A segregated model for plasmid content and product synthesis in unstable binary fission recombinant organisms

Plasmid propagation in populations of unstable, binary fission recombinant organisms has been studied using a segregated, population balance mathematical model. Segregated models have the advantage of direct incorporation of basic information on mechanisms and kinetics of plasmid replication and segregation at the single-cell level. The distribution of cellular plasmid content and specific rates of plasmid gene expression have been obtained for several single-cell models of plasmid replication, partition, and gene expression. Plasmid replication kinetics during cell growth significantly influence the plasmid content distribution. In the case of transient growth of plasmid-containing and plasmid-free cells in partially selective medium, the degree of selection required for stable maintenance of plasmid-containing cells has been determined. Guidelines are presented for applicability of simpler, nonsegregated models and for evaluation of the parameters in these models based on single-cell mechanisms and associated parameters.     

Plasmid stability in budding yeast populations: Steady-state growth with selection pressure

Plasmid gene product accumulation in a cell population depends on the fraction of plasmid-containing cells and the distribution of single-cell plasmid content. These important population properties have been related to plasmid replication regulation and kinetics and to plasmid segregation rules at the single-cell level using population balance mathematical models. Budding yeast populations are considered in detail because of the practical potential of yeast host-vector systems and because of the model complications introduced by the asymmetric division pattern observed for Saccharomyces cerevisiae at all but the largest growth rates. Solutions are presented for several different reasonable models of plasmid replication and segregation. The results offer potential for identification of important qualitative features of yeast plasmid replication and of model parameter values from average and segregated experimental data on yeast populations.     

Study of recombinant micro-organism populations characterized by their plasmid content per cell using a segregated model

Numerous observations from recombinant systems have shown that properties such as the specific cell growth rate and the plasmid-free cell formation rate are related, not only to the average plasmid content per cell, but also to the plasmid distribution within a population. The plasmid distribution in recombinant cultures can have an effect on the culture productivity that cannot be modelled using average values of the overall culture. The prediction of the behaviour of a plasmid content distribution and its causes and effects can only be studied using segregated models. A segregated model that describes populations of recombinant cells characterized by their plasmid content distribution has been developed. This model includes critical causes of recombinant culture instability such as the plasmid partition mechanism at cell division, plasmid replication kinetics and the effect of the plasmid content on the specific growth rate. The segregated model allows investigation of the effect of each of these causes and that of the plasmid content distribution on the observable behaviour of a recombinant culture.The effect of two partitioning mechanisms (Gaussian distribution and binomial distribution) on culture stability was investigated. The Gaussian distribution is slightly more stable. A small plasmid replication rate constant results in a very unstable culture even after short periods of time. This instability is dramatically improved for a larger value of this constant, hence improving protein synthesis. For a very narrow initial plasmid distribution, a given plasmid replication rate and partitioning mechanism can become broad even after a relatively short period of time. In contrast, a very "broad" initial distribution gave rise to a "Gamma-like" distribution profile. If we compare the results obtained in the simulations of the segregated model with those of the non-segregated one (average model), the latter model predicts much more stable behaviour, thus these average models cannot predict culture instability with the same precision.When compared with the experimental results, the segregated model was able to predict the practical behaviour with accuracy even in a system with a high plasmid content per cell and a high rate of plasmid-free cell formation which could not be achieved with a non-segregated model.     

A novel structured kinetic modeling approach for the analysis of plasmid instability in recombinant bacterial cultures

The instantaneous specific growth rate of a recombinant bacterial culture is directly calculated using a simple structured kinetic modeling approach. Foreign plasmid replication and foreign protein expression represent metabolic burdens to the host cell. The individual effects of these plasmid-mediated activities on the growth rate of plasmid-bearing cells are estimated separately. The dynamic and steady state simulations of the model equations show remarkable agreement with widely observed experimental trends in plasmid copy number and foreign protein content. The model provides an important tool for understanding and controlling plasmid instability in recombinant bacterial fermentations. The modeling framework employed here is suitable for studying the metabolism and growth of a variety of microbial cultures.     

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

The physiology of ColE1-type plasmid replication in a growing host has been examined both theoretically, using computer simulation, and experimentally, by observing replication of the plasmid pBR322 after a nutritional shift-up from glycerol minimal medium (doubling time 71 min) to LB medium (doubling time 24 min). The theory was based on a negative control model and uses three rate equations: for the accumulation of cell mass, for the accumulation of the replication inhibitor, and for the rate of plasmid synthesis. The implications of the theory were explored by simulating the effects of changes in the expression of replication control genes. The nutritional shift-up experiment showed that plasmid replication was blocked immediately after the shift for about half a mass doubling time; after that time, replication rapidly increased until plasmid numbers per unit volume of culture parallelled the increase in culture mass. After the establishment of steady-state growth in the post-shift medium, the plasmid concentration (plasmids per cell mass) was reduced in comparison to pre-shift growth in the same proportion as the culture doubling time. The results showed that plasmid replication factors are under metabolic control and that the changes in the control of these factors compensate one another during steady-state growth, but not immediately after the medium shift.     

A segregated model of recombinant multicopy plasmid propagation

A segregated model of multicopy plasmid propagation has been formulated which incorporates plasmid replication and partition functions, as well as the effect of plasmid presence on host growth rate. Growth of plasmid-free cells in selective medium is explicitly analyzed. The model parameters can be determined from experimentally measurable quantities. Propagation of a recombinant multicopy plasmid in the yeast Saccharomyces cerevisiae is analyzed using this model.     

Surprising dependence on postsegregational killing of host cells for maintenance of the large virulence plasmid of Shigella flexneri

Low-copy-number plasmids all encode multiple systems to ensure their propagation, including replication, partition (active segregation), and postsegregational killing (PSK) systems. PSK systems kill those rare cells that lose the plasmid due to replication or segregation errors. PSK systems should not be used as the principle means of maintaining the plasmid. The metabolic cost of killing the many cured cells that would arise from random plasmid segregation is far too high. Here we describe an interesting exception to this rule. Maintenance of the large virulence plasmid of Shigella flexneri is highly dependent on one of its PSK systems, mvp, at 37 degrees C, the temperature experienced during pathogenesis. At 37 degrees C, the plasmid is very unstable and mvp efficiently kills the resulting cured bacterial cells. This imposes a major growth disadvantage on the virulent bacterial population. The systems that normally ensure accurate plasmid replication and segregation are attenuated or overridden at 37 degrees C. At 30 degrees C, a temperature encountered by Shigella in the outside environment, the maintenance systems function normally and the plasmid is no longer dependent on mvp. We discuss why the virulent pathogen tolerates this self-destructive method of propagation at the temperature of infection.     

A mathematical model for prediction of plasmid copy number and genetic stability in Escherichia coli

The design of bioreactors for genetically modified bacterial cultures would benefit from predictive models. Of particular importance is the interaction of the external environment, cell physiology, and control of plasmid copy number. We have recently developed a model based on the molecular mechanisms for control of replication of Co1E1 type plasmids. The inclusion of the plasmid model into a single-cell E. coli model allows the explicit prediction of the interaction of cell physiology and plasmid-encoded functions. The model predictions of the copy number of plasmids with the Co1E1 origin of replication carrying a variety of regulatory mutations is very close to that observed experimentally.All of the model parameters for plasmid replication control can be obtained independently and no adjustable parameters are needed for the plasmid model. In this article we discuss the model's use in predicting the effect of operating conditions on production of a protein from a plasmid encoded gene and the stability of the recombinant cells in a continuous culture.     

Involvement of proliferating cell nuclear antigen (cyclin) in DNA replication in living cells.

Proliferating cell nuclear antigen (PCNA) (also called cyclin) is known to stimulate the activity of DNA polymerase delta but not the other DNA polymerases in vitro. We injected a human autoimmune antibody against PCNA into unfertilized eggs of Xenopus laevis and examined the effects of this antibody on the replication of injected plasmid DNA as well as egg chromosomes. The anti-PCNA antibody inhibited plasmid replication by up to 67%, demonstrating that PCNA is involved in plasmid replication in living cells. This result further implies that DNA polymerase delta is necessary for plasmid replication in vivo. Anti-PCNA antibody alone did not block plasmid replication completely, but the residual replication was abolished by coinjection of a monoclonal antibody against DNA polymerase alpha. Anti-DNA polymerase alpha alone inhibited plasmid replication by 63%. Thus, DNA polymerase alpha is also required for plasmid replication in this system. In similar studies on the replication of egg chromosomes, the inhibition by anti-PCNA antibody was only 30%, while anti-DNA polymerase alpha antibody blocked 73% of replication. We concluded that the replication machineries of chromosomes and plasmid differ in their relative content of DNA polymerase delta. In addition, we obtained evidence through the use of phenylbutyl deoxyguanosine, an inhibitor of DNA polymerase alpha, that the structure of DNA polymerase alpha holoenzyme for chromosome replication is significantly different from that for plasmid replication.     

Cell cycle analysis of plasmid-containing Escherichia coli HB101 populations with flow cytometry

The relationship between cell mass and cell number dynamics for bacteria such as Escherichia coli depends on the cell cycle parameters C and D. Effects of plasmid copy number on these cell cycle parameters have been studied for Escherichia coli HB101 containing pMB1 plasmids propagated at different copy numbers ranging from 12 to 122. Determination of cell cycle and cell size parameters was accomplished using flow cytometry data on single-cell light scattering and DNA content frequency functions in conjunction with a mathematical model of cell population statistics. Two independent methods for estimating C and D intervals based on flow cytometry were developed and applied with essentially identical results. The presence of plasmids decreases the C and D periods, mean cell sizes, and initiation masses for chromosome replication by 14, 24, 38, and 18%, respectively, relative to corresponding values for plasmid-free host cells. Plasmid copy number has a negligible influence on these parameters, suggesting that host-plasmid inter actions which determine these properties are centered on the single plasmid selected for replication according to the random selection model established for ColE1-type plasmids.     

On plasmid incompatibility

In this paper is presented a brief review of the current state of information on plasmid incompatibility followed by a detailed mathematical model dealing with incompatibility between autonomous homogenic plasmids and based on the assumption that the intracellular plasmid copy pool is randomized with respect to assortment during cell division. Two cases are considered: one in which each plasmid copy replicates once in each generation of cell growth (regular replication) and one in which plasmids are chosen at random for replication from a common pool, irrespective of their replication history (random replication). In both cases, it is assumed that the partition of plasmid copies to daughter cells at cell division is regular—existing plasmid copies are divided equally among the two daughter cells (equipartition). In the case of regular replication coupled with equipartition, it is shown that the survival of heteroplasmid cells (cells containing at least one copy of each of two incompatible plasmids) during exponential growth in a nonselective medium is given by H = H₀[1 − 1/(2N − 1)]ⁿ, where H₀ and H are the numbers of heteroplasmid cells after 0 and n generations of growth, respectively, and N is the plasmid copy number in newborn cells. In the second case, (random replication-equipartition), it is shown that the survival of the heteroplasmid population during exponential growth under nonselective conditions is given by H = H₀[(N − 1)(2N + 1)/(2N − 1)(N + 1)ⁿ. Sample calculations are presented to show that segregation is more rapid in the latter than in the former case. Finally, some of the plasmid-linked genetic determinants that might be expected to affect the expression of incompatibility between nonisogenic plasmids are briefly considered. These determinants include recognition specificity for replication origins, recognition specificity, specific activity of copy number control systems, and recognition specificity of partition systems.     

Growth-rate dependence reveals design principles of plasmid copy number control

Genetic circuits in bacteria are intimately coupled to the cellular growth rate as many parameters of gene expression are growth-rate dependent. Growth-rate dependence can be particularly pronounced for genes on plasmids; therefore the native regulatory systems of a plasmid such as its replication control system are characterized by growth-rate dependent parameters and regulator concentrations. This natural growth-rate dependent variation of regulator concentrations can be used for a quantitative analysis of the design of such regulatory systems. Here we analyze the growth-rate dependence of parameters of the copy number control system of ColE1-type plasmids in E. coli. This analysis allows us to infer the form of the control function and suggests that the Rom protein increases the sensitivity of control.     

Analysis of pBR322 replication kinetics and its dependency on growth rate

Accurate estimates of plasmid copy number in a cell are a prerequisite for predicting plasmid stability and protein production. A refined version of a structured model for the pBR322 plasmid replication mechanism is described. The model is capable of accurately predicting pBR322 plasmid copy number in Escherichia coli B/r for a wide range of growth rates. The refinements include better estimates of promoter strength, the degradation rate of RNA species, binding constant of RNAI-RNAII reaction, and dependency of promoter strength on growth rate. The predictions of the model are verified by recent experimental observations but differ from some previous reports. This model can also be used to predict the binding constant of the RNAI-RNAII reaction of ColE1 type plasmids. At 37 degrees C, the binding constant is estimated to be 77 +/- 11 x 10(-13) mL/molecule-h for pBR322.     

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.     

An evaluation of models for the effect of plasmid copy number on bacterial growth rate

The rates of growth of recombinant bacteria depend on their plasmid content. This is modelled by expressing the specific growth rate in terms of the number of copies of the plasmid per cell. Three models in common use have been tested with different Escherichia coli strains and one strain of Bacillus stearothermophilus containing different plasmids. While no particular model was decisively better than others for all data, that of Bentley & Quiroga (Biotechnol. Bioeng. 1993, 42: 222–234) was the best for specific growth rates which vary inversely with the plasmid copy number, and a modified form of the model of Satyagal & Agarwal (Biotechnol. Bioeng. 1989, 33: 1135–1144) was the best for growth rates which increase with the copy number. The differences appear to be linked to the plasmid replication mechanisms. Contrary to some claims, no model portrayed the experimentally observed inflection points.