Luigi Mariani

A bimolecular mechanism for the cell size control of the cell cycle

A molecular model for the control of cell size has been developed. It is based on two molecules, one (I) acts as an inhibitor of the entrance into S phase, and it is synthetised just after cell separation in a fixed amount per nucleus. The other (A) is an activator of the S phase, and it is synthetised at a ratio proportional to the overall protein accumulation. The activator reacts stoichiometrically with (I), and after all the (I) molecules have been titrated, (A) begins to accumulate. When it reaches a threshold value, it triggers the onset of DNA replication. This model was tested by simulation and when applied to the case of unequal division explains a number of features of an exponentially growing yeast cell population: (a) the lengths of TP (cycle time of parent cells) and TD (cycle time of daughter cells) verify the condition exp(- KTP ) + exp(- KTD ) = 1; (b) the changes of the average cell size of populations at different growth rates; (c) the frequency of parents and daughters at various growth rates; (d) the increase of cell size at bud initiation for cells of increasing genealogical age; (e) the existence of a TP - TB period (difference between the cycle time of parents and the length of budded phase) that depends linearly upon the doubling time of the population.

Cell cycle modelling

Models able to describe the events of cellular growth and division and the dynamics of cell populations are useful for the understanding of functional control mechanisms and for the theoretical support for automated analysis of flow cytometric data and of cell volume distributions. This paper reports on models that we have developed with this aim for different kinds of cells. The models are composed by two subsystems: one describes the growth dynamics of RNA and protein, and the second accounts for DNA replication and cell division, and describe in a rather unitary frame the cell cycle of eukaryotic cells, like mammalian cells and yeast, and of prokaryotic cells. The model is also used to study the effects of various sources of variability on the statistical properties of cell populations, and we find that in microbial cells the main source of variability appears to be an inaccuracy of the molecular mechanism that monitors cell size. In normal mammalian cells another source of variability, that depends upon the interaction with growth factors which give competence, is apparent. An extended version of the model, which comprises also this additional variability, is presented and used to describe the properties of mammalian cell growth.

A simulation program based on a structured population model for biotechnological yeast processes

SummaryA segregated population model for budding yeasts and a simulation program based on it are presented. They enable the study of bioprocesses utilizing yeasts in steady and perturbed conditions and in particular the comparison between the model predictions and the experimental results obtained by flow cytometry, which allows the measurement of segregated parameters of cell populations.

Analysis of a cell cycle model for Escherichia coli

SummaryRibosome and protein synthesis, DNA replication and cell division in Escherichia coli cells are described by a mathematical model that integrates previous descriptions in quantitative terms and proposes a new formalization to relate ribosome net synthesis to cell growth. The model assumes a cell size control of DNA replication and therefore is structurally divided into two subsystems: the first, whose state variables are ribosomes and protein, and the second, which is activated when the protein level reaches a threshold and which is comprised of DNA replication and cell division. The dynamics of the entire system is set only by the first subsystem: the values of its parameters determine whether the cells will be in a resting condition or will grow exponentially and in the latter case the resulting duplication time, while the structure and the parameter values of the second subsystem determine the size and the composition of the cell and the timing of DNA replication during the cycle. Relationships are derived that allow a simple determination of the time of initiation and of termination of DNA replication and the number of chromosome origins involved in any possible cell cycle as well as the macromolecular levels at the beginning of a cycle and on the average in a population of cells in balanced exponential growth.

ANALYSIS OF PROTEIN DISTRIBUTION IN POPULATIONS OF BUDDING YEAST BASED ON A STRUCTURED MODEL OF CELL GROWTH

Abstract Recent technological developments allow to measure segregated parameters of cell populations (cell size; protein, DNA, RNA content) on significant samples of the population (10 - 10 cells). To exploit these information and to develop control approaches based on these parameters, which are more directly related to the growth metabolism, it is necessary to use structured mathematical models of cell population. In the present paper a structured model able to describe cell growth and unequal division of budding yeast Saccharomyces cerevisiae is presented and from it age and size distributions for populations in exponential steady states of growth are derived. In several conditions the experimental protein distributions, obtained by flow cytometry, are shown to accurately fit those predicted by the model and to contain relevant information on the conditions of growth of the microbial biomass. These findings may have a predictive value on process dynamics being very sensitive to changes in synthesis and division rates, and may find a utilization in the development of new control approaches for microbial reactors.

Yeast Biotechnological Processes Monitored by Analysis of Segregated Data with Structured Models

Abstract Several biological parameters have been measured in populations of budding yeast growing in a glucose-limited chemostat, both in steady state and during perturbed growth conditions. The population structure has been determined with a segregated data analysis performed on protein distribution and on volume distributions. A new structured model for budding yeast population is presented, in which the entire system is described only in terms of critical cell mass parameters. This approach allows to integrate in a fairly simple way the population model with the bioreactor performance and to describe transient states of growth.

Generalized polynomial programming : Its approach to the solution of some management science problems

Abstract Generalized Polynomial Programming is used to obtain a numerical solution to some general problems in management science, modeled by discrete nonlinear systems with nonlinear performance indices, when the nonlinearities are modeled as generalized polynomials. Two general applications to the structural control in a graded manpower system and to advertising scheduling are considered. Numerical results are discussed.

Control of Continuous Fermentation Processes by Sliding Mode Design

Abstract Even if various linear control techniques have been used for continuous fermentation processes, which are intrinsically non-linear, it is generally acknowledged that the performance could be significantly improved by using non-linear control methods. In this paper, the variable structure control is considered and some examples of application to a fermentation process are shown by simulation. The proposed solutions are designed to achieve robustness against model uncertainties and to ensure chattering free control input. In fact, due to the process complexity, the model cannot be defined without some amount of uncertainty, and, due to physical constraints, the input variables are usually required to show a smooth behavior.

Structured Modeling and Parameter Identification of Budding Yeast Populations

The present paper investigates the possibility to obtain, from experimental data, reasonable and plausible parameter estimates of a particular model of budding yeast population, which accounts for unequal division and structural heterogeneity by genealogical age. The optimal parameter estimates are produced by fitting distributions predicted by the model to protein distributions obtained by flow-cytometry from steady-state cultures of S. cerevisiae at different growth conditions. Calculations were carried out, with the aid of a standard Levenberg-Marquardt algorithm for nonlinear least-squares, by minimizing the sum of squares between measured and simulated data. The best fit values provide information, related to the cell cycle, which satisfactorily agrees with previous experimental studies. Moreover, the reliability of the model is investigated through a statistical analysis based on the accuracy of estimation.

Mathematical Modelling of Cell Growth and Proliferation

Abstract Models able to describe the events of cellular growth and division and the dynamics of cell populations are useful for the understanding of control mechanisms and for theoretical support for the automated analysis of flow cytometric data and of cell volume distributions. This paper reports on models that have been developed by the Authors with this aim, describing in a rather unitary frame the cell cycle of eukaryotic cells, like mammalian cells and yeast, and of prokaryotic cells. The model is based on the assumption that the progression of the nuclear division cycle is regulated by a sequential attainment of two threshold protein levels. It accounts for a number of features of cell growth and division in population of actively growing cells, it explains all the different patterns of cell cycle which are experimentally found and yields quantitative relations between timing of the cell cycle and macromolecular composition of the cells. The model is also used to study the effect of various sources of variability on the statistical properties of cell populations and the main source of variability appears to be an inaccuracy of the molecular mechanism that monitors the cell size. Besides in normal mammalian cells a second source of variability is apparent, which depends upon the interaction with growth factors which give competence. An extended version of the model, which comprises also this additional variability, is also considered and used to describe properties of normal and transformed cell growth.