Analysis of a cell cycle model for Escherichia coli

SummaryRibosome and protein synthesis, DNA replication and cell division in Escherichia coli cells are described by a mathematical model that integrates previous descriptions in quantitative terms and proposes a new formalization to relate ribosome net synthesis to cell growth. The model assumes a cell size control of DNA replication and therefore is structurally divided into two subsystems: the first, whose state variables are ribosomes and protein, and the second, which is activated when the protein level reaches a threshold and which is comprised of DNA replication and cell division. The dynamics of the entire system is set only by the first subsystem: the values of its parameters determine whether the cells will be in a resting condition or will grow exponentially and in the latter case the resulting duplication time, while the structure and the parameter values of the second subsystem determine the size and the composition of the cell and the timing of DNA replication during the cycle. Relationships are derived that allow a simple determination of the time of initiation and of termination of DNA replication and the number of chromosome origins involved in any possible cell cycle as well as the macromolecular levels at the beginning of a cycle and on the average in a population of cells in balanced exponential growth.

[1]  J. Forchhammer,et al.  Growth rate of polypeptide chains as a function of the cell growth rate in a mutant of Escherichia coli 15. , 1971, Journal of molecular biology.

[2]  P. Dennis,et al.  Macromolecular Composition During Steady-State Growth of Escherichia coli B/r , 1974, Journal of bacteriology.

[3]  G. Churchward,et al.  An examination of the Cooper-Helmstetter theory of DNA replication in bacteria and its underlying assumptions. , 1977, Journal of theoretical biology.

[4]  J. Gallant,et al.  Two Compounds implicated in the Function of the RC Gene of Escherichia coli , 1969, Nature.

[5]  R. Lazzarini,et al.  Altered metabolism of the guanosine tetraphosphate, ppGpp, in mutants of E. coli , 1974 .

[6]  M. Cashel.  Regulation of bacterial ppGpp and pppGpp. , 1975, Annual review of microbiology.

[7]  P. Dennis,et al.  Regulation of ribonucleic acid synthesis in Escherichia coli B-r: an analysis of a shift-up. 1. Ribosomal RNA chain growth rates. , 1973, Journal of molecular biology.

[8]  W. Donachie,et al.  Relationship between Cell Size and Time of Initiation of DNA Replication , 1968, Nature.

[9]  O. Maaløe,et al.  Regulation of the Protein-Synthesizing Machinery—Ribosomes, tRNA, Factors, and So On , 1979 .

[10]  A. Ishihama,et al.  Biosynthesis of RNA polymerase in Escherichia coli. IV. Accumulation of intermediates in mutants defective in the subunit assembly. , 1977, Journal of molecular biology.

[11]  A. Ishihama,et al.  Autogenous regulation of RNA polymerase beta subunit synthesis in vitro. , 1978, The Journal of biological chemistry.

[12]  H. Bremer,et al.  RNA chain growth-rate in Escherichia coli. , 1968, Journal of molecular biology.

[13]  A. Gierer,et al.  Synthesis of ribosomal proteins and formation of ribosomes in Escherichia coli. , 1968, Journal of molecular biology.

[14]  W. Knorre,et al.  M. A. Savageau, Biochemical Systems Analysis. A Study of Function and Design in Molecular Biology. 396 S., 115 Abb., 14 Tab. Reading, Mass. 1976. Addison‐Wesley Pbl. Co./Advanced Book Program. £ 26,50 , 1979 .

[15]  J. Scaife.  Bacterial RNA Polymerases: The Genetics and Control of Their Synthesis , 1976 .

[16]  O. Maaløe,et al.  Chain growth rate of -galactosidase during exponential growth and amino acid starvation. , 1973, Journal of molecular biology.

[17]  R. Hayward,et al.  Evidence for specific control of RNA polymerase synthesis in Escherichia coli. , 1973, Nature: New biology.

[18]  D. Nierlich.  Regulation of bacterial growth, RNA, and protein synthesis. , 1978, Annual review of microbiology.

[19]  R. H. Pritchard,et al.  Changes in Cell Size and Shape Associated with Changes in the Replication Time of the Chromosome of Escherichia coli , 1973, Journal of bacteriology.

[20]  R. Goldberger.  Autogenous Regulation of Gene Expression , 1974, Science.

[21]  S. Molin,et al.  Control of Protein Synthesis in Escherichia coli: Analysis of an Energy Source Shift-Down , 1977, Journal of bacteriology.

[22]  H. Yang,et al.  Effects of guanosine tetraphosphate on cell-free synthesis of Escherichia coli ribosomal RNA and other gene products. , 1975, Proceedings of the National Academy of Sciences of the United States of America.

[23]  R. H. Pritchard,et al.  Effect of Thymine Concentration on the Replication Velocity of DNA in a Thymineless Mutant of Escherichia coli , 1970, Nature.

[24]  W. Haseltine,et al.  Synthesis of guanosine tetra- and pentaphosphate requires the presence of a codon-specific, uncharged transfer ribonucleic acid in the acceptor site of ribosomes. , 1973, Proceedings of the National Academy of Sciences of the United States of America.

[25]  S. Cooper,et al.  Chromosome replication and the division cycle of Escherichia coli B/r. , 1968, Journal of molecular biology.

[26]  S. Cooper,et al.  On the bacterial life sequence. , 1968, Cold Spring Harbor symposia on quantitative biology.

[27]  M. Savageau.  Biochemical Systems Analysis: A Study of Function and Design in Molecular Biology , 1976 .

[28]  H. A. Boer,et al.  Specific inhibition of ribosomal RNA synthesis in vitro by guanosine 3′ diphosphate, 5′ diphosphate , 1975, Nature.

[29]  H. Bremer,et al.  Regulation of ribonucleic acid synthesis in Escherichia coli B-r: an analysis of a shift-up. II. Fraction of RNA polymerase engaged in the synthesis of stable RNA at different steady-state growth rates. , 1973, Journal of molecular biology.

[30]  O. Maaløe.  An Analysis of Bacterial Growth , 1970 .

[31]  R. Lazzarini,et al.  The control of ribonucleic acid synthesis during amino acid deprivation in Escherichia coli. , 1971, The Journal of biological chemistry.

[32]  E. Powell.  An outline of the pattern of bacterial generation times. , 1958, Journal of general microbiology.

[33]  H. Juarez,et al.  Relationships Among Deoxyribonucleic Acid, Ribonucleic Acid, and Specific Transfer Ribonucleic Acids in Escherichia coli 15T− at Various Growth Rates , 1973, Journal of bacteriology.

[34]  J. Gallant,et al.  On the regulation of guanosine tetraphosphate levels in stringent and relaxed strains of Escherichia coli. , 1971, The Journal of biological chemistry.