Quantitative model of ColE1 plasmid copy number control. 1993

V Brendel, and A S Perelson
Department of Mathematics, Stanford University, CA 94305.

Initiation of replication of the Escherichia coli plasmid ColE1 is inhibited by formation of a complex between a small plasmid RNA (RNA I) and the pre-primer for DNA synthesis (RNA II). Complex formation (and inhibition of replication) is enhanced by the plasmid-encoded Rom protein. The in vitro kinetics of complex formation were previously studied both experimentally and theoretically. The in vivo concentrations and half-lives of RNA I, RNA II and Rom protein have been measured recently. We present a dynamic model for the in vivo replication control mechanism that accounts for the measured concentration values. From the model we deduce a simple formula for the steady-state plasmid concentration. Our results agree with a previous simple steady-state analysis done by Brenner and Tomizawa, in that plasmid copy number is most strongly dependent on the per plasmid rate of RNA I synthesis. However, our model predicts other parameter dependencies that are not evident from or at variance with the previous analysis. Accordingly, we predict that plasmid copy number is greatly influenced by changes in the rate constant describing the formation of an initial unstable RNA I-RNA II complex, but is only slightly influenced by changes in the dissociation rate of this complex. Plasmid copy number per average cell volume is predicted to increase linearly with increases in the RNA II synthesis rate and with increases in the generation time of the host culture. Rom protein, which promotes conversion of the unstable RNA I-RNA II complex to a stable complex, serves to decrease copy number; however, its presence or absence does not seem to qualitatively alter the copy number control mechanism. Our model predicts the quantitative increase of plasmid copy number in rom- mutants. Several experiments are suggested to investigate the predictions of the model.

UI MeSH Term Description Entries
D007700 Kinetics The rate dynamics in chemical or physical systems.
D008433 Mathematics The deductive study of shape, quantity, and dependence. (From McGraw-Hill Dictionary of Scientific and Technical Terms, 6th ed) Mathematic
D008957 Models, Genetic Theoretical representations that simulate the behavior or activity of genetic processes or phenomena. They include the use of mathematical equations, computers, and other electronic equipment. Genetic Models,Genetic Model,Model, Genetic
D003086 Bacteriocin Plasmids Plasmids encoding bacterial exotoxins (BACTERIOCINS). Bacteriocin Factors,Col Factors,Colicin Factors,Colicin Plasmids,Bacteriocin Factor,Bacteriocin Plasmid,Col Factor,Colicin Factor,Colicin Plasmid,Factor, Bacteriocin,Factor, Col,Factor, Colicin,Factors, Bacteriocin,Factors, Col,Factors, Colicin,Plasmid, Bacteriocin,Plasmid, Colicin,Plasmids, Bacteriocin,Plasmids, Colicin
D004261 DNA Replication The process by which a DNA molecule is duplicated. Autonomous Replication,Replication, Autonomous,Autonomous Replications,DNA Replications,Replication, DNA,Replications, Autonomous,Replications, DNA
D001426 Bacterial Proteins Proteins found in any species of bacterium. Bacterial Gene Products,Bacterial Gene Proteins,Gene Products, Bacterial,Bacterial Gene Product,Bacterial Gene Protein,Bacterial Protein,Gene Product, Bacterial,Gene Protein, Bacterial,Gene Proteins, Bacterial,Protein, Bacterial,Proteins, Bacterial
D012313 RNA A polynucleotide consisting essentially of chains with a repeating backbone of phosphate and ribose units to which nitrogenous bases are attached. RNA is unique among biological macromolecules in that it can encode genetic information, serve as an abundant structural component of cells, and also possesses catalytic activity. (Rieger et al., Glossary of Genetics: Classical and Molecular, 5th ed) RNA, Non-Polyadenylated,Ribonucleic Acid,Gene Products, RNA,Non-Polyadenylated RNA,Acid, Ribonucleic,Non Polyadenylated RNA,RNA Gene Products,RNA, Non Polyadenylated
D012329 RNA, Bacterial Ribonucleic acid in bacteria having regulatory and catalytic roles as well as involvement in protein synthesis. Bacterial RNA

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