fitVolDist: Fit a model for cell volume distribution under least squares criteria.

Description

This function fits a model for cell volume distribution under least squares criteria; free model parameters are the cell growth rate r (\(\mu m^3/h\)), the variability in cell growth rate sigma_r (\(\mu m^3/h\)) and a linear scaling factor A.

Usage

fitVolDist(vol, freq, r = 100, sigma_r = 44, t = 40,
           sigma_t = 0.3 * t, maxiter = 100, nprint = 1,
           alg="leastsq")

Arguments

vol

a vector of numeric values representing volumes (\(\mu m^3\))

freq

a vector of numeric values with the same length as vol, representing the frequency of cells of the volumes given in vol

a numeric value that represents the starting value for the rate (\(\mu m^3/h\)) of cell growth parameter

sigma_r

a numeric value that represents the starting value for the variability in the rate of cell growth parameter r (\(\mu m^3/h\))

a numeric value representing the average cell cycle time (\(h\))

sigma_t

a numeric value representing the variability in the average cell cycle time t (\(h\))

maxiter

numeric value representing the maximum number of iterations used by nls.lm in model fitting under least squares criteria

nprint

optimization output is printed every nprint iterations

alg

character string indicating the algorithm to use; the choices are now "leastsq", so that that sum square error sum((data - model)^2) is minimized, or "chisq", so that the multinomial likelihood chi-square

2*sum(data*log(data/model)) is minimized.

Value

fitVolDist returns an object of class "fitVolDist".

The generic accessor functions coefficients, vcov, deviance, fitted and residuals extract various useful features of the value returned by fitVolDist.

An object of class "fitVolDist" is a list containing the following components:

the value for t (\(h\)) used

sigma_t

the value for sigma_t (\(h\)) used

fitted

the model fit.

fit.res

the output object returned from nls.lm.

summary.fit.res

the summary of the output object returned from nls.lm.

References

Halter M, Elliott JT, Hubbard JB, Tona A, Plant AL (2009), "Cell Volume Distributions Reveal Cell Growth Rates and Division Times", Journal of Theoretical Biology, Vol 257, pp 124 - 130, DOI: 10.1016/j.jtbi.2008.10.031.

Examples

Run this code

# NOT RUN {
# }
# NOT RUN {
#############################################################
# Fit volume distribution data for A10 vSMC cell cultures
# as described in the above referenced paper
#############################################################

## load the volume distributions in the "A10_vSMC_volume_data" dataset
data("A10_vSMC_volume_data")  
labs <- c("a","b","c","d")

## the volume distributions representing 0 nM aphidicolin concentration
Aph0 <- list(Aph0_a, Aph0_b, Aph0_c, Aph0_d)
## the associated cell cycle times
tAph0 <- c(tAph0_a, tAph0_b, tAph0_c, tAph0_d)   
## fit each dataset
Aph0res <- list()
Aph0tab <- matrix(ncol=2,nrow=4)
for(i in 1:length(Aph0)) {
  Aph0res[[i]] <- fitVolDist(vol=volumes_A10_vSMC, freq=Aph0[[i]],
                             r=100,sigma_r=44, t=tAph0[i])

  Aph0tab[i,] <- coef(Aph0res[[i]])
}
Aph0tab <- rbind(Aph0tab, colMeans(Aph0tab))
colnames(Aph0tab) <- c("r", "sigma_r")
rownames(Aph0tab) <- c(labs, "mean values")

## plot results 
par(mfrow=c(3,2))

for(i in 1:length(Aph0)) {
  pe <- signif(coef(Aph0res[[i]]),3)
  plot(volumes_A10_vSMC, Aph0[[i]], type="l", main= substitute(paste(
  "r: ", p1, ", ", sigma[r],": ",p2), 
  list(p1=pe[1], p2=pe[2])),
  xlab = expression(paste("volume (",mu, m^3,")", sep="")), 
  sub=paste("vol. dist. Aphidicolin 0 nM", labs[i]), ylab="frequency")
  
  lines(volumes_A10_vSMC, fitted(Aph0res[[i]]), col=2)
}
textplot("(Above) Volume distribution data
representing A10 vSMC cells 
cultured with 0 nM aphidicolin 
concentration (black) 
and model fit (red).  
(Right) Parameter estimates and 
mean estimates over the four fits",fixed.width=FALSE)
textplot(signif(Aph0tab,3))

## the volume distributions representing 50 nM aphidicolin concentration
Aph50 <- list(Aph50_a, Aph50_b, Aph50_c, Aph50_d)
## the associated cell cycle times
tAph50 <- c(tAph50_a, tAph50_b, tAph50_c, tAph50_d)   
## fit each dataset
Aph50res <- list()
Aph50tab <- matrix(ncol=2,nrow=4)
for(i in 1:length(Aph50)) {
  Aph50res[[i]] <- fitVolDist(vol=volumes_A10_vSMC, freq=Aph50[[i]],
                             r=100,sigma_r=44, t=tAph50[i]) 

  Aph50tab[i,] <- coef(Aph50res[[i]])
}
Aph50tab <- rbind(Aph50tab, colMeans(Aph50tab))
colnames(Aph50tab) <- c("r", "sigma_r")
rownames(Aph50tab) <- c(labs, "mean values")
  
## plot results 
par(mfrow=c(3,2))

for(i in 1:length(Aph50)) {
  pe <- signif(coef(Aph50res[[i]]),3)
  plot(volumes_A10_vSMC, Aph50[[i]], type="l", main= substitute(paste(
  "r: ", p1, ", ", sigma[r],": ",p2),
  list(p1=pe[1], p2=pe[2])),
  xlab = expression(paste("volume (", mu, m^3,")", sep="")),
  sub=paste("vol. dist. Aphidicolin 50 nM", labs[i]), ylab="frequency")
  
  lines(volumes_A10_vSMC, fitted(Aph50res[[i]]), col=2)
}
textplot("(Above) Volume distribution data
representing A10 vSMC cells 
cultured with 50 nM aphidicolin 
concentration (black) 
and model fit (red).  
(Right) Parameter estimates and 
mean estimates over the four fits",fixed.width=FALSE)
textplot(signif(Aph50tab,3))

## the volume distributions representing 100 nM aphidicolin concentration
Aph100 <- list(Aph100_a, Aph100_b, Aph100_c, Aph100_d)
## the associated cell cycle times
tAph100 <- c(tAph100_a, tAph100_b, tAph100_c, tAph100_d)   
## fit each dataset
Aph100res <- list()
Aph100tab <- matrix(ncol=2,nrow=4)
for(i in 1:length(Aph100)) {
  Aph100res[[i]] <- fitVolDist(vol=volumes_A10_vSMC, freq=Aph100[[i]],
                             r=100,sigma_r=44, t=tAph100[i]) 
  Aph100tab[i,] <- coef(Aph100res[[i]])
}
Aph100tab <- rbind(Aph100tab, colMeans(Aph100tab))
colnames(Aph100tab) <- c("r", "sigma_r")
rownames(Aph100tab) <- c(labs, "mean values")

## plot results 
par(mfrow=c(3,2))

for(i in 1:length(Aph100)) {
  pe <- signif(coef(Aph100res[[i]]),3)
  plot(volumes_A10_vSMC, Aph100[[i]], type="l", main= substitute(paste(
  "r: ", p1, ", ", sigma[r],": ",p2),
  list(p1=pe[1], p2=pe[2])),
  xlab = expression(paste("volume (",mu, m^3,")", sep="")),
  sub=paste("vol. dist. Aphidicolin 100 nM", labs[i]), ylab="frequency")
  
  lines(volumes_A10_vSMC, fitted(Aph100res[[i]]), col=2)
}
textplot("(Above) Volume distribution data
representing A10 vSMC cells 
cultured with 100 nM aphidicolin 
concentration (black) 
and model fit (red).  
(Right) Parameter estimates and 
mean estimates over the four fits",fixed.width=FALSE)
textplot(signif(Aph100tab,3))

# }
# NOT RUN {
#############################################################
# Fit volume distribution data for NIH3T3 cell cultures
# as described in the above referenced paper
#############################################################

## load the volume distributions in the "NIH3T3_volume_data" dataset
data("NIH3T3_volume_data")  
labs <- c("a","b","c","d")

## the volume distributions representing NIH3T3 cells 
NIH3T3 <- list(NIH3T3_a, NIH3T3_b, NIH3T3_c, NIH3T3_d)
## the associated cell cycle times
tNIH3T3 <- c(tNIH3T3_a, tNIH3T3_b, tNIH3T3_c, tNIH3T3_d)   
## fit each dataset
NIH3T3res <- list()
NIH3T3tab <- matrix(ncol=2,nrow=4)
for(i in 1:length(NIH3T3)) {
  NIH3T3res[[i]] <- fitVolDist(vol=volumes_nih3t3, freq=NIH3T3[[i]],
                               r=100,sigma_r=44, t=tNIH3T3[i])
  NIH3T3tab[i,] <- coef(NIH3T3res[[i]])
}
NIH3T3tab <- rbind(NIH3T3tab, colMeans(NIH3T3tab))
colnames(NIH3T3tab) <- c("r", "sigma_r")
rownames(NIH3T3tab) <- c(labs, "mean values")

## plot results 
par(mfrow=c(3,2))

for(i in 1:length(NIH3T3)) {
  pe <- signif(coef(NIH3T3res[[i]]),3)
  plot(volumes_nih3t3, NIH3T3[[i]], type="l", main= substitute(paste(
  "r: ", p1, ", ", sigma[r],": ",p2),
  list(p1=pe[1], p2=pe[2])),
  xlab = expression(paste("volume (",mu, m^3,")", sep="")),
  sub=paste("vol. dist. NIH3T3", labs[i]), ylab="frequency")
  
  lines(volumes_nih3t3, fitted(NIH3T3res[[i]]), col=2)
}
textplot("(Above) Volume distribution data
representing NIH3T3 cells 
cultured under normal
conditions (black) 
and model fit (red). 
(Right) Parameter estimates and 
mean estimates over the four fits",fixed.width=FALSE)
textplot(signif(NIH3T3tab,3))

# }