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Calculation of Doubling Time

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Weathered
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Topic Started by Weathered
on 3/29/2010 4:30 AM   
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Hi all,

I've been looking in the archives to get a method of accurately measuring cell doubling time and I found posts that pointed to this website here.

Seems very useful, however, when i plug in the following data for an experiment ........

0

500000

5

640000

24

1880000

29

3000000

48

4200000

53

4320000

77

11760000

96

16640000


...... it generates a graph giving an equation of ......... "amount=946090.4145*e0.0307*time"

My problem is that when I plug the same data into excel and generate the graph there with an exponential trendline, the equation comes out as ......... y = 664510e0.0362x

Using the "doubling time = ln(2)/growth rate" formula, this results in quite a different answer.

Can anyone explain the discrepancy to me? Does the website use a different trendline calculation?

Many thanks


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Suola
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Posted By Suola
on 3/29/2010 7:15 AM   
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Weathered,

The reason for differing parameters could be the way the datapoints are weighed in the regression process. In the Mathworld page (link from the Doubling Time's page) they say that they use form of the target function where the weight of the datapoints is evenly distributed among all the datapoints.
Excel maybe uses the version of the target function in which the datapoints in the lower end of the range are weighed more... If you compare the curves from these two programs, it indeed looks like in Excel's fit, the curve fits the early datapoints better than that of Doubling Time's and diverges more at the end.


The doubling times (22.5 in Doubling Time vs. 19.1 in Excel) are reasonable close for this noisy data. If you are doing cell counting for some analytical purposes and want to be super careful about the values, you should count the cell number in duplicate or triplicate for each time point and weight the data with the averages and use the inverse of the standard deviation as a weighing factor. It would also help to have at least one more datapoint between each of the 20 hour intervals, because the measuring interval should be way smaller than the time constant of the system (here doubling time).

Note also that the cell doubling time is constant (or close to constant) only at the logarithmic phase of the growth. There is a lag period and upper plateau as well which do not fit to the exponential curve at all and which should not be included in the fitting.

Cheers,


Certainty of death, small chance of success... What are we waiting for? - Gimli


Last edited Mar 29, 2010, 9:38 AM by Suola

Weathered
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Posted By Weathered
on 3/29/2010 12:08 PM   
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Hi Suola,

Thanks for a great explaination!

So, for the lag and plateau phases, would you simply eliminate the data points from the calculation?

Do you just eyeball the data to see what points to eliminate or is there a more robust way to identify the log growth phase?

Many thanks!



samm
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Posted By samm
on 4/1/2010 11:20 AM   
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Suola, thanks again for that fab explanation.
Weathered, as for your second question, graphing software such as Prizm (and maybe the 'new' Excel with the Math/Analysis toolpak) can do modal curve fitting, to give you a very accurate log phase equation, and sort-of-acceptible ones for lag/plateau.



Suola
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Posted By Suola
on 4/2/2010 6:01 AM   
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Weathered, Samm,

Sorry for my absence and delay in replying...

Indeed, in order to get the doubling time, you should take into account only the logarithmic phase... Here are links to some papers and tutorials...

http://www.bdbiosciences.com/external_files/dl/doc/tech_bulletin/live/web_enabled/tb438.pdf
http://www.docstoc.com/docs/28023447/APPENDIX-I-Determination-of-doubling-time/
http://www.mpi-bremen.de/Binaries/Binary5381/Wachstumsversuch%283%29.pdf
http://media.wiley.com/product_data/excerpt/59/04716293/0471629359.pdf

Cheers,

Certainty of death, small chance of success... What are we waiting for? - Gimli



Weathered
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Posted By Weathered
on 4/7/2010 3:52 AM   
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Thanks all, I'll install that math toolpack on excel and see how it goes.



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