# 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 (a_{i}) 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 (a_{i}) can be found from the theoretical age distribution described by this formula,

**[math]\displaystyle{ F=2-2^{\frac{(\tau-a_i)}{\tau}} }[/math]**

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:

**[math]\displaystyle{ a_i=\tau-\frac{log(2-F)}{log2}*\tau }[/math]**

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

**[math]\displaystyle{ a_i=\tau-log(2-F)*\tau }[/math]**

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

**[math]\displaystyle{ a_i=84-log(2-0.66)*84=48.5 }[/math]**

The C+D period is estimated from the initiation age (a_{i}), 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 (a_{i}): 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):

**[math]\displaystyle{ \frac{oriC}{terC}=2^{\frac{C}{\tau}} }[/math]**

which gives:

**[math]\displaystyle{ C=log_2(\frac{oriC}{terC})*{\tau} }[/math]**

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

**[math]\displaystyle{ D = (C+D) - C }[/math]**

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

a_{i} = 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