Cell cycle analysis

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(Determination of initiation age (ai) and C+D:)
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C period = the time for a round of chromosome replication
C period = the time for a round of chromosome replication
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D period = the time between the end of a round of chromosome replication and cell                division
D period = the time between the end of a round of chromosome replication and cell                division
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#Determination of initiation age (a<sub>i</sub>) and C+D:  
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===Determination of initiation age (a<sub>i</sub>) and C+D:===
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[[Image:Theoretical_age_distr.jpg|left|250px]]
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[[Image:Theoretical_age_distr.jpg|left|200px]]
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From flow cytometry analysis of cells treated with rifampicin and cephalexin (run-out histogram) the proportions of cells that had notinitiated replication at the time of drug action (4-origin-cells, streaked) and cells that initiated (8-origin-cells) can be estimated.The initiation age (ai) can be found from thetheoretical age distribution described by this formula,
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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<sub>i</sub>) can be found from the theoretical age distribution described by this formula,
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'''<math>F=2-2^{\frac{(\tau-a_i)}{\tau}}</math>'''
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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).                                                                                                                                                                                   
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This gives:
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'''<math>a_i=\tau-\frac{log(2-F)}{log2}*\tau</math>''' 
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which is the same as this (log2 is 1):
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'''<math>a_i=\tau-log(2-F)*\tau</math>'''
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If you have for example a generation time τ=84 minutes and the portion of cells with 4 origins is 66% the formula gives:                                                           
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'''<math>a_i=84-log(2-0.66)*84=48.5</math>'''
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The C+D period is estimated from the initiation age (a<sub>i</sub>), the generation time (τ) and the number of generations spanned per cell cycle.
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Example:
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[[Image:DNAHistogram.jpg|left|100px]]
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4-origin-cells: 23 %
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Generation time (τ): 27 min                                                   
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Initiation age (a<sub>i</sub>): 5 min
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[[Image:C+D_1.jpg|left|250px]]
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===Determination of the C and D periods:===
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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):
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'''<math>\frac{oriC}{terC}=2^{\frac{C}{\tau}}</math>'''
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which gives:
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'''<math>C=log(\frac{oriC}{terC})*{\tau}</math>'''
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The D period is found from the C+D and C period:
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'''<math>D = (C+D) - C</math>'''
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Example (continues):
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C period calculated from the ''oriC/terC'' ratio: 49 min
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D period = (C+D) – C
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D period = 76 min – 49 min = 27 min
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[[Image:C+D_2.jpg|left|250px]]
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===The theoretical exponential DNA histogram:===
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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.
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Example:
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[[Image:Theoretical_exp_histogram.jpg|left|400px]]
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[[Image:Theoretical_exp_histogram2.jpg|left|200px]]
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The individual values of C and D can be varied
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to obtain a shape of the theoretical histogram
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that gives the best fit to the experimental histogram.
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===Calculation of the average number of replication forks when D=τ:===
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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:
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(4 x 0.23) + (12 x 0.77) = 10.2 forks
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===Calculation of the average number of replication forks when D≠τ:===
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Example:
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4-origin-cells: 23%
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8-origin-cells: 77%
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τ = 27 min
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a<sub>i</sub> = 5 min
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C = 51 min
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D = 25 min
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C+D = 76 min
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[[Image:C+D_3.jpg|left|350px]]
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12 forks → 8-origin peak in run-out histogram = 77% of the cells
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6 and 4 forks → 4-origin peak in run-out histogram = 23% of the cells
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The fraction of cells containing 6 forks: F = 2 - 2<sup>((τ-a<sub>t</sub>)/τ)</sup> = 2 – 2<sup>((27-2)/27)</sup> = 0.10
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The fraction of cells containing 4 forks: 0.23 – 0.10 = 0.13
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'''F = 2 - 2<sup>((τ-ai))</sup>'''
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The average number of replication forks: (6 x 0.10) + (4 x 0.13) + (12 x 0.77) = 10.4 forks
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where F is the fraction of cells that had not initiated and  is the generation time, or from the estimated graph of the theoretical age distribution (streaked portion).                                                                                                                                                                                   
 
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The C+D period is estimated from the initiation age (ai), the generation time () and the number of generations spanned per cell cycle.
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[[Category:Protocol]][[Category:Escherichia coli]]

Revision as of 13:20, 4 May 2011

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


Contents

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):

ai = τ − log(2 − F) * τ

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


ai = 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

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