Towards a blueprint of the cell cycle.

The understanding of the organisation of cell cycle events is of utmost importance to devise effective therapeutic strategies for cancer. In this article we gather evidences from the literature in support of a system model of the cell cycle, in which a growth-sensitive threshold controls entry into S phase and the sequential activation of cyclin-dependent kinases. The cycle is terminated by an End function, that comprises events from the onset of mitosis to cell division and that may also be modulated by the increase of cell size. This blueprint allows quantitative predictions by computer simulations of steady and transitory states. In fact, we show that the proposed control system applies to budding yeast populations during nutritional shift-up and following hyperactivation of the cAMP signalling pathway. Besides the growth-sensitive control system it is shown to apply to mammalian cells both in the exit from quiescence and in active proliferation. The putative molecular determinants that set the threshold controlling S phase entry are consistently altered in cancer cells. Finally, we discuss an input/output analysis based on the simulated behaviour derived from the blueprint as a new tool to investigate the road to cancer.

Characterization of cell population growth by cell cycle parameters.

The quantitative description of the relationships between global properties, defined at the cellular population level, and individual properties, defined at the single cell level, is considered in this communication along with the analysis of some segregated models of yeast and hybridoma cell cultures.

Nonlinear estimation of specific growth rate for aerobic fermentation processes.

The specific growth rate of the biomass, a very important parameter of almost every fermentation process, cannot be measured directly or estimated from related variables, as the concentrations of biomass, substrates, or products, due to the lack of reliable and cheap sensors. In this article a stable adaptive estimator of the specific growth rate is designed for those aerobic processes where the measurement of the oxygen uptake rate is available on-line. This particular approach can be applied also for other reaction rates if the model of the process satisfies some very general assumptions, which make the dynamics of the measured reaction rate a nonlinear function only of two unknown parameters, the specific growth rate and its time derivative. With respect to a previous similar approach, the new estimator has one additional parameter and a different nonlinear structure. From the analysis of the dynamics of the estimation error, a tuning criterion is derived, by which the two different algorithms can be compared under similar conditions. Simulation results show a good performance of both estimators for various kind of processes and disturbances. (c) 1995 John Wiley & Sons, Inc.

Growth and production modeling in hybridoma continuous cultures.

Several experimental data on continuous cultures of hybridoma cells show that monoclonal antibody productivity is a decreasing function of dilution rate. It has been suggested that this unusual behavior may be due to the arrest of a fraction of cycling cells at a critical point of Phase G(1). Although this hypothesis has been recently investigated by using population balance models, mathematical analysis has been performed without accounting for the dynamics of the arrested cells properly. In this article, a more general and accurate approach is presented and new specific assumptions are introduced to characterize the arrest and the later progress through the cycle. Two different models (stochastic and deterministic) and two different critical points for the arrest (at the beginning and at the end of G(1)) are considered. The cell cycle parameters are estimated so that data predicted by the model fit those reported in the literature. In particular, the fraction of arrested cells, the cell arrest probability, and the mean cell generation time are computed as functions of the dilution rate. Results so far obtained predict that there is an optimal value of dilution rate for maximizing specific production rate of monoclonal antibody.

Analysis of oscillations in yeast continuous cultures by a new simplified model.

The autonomous oscillations in yeast continuous cultures are investigated analytically and related to the behaviour of the single cell by means of a suitable modified version of Monod's classical chemostat model. Two main cell phases or states are considered to account for the experimentally observed changes occurring in the cell growth course: the budded phase and the unbudded one. Thus, a sort of two compartment structure is given to the total biomass. The model so far obtained allows one to analyse the local properties of the predicted steady states under various assumptions, both on the yield coefficients and the specific growth rates. Necessary conditions for the local instability are derived and the existence of stable limit cycles is shown by computer simulation. With respect to the qualitative changes in the metabolic parameters, this analysis agrees with the results obtained by simulation of complex structured and segregated models. However, the oscillation period is too long compared with the experimental one and this fact may be mainly due to the strong simplifying assumptions on the dynamic evolution of the transfer rates between the two compartments. The model's usefulness seems until now restricted to the identification of the relationships between the cell cycle regulation and the oscillation triggering.

On the optimal control of fed-batch reactors with substrate-inhibited kinetics.

The optimal feed rate profiles, for fed-batch fermentation that maximizes the biomass production and accounts for time, are analyzed. The solution can be found only if the final arc of the optimal control is a batch arc, since in this case the final concentrations of substrate and biomass can be determined by ulterior conditions on the mass balance and on the final growth rate of biomass and thus it is possible to solve the resulting time optimal problem by using Green's theorem. This evidences the "turnpike property" of the solution, which tries to spend the maximum time on or at least near the singular arc along which the substrate concentration is maintained constant. The optimality of the final batch arc is related to the time operational cost in the performance index. The sequence of the control depends on the initial conditions for which six different regions, with the respective patterns, have been identified, in case the performance index allows the control sequence to have a final batch.