title: A Markov model approach shows a large variation in the length of S phase in MCF-7 breast cancer cells.
abstract: 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.
authors.affiliation: Centre for Mathematical Sciences, Division of Mathematical Statistics, Lund University, Lund, Sweden. sara@maths.lth.se
authors.forename: Sara
authors.initials: S
authors.lastname: Larsson
authors.forename: Maria
authors.initials: M
authors.lastname: Johansson
authors.forename: Stina
authors.initials: S
authors.lastname: Oredsson
authors.forename: Ulla
authors.initials: U
authors.lastname: Holst
mesh_terms: D000704:Analysis of Variance; D001943:Breast Neoplasms / Q000473:pathology / Q000503:physiopathology*; D001973:Bromodeoxyuridine; D045744:Cell Line, Tumor; D004247:DNA / Q000032:analysis / Q000096:biosynthesis; D005434:Flow Cytometry / Q000379:methods; D006801:Humans; D008390:Markov Chains; D012044:Regression Analysis; D012093:Replicon / Q000502:physiology; D016196:S Phase / Q000502:physiology; D013997:Time Factors
chemical_list: D004247:DNA; D001973:Bromodeoxyuridine