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.     

Partitioning of the 2-microm circle plasmid of Saccharomyces cerevisiae. Functional coordination with chromosome segregation and plasmid-encoded rep protein distribution

The efficient partitioning of the 2-microm plasmid of Saccharomyces cerevisiae at cell division is dependent on two plasmid-encoded proteins (Rep1p and Rep2p), together with the cis-acting locus REP3 (STB). In addition, host encoded factors are likely to contribute to plasmid segregation. Direct observation of a 2-microm-derived plasmid in live yeast cells indicates that the multiple plasmid copies are located in the nucleus, predominantly in clusters with characteristic shapes. Comparison to a single-tagged chromosome or to a yeast centromeric plasmid shows that the segregation kinetics of the 2-microm plasmid and the chromosome are quite similar during the yeast cell cycle. Immunofluorescence analysis reveals that the plasmid is colocalized with the Rep1 and Rep2 proteins within the yeast nucleus. Furthermore, the Rep proteins (and therefore the plasmid) tend to concentrate near the poles of the yeast mitotic spindle. Depolymerization of the spindle results in partial dispersion of the Rep proteins in the nucleus concomitant with a loosening in the association between plasmid molecules. In an ipl1-2 yeast strain, shifted to the nonpermissive temperature, the chromosomes and plasmid almost always missegregate in tandem. Our results suggest that, after DNA replication, plasmid distribution to the daughter cells occurs in the form of specific DNA-protein aggregates. They further indicate that the plasmid partitioning mechanism may exploit at least some of the components of the cellular machinery required for chromosomal segregation.     

Clustering versus random segregation of plasmids lacking a partitioning function: a plasmid paradox?

Plasmids lacking a functional partition system are randomly distributed to the daughter cells; plasmid-free daughter cells are formed with a frequency of (1/2)2n per cell and cell generation where 2n is the (average) copy number at cell division. Hence, the unit of segregation is one plasmid copy. However, plasmids form clusters in the cells. A putative solution to this potential paradox is presented: one plasmid copy at a time is recruited from the plasmid clusters to the replication factories that are located in the cell centres. Hence, replication offers the means of declustering that is necessary in a growing host population. The daughter copies diffuse freely and each copy may with equal probability end up in either of the two cell halves. In this way, the random segregation of the plasmids is coupled to replication and occurs continuously during the cell cycle, and is not linked to cell division. The unit of segregation is the plasmid copy and not the plasmid clusters. In contrast, the two daughters of a Par+ plasmid are directed in opposite directions by the plasmid-encoded partition system, thereby assuring that each daughter cell receives the plasmid.     

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.     

A comparison of sexual and asexual replication strategies in a simplified model based on the yeast life cycle

This paper develops simplified mathematical models describing the mutation-selection balance for the asexual and sexual replication pathways in Saccharomyces cerevisiae, or Baker’s yeast. The simplified models are based on the single-fitness-peak approximation in quasispecies theory. We assume diploid genomes consisting of two chromosomes, and we assume that each chromosome is functional if and only if its base sequence is identical to some master sequence. The growth and replication of the yeast cells is modeled as a first-order process, with first-order growth rate constants that are determined by whether a given genome consists of zero, one, or two functional chromosomes. In the asexual pathway, we assume that a given diploid cell divides into two diploids. For the sake of generality, our model allows for mitotic recombination and asymmetric chromosome segregation. In the sexual pathway, we assume that a given diploid cell divides into two diploids, each of which then divide into two haploids. The resulting four haploids enter a haploid pool, where they grow and replicate until they meet another haploid with which to fuse. In the sexual pathway, we consider two mating strategies: (1) a selective strategy, where only haploids with functional chromosomes can fuse with one another; (2) a random strategy, where haploids randomly fuse with one another. When the cost for sex is low, we find that the selective mating strategy leads to the highest mean fitness of the population, when compared to all of the other strategies. When the cost for sex is low, sexual replication with random mating also has a higher mean fitness than asexual replication without mitotic recombination or asymmetric chromosome segregation. We also show that, at low replication fidelities, sexual replication with random mating has a higher mean fitness than asexual replication, as long as the cost for sex is low. If the fitness penalty for having a defective chromosome is sufficiently high and the cost for sex sufficiently low, then at low replication fidelities the random mating strategy has a mean fitness that is a factor of larger than the asexual mean fitness. We argue that for yeast, the selective mating strategy is the one that is closer to reality, which if true suggests that sex may provide a selective advantage under considerably more relaxed conditions than previous research has indicated. The results of this paper also suggest that S. cerevisiae switches from asexual to sexual replication when stressed, because stressful growth conditions provide an opportunity for the yeast to clear out deleterious mutations from their genomes. That being said, our model does not contradict theories for the evolution of sex that argue that sex evolved because it allows a population to more easily adapt to changing conditions.     

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.     

ARS replication during the yeast S phase

A 1.45 kb circular plasmid derived from yeast chromosome IV contains the autonomous replication element called ARS1. Isotope density transfer experiments show that each plasmid molecule replicates once each S phase, with initiation depending on two genetically defined steps required for nuclear DNA replication. A density transfer experiment with synchronized cells demonstrates that the ARS1 plasmid population replicates early in the S phase. The sequences adjacent to ARS1 on chromosome IV also initiate replication early, suggesting that the ARS1 plasmid contains information which determines its time of replication. The times of replication for two other yeast chromosome sequences, ARS2 and a sequence referred to as 1OZ, indicate that the temporal order of replication is ARS1 leads to ARS2 leads to 1OZ. These experiments show directly that specific chromosome regions replicate at specific times during the yeast S phase. If ARS elements are origins of chromosome replication, then the experiment reveals times of activation for two origins.     

Measurements and models of synchronous growth of fission yeast induced by temperature oscillations

Pulsing of temperature in a fermentor at intervals coincident with cell generation time was used to induce synchrony in a population of the fission yeast Schizosaccharomyces pombe. Measurements of culture protein, RNA, and DNA during synchronous growth confirm continuous synthesis of protein and RNA and discontinuos synthesis of DNA as previously reported. Flow microfluorometry of populations at different times during the synchrony cycle was used to monitor the changes in single-cell protein. RNA, and DNA frequency functions. These measurements illustrate very clearly the degree of synchrony and patterns of macromolecular synthesis and also confirm previous estimates of the cellular protein contents characteristic of dividing cells. Additional insights into single-cell kinetics and division controls are provided by two-parameter flow microfluorometry measurements and by mathematical modeling of population dynamics. Such data are necessary foundations for robust population balance models of microbial processes.     

A novel role for the mitotic spindle during DNA segregation in yeast: promoting 2 microm plasmid-cohesin association

The 2 microm circle plasmid in Saccharomyces cerevisiae is a model for a stable, high-copy-number, extrachromosomal "selfish" DNA element. By combining a partitioning system and an amplification system, the plasmid ensures its stable propagation and copy number maintenance, even though it does not provide any selective advantage to its host. Recent evidence suggests that the partitioning system couples plasmid segregation to chromosome segregation. We now demonstrate an unexpected and unconventional role for the mitotic spindle in the plasmid-partitioning pathway. The spindle specifies the nuclear address of the 2 microm circle and promotes recruitment of the cohesin complex to the plasmid-partitioning locus STB. Only the nuclear microtubules, and not the cytoplasmic ones, are required for loading cohesin at STB. In cells recovering from nocodazole-induced spindle depolymerization and G(2)/M arrest, cohesin-STB association can be established coincident with spindle restoration. This postreplication recruitment of cohesin is not functional in equipartitioning. However, normally acquired cohesin can be inactivated after replication without causing plasmid missegregation. In the mtw1-1 mutant yeast strain, the plasmid cosegregates with the spindle and the spindle-associated chromosomes; by contrast, a substantial number of the chromosomes are not associated with the spindle. These results are consistent with a model in which the spindle promotes plasmid segregation in a chromosome-linked fashion.     

Segregation of the yeast plasmid: similarities and contrasts with bacterial plasmid partitioning

The high copy yeast plasmid 2 microm circle, like the well-studied low copy bacterial plasmids, utilizes two partitioning proteins and a cis-acting 'centromere'-like sequence for its stable propagation. Functionally, though, the protein and DNA constituents of the two partitioning systems are quite distinct. Key events in the yeast and bacterial segregation pathways are plasmid organization, localization, replication, 'counting' of replicated molecules and their distribution to daughter cells. We suggest that the two systems facilitate these common logistical steps by adapting to the physical, biochemical, and mechanical contexts in which the host chromosomes segregate.     

From intracellular signaling to population oscillations: bridging size- and time-scales in collective behavior

Collective behavior in cellular populations is coordinated by biochemical signaling networks within individual cells. Connecting the dynamics of these intracellular networks to the population phenomena they control poses a considerable challenge because of network complexity and our limited knowledge of kinetic parameters. However, from physical systems, we know that behavioral changes in the individual constituents of a collectively behaving system occur in a limited number of well-defined classes, and these can be described using simple models. Here, we apply such an approach to the emergence of collective oscillations in cellular populations of the social amoeba Dictyostelium discoideum. Through direct tests of our model with quantitative in vivo measurements of single-cell and population signaling dynamics, we show how a simple model can effectively describe a complex molecular signaling network at multiple size and temporal scales. The model predicts novel noise-driven single-cell and population-level signaling phenomena that we then experimentally observe. Our results suggest that like physical systems, collective behavior in biology may be universal and described using simple mathematical models.     

A DNA replication origin and a replication fork barrier used in vivo in the circular plasmid pKD1

As in other yeasts, ARS-containing plasmids can be maintained extrachromosomally in Kluyveromyces lactis. Although some fragments of K. lactis DNA have ARS activity in both K. lactis and Saccharomyces cerevisiae, it appears that the sequences required for ARS activity in the two yeasts are different. As an approach to a better understanding of ARS structure and function in K. lactis, we analyzed the replication of the circular plasmid pKD1. We identified a 159-bp sequence able to promote autonomous replication of pKD1 in both yeasts; this fragments contains both a sequence related to the S. cerevisiae ARS consensus sequence and a region of 53% identity to the 40-bp sequence essential for K. lactis KARS101 function. By the analysis of in vivo replication intermediates we provide the first direct evidence that DNA replication initiates at or near the K. lactis ARS element. Replication terminates at the cisacting stability locus of pKD1, which functions as a replication fork barrier (RFB) and is necessary for proper plasmid segregation. RFB activity requires the pKDI gene products that are important for plasmid segregation, suggesting a link between DNA replication termination and plasmid segregation in a eukaryotic organism.     

Transient response simulations of recombinant microbial populations

An asynchronous bacterial population has been approximated using a finite number of "computer" cells, each based on a complex single-cell model for Escherichia coli. This formulation correctly simulates the transient responses of protein and total cell mass synthesis rate to the sudden increase in the concentration of limiting energy source in the growth medium. Experimentally observed responses of rRNA and mRNA synthesis rates to growth rate shifts are qualitatively mirrored by the model. Simulation trends following those of a rel(-) mutant suggest that model modifications are needed to describe the dynamics of the stringent response. Simulations of the responses of recombinant populations to plasmid amplification or plasmid promoter induction also result in behavior similar to that determined experimentally. The calculated responses for recombinant populations subjected to constant promoter induction or cyclic induction-noninduction lead to the conclusion that inducible systems give greater productivity than those with fixed promoter strength. This formulation may be utilized as a basis for exploring other aspects of recombinant population dynamics.     

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.     

Temperature sensitive replication plasmids are passively distributed during cell division at non-permissive temperature: a new model for replicon duplication and partitioning

Summary To see whether plasmid molecules in bacteria are equally partitioned or randomly distributed at cell division, the segregation properties of temperature sensitive replication mutants of the E. coli plasmid pSC101 were tested at non-permissive temperature. The results support the idea that at least unreplicated molecules are passively distributed and thus the Equipartition Model is unlikely even under physiological conditions if plasmids replicate randomly. Therefore, we developed a new model which involves the Random Replication Hypothesis and assumes that only the two products of the last plasmid replication event are actively partitioned into two daughter cells and the others are randomly distributed. Mathematical studies revealed that the incompatibility segregation rate predicted by this model fits the experimental data.     

The DNA-A component of a plant geminivirus (Indian mung bean yellow mosaic virus) replicates in budding yeast cells

Understanding the biochemistry of DNA replication of the plant DNA viruses is important for the development of antiviral strategies. Since DNA replication is little studied in plants, a genetically tractable, easily culturable, eukaryotic model system is required to pursue such studies in a facile manner. Here we report the development of a yeast model system that supports DNA replication of a chosen geminivirus strain, Indian mung bean yellow mosaic virus. The replication of plasmid DNA in the model system relies specifically on the virus-derived elements and factors. Usage of this model system revealed the role of at least one hitherto unknown viral factor for viral DNA replication. The episomal characteristic of single-strandedness of replicated plasmid DNA was shown, and the expression of viral genes was also confirmed. This model system is expected to shed light on the machinery and mechanism involved in geminiviral DNA replication in plants.     

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.