Difference between revisions of "Cell cycle analysis"

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(Determination of the C and D periods:)
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This gives:
 
This gives:
  
'''<math>a_i=\tau-\frac{log(2-F)}{log2}*\tau</math>'''    
+
'''<math>a_i=\tau-\frac{log(2-F)}{log2}*\tau</math>'''  
 +
 
 +
which is the same as this (log2 is 1):
 +
 
 +
'''<math>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:                                                             
 
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>a_i=84-\frac{log(2-0.66)}{log2}*84=48.5</math>'''  
+
'''<math>a_i=84-log(2-0.66)*84=48.5</math>'''  
  
  
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[[Image:C+D_1.jpg|left|250px]]
 
[[Image:C+D_1.jpg|left|250px]]
 
 
 
 
 
 
 
 
 
 
  
 
===Determination of the C and D periods:===
 
===Determination of the C and D periods:===
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'''<math>C=log(\frac{oriC}{terC})*{\tau}</math>'''
+
'''<math>C=log2(\frac{oriC}{terC})*{\tau}</math>'''
  
  

Revision as of 03:24, 1 July 2013

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:

Theoretical age distr.jpg

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,

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle 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:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle a_i=\tau-\frac{log(2-F)}{log2}*\tau}

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

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle 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:


Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle 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:

DNAHistogram.jpg

4-origin-cells: 23 %

Generation time (τ): 27 min

Initiation age (ai): 5 min


C+D 1.jpg

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):

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle \frac{oriC}{terC}=2^{\frac{C}{\tau}}}


which gives:


Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle C=log2(\frac{oriC}{terC})*{\tau}}


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

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): {\displaystyle 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


C+D 2.jpg

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:

Theoretical exp histogram.jpg















Theoretical exp histogram2.jpg



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


C+D 3.jpg














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