Ovide Arino

Analysis of a cell cycle model based on unequal division of metabolic constituents to daughter cells during cytokinesis

We demonstrate that the unequal division of RNA during cytokinesis explains the dispersion of cell generation times in CHO cell cultures. Experimental cytometric results reported previously serve as a basis for a probabilistic model of cytokinesis. Unequal RNA division to daughter cells, together with two simple laws of RNA production, are used as a source of randomness within the cell cycle. The model reproduces the experimental growth of the CHO cell population, including the observed variability in RNA content. The model has stabilizing properties which explain why a cell population with increased RNA content characteristics, a few cell cycles, to the original pattern. Other cell cycle characteristics, like sister-to-sister and mother-to-daughter generation time correlations implied by the model, are close to their experimental analogs. The conceptual basis of the model is general enough to include unequal division of factors other than RNA (cell mass, cell proteins, etc.) as sources of generation time variability. It seems that the observed dispersion of cell generation times, explained previously in the terms of random transitions in some part of the cell cycle (the Smith & Martin A and B state hypothesis), can be reduced to the single random event of unequal division. This supplies a new convenient tool in the investigation of cell cycle kinetics.

Stability analysis of models of cell production systems

Abstract We investigate the qualitative behaviour of the models of cell production systems, in the form of systems of nonlinear delay differential equations. Considered are three general models of a system involving the subpopulations of stem cells, precursor cells and mature cells, with different configurations of regulation feedbacks. The models correspond basically to the blood cell production process; however, other applications are possible. First, the simplified version (describable by ordinary differential equations) is considered. Fairly complete characterization of the trajectories is possible in this case, using the Lyapunov functions and phase plane techniques. Next, for the general models, the stability of equations linearized around the equilibria is investigated. Certain results can be obtained here, using both exact methods and numerical procedures based on an original lemma on the zeros of exponential polynomials. Then global properties (boundedness, attractivity, etc.) are examined for the nonlinear, delay case using a range of methods: Lyapunov functionals, Razumikhin functions and direct estimates on solutions. Certain special cases of our models reduce to previous literature models of blood production. Results of our analysis enable to exclude these configurations of regulation feedbacks which yield model behaviour not compatible with biological and medical observations. Techniques developed in this paper are applicable to a wide range of possible models of cell production systems.

Comparison of approaches to modeling of cell population dynamics

This paper reviews structured cell population models. A typical formulation is the partial differential equation (PDE) \[ \frac{{\partial p}}{{\partial t}} + \frac{{\partial p}}{{\partial a}} + \frac{{\partial ( {gp} )}}{{\partial a}} = B - D, \] the Lotka–von Forster equation, generalized by Webb, where t is the chronological time, a is cell age,

Asymptotic analysis of a cell cycle model based on unequal division

p = p( {a,t} )

A mathematical model of growth of population of fish in the larval stage: Density-dependence effects

is the population density, and g is the cell growth rate, while B and D are birth and death terms, respectively. Essentially, it is a transport equation with additional nonlocal boundary conditions.Another approach, apparently not involving a transport equation, and related to the theory of branching processes has been originally derived by Kimmel and analyzed by the authors. It is shown that this latter approach fits in the framework of PDE models and has comparable generality.The relationships between both types of models are generally nontrivial and seem important for their applicability.

A semigroup representation and asymptotic behavior of certain statistics of the fisher-wright-moran coalescent

We provide an analysis of the asymptotic behavior of a novel cell cycle model offering a uniform description of the processes of RNA production and division and explaining the cell generation time variability, at least in certain cell lines. We prove that the distribution

Cell cycle kinetics with supramitotic control, two cell types, and unequal division: a model of transformed embryonic cells.

m( t,x )

A MATHEMATICAL MODEL FOR PHYTOPLANKTON

of the RNA level

AN INTEGRAL EQUATION OF CELL POPULATION DYNAMICS FORMULATED AS AN ABSTRACT DELAY EQUATION — SOME CONSEQUENCES

( x )

Asymptotic Analysis of a Functional-Integral Equation Related to Cell Population Kinetics

in the dividing cells at a given time