Cell cycle analysis

Cell cycle analysis of Escherichia coli cells

C period = the time for a round of chromosome replication

D period = the time between the end of a round of chromosome replication and cell                division

Determination of initiation age (ai) and C+D:
From flow cytometry analysis of cells treated with rifampicin and cephalexin (run-out histogram) the proportions of cells that had not initiated replication at the time of drug action (4-origin-cells, streaked) and cells that had initiated (8-origin-cells) can be estimated.The initiation age (ai) can be found from the theoretical age distribution described by this formula,

$$F=2-2^{\frac{(\tau-a_i)}{\tau}}$$

where F is the fraction of cells that had not initiated and τ is the generation time, or from the estimated graph of the theoretical age distribution (streaked portion). This gives:

$$a_i=\tau-\frac{log(2-F)}{log2}*\tau$$

which is the same as this (log2 is 1):

$$a_i=\tau-log(2-F)*\tau$$

If you have for example a generation time τ=84 minutes and the portion of cells with 4 origins is 66% the formula gives:

$$a_i=84-log(2-0.66)*84=48.5$$

The C+D period is estimated from the initiation age (ai), the generation time (τ) and the number of generations spanned per cell cycle.

Example:

4-origin-cells: 23 %

Generation time (τ): 27 min Initiation age (ai): 5 min



Determination of the C and D periods:
The C period is found from the oriC/terC ratio obtained by Southern blot or qPCR analysis (oriC/ter ratio determination) and the generation time (τ):

$$\frac{oriC}{terC}=2^{\frac{C}{\tau}}$$

which gives:

$$C=log(\frac{oriC}{terC})*{\tau}$$

The D period is found from the C+D and C period:

$$D = (C+D) - C$$

Example (continues):

C period calculated from the oriC/terC ratio: 49 min

D period = (C+D) – C

D period = 76 min – 49 min = 27 min



The theoretical exponential DNA histogram:
A theoretical exponential DNA histogram can be drawn to check whether the obtained values fit with the experimental data. From the C+D period the DNA content of the cells at different time points in the cell cycle can be calculated.

Example:





The individual values of C and D can be varied

to obtain a shape of the theoretical histogram

that gives the best fit to the experimental histogram.

Calculation of the average number of replication forks when D=τ:
In the example given above, 23% of the cells contain 4 replication forks (4-origin peak in run-out histogram) and 77% contain 12 replication forks (8-origin peak), hence the average number of replication forks in the cell population will be:

(4 x 0.23) + (12 x 0.77) = 10.2 forks

Calculation of the average number of replication forks when D≠τ:
Example:

4-origin-cells: 23%

8-origin-cells: 77%

τ = 27 min

ai = 5 min

C = 51 min D = 25 min

C+D = 76 min



12 forks → 8-origin peak in run-out histogram = 77% of the cells

6 and 4 forks → 4-origin peak in run-out histogram = 23% of the cells

The fraction of cells containing 6 forks: F = 2 - 2((τ-at)/τ) = 2 – 2((27-2)/27) = 0.10

The fraction of cells containing 4 forks: 0.23 – 0.10 = 0.13

The average number of replication forks: (6 x 0.10) + (4 x 0.13) + (12 x 0.77) = 10.4 forks