1. Bacterial Cell Cycle
   
2. DNA Replication
   1. Initiation of DNA Replication and DnaA
   2. Elongation and the C Period
   3. Mathematical Model
   4. Simulations
3. Cell Growth
   1. Schematic of Primary Cell Components
   2. Mathematical Model
   3. Results
4. Future Directions

1. Slow growing cells: Similar to Eukaryotes
   1. B period like G₀/G₁
   2. C period like S
   3. D period like M
2. Fast growing Procaryotic cells have overlapping periods

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Initiation of DNA Replication and DnaA

• Initiation begins at a single site, oriC, with a complex of proteins and a primer mRNA
• The oriC gene in E. coli has 4 sites with the consensus sequence TTAT(C/A)CA(C/A)A, which binds DnaA
• 20-40 monomers of DnaA^.ATP bind to oriC as a first step to initiation of DNA replication (only this active form allows in vitro initiation)
• Immediately following replication, the DNA is in a hemimethylated state, and oriC binds to the cell membrane for 8-10 minutes.
  

 

DnaA

• DnaA is a stable protein that has several forms: Unbound, bound to either ATP or ADP, bound to cardiolipin, and bound to the chromosome
• The dnaA gene is autoregulated and located near oriC
• DnaA appears to not binds hemimethylated DNA

Elongation and the C Period

• Replication of the DNA proceeds in a bidirectional manner with another set of proteins
• The C Period is roughly constant at about 45 minutes for many growth conditions

 

Mathematical Model

Below is a schematic representing one model for the Control of Initiation of DNA Replication by the protein DnaA.

1. Probabilistic Part of the Model

A Monte Carlo simulation is used to determine if the active DnaA, DnaA^.ATP, binds to oriC at any of the 4 binding sites with the consensus sequence. The probability that one molecule of DnaA^.ATP binds to oriC is approximately

It is assumed that there is at most one binding event during the time interval, Dt/J. The probability that one molecule dissociates is

where N is the number of exposed molecules. The simulation follows how many DnaA molecules are bound to the 4 binding sites of oriC for each time step in the program.

2. Deterministic Part of the Model

To determine the random binding of DnaA to the consensus sequence elsewhere along the replicating DNA forks (GS), we evaluate

where k_gs is the rate of formation of consensus sequence sites per elongating chromosome, AC.

The differential equation for the dynamics of the concentration of the various forms of DnaA protein (bound to the chromosome, inactive, and free with ATP are given by the following:

where the k's are the kinetic constants, m = ln(2)/t for t the generation time, and g a fraction representing both different available quantities of [DnaA_i] and differing binding rates for these forms.

3. Program Controls - Initiation and Division

Whenever 30 or more molecules of DnaA-ATP bind to oriC, then initiation is assumed to occur and a new oriC is created. The new oriC and the one that initiated are not allowed to bind DnaA for 8 min.

The length of the C and D periods for replication are fixed, so it is assumed that 70 min after initiation, division occurs. Note that this initiation event will have occurred in a past generation, so the program tracks specific oriCs. At division, the volume and quantities of the chemical species are halved, and the generation time t is reset to reflect the length of the last generation.

4. Simulations of the Model

Below are graphs showing typical simulations of the model for a given set of growth parameters.

• Model produced regular synchronous initiation events
• Variation in synchrony matched Skarstad et al data
• Matched Zyskind data for DnaA concentration
• Suggest key role of active/inactive pool of DnaA
• Models required input of growth information

• Growth and Initiation of DNA Replication are linked
• Bremer and Dennis have extensive data on important cellular components at different growth rates

  • Protein, RNA, and DNA/mass - Cell size
  • RNA polymerase - % active, elongation rates (Transcription)
  • Stable and unstable RNA and production rates
  • Ribosomes - % active, elongation rates (Translation)
  • DNA replication rates rates
  • oriCs/mass
• Stringent control (Negative feedback) by tetraphosphoguanine, ppGpp
• Details of biochemical processes fairly well known

 

 

Transcription

• RNA polymerase is main component
• Proteins are produced at differing rates
• Ribosomal RNA (rRNA) and transfer RNA (tRNA) have the most active genes
• Passive control by gene dosage
• ppGpp affects s₇₀ factor of RNA polymerase

 

 

 

 

Translation

• Ribosomes and tRNA⁺ are main components
• Transcription and Translation coupled in bacteria
• mRNA short half-life

 

 

Production of ppGpp

• RelA detecting tRNA^- primary control
• Alternate controls through SpoT
• Negative Feedback

 

 

 

Mathematical Model

• Biochemical reactions formed from primary components above
• Derive differential equations for components (12 equations)
• Conservation of mass used
• Parameters fit to data as best possible
• Nutrient accumulated into mass followed

• Wai Lee (Master's Thesis) followed early exponential growth, but failed to match all key experimental data
• Model being revised - Add better functional controls
• Plan to link to DnaA model and fit size data
• Include new data on initiation controls