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.     

Phytoplankton dynamics

We present a model of the phytoplankton dynamics. The distribution of the size of the phytoplankton aggregates is described by a non-linear transport equation that contains terms responsible for the growth of phytoplankton aggregates, their fragmentation and coagulation. We study asymptotic behaviour of moments of the solutions and we explain why phytoplankton tends to create large aggregates.     

Organization of the cytokeratin network in an epithelial cell

The cytoskeleton is a dynamic three-dimensional structure mainly located in the cytoplasm. It is involved in many cell functions such as mechanical signal transduction and maintenance of cell integrity. Among the three cytoskeletal components, intermediate filaments (the cytokeratin in epithelial cells) are the best candidates for this mechanical role. A model of the establishment of the cytokeratin network of an epithelial cell is proposed to study the dependence of its structural organization on extracellular mechanical environment. To implicitly describe the latter and its effects on the intracellular domain, we use mechanically regulated protein synthesis. Our model is a hybrid of a partial differential equation of parabolic type, governing the evolution of the concentration of cytokeratin, and a set of stochastic differential equations describing the dynamics of filaments. Each filament is described by a stochastic differential equation that reflects both the local interactions with the environment and the non-local interactions via the past history of the filament. A three-dimensional simulation model is derived from this mathematical model. This simulation model is then used to obtain examples of cytokeratin network architectures under given mechanical conditions, and to study the influence of several parameters.     

Effect of a sharp change of the incidence function on the dynamics of a simple disease

We investigate two cases of a sharp change of incidencec functions on the dynamics of a susceptible-infective-susceptible epidemic model. In the first case, low population levels have mass action incidence, while high population levels have proportional incidence, the switch occurring when the total population reaches a certain threshold. Using a modified Dulac theorem, we prove that this system has a single equilibrium which attracts all solutions for which the disease is present and the population remains bounded. In the second case, an increase of the number of infectives leads to a mass action term being added to a standard incidence term. We show that this allows a Hopf bifurcation to occur, with periodic orbits being generated when a locally asymptotically stable equilibrium loses stability.     

Modelization of the role of currents and turbulence on the growth and dispersion of marine phytoplankton

This note introduces a model of growth and dispersion of marine phytoplankton, focusing on the effects of currents (3D) and vertical mixing. Our method consists in describing these effects as the product of the horizontal current, which is solved along characteristic lines, and the coupled action of vertical current and vertical diffusion, restricted on each characteristic line of the horizontal current. One thus obtains explicit formulae, which it will be possible to use in the study of the phytoplankton distribution.     

Editorial

Acta Biotheoretica -     

Abnormalities of ADP/ATP carrier protein in J-2-N cardiomyopathic hamsters

ADP/ATP carrier protein (AAC) is located in the mitochondrial inner membrane and has an important function in mitochondrial energy supply. This protein transports ATP to the cytoplasm and counter transports ADP into the mitochondria. J-2-N cardiomyopathic hamsters were investigated to determine the AAC content in cardiac mitochondria. After recording an electrocardiogram and collecting blood, the cardiac mitochondria were isolated. The mitochondrial membranes were labelled with eosin-5-maleimide (EMA) and separated on SDS polyacrylamide gels. The position of the AAC component was identified by exposing the gel under UV light, and the AAC content was determined by densitometry after staining with Coomassie blue. The AAC content ratio was significantly decreased in both 10-week-old and 1-year survived J-2-N hamsters when compared to control Golden hamster. Among 10-week-old J-2-N hamsters, the decrease in the AAC content ratio was more marked for the animals with more severe myocardial damage. The H⁺-ATPase activities of mitochondrial membrane were higher in 10-week-old J-2-N hamsters than in control hamsters. These results suggest that the decrease of AAC in J-2-N hamster plays an important role in the pathogenesis of cardiomyopathy in J-2-N hamsters.     

A periodicity result for a nonlinear functional integral equation

In this paper, we study the effect of introducing a delay in a model of cell proliferation considered originally by O. Arino and M. Kimmel (J. Math. Biol. 27, 341–354 (1989)). We prove that slow oscillations take place and periodic oscillations appear for appropriate values of a parameter.