title: Cell cycle progression.
abstract: In this paper we consider cell cycle models for which the transition operator for the evolution of birth mass density is a simple, linear dynamical system with a stochastic perturbation. The convolution model for a birth mass distribution is presented. Density functions of birth mass and tail probabilities in n-th generation are calculated by a saddle-point approximation method. With these probabilities, representing the probability of exceeding an acceptable mass value, we have more control over pathological growth. A computer simulation is presented for cell proliferation in the age-dependent cell cycle model. The simulation takes into account the fact that the age-dependent model with a linear growth is a simple linear dynamical system with an additive stochastic perturbation. The simulated data as well as the experimental data (generation times for mouse L) are fitted by the proposed convolution model.
authors.affiliation: Department of Mathematical Statistics, Institute of Mathematics, Stockholm University, S-106 91 Stockholm, Sweden. joanna@math.su.se
authors.forename: Joanna
authors.initials: J
authors.lastname: Tyrcha
mesh_terms: D000818:Animals; D002453:Cell Cycle; D002455:Cell Division; D003198:Computer Simulation; D016013:Likelihood Functions; D008433:Mathematics; D051379:Mice; D008954:Models, Biological; D013997:Time Factors