number of mutant cells distribution: The distribution of mutant cell counts

Description

Density, distribution function, quantile function and random generation for mutant cell counts.

Usage

dflan(m, mutations = 1., fitness = 1., death = 0., plateff = 1.,
        model = c("LD", "H", "I"), muinf = +Inf)
  pflan(m, mutations = 1., fitness = 1., death = 0., plateff = 1.,
        model = c("LD", "H", "I"), muinf = +Inf, lower.tail = TRUE)
  qflan(p, mutations = 1., fitness = 1., death = 0., plateff = 1.,
        model = c("LD", "H", "I"), muinf = +Inf, lower.tail = TRUE)
  rflan(n, mutations = 1., mutprob = NULL, fitness = 1., death = 0., plateff = 1.,
        dist = list(name = "lnorm", meanlog = -0.3795851, sdlog = 0.3016223),
        distfn = NULL,
        mfn = 1e9, cvfn = 0,
        muih = list(mu = NULL, muinv0 = NULL),
        ...)

Value

dflan gives the density, pflan gives the distribution function, qflan gives the quantile function, and rflan

generates a random sample.

rflan returns a list with two arguments, each with length n: a vector of integers

$mc (mutant counts), and a vector of numeric $fn (final numbers of cells).

Arguments

m: vector of quantiles.
p: vector of probabilities.
n: number of observations. If length(n) > 1, the length is taken to be the number required.
mutations: mean number of mutations: positive integer. Ignored if mutprob is non-empty.
mutprob: mutation probability: numeric between 0 and 1. By default empty. See details.
fitness: fitness parameter: numeric positive. By default 1.
death: death probability: numeric between 0 and 0.5. By default 0.
plateff: plating efficiency parameter: numeric number between 0 and 1. By default 1. See Details.
dist: lifetime distribution for mutant cells. See Details.
model: statistical lifetime model. Must be one of "LD" (default) for Luria-Delbrück model (exponential lifetimes), "H" for Haldane model (constant lifetimes), or "I" for Inhomogeneous model
distfn: final number of cells distribution. Must be one of "lnorm" (default if cvfn is positive) or "gamma".
mfn: mean final number of cells: numeric positive.
cvfn: coefficient of variation of final numbers of cells: numeric, default 0. If non-zero and if mutprob is empty, compute the sample with mutprob = mutations/mfn
muih: functions for inhomogeneous model. See details.
muinf: parameter used only if model is I. See details.
lower.tail: logical: if TRUE (default), probabilities are P[X <= x] otherwise, P[X > m].
...: Arguments to be passed for muih, such that hyperparameters.

Details

The argument dist is a list beginning with the distribution name followed by its parameters, and must be one the 4 following distributions: "dirac", "exp", "lnorm"(meanlog, sdlog), "gamma"(shape, scale). Note that the parameters related to the "dirac" and "exp" cases are directly computed with inputs fitness and death.

If muih$mu is non-empty, a time dependent growth model is performed. The function muih$mu is a bivariate function which represents roughly the mean growth of clone durig an time interval. The function muih$muinv0 is the inverse function of muih$mu(0,.). If muih$muinv0 is empty, it is approximated using muih$mu.

muinf corresponds to the cumulative division rate on the interval [0 ; +Inf). It is the limit as t tends to infinity of muih$mu(0,t). If model is I, muinf has to be finite, else model is set to "LD"

If mutprob is non-empty and if cvfn is zero, the sample of mutants is computed with mutations as the product of mutprob by mfn. If cvfn is positive, the final numbers of cells are generated with the log-normal (if distfn is "lnorm" or empty) or the gamma (if distfn is "gamma") distribution with mean mfn and coefficient of variation cvfn. The sample of mutants is then generated conditionally to the sample of final numbers of cells.

A plating efficiency plateff smaller than 1 can be taken into account in the dflan, pflan and qflan functions only under LD model.

If the plating efficiency plateff is smaller than 1 in the flan function, then each mutant count mc is replaced by a binomial number with parameters size = mc and prob = plateff.

Examples

Run this code

#----------------------- distributions ----------------------------------

# Luria-Delbrück model, mean number of mutations 1, fitness parameter 1
dflan(0:10)
pflan(0:10)
qflan(c(0.95, 0.99))

# Luria-Delbrück model, mean number of mutations 2, fitness parameter 0.5
qflan(c(0.95, 0.99), mutations = 2, fitness = 0.5)
# \donttest{
qflan(c(0.05, 0.01), mutations = 2, fitness = 0.5, lower.tail = FALSE)

# Haldane model, mean number of mutations 2, fitness parameter 0.5
qflan(c(0.95, 0.99), mutations = 2, fitness = 0.5, model = "H")
# }
#---------------------- random samples ----------------------------------
# lognormal lifetime distribution, lognormal final numbers
X <- rflan(100, cvfn = 0.3)
X$mc              # mutant counts
X$fn              # final numbers

# lognormal lifetime distribution, gamma final numbers
X <- rflan(100, distfn = "gamma", cvfn = 0.3)
X$mc              # mutant counts
X$fn              # final numbers

# mean number of mutations 2, fitness parameter 0.5 (realistic model, but slow)
# \donttest{
# lognormal lifetimes
rflan(1000, mutations = 2, fitness = 0.5)$mc
# gamma lifetimes
rflan(1000, mutations = 2, fitness = 0.5, dist = list(name = "gamma", shape = 10, scale = 0.05))$mc
# }
# exponential lifetimes (Luria-Delbrück model, fast)
rflan(1000, mutations = 2, fitness = 0.5, dist = list("exp"))$mc

# constant lifetimes (Haldane model, fast)
rflan(1000, mutations = 2, fitness = 0.5, dist = "dirac")$mc

# specifying mutation probability and mean final number
# \donttest{
rflan(1000, mutprob = 2e-9, mfn = 2e9, fitness = 0.5, dist = list("dirac"))$mc


# positive cell death probability
rflan(1000, mutprob = 2e-9, mfn = 2e9, death = 0.1, fitness = 0.5, dist = list("exp"))$mc
# }
#------------- Inhomogeneous model ---------
f <- function(t,n0,nf) nf/(1+(nf/n0-1)*exp(-t))  # Logistic function: mean growth of a clone
finv <- function(s,n0,nf) -log((nf/s-1)/(nf/n0-1))  # Inverse function of f

mu <- function(s,t,n0,nf) log(f(t,n0,nf)/f(s,n0,nf))   # Definition of mu
muinv0 <- function(u,n0,nf) finv(f(0.,n0,nf)*exp(u),n0,nf)   # Inverse function of mu

rflan(1000, muih = list(mu = mu, muinv0 = muinv0), n0 = 1e2, nf = 1e6)$mc