ABSTRACT
Increasing the knowledge of various cell cycle kinetic parameters, such as the length of the cell cycle and its different phases, is of considerable importance for several purposes including tumor diagnostics and treatment in clinical health care and a deepened understanding of tumor growth mechanisms. Of particular interest as a prognostic factor in different cancer forms is the S phase, during which DNA is replicated. In the present paper, we estimate the DNA replication rate and the S phase length from bromodeoxyuridine-DNA flow cytometry data. The mathematical analysis is based on a branching process model, paired with an assumed gamma distribution for the S phase duration, with which the DNA distribution of S phase cells can be expressed in terms of the DNA replication rate. Flow cytometry data typically contains rather large measurement variations, however, and we employ nonparametric deconvolution to estimate the underlying DNA distribution of S phase cells; an estimate of the DNA replication rate is then provided by this distribution and the mathematical model.
Subject(s)
DNA/analysis , DNA/metabolism , Models, Genetic , S Phase/genetics , Statistical Distributions , Bromodeoxyuridine/analysis , Bromodeoxyuridine/metabolism , Cell Line, Tumor , Female , Flow Cytometry , Humans , Kinetics , Reference Values , Stochastic ProcessesABSTRACT
A stochastic model for interpreting BrdUrd DNA FCM-derived data is proposed. The model is based on branching processes and describes the progression of the DNA distribution of BrdUrd-labelled cells through the cell cycle. With the main focus on estimating the S phase duration and its variation, the DNA replication rate is modelled by a piecewise linear function, while assuming a gamma distribution for the S phase duration. Estimation of model parameters was carried out using maximum likelihood for data from two different cell lines. The results provided quite a good fit to the data, suggesting that stochastic models may be a valuable tool for analysing this kind of data.
Subject(s)
Flow Cytometry/methods , Models, Biological , S Phase/physiology , Breast/cytology , Breast Neoplasms/pathology , Cell Line , DNA Replication , Humans , Stochastic ProcessesABSTRACT
A mathematical model, based on branching processes, is proposed to interpret BrdUrd DNA FCM-derived data. Our main interest is in determining the distribution of the G(2) phase duration. Two different model classes involving different assumptions on the distribution of the G(2) phase duration are considered. Different assumptions of the G(2) phase duration result in very similar distributions of the S phase duration and the estimated means and standard deviations of the G(2) phase duration are all in the same range.
Subject(s)
Flow Cytometry/methods , G2 Phase/physiology , Models, Biological , Statistical Distributions , Algorithms , Bromodeoxyuridine/analysis , Bromodeoxyuridine/metabolism , Cell Cycle/physiology , Cell Line, Tumor , Computer Simulation , DNA/biosynthesis , DNA Replication , Humans , Kinetics , Likelihood Functions , S Phase/physiology , Stochastic ProcessesABSTRACT
BACKGROUND: The potential doubling time of a tumor has been suggested to be a measurement of tumor aggressiveness; therefore, it is of interest to find reliable methods to estimate this time. Because of variability in length of the various cell cycle phases, stochastic modeling of the cell cycle might be a suitable approach. METHODS: The relative movement curve and the DNA synthesis time were estimated by using local polynomial regression methods. Further, the rate of nucleotide incorporation was estimated by using a Markov pure birth process with one absorbing state to model the progression of the DNA distribution through S phase. RESULTS: An estimate of the DNA synthesis time, with confidence intervals, was obtained from the relative movement curve. The Markov approach provided an estimate of the distribution of the time to complete S phase given the initial distribution. Using the Markov approach we also made an estimate of the mean number of active replicons during S phase. CONCLUSIONS: A Markov pure birth process has shown to be useful to model the progression of cells through S phase and to increase knowledge about the variability in the length of S phase and a large variation is shown.
