Evolutionary model for the unequal segregation of high copy plasmids

Plasmids are extrachromosomal DNA elements of microorganisms encoding beneficial genetic information. They were thought to be equally distributed to daughter cells during cell division. Here we use mathematical modeling to investigate the evolutionary stability of plasmid segregation for high-copy plasmids—plasmids that are present in up to several hundred copies per cell—carrying antibiotic resistance genes. Evolutionary stable strategies (ESS) are determined by numerical analysis of a plasmid-load structured population model. The theory predicts that the evolutionary stable segregation strategy of a cell depends on the plasmid copy number: For low and medium plasmid load, both daughters receive in average an equal share of plasmids, while in case of high plasmid load, one daughter obtains distinctively and systematically more plasmids. These findings are in good agreement with recent experimental results. We discuss the interpretation and practical consequences.

In the last years, it becomes more and more clear that heterogeneity in isogenic bacterial populations is rather the rule than the exception. This observation is interesting as it reveals the complex social life of bacteria, and also because of tremendous practical implications in medicine, biotechnology, and ecology. The central questions in this field are the identification of the underlying proximate causes (molecular mechanisms) on the one hand and on the other hand the identification of ultimate causes (evolutionary forces) that shape the social life of bacteria. We focus on plasmid dynamics, in particular on plasmid segregation. Recent experiments showed that plasmid segregation depends on the plasmid load. We identify possible evolutionary factors that shaped this process. It turns out that the ambivalence in the effect of plasmids—advantageous if present in low copy numbers, a metabolic burden if present in high copy numbers—is able to explain the experimental observations. The experimental findings can be interpreted as a variant of the principle of division of labor, as it is well known from e.g. persister cells or sporulation. Our model extends the theory of unequal segregation of damage to the ambivalent role of plasmids. Similarly, it is known that certain gene regulatory proteins are acting in a dose-dependent manner. Due to differences in their cellular concentrations and in their affinities to various target promoters, differential gene expression patterns are achieved. Consequently, tight concentration control is observed [1]. Another example is the strict copy-dependent utilization of autolysins during cell division. These enzymes carefully open the bacterial cell wall to allow for its extension [2]. Overproduction of these enzymes leads to cell lysis [3]. These molecules are in principle also candidates for a segregation characteristic similar to that of high copy plasmids described here.

Evolution of the first genetic cells and the universal genetic code: a hypothesis based on macromolecular coevolution of RNA and proteins

A qualitative hypothesis based on coevolution of protein and nucleic acid macromolecules was developed to explain the evolution of the first genetic cells, from the likely organic chemical-rich environment of early earth, through to the Last Universal Common Ancestor (LUCA). The evolution of the first genetic cell was divided into three phases, proto-genetic cells I, II and III, and the transition to each milestone is described, based on development of chemical cross-catalysis, bio-cross-catalysis, and the universal genetic code, respectively. Selection of macromolecular properties of both peptides and nucleic acids, in response to environmental factors, was likely to be a key aspect of early evolution. The development of hereditable nucleic acids with various key functions; translation, transcription and replication, is described. These functions are envisaged to have coevolved with protein enzymes, from simple organic precursors. Genetically heritable nucleotides may have developed after the local earth environment had cooled below 63 °C. Around this temperature G-C bases would have been preferentially utilized for nucleotide synthesis. Under these conditions RNA type nucleotides were then likely selected from a range of different types of nucleotide backbones through template-based synthesis. Initial development of the genetic coding system was simplified by the availability of proto-messenger RNA sequences that contained only G and C bases, and the need to encode only four amino acids. The step-wise addition of further amino acids to the code was predicted to parallel the growing metabolic complexity of the proto-genetic cell. On completion of this evolutionary process the proto-genetic cell is envisaged to have become the LUCA, the last common ancestor of bacteria, eukaryote and archaea domains. Key issues addressed by the model include: (a) the transition from non-hereditable random sequences of peptides and nucleic acids to specific proteins coded by hereditable nucleotide sequences, (b) the origin of homochiral amino acids and sugars, and (c) the mutation limits on the sizes of early nucleic acid genomes. The first genome was limited to a size of about 200 base pairs.

Modeling a minimal cell

One important aim of synthetic biology is to develop a self-replicating biological system capable of performing useful tasks. A mathematical model of a synthetic organism would greatly enhance its value by providing a platform in which proposed modifications to the system could be rapidly prototyped and tested. Such a platform would allow the explicit connection of genomic sequence information to physiological predictions. As an initial step toward this aim, a minimal cell model (MCM) has been formulated. The MCM is defined as a model of a hypothetical cell with the minimum number of genes necessary to grow and divide in an optimally supportive culture environment. It is chemically detailed in terms of genes and gene products, as well as physiologically complete in terms of bacterial cell processes (e.g., DNA replication and cell division). A mathematical framework originally developed for modeling Escherichia coli has been used to build the platform MCM. A MCM with 241 product-coding genes (those which produce protein or stable RNA products) is presented. This gene set is genomically complete in that it codes for all the functions that a minimal chemoheterotrophic bacterium would require for sustained growth and division. With this model, the hypotheses behind a minimal gene set can be tested using a chemically detailed, dynamic, whole-cell modeling approach. Furthermore, the MCM can simulate the behavior of a whole cell that depends on the cell's (1) metabolic rates and chemical state, (2) genome in terms of expression of various genes, (3) environment both in terms of direct nutrient starvation and competitive inhibition leading to starvation, and (4) genomic sequence in terms of the chromosomal locations of genes.

Investigation of subpopulation heterogeneity and plasmid stability in recombinant escherichia coli via a simple segregated model

Many microbial and cell cultures exhibit phenomena that can best be described using a segregated modeling approach. Heterogeneties are more marked in recombinant cell cultures because subpopulations, which often exhibit different growth and productivity characteristics, are more easily identified by selective markers. A simple segregated mathematical model that simulates the growth of recombinant Escherichia coli cells is developed. Subpopulations of different growth rate, plasmid replication rate, and plasmid segregation probability are explicitly considered. Results indicate that a third mechanism of plasmid instability, referred to here as a "downward selective pressure," is significant when describing plasmid loss in batch and chemostat cultures. Also, the model agrees well with experimental data from cultures under antibiotic selective pressure. Finally, model simulations of chemostat cultures reveal the importance of initial conditions on culture stability and the possible presence of nonrandom partitioning functions.

Optimizing initial plasmid copy number distribution for improved protein activity in a recombinant fermentation

Recombinant bacterial cells in a fermentation broth rarely contain the same number of plasmids, even though this simplification is often used. Recent work has however indicated limitations of the simplified approach. Based on these studies, the distribution of plasmid copy numbers per cell has been represented macroscopically here in a Gaussian form for the fraction of biomass as a function of the copy number. Applying this distribution and an experimentally validated kinetic model to glyceraldehyde-3-phosphate dehydrogenase (GAPDH) synthesis by Escherichia coli containing the plasmid pBR Eco gap, it is seen that GAPDH production in a batch fermentation is maximized by a particular initial (non-zero) copy number variance and an optimal duration. To implement this distribution in a bioreactor, it is suggested that the profile may be discretized, inocula corresponding to the mean copy number of each fraction prepared, and then combined to obtain the seed culture.

Single-cell models: promise and limitations

This article describes the development of single-cell models, their uses and accomplishments, the barriers to the greater adoption, and a perspective on challenges to the biochemical engineering community where the single-cell model approach may be used advantageously. In particular, it may become an important tool in relating genomic information to cellular regulation and dynamics.

Stability of a recombinant shuttle plasmid in Bacillus subtilis and Escherichia coli

The recombinant shuttle plasmid pCPPS-31, which confers carboxymethylcellulase (CMCase) production and neomycin resistance (Ner), was segregationally but not structurally unstable in both B. subtilis (50-60%) and Escherichia coli (80-90%) when grown in serial batch cultures for 72 h diluting 1:1,000 with fresh medium every 24 h. The plasmid showed 80-100% segregational and complete structural stability in B. subtilis during batch, fed-batch, and continuous culture fermentations in minimal M9 medium. In E. coli the instability was > or = 50% in 36 h of batch or continuous culture and approached 100% in 72 h of continuous fermentation. The plasmid was more stable (> or = 60%) during fed-batch fermentation. Stability in B. subtilis and instability in E. coli may be attributed to (i) the significant growth-rate advantage of plasmid-free (P-) cells over plasmid-harboring (P+) cells in the case of E. coli, an advantage that was absent in B. subtilis, and (ii) the existence of plasmid in oligomeric forms in E. coli and in mainly monomeric forms in B. subtilis.