124 Uppsala, Sweden ABSTRACT Initiation of replication of the plasmid ColEl is primed by the cis-acting RNA 11. Copy numbers are regulated by inhibition of RNA 11 by the antisense RNA 1, whose concentration is proportional to the plasmid concentration. This inhibition is enhanced by a protein, Rom, and takes place during a time set by the transcription of 250 bases of the gene for RNA 11. When this transcription is dominated by several steps of about equal duration, the probability for RNA 11 to prime DNA replication is approximately determined by e-constant[RNA '1. For large values of the "constant" small changes in [RNA I] give large variations in the priming probability. It is shown, first, that this type of mechanism can reduce the rate of plasmid loss and enable single copies of ColEl to duplicate at a well-defined time in the cell cycle; second, that when the rate of initiation of transcription of RNA 11 increases, plasmid losses decrease and the distribution of single copy duplication times becomes narrower; third, that the action of Rom may further reduce plasmid losses and further narrow the distribution of duplication times in the single-copy case. INTRODUCTION Replication of the E. coli plasmid ColEl is initiated by a whereas it comes out in the argument of a natural logarithm cis-acting RNA (RNA II, RI,), which can form a duplex in the B and T study. In the present work the difference with a complementary stretch of DNA at the origin of between these two models is traced to different assumptions plasmid replication. Subsequent cleavage of the hybridized concerning how RI inhibits RII. B and T assume, with part of RII by RNase H creates a primer for DNA synthesis support from experiments (Tomizawa, 1986), that RI, can be (Itoh and Tomizawa, 1980). Copy numbers are controlled attacked by RI during a time window defined by the tran- by inhibition of RII by the transacting RNA I (RI) (Tomi- scription of bases 110 to 360 of the gene for RI,. They zawa and Itoh, 1981; Tomizawa, 1984; Masukata and assume, furthermore, that transcription proceeds in 250 Tomizawa, 1986), which is antisense to the 5' region of RI, steps of about equal duration. Thereby, the length of the (Morita and Oka, 1979). The concentration of RI is nearly time window has a narrow distribution, and inhibition of proportional to the concentration of plasmid (Brenner and RNA II by RNA I occurs in multiple steps, where each Tomizawa, 1991; Brendel and Perelson, 1993). Inhibition is contributes in the same proportion to the overall inhibition. enhanced by a protein, Rom, which binds to the initial Implicit in the model of B and P is, instead, that the complex between RI and RI,, and increases the probability inhibition time is dominated by a single step (cf. Keasling of duplex formation between the two RNAs (Cesareni et al., and Palsson, 1989a). 1982; Lacatena et al., 1984; Tomizawa and Som, 1984; The present work compares a number of consequences of Eguchi et al., 1991; Eguchi and Tomizawa, 1991; Brendel the B and P and B and T models, and it suggests experi- and Perelson, 1993). The concentration of Rom is also mental designs to discriminate between them. It also ex- nearly proportional to plasmid concentration (Brendel and plores a number of general consequences of multiple step Perelson, 1993). Recently, Brenner and Tomizawa (1991) inhibition as suggested by B and T: when suitably tuned and (B and T) and Brendel and Perelson (1993) (B and P) combined with a mechanism for plasmid partitioning presented quantitative models for ColEl copy number con- (Gerdes et al., 1985) the B and T model has remarkable trol. According to B and T the steady-state plasmid concen- properties. These may be of general interest because they tration is proportional to the logarithm of the ratio between reveal new options concerning replication control and, pos- the initiation rate of transcription of RII (kII) and the growth sibly, regulation of gene expression. rate (kH) of the host cells. In contrast, B and P find a linear We discuss how plasmid duplications are distributed relation between the plasmid concentration and kII/kH. The through the cell cycle and demonstrate several dramatic two models were recently compared by Merlin and Polisky consequences of multiple-step inhibition of RNA II by (1995). The comparison did not clarify, however, why the RNA I according to the B and T model: ratio kII/kH appears as a linear term in the B and P model, First, single copies of ColEl in a cell can, in principle, precisely coordinate their duplication time with the cell cycle. In the multiple-copy number case the new mechanism Receivedfor publication 15 June 1995 and in final form 2 October 1995. may lead to small copy number fluctuations and extremely Address reprint requests to Dr. Mans Ehrenberg, Department of Mo- lecular Biology, Uppsala University, BMC Box 590, S-751 24 Uppsala, small plasmid loss rates. Sweden. Tel.: 46 18 174213; Fax: 46 18 557723; E-mail: ehrenberg@ Second, for single-copy plasmids the distribution of the xray.bmc.uu.se. duplication time becomes narrower as the ratio kII/kH in- C 1996 by the Biophysical Society creases, given a fixed rate of initiation of plasmid replica- 0006-3495/96/01/135111 $2.00 tion. When this ratio increases, the probability that RII 136 Biophysical Journal Volume 70 January 1996 survives the time window where it can be attacked by RI Scheme 2 the probability, P(duplex), that CI is converted to decreases. This means that the plasmids can accomplish an a stable duplex between RI and RI, and that RII becomes improved coordination with the cell cycle, at the cost of degraded is given by increased turnover rates of both RI and RI,. In the multiple-copy number case increasing kII/kH results + kaR * [Rom] P(duplex) = kdl in ever smaller plasmid losses. k-a + kdl + kaR [Rom]' (3) Third, the action of Rom can further narrow the distribu- tion of duplication times in the single-copy case and dra- Both RI and Rom are constitutively expressed from ColEl matically lower plasmid losses in the multiple-copy case. plasmids and both are rapidly degraded, so that their con- The possibility for precise timing between cell and plas- centrations are nearly proportional to the plasmid concen- mid cycles has recently been discussed for the plasmid RI. tration y (cf. Brenner and Tomizawa, 1991; Brendel and Here, however, the mechanism of such coordination would Perelson, 1993; Keasling and Palsson, 1989a,b; Bremer and be quite different (Ehrenberg and Sverredal, 1995). Lin-Chao, 1986). Denoting the production rates per plasmid When there are several ColEl copies per cell, the present of RI and Rom by k1 and kR, respectively, and their respec- analysis suggests that their duplication times are spread in tive degradation rate constants by E, and ER, their concen- the cell cycle, in accordance with experiments (Leonard and trations can be written as Helmstetter, 1988). A similar behavior characterizes the plasmid RI, as shown by experiment (Nordstrom, 1983) and [RI] = -_k and [Rom] = R (4) as suggested by theory (Ehrenberg and Sverredal, 1995). ER These relations are derived in Appendix 2, along with a MACROSCOPIC FEATURES OF THE ColEI COPY discussion of their range of validity. The main point is that NUMBER CONTROL the larger the parameters k1, El, kR and ER (Table 1) are, for given ratios k1/E1 and kR/ER, the better are the approxima- The inhibition of RII priming of ColEl replication is, first, tions in Eq. 4 (cf. Ehrenberg and Sverredal, 1995). We note governed by the concentrations of RI and Rom in the cells that this is one of several cases where increasing precision ([RI] and [Rom]). Second, it is also determined by the of the control system is bought at increasing energy cost second-order, effective association rate constant k12 for (see Discussion). binding and duplex formation between RI and RI,. The The rate of change of the plasmid concentration y is effective rate constant k12 is, in turn, determined by the governed by the differential equation (cf. Bremer and association rate constant ka for initial complex formation Lin-Chao, 1986; Keasling and Palsson, 1989a,b; Brenner between RI and RII multiplied by the probability P(duplex) and Tomizawa, 1991; Brendel and Perelson, 1993) that this initial encounter leads to duplex formation and breakdown of RI,: dy = ki* Qo y - kH*Y- (5) k12= kg * P(duplex). (1) This simple form for the rate of inhibition, k,2, is derived in k11 is the rate constant of initiation of transcription of RII. Qo Appendix 1, and its range of validity is specified in terms of is the probability that R1I is not inhibited by RI, so that it can the underlying microscopic rate constants (see also below form a primer for intiation of plasmid replication. The Eq. 13, where this point is further discussed). parameter kH is the (exponential) growth rate of the host The probability P(duplex) is enhanced by the action of cells, and the negative term to the right in Eq. 5 describes Rom, according to the simplified scheme (Eguchi et al., the dilution of plasmids by the exponential volume expan- 1991; Eguchi and Tomizawa, 1991; Brendel and Perelson, sion with time (Ehrenberg and Kurland, 1984; Brendel and 1993): Perelson, 1993; Ehrenberg and Sverredal, 1995).