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

Washout and non-washout solutions of a system describing microbial fermentation process under the influence of growth inhibitions and maximal concentration of yeast cells

An unstructured model for the growth of yeast cell on glucose due to growth inhibitions by substrate, products, and cell density is discussed. The proposed model describes the dynamical behavior of fermentation system that shows multiple steady states for a certain regime of operating parameters such as inlet glucose and dilution rate. Two types of steady state solutions are found, namely washout and non-washout solutions. Furthermore, different numerical impositions to the two parameters put in evidence three results regarding non-washout solution: a unique locally stable non-washout solution, a unique locally stable non-washout solution towards which other nearby solutions exhibit damped oscillations, and multiple non-washout solutions where one is locally stable while the other is unstable. It is also found an optimal inlet glucose which produces the highest cell and ethanol concentration.

Application of statistical techniques for elucidating flow cytometric data of batch and fed-batch cultures

The objective of this work is to develop structured, segregated stochastic models for bioprocesses using time-series flow cytometric (FC) data. To this end, mammalian CHO cells were grown in both batch and fed-batch cultures, and their viable cell numbers (VCDs), monoclonal antibody (MAb), cell cycle phases, mitochondria membrane potential/mitochondria mass, Golgi apparatus, and endoplasmic reticulum (ER) were analyzed. For the fed-batch mode, soy hydrolysate was introduced at 24-H intervals. The cytometric data were analyzed for early indicators of growth and productivity by multiple linear regression analysis, which involved taking into account multicollinearity diagnostics, Durbin-Watson statistics, and Houston tests to determine and refine statistically significant correlations between categorical variables (FC parameters) and response variables (yield parameters). The results indicate that the percentage of G1 cells and ER was significantly correlated with VCD and MAb in the case of batch culture, whereas for fed-batch culture, the percentage of G2 cells and ER was correlated significantly. There was a significant difference between cells in the batch and fed-batch cultures in their ER content, suggesting that the increase in protein synthesis as reflected by the ER content and consequent increase in growth rate and MAb productivity both can be monitored at the cellular level by FC analysis of ER content.

THE EFFECT OF THE ORGANISMS' BODY SIZE AND ENERGY RESERVES IN MODELS FOR POPULATION DYNAMICS

We present two models suitable for describing dynamics of a population of unicellular organisms residing in chemostat. These models are based on biologically motivated Dynamic Energy Budget (DEB) theory and take into account the dynamics of mean energy reserves and body length of organisms in the population. The difference between the models is in the construction of the reproduction rate. In model A it is the ordinary reproduction rate used in DEB theory. In model B it is adjusted to take into account a saturation effect in the dynamics of mean body length. Our modeling approach is illustrated by considering population of E. coli developing in the chemostat. We consider realistic situations of growth of population of E. coli at fixed and varied environmental and biological factors. We show that unlike model B in model A the dynamics of body length does not affect directly population development. Nevertheless, taking such dynamics into account is essential in both models since it provides additional constrains to population development. The models can be easily extended to include description of individual characteristics other than body size (e.g., reproduction rate, mortality rate). The models predict two types of transient dynamics: one type is similar to that in a logistic model; the other type is damped oscillations. The essential difference between the models is that model B better predicts the extinction threshold of the population.

A Simple Unforced Oscillatory Growth Model in the Chemostat

In a chemostat, transient oscillations in cell number density are often experimentally observed during cell growth. The aim of this paper is to propose a simple autonomous model which is able to generate these oscillations, and to investigate it analytically. Our point of view is based on a simplification of the cell cycle in which there are two states (mature and immature) with the transfer between the two dependent on the available resources. We use the mathematical global properties of competitive differential systems to prove the existence of a limit cycle. A comparison between our model and a more complex model consisting of partial differential equations is made with the help of numerical simulations, giving qualitatively similar results.

Morphologically-structured models of growing budding yeast populations

It has been well recognized that many key aspects of cell cycle regulation are encoded into the size distributions of growing budding yeast populations due to the tight coupling between cell growth and cell division present in this organism. Several attempts have been made to model the cell size distribution of growing yeast populations in order to obtain insight on the underlying control mechanisms, but most were based on the age structure of asymmetrically dividing populations. Here we propose a new framework that couples a morphologically-structured representation of the population with population balance theory to formulate a dynamic model for the size distribution of growing yeast populations. An advantage of the presented framework is that it allows derivation of simpler models that are directly identifiable from experiments. We show how such models can be derived from the general framework and demonstrate their utility in analyzing yeast population data. Finally, by employing a recently proposed numerical scheme, we proceed to integrate numerically the full distributed model to provide predictions of dynamics of the cell size structure of growing yeast populations.

Hxt-carrier-mediated glucose efflux upon exposure of Saccharomyces cerevisiae to excess maltose

When wild-type Saccharomyces cerevisiae strains pregrown in maltose-limited chemostat cultures were exposed to excess maltose, release of glucose into the external medium was observed. Control experiments confirmed that glucose release was not caused by cell lysis or extracellular maltose hydrolysis. To test the hypothesis that glucose efflux involved plasma membrane glucose transporters, experiments were performed with an S. cerevisiae strain in which all members of the hexose transporter (HXT) gene family had been eliminated and with an isogenic reference strain. Glucose efflux was virtually eliminated in the hexose-transport-deficient strain. This constitutes experimental proof that Hxt transporters facilitate export of glucose from S. cerevisiae cells. After exposure of the hexose-transport-deficient strain to excess maltose, an increase in the intracellular glucose level was observed, while the concentrations of glucose 6-phosphate and ATP remained relatively low. These results demonstrate that glucose efflux can occur as a result of uncoordinated expression of the initial steps of maltose metabolism and the subsequent reactions in glucose dissimilation. This is a relevant phenomenon for selection of maltose-constitutive strains for baking and brewing.

A size-structured, non-conservative ODE model of the chemostat

We study a class of size-structured, ODE models of growth in the chemostat, that take into account cell maintenance and substrate dependent cell mortality. Unlike most classical chemostat models, they are supposed to be non-conservative, in the sense that they do not verify the mass conservation principle. However, using a change of time scale, we are able to obtain qualitative results. Then, using a Lyapunov functional, we prove the global stability of the non-trivial equilibrium. Some examples of the possible structure of the models are given to finish with.

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.

Population balance models of autonomous microbial oscillations

Autonomous oscillations in continuous microbial cultures is well documented for the case of baker's yeast, Saccharomyces cerevisiae, for which it has been observed under a range of operating conditions. We have found that autonomous microbial oscillations can be modeled by unstructured population balance models in which a key cell cycle parameter is a function of the environmental conditions, e.g., the concentration of a substrate or product. Although these models are remarkably simple, they can display a wide range of dynamic behaviors. These behaviors include, for binary fission organisms, solutions containing a single synchronous population and, for budding yeasts, two synchronized subpopulations with a period of oscillation similar to that of the cell cycle length, a pattern that has been observed experimentally in S. cerevisiae. Numerical simulations of the model equations also show that complex periodic solutions with periods very different from the cell cycle length are possible. The ability of the population balance approach to accurately describe the available data of yeast culture dynamics will be discussed.