3 research outputs found
Multiscale Estimation of Cell Kinetics
We introduce a methodology based on the Luria–Delbrück fluctuation model for estimating the cell kinetics of clonally expanding populations. In particular, this approach allows estimation of the net cell proliferation rate, the extinction coefficient and the initial (viable) population size. We present a systematic approach based on spatial partitioning, which captures the local fluctuations of the number and sizes of individual clones. However, partitioning introduces measurement error by inflating the number of clones, which is dependent on time and the degree of cell migration. We perform various in silico experiments to explore the properties of the estimators and we show that there exists a direct relationship between precision and observation time. We also explore the trade-off between the measurement error and the estimation accuracy. By exploring different scales of cellular fluctuations, from the entire population down to those of individual clones, we show that this methodology is useful for inferring important parameters in neoplastic progression
Statistics for the Luria-Delbr\"uck distribution
The Luria-Delbr\"uck distribution is a classical model of mutations in cell
kinetics. It is obtained as a limit when the probability of mutation tends to
zero and the number of divisions to infinity. It can be interpreted as a
compound Poisson distribution (for the number of mutations) of exponential
mixtures (for the developing time of mutant clones) of geometric distributions
(for the number of cells produced by a mutant clone in a given time). The
probabilistic interpretation, and a rigourous proof of convergence in the
general case, are deduced from classical results on Bellman-Harris branching
processes. The two parameters of the Luria-Delbr\"uck distribution are the
expected number of mutations, which is the parameter of interest, and the
relative fitness of normal cells compared to mutants, which is the heavy tail
exponent. Both can be simultaneously estimated by the maximum likehood method.
However, the computation becomes numerically unstable as soon as the maximal
value of the sample is large, which occurs frequently due to the heavy tail
property. Based on the empirical generating function, robust estimators are
proposed and their asymptotic variance is given. They are comparable in
precision to maximum likelihood estimators, with a much broader range of
calculability, a better numerical stability, and a negligible computing time
Fluctuation analysis: can estimates be trusted?
The estimation of mutation probabilities and relative fitnesses in
fluctuation analysis is based on the unrealistic hypothesis that the
single-cell times to division are exponentially distributed. Using the
classical Luria-Delbr\"{u}ck distribution outside its modelling hypotheses
induces an important bias on the estimation of the relative fitness. The model
is extended here to any division time distribution. Mutant counts follow a
generalization of the Luria-Delbr\"{u}ck distribution, which depends on the
mean number of mutations, the relative fitness of normal cells compared to
mutants, and the division time distribution of mutant cells. Empirical
probability generating function techniques yield precise estimates both of the
mean number of mutations and the relative fitness of normal cells compared to
mutants. In the case where no information is available on the division time
distribution, it is shown that the estimation procedure using constant division
times yields more reliable results. Numerical results both on observed and
simulated data are reported