Analysis of the physiological control of replication of ColE1-type plasmids

Mathematical Models of Plasmid Population Dynamics

With plasmid-mediated antibiotic resistance thriving and threatening to become a serious public health problem, it is paramount to increase our understanding of the forces that enable the spread and maintenance of drug resistance genes encoded in mobile genetic elements. The relevance of plasmids as vehicles for the dissemination of antibiotic resistance genes, in addition to the extensive use of plasmid-derived vectors for biotechnological and industrial purposes, has promoted the in-depth study of the molecular mechanisms controlling multiple aspects of a plasmids' life cycle. This body of experimental work has been paralleled by the development of a wealth of mathematical models aimed at understanding the interplay between transmission, replication, and segregation, as well as their consequences in the ecological and evolutionary dynamics of plasmid-bearing bacterial populations. In this review, we discuss theoretical models of plasmid dynamics that span from the molecular mechanisms of plasmid partition and copy-number control occurring at a cellular level, to their consequences in the population dynamics of complex microbial communities. We conclude by discussing future directions for this exciting research topic.

ColE1-Plasmid Production in Escherichia coli: Mathematical Simulation and Experimental Validation

Plasmids have become very important as pharmaceutical gene vectors in the fields of gene therapy and genetic vaccination in the past years. In this study, we present a dynamic model to simulate the ColE1-like plasmid replication control, once for a DH5α-strain carrying a low copy plasmid (DH5α-pSUP 201-3) and once for a DH5α-strain carrying a high copy plasmid (DH5α-pCMV-lacZ) by using ordinary differential equations and the MATLAB software. The model includes the plasmid replication control by two regulatory RNA molecules (RNAI and RNAII) as well as the replication control by uncharged tRNA molecules. To validate the model, experimental data like RNAI- and RNAII concentration, plasmid copy number (PCN), and growth rate for three different time points in the exponential phase were determined. Depending on the sampled time point, the measured RNAI- and RNAII concentrations for DH5α-pSUP 201-3 reside between 6 ± 0.7 and 34 ± 7 RNAI molecules per cell and 0.44 ± 0.1 and 3 ± 0.9 RNAII molecules per cell. The determined PCNs averaged between 46 ± 26 and 48 ± 30 plasmids per cell. The experimentally determined data for DH5α-pCMV-lacZ reside between 345 ± 203 and 1086 ± 298 RNAI molecules per cell and 22 ± 2 and 75 ± 10 RNAII molecules per cell with an averaged PCN of 1514 ± 1301 and 5806 ± 4828 depending on the measured time point. As the model was shown to be consistent with the experimentally determined data, measured at three different time points within the growth of the same strain, we performed predictive simulations concerning the effect of uncharged tRNA molecules on the ColE1-like plasmid replication control. The hypothesis is that these tRNA molecules would have an enhancing effect on the plasmid production. The in silico analysis predicts that uncharged tRNA molecules would indeed increase the plasmid DNA production.

Oscillations by minimal bacterial suicide circuits reveal hidden facets of host-circuit physiology

Synthetic biology seeks to enable programmed control of cellular behavior though engineered biological systems. These systems typically consist of synthetic circuits that function inside, and interact with, complex host cells possessing pre-existing metabolic and regulatory networks. Nevertheless, while designing systems, a simple well-defined interface between the synthetic gene circuit and the host is frequently assumed. We describe the generation of robust but unexpected oscillations in the densities of bacterium Escherichia coli populations by simple synthetic suicide circuits containing quorum components and a lysis gene. Contrary to design expectations, oscillations required neither the quorum sensing genes (luxR and luxI) nor known regulatory elements in the P_luxI promoter. Instead, oscillations were likely due to density-dependent plasmid amplification that established a population-level negative feedback. A mathematical model based on this mechanism captures the key characteristics of oscillations, and model predictions regarding perturbations to plasmid amplification were experimentally validated. Our results underscore the importance of plasmid copy number and potential impact of “hidden interactions” on the behavior of engineered gene circuits - a major challenge for standardizing biological parts. As synthetic biology grows as a discipline, increasing value may be derived from tools that enable the assessment of parts in their final context.

A structured, segregated model for genetically modified Escherichia coli cells and its use for prediction of plasmid stability

A structured, segregated model is presented for an asynchronously growing population of genetically modified Escherichia coli cells. A finite representation method was modified so that 272 cells could be used to represent a microbial population. The concept of a "limbo" compartment was introduced to allow random plasmid distribution to daughter cells upon cell division while restricting the number of computer cells included in the calculation. This scheme enabled us to predict plasmid instability and distribution of plasmid-originated properties in a population without a priori determination of growth rates or probability of forming plasmid-free cells from plasmid-containing cells. Predictions of population behavior using a single-cell model requires no adjustable parameters. The results comparing different induction strategies suggest that in continuous culture, there exists an optimum efficiency of partial induction that maximizes the long-term productivity of the gene product due to plasmid stability. With the optimum efficiency of partial induction, constant induction appears to prove more stable than cycling induction.

Multileveled selection on plasmid replication

The replication control genes of bacterial plasmids face selection at two conflicting levels. Plasmid copies that systematically overreplicate relative to their cell mates have a higher chance of fixing in descendant cells, but these cells typically have a lower chance of fixing in the population. Apart from identifying the conflict, this mathematical discussion characterizes the efficiency of the selection levels and suggests how they drive the evolution of kinetic mechanisms. In particular it is hypothesized that: (1) tighter replication control is more vulnerable to selfishness; (2) cis-acting replication activators are relics of a conflict where a plasmid outreplicated its intracellular competitors by monopolizing activators; (3) high-copy plasmids with sloppy replication control arise because intracellular selection favors overreplication, thereby relieving intercellular selection for lower loss rates; (4) the excessive synthesis of cis-acting replication activators and trans-acting inhibitors is the result of an arms race between cis selfishness and trans retaliations; (5) site-specific recombination of plasmid dimers is equivalent to self-policing; and (6) plasmids modify their horizontal transfer to spread without promoting selfishness. It is also discussed how replication control may be subject to a third level of selection acting on the entire population of plasmid-containing cells.

A model for regulation of ColE1-like plasmid replication by uncharged tRNAs in amino acid-starved Escherichia coli cells

It has been previously observed that various ColE1-like plasmids replicate differentially in Escherichia coli cells during the relaxed response to amino acid starvation. Here we develop a kinetic model to explain these observations based on the possibility of interaction of the 3' CCA-OH sequence with the UGG triplets in loops of RNA I and RNA II encoded by ColE1-like plasmids. According to our model, when the interaction of uncharged CCA with RNA I is possible, the replication of the ColE1-like plasmid is affected by differences in the concentration of various tRNAs in the starved cell, but it is not affected by the tRNA concentration if the hypothetical pairing occurs between the CCA-OH and RNA II. Using the previously determined parameters for the pBR322 plasmid, the concentration of uncharged tRNAs in the amino acid starved relaxed strains and the assumed efficiency of binding of tRNA and RNA I, we show that our model explains the differences in pBR322 copy number in the relaxed strain starved for several amino acids.

The RepA protein of plasmid pSC101 controls Escherichia coli cell division through the SOS response

Although plasmid copy number varies widely among different plasmid species, normally copy number is maintained within a narrow range for any given plasmid. Such copy number control has been shown to occur by regulation of the rate of plasmid DNA replication. Here we report a novel mechanism by which the pSC101 plasmid also can detect an imbalance between the cellular level of its replication protein, RepA, and plasmid-borne RepA binding sites to inhibit bacterial DNA replication and delay host cell division when RepA is in relative excess. We show that delayed cell division occurs by RepA-mediated induction of the SOS response and can be reversed by over-expression of the host DNA primase, DnaG. The effects of RepA excess are prevented by introducing a surfeit of RepA binding sites. The mechanism reported here may help to limit variation in plasmid copy number and allow repopulation of cells with plasmids when copy number falls--potentially pre-empting plasmid loss in cultures of dividing cells.

Activities of constitutive promoters in Escherichia coli

The in vivo activities of seven constitutive promoters in Escherichia coli have been determined as functions of growth rate in wild-type relA+ spoT+ strains with normal levels of guanosine tetraphosphate (ppGpp) and in ppGpp-deficient DeltarelADeltaspoT derivatives. The promoters include (i) the spc ribosomal protein operon promotor Pspc; (ii) the beta-lactamase gene promotor Pblaof plasmid pBR322; (iii) the PLpromoter of phage lambda; (iv) and (v) the replication control promoters PRNAIand PRNAIIof plasmid pBR322; and (vi) and (vii) the P1 and P2 promoters of the rrnB ribosomal RNA operon. Each strain carried an operon fusion consisting of one of the respective promoter regions linked to lacZ and recombined into the chromosome at the mal locus of a lac deletion strain. The amount of 5'-terminal lacZ mRNA and of beta-galactosidase activity expressed from these promoters were determined by standard hybridization or enzyme activity assays, respectively. In addition, DNA, RNA and protein measurements were used to obtain information about gene dosage, rRNA synthesis and translation rates. By combining lacZ mRNA hybridization data with gene dosage and rRNA synthesis data, the absolute activity of the different promoters, in transcripts/minute per promoter, was determined. In ppGpp-proficient (relA+ spoT+) strains, the respective activities of rrnB P1 and P2 increased 40 and fivefold with increasing growth rate between 0.7 and 3.0 doublings/hour. The activities of Pspc, PL, Pbla, and PRNAIincreased two- to threefold and reached a maximum at growth rates above 2.0 doublings/hour. In contrast, PRNAIIactivity decreased threefold over this range of growth rates. In ppGpp-deficient (DeltarelA DeltaspoT) bacterial strains, the activities of rrnB P1 and P2 promoters both increased about twofold between 1.6 and 3.0 doublings/hour, whereas the activities of Pspc, PL, Pbla, and PRNAI, and PRNAIIwere about constant. To explain these observations, we suggest that the cellular concentration of free RNA polymerase increases with increasing growth rate; for saturation the P1 and P2 rRNA promoters require a high RNA polymerase concentration that is approached only at the highest growth rates, whereas the other promoters are saturated at lower polymerase concentrations achieved at intermediate growth rates. In addition, the data indicate that the respective rrnB P1 and PRNAIIpromoters were under negative and positive control by ppGpp. This caused a reduced activity of rrnB P1 and an increased activity of PRNAIIduring slow growth in wild-type (relA+ spoT+) relative to ppGpp-deficient (DeltarelA DeltaspoT) bacterial strains.

Role of the rom protein in copy number control of plasmid pBR322 at different growth rates in Escherichia coli K-12

The copy number per cell mass of plasmid pBR322 and a rom- derivative was measured as a function of generation time. In fast growing cells the copy number per cell mass was virtually identical for rom+ and rom- derivatives. However, the copy number of pBR322 only increased 3- to 4-fold from a 20- to 80-min generation time, whereas the copy number of the rom- derivative increased 7- to 10-fold. The copy number stayed constant for the rom+ and rom- plasmids at generation times longer than 80-100 min. Thus, the presence of the rom gene decreased the copy number of plasmid pBR322 in slowly growing cells at least 2-fold when compared with the rom- plasmid. To study the effect of the rom gene in trans we cloned the gene into the compatible P15A-derived rom- plasmid pACYC184. In cells carrying both pACYC184 rom+ and pBR322 rom- the presence of the rom gene in trans had little effect on the copy number of pBR322 rom- at fast growth, but it decreased its copy number at slow growth to the same level as found for pBR322, i.e., complemented the pBR322 rom- plasmid. The pACYC184 plasmid and its rom+ derivatives showed copy numbers similar to those of pBR322 rom- and pBR322 itself, respectively, at fast and slow growth. We conclude that the rom gene product-the Rom protein-is an important element in copy number control of ColE1-type plasmids especially in slowly growing cells.

Trade-off between segregational stability and metabolic burden: a mathematical model of plasmid ColE1 replication control

A model of ColE1 copy number control has been developed where molecular details of replication are connected both to segregational stability and metabolic burden. Efficient replication control reduces copy number variation and increases segregational stability for a given average copy number. Copy number variation is predicted to depend on the type of inhibition mechanism as well as RNA I and RNA II turnover rate constants. It is shown that when both RNA I and RNA II transcription frequencies and the rate constant for degradation of free RNA I are very large, a hyperbolic inhibition mechanism must compensate with a 1.4 times greater average copy number to obtain the same segregational stability as an exponential inhibition mechanism. How sensitively the replication frequency responds to changes in RNA I concentration depends on the type of inhibition mechanism and the number of attempts to form an RNA II replication primer per plasmid and cell cycle. If RNA I is too stable, it will not follow changes in plasmid concentration closely, and when the transcription frequency for RNA I is only slightly higher than for RNA II, RNA I concentration becomes randomized. In both these cases, the proportionality between the single cell RNA I and plasmid concentrations is lost and this impairs copy number control. Thresholds in the rate for degradation of free RNA I as well as in RNA I and RNA II transcription frequencies have been computed, where an increase in these rate constants has a negligible effect on segregational stability but a corresponding decrease leads to segregational disaster. This indicates that there exists a well defined optimal set of rate constants where the regulation system works well without excessive metabolic load. A number of new experiments are suggested to address features of particular importance for the evolution of ColE1 copy number control.

Requirements for rapid plasmid ColE1 copy number adjustments: a mathematical model of inhibition modes and RNA turnover rates

The random distribution of ColE1 plasmids between the daughter cells at cell division introduces large copy number variations. Statistic variation associated with limited copy number in single cells also causes fluctuations to emerge spontaneously during the cell cycle. Efficient replication control out of steady state is therefore important to tame such stochastic effects of small numbers. In the present model, the dynamic features of copy number control are divided into two parts: first, how sharply the replication frequency per plasmid responds to changes in the concentration of the plasmid-coded inhibitor, RNA I, and second, how tightly RNA I and plasmid concentrations are coupled. Single (hyperbolic)- and multiple (exponential)-step inhibition mechanisms are compared out of steady state and it is shown how the response in replication frequency depends on the mode of inhibition. For both mechanisms, sensitivity of inhibition is "bought" at the expense of a rapid turnover of a replication preprimer, RNA II. Conventional, single-step, inhibition kinetics gives a sloppy replication control even at high RNA II turnover rates, whereas multiple-step inhibition has the potential of working with unlimited precision. When plasmid concentration changes rapidly, RNA I must be degraded rapidly to be "up to date" with the change. Adjustment to steady state is drastically impaired when the turnover rate constants of RNA I decrease below certain thresholds, but is basically unaffected for a corresponding increase. Several features of copy number control that are shown to be crucial for the understanding of ColE1-type plasmids still remain to be experimentally characterized. It is shown how steady-state properties reflect dynamics at the heart of regulation and therefore can be used to discriminate between fundamentally different copy number control mechanisms. The experimental tests of the predictions made require carefully planned assays, and some suggestions for suitable experiments arise naturally from the present work. It is also discussed how the presence of the Rom protein may affect dynamic qualities of copy number control.

Hypothesis: hypersensitive plasmid copy number control for ColE1

Initiation of replication of the plasmid ColE1 is primed by the cis-acting RNA II. Copy numbers are regulated by inhibition of RNA II by the antisense RNA I, 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 II. When this transcription is dominated by several steps of about equal duration, the probability for RNA II to prime DNA replication is approximately determined by e-constant[RNA I]. 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 ColE1 to duplicate at a well-defined time in the cell cycle; second, that when the rate of initiation of transcription of RNA II 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.

Assessment of quantitative models for plasmid ColE1 copy number control

Two quantitative models of plasmid ColE1 copy number control are compared with respect to mathematical logic of derivation and application to experimental observations. Explanatory background material and clarifications are supplied for selected aspects of each model. Contrasting features are emphasized and experiments are suggested to distinguish between predictions of the models.

Maintenance of pBR322-derived plasmids without functional RNAI

pBR322-derived plasmids that lack the bla gene and 40% of the gene for the replication inhibitor, RNAI, have been constructed. Since the RNAI gene totally overlaps with the gene for the replication primer, RNAII, this primer is similarly defective and also lacks its normal promoter. The primer is presumed to by synthesized either from the counter-tet promoter (plasmid pCL59) or from an inserted lacUV5 promoter (plasmid pCL59-65). Based mainly on the observation that the plasmid Rom protein, which normally assists in the RNAI/RNAII interaction, has no effect on the replication of the RNAI/RNAII-defective plasmids, we suggest that the defective RNAI is not functional while the defective RNAII primer, although less efficient, still allows plasmid replication. The defective plasmids are fully compatible with the intact parent plasmid, indicating that they do not share a common control of replication. In the absence of antibiotics, the bacteria lose the defective plasmid, beginning after 80 generations; under the same conditions, the parent plasmid is retained even after 140 generations. During exponential growth of their host, the number of defective plasmids in a culture increases exponentially with a doubling time either smaller or greater than that of the host cell growth, depending on the growth medium and, in the case of pCL59-65, on the presence or absence of lac inducer IPTG. As a result of these differences in host cell growth and plasmid replication, the plasmids are either gradually diluted out or their copy number continually increases. This shows that, without RNAI, plasmid replication is uncoupled from the host cell growth and not, as usual, adjusted to it. It also implies that the RNAI mechanism is the only means of replication control for ColE1-type plasmids that senses and adjusts the copy number; limiting host factors cannot provide a back-up control to stabilize copy numbers.

Control of cyclic chromosome replication in Escherichia coli

The biochemical basis for cyclic initiation of bacterial chromosome replication is reviewed to define the processes involved and to focus on the putative oscillator mechanism which generates the replication clock. The properties required for a functional oscillator are defined, and their implications are discussed. We show that positive control models, but not negative ones, can explain cyclic initiation. In particular, the widely accepted idea that DnaA protein controls the timing of initiation is examined in detail. Our analysis indicates that DnaA protein is not involved in the oscillator mechanism. We conclude that the generations of a single leading to cyclic initiation is separate from the initiation process itself and propose a heuristic model to focus attention on possible oscillator mechanisms.

ColE1 plasmid replication: a simple kinetic description from a structured model

Time constant analysis illustrates how a complex model for ColE-1-type plasmid replication can be reduced to a simple, realistic description of the overall replication kinetics. The analysis leads to the identification of the key parameters governing plasmid replication and to the estimation of parameters that are difficult to determine experimentally. The overall kinetics of ColE1-type plasmid replication are zerothorder in production and first order in dilution. Experimental data confirm our predictions. Similar analysis of the postulated mechanism for the action of the Rom protein reveals that it has no significant effect on plasmid replication dynamics.

RelA mutation and pBR322 plasmid amplification in amino acid-starved cells of Escherichia coli

Plasmid pBR322 is amplified following amino-acid limitation in Escherichia coli relA hosts. In relA+ hosts there was no significant amplification or a much smaller one. Plasmid amplification is due to the relA mutation; when the relA+ allele is transferred into the relA mutant CP79 this strain no longer amplifies plasmid DNA during amino acid starvation. It is concluded that ppGpp is a negative effector of plasmid replication. Amplification is temperature dependent, being maximal at 32 degrees C and negligible at 37 degrees C.

Activities of the RNAI and RNAII promoters of plasmid pBR322

The synthesis rates of the replication control RNAs of plasmid pBR322, RNAI, an inhibitor of replication, and RNAII, the preprimer, have been determined by hybridizing in vivo pulse-labeled RNA to specific, single-stranded DNA probes for RNAI and RNAII. In Escherichia coli growing in glycerol minimal medium, RNAI transcripts were made at a rate of one molecule per 30 s per plasmid; RNAII was transcribed fivefold less, at a rate of one molecule per 3 min per plasmid. It is estimated that only 1 in 20 prepriming events leads to replication.