Using R to examine a Growth Curve and calculate Doubling Time
The doubling time of cells growing exponentially in liquid culture can be a useful phenotype to quantify. A plot of the log of the OD (optical density) versus time can be used to determine growth rate. The slope of the fit line is the growth rate: k and the doubling time is given by: log(2)/k. The following is an example using the R environment to plot and fit a growth curve and find doubling time.
Pichia pastoris was grown in liquid culture. Aliquots were taken at various times post-innoculation, and measured by OD600. When the aliquots surpassed the linear range of the spectrophotometer they were diluted before reading. Thus the input data file has 5 columns: time post-innoculation, minutes, dilution factor, OD reading, derived OD.
R_growth_curve_example.pdf (this example with figures)
1.) Read the data into R
# read the data into R from a tab-delimited text file gdata <- read.table(file="yeast_timecourse.txt", sep="\t", header=T) # what are the column names? colnames(gdata)
2.) plot the derived OD600 readings as a function of time
# columns of interest are: # minutes (2nd column) and dOD600 (5th column, derived OD600) # examine a plot of OD versus time plot(gdata[,2], gdata[,5]) # could also use column names to specify columns: plot(gdata[,"minutes"], gdata[,"dOD600"]) # make the plot look nicer plot(gdata[,2], gdata[,5], main="OD versus Time", xlab="minutes", ylab="OD600")
3.) Find the portion of the curve which is linear during exponential phase growth
(hint: plot log of OD versus time)
# since this is a growth curve, we want to plot the log # of the OD plot(gdata[,2], log(gdata[,5]), main="OD versus Time", xlab="minutes", ylab="log(OD600)") # pick the part of the curve that looks linear # maybe points 3 through 6?
4.) use the linear modeling function to to perform regression
The resulting slope can be used to find the yeast doubling time.
# use lm() to fit this part of the curve # fit y as a function of x (or OD as a function of time) # but only use the points of interest lm(log(gdata[3:6,"dOD600"]) ~ gdata[3:6,"minutes"]) # save the linear fit to an object called "fit" fit <- lm(log(gdata[3:6,"dOD600"]) ~ gdata[3:6,"minutes"]) # give the fit to the abline() function to draw a line on the plot abline(fit) # the fit object is kind of complicated # it's got lots of stuff in it names(fit) # however the slope of the line can be found by looking # at the second coefficient fit$coef # use the slope to calculate the doubling time of the # cells during their exponential growth phase # the formula is log(2)/k where k is the growth rate (slope from the curve) log(2)/fit$coef # write the doubling time on the curve text(800,-2,"Doubling Time = 130 minutes")
R is available from CRAN