I am attempting to determine the growth rate for a cell line. My method for doing so is simply by doing a cell count of my culture every 6 hours. However, my problem is the growth rate should be determined from the period of linear growth (a constant rate of growth). I can subjectively state that the period of growth, for example, begins at 12 hours and ends at 72 hours, however I am looking for a more robust and ultimately a quantitative method, so I can apply it non-subjectively to various growth curves.
I am not sure you will see continual/constant growth over time. I think if you started with 1 cell in a culture flask, under appropriate conditions it would divide to 2 cells, 4, then 8, 16, 32 etc. until confluence or cell density reaches the point where cells stop dividing. For some cell lines this is less than 1 x 10^6/mL. If you were to keep some cell lines growing for 72 hours, the growth curve would flatten out as cells stop growing. I think it would be best to determine with cell line you are using the point where cells stop growing. Then keep cell # below this point to see growth or doubling every X minutes/hours. You should also be aware that depending upon how many passages, the cell lines have been through, their growth changes (may slow down).
It may be best to look at the cell line you are working with, start with early passage # cells and then inoculate culture flask with a known number of cells and determine point where growth flattens out.
One option is to fit a logistic growth curve to the data. That is a simple population dynamics equation that has a maximal growth rate and a "carrying capacity" representing the maximum # cells the culture can reach. I have some R code to do this if you are interested. There are more complex models you can use - e.g. models that can take into account a lag phase - and we are developing some software to do that.
Matthew here is some R code. r is the maximal growth rate. I realize you are in Loughborough. I live in Leicester and work in Sutton Bonington so we can easily meet for a chat if that would help.
Dov
library(minpack.lm)
# HERE ARE THE FITTING FUNCTIONS
logistic.fits = function(time,density,platform="windows") {
# how many time points
ntime = length(time)
# initial estimates for each of the three parameters; for x0 we use the first data point, for xc we use the last data point and for r we use the gradient of the straight line between the logs of the first and last data points
guess = list (x0 = density[1], xc = density[ntime], r = ((log(density[ntime]) - log(density[1]))/(time[ntime] - time[1])))
# call the nonlinear fitting function
nl = nls(density~xc*x0*exp(r*time)/(xc+x0*(exp(r*time)-1)),start=guess)
if (platform=="windows"){
windows()
}
else {
quartz()
}
# add a red line with the fitted values to the graph
plot(time,density)
lines(time,predict(nl),col="blue")
nl
}
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