A population balance model describing the cell cycle dynamics of myeloma cell cultivation

A multi-staged population balance model is proposed to describe the cell cycle dynamics of myeloma cell cultivation. In this model, the cell cycle is divided into three stages, i.e., G1, S, and G2M phases. Both DNA content and cell volume are used to differentiate each cell from other cells of the population. The probabilities of transition from G1 to S and division of G2M are assumed to be dependent on cell volume, and transition probability from S to G2M is determined by DNA content. The model can be used to simulate the dynamics of DNA content and cell volume distributions, phase fractions, and substrate and byproduct concentrations, as well as cell densities. Measurements from myeloma cell cultivations, especially the FACS data with respect to DNA distribution and cell fractions in different stages, are employed for model validation.     

Synchronized mammalian cell culture: Part II—population ensemble modeling and analysis for development of reproducible processes

The consideration of inherent population inhomogeneities of mammalian cell cultures becomes increasingly important for systems biology study and for developing more stable and efficient processes. However, variations of cellular properties belonging to different sub‐populations and their potential effects on cellular physiology and kinetics of culture productivity under bioproduction conditions have not yet been much in the focus of research. Culture heterogeneity is strongly determined by the advance of the cell cycle. The assignment of cell‐cycle specific cellular variations to large‐scale process conditions can be optimally determined based on the combination of (partially) synchronized cultivation under otherwise physiological conditions and subsequent population‐resolved model adaptation. The first step has been achieved using the physical selection method of countercurrent flow centrifugal elutriation, recently established in our group for different mammalian cell lines which is presented in Part I of this paper series. In this second part, we demonstrate the successful adaptation and application of a cell‐cycle dependent population balance ensemble model to describe and understand synchronized bioreactor cultivations performed with two model mammalian cell lines, AGE1.HN_AAT and CHO‐K1. Numerical adaptation of the model to experimental data allows for detection of phase‐specific parameters and for determination of significant variations between different phases and different cell lines. It shows that special care must be taken with regard to the sampling frequency in such oscillation cultures to minimize phase shift (jitter) artifacts. Based on predictions of long‐term oscillation behavior of a culture depending on its start conditions, optimal elutriation setup trade‐offs between high cell yields and high synchronization efficiency are proposed. © 2014 American Institute of Chemical Engineers Biotechnol. Prog., 31:175–185, 2015     

Towards understanding of the complex structure of growing yeast populations

In a growing Saccharomyces cerevisiae population, cell size is finely modulated according to both the chronological and genealogical ages. This generates the complex heterogeneous structure typical of budding yeast populations. In recent years, there has been a growing interest in developing mathematical models capable of faithfully describing population dynamics at the single cell level. A multistaged morphologically structured model has been lately proposed based on the population balance theory. The model was able to describe the dynamics of the generation of a heterogeneous growing yeast population starting from a sub-population of daughter unbudded cells. In this work, which aims at validating the model, the simulated experiment was performed by following the release of a homogeneous population of daughter unbudded cells. A biparametric flow cytometric approach allowed us to analyse the time course joint distribution of DNA and protein contents at the single cell level; this gave insights into the coupling between growth and cell cycle progression that generated the final population structure. The comparison between experimental and simulated size distributions revealed a strong agreement for some unexpected features as well. Therefore, the model can be considered as validated and extendable to more complex situations.     

In vitro ovine articular chondrocyte proliferation: experiments and modelling

This study focuses on analysis of in vitro cultures of chondrocytes from ovine articular cartilage. Isolated cells were seeded in Petri dishes, then expanded to confluence and phenotypically characterized by flow cytometry. The sigmoidal temporal profile of total counts was obtained by classic haemocytometry and corresponding cell size distributions were measured electronically using a Coulter Counter. A mathematical model recently proposed ( 1 ) was adopted for quantitative interpretation of these experimental data. The model is based on a 1‐D (that is, mass‐structured), single‐staged population balance approach capable of taking into account contact inhibition at confluence. The model’s parameters were determined by fitting measured total cell counts and size distributions. Model reliability was verified by predicting cell proliferation counts and corresponding size distributions at culture times longer than those used when tuning the model’s parameters. It was found that adoption of cell mass as the intrinsic characteristic of a growing chondrocyte population enables sigmoidal temporal profiles of total counts in the Petri dish, as well as cell size distributions at ‘balanced growth’, to be adequately predicted.     

Implementation of a Fully Automated Microbial Cultivation Platform for Strain and Process Screening

Advances in molecular biotechnology have resulted in the generation of numerous potential production strains. Because every strain can be screened under various process conditions, the number of potential cultivations is multiplied. Exploiting this potential without increasing the associated timelines requires a cultivation platform that offers increased throughput and flexibility to perform various bioprocess screening protocols. Currently, there is no commercially available fully automated cultivation platform that can operate multiple microbial fed‐batch processes, including at‐line sampling, deep freezer off‐line sample storage, and complete data handling. To enable scalable high‐throughput early‐stage microbial bioprocess development, a commercially available microbioreactor system and a laboratory robot are combined to develop a fully automated cultivation platform. By making numerous modifications, as well as supplementation with custom‐built hardware and software, fully automated milliliter‐scale microbial fed‐batch cultivation, sample handling, and data storage are realized. The initial results of cultivations with two different expression systems and three different process conditions are compared using 5 L scale benchmark cultivations, which provide identical rankings of expression systems and process conditions. Thus, fully automated high‐throughput cultivation, including automated centralized data storage to significantly accelerate the identification of the optimal expression systems and process conditions, offers the potential for automated early‐stage bioprocess development.     

Quantitative studies of bacterial chemotaxis and microbial population dynamics

Although there is a long history of conjecture regarding the role and significance of bacterial chemotaxis in microbial ecology, only recently has a significant body of work appeared attempting to address this issue. The purpose of this paper is to provide a concise overview of this work, which combined mathematical modeling of bacterial population migration and experimental measurement of the model parameters with modeling of competitive microbial population dynamics in a nonmixed environment. Predictions from the population dynamics models, based on experimental estimates of the various motility and growth parameter values, are related to the small number of experimental observations available to date dealing with the effects of bacterial motility on competition in a nonmixed environment. Current results indicate that cell motility and chemotaxis properties can be as important to population dynamics as cell growth kinetic properties, so that greater attention to this aspect of microbial behavior is warranted in future studies of microbial ecology.     

Modeling and optimization of alpha-amylase production in a recombinant yeast fed-batch culture taking account of the cell cycle population distribution.

A simple mathematical model describing the cell cycle dependency of rice alpha-amylase production by a recombinant yeast was constructed to investigate the efficiency of cell cycle population control. First, the effects of the glucose concentration and cultivation temperature on the specific growth rate, the specific production rate of rice alpha-amylase, and the distribution of the cell cycle population were studied under balanced growth conditions. On the basis of the results, parameter values for the mathematical model were then estimated. The proposed model was shown to be applicable for unbalanced as well as balanced growth phases. The optimal control strategy in respect of temperature and glucose concentration for maximum rice alpha-amylase production, taking into account the cell cycle population, was determined and the result was compared with that obtained by a simple mathematical model in which cell cycle distribution was not considered. Finally, the effect of the initial population of each cell cycle phase on the final amount of the product under optimal operational conditions was investigated. The simulation and experimental data coincided well with each other, and the model was used to optimize the control strategy for maximum alpha-amylase production.     

Simulation of penicillin production in fed-batch cultivations using a morphologically structured model

A mathematical model is formulated to describe trends in biomass and penicillin formation as well as substrate consumption for fed-batch cultivations. The biomass is structured into three morphological compartments, and glucose and corn steep liquor are considered as substrates for growth. Penicillin formation is assumed to take place in the subapical compartment and in the growing region of the hyphal compartment. Furthermore, it is inhibited by glucose. Model parameters are estimated using an evolutionary algorithm and fitting the model to a standard fed-batch cultivation. The model is validated on experimental data from three different fed-batch cultivations, including two repeated fed-batch cultivations. The model predictions show good agreement with the measurements of biomass and pencillin concentrations for all fed-batch cultivations. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 56: 593-604, 1997.     

The MYpop toolbox: Putting yeast stress responses in cellular context on single cell and population scales

Systems biology holds the promise to integrate multiple sources of information in order to build ever more complete models of cellular function. To do this, the field must overcome two significant challenges. First, the current strategy to model average cells must be replaced with population based models accounting for cell‐to‐cell variability. Second, models must be integrated with each other and with basic cellular function. This requires a core model of cellular physiology as well as a multiscale simulation platform to support large‐scale simulation of culture or tissues from single cells. Here, we present such a simulation platform with a core model of yeast physiology as scaffold to integrate and simulate SBML models. The software automates this integration helping users simulate their model of choice in context of the cell division cycle. We benchmark model merging, simulation and analysis by integrating a minimal model of osmotic stress into the core model and analyzing it. We characterize the effect of single cell differences on the dynamics of osmoadaptation, estimating when normal cell growth is resumed and obtaining an explanation for experimentally observed glycerol dynamics based on population dynamics. Hence, the platform can be used to reconcile single cell and population level data.     

Kinetics of microbial cell growth

As a rate equation of microbial cell growth, the Monod equation is widely used. However, this equation cannot fully correspond to real courses of microbial cell growth in many batch cultivations. Especially, predicted values based on this equation do not agree with observed values in many continuous cultivations. In this paper, which introduces new concepts of critical concentration and coefficient of consumption activity, the growth rate equation which corresponds to the whole period including lag period is newly derived and characteristics of microbial cell growth in batch cultivation are clarified. Further, applying the new rate equation to continuous cultivation, a general equation with which to calculate cell concentration is derived and characteristics of microbial cell growth in continuous cultivation are clarified. The calculated values of cell concentration based on the new theory showed quite good agreement with the observed values in both batch and continuous cultivation.     

Competition between two microbial populations in a sequencing fed-batch reactor: theory, experimental verification, and implications for waste treatment applications

Competition between two microbial populations for a single pollutant (phenol) was studied in a sequencing fed-batch reactor (SFBR). A mathematical model describing this system was developed and tested experimentally. It is based on specific growth rate expressions revealed from pure culture batch experiments. The species employed were Pseudomonas putida (ATCC 17514) and Pseudomonas resinovorans (ATCC 14235). It was found that both species biodegrade phenol following inhibitory kinetics which can be described by Andrews' expression. The model predicts that the dynamics of a SFBR, and the kinetics of biodegradation, result in a complex set of operating regimes in which neither species, only one species, or both species can survive at steady cycle. The model also predicts the existence of multiple outcomes, achievable from different start-up conditions, in some domains of the operating parameter space. Experimental results confirmed the model predictions. There was excellent agreement between predicted and measured concentrations of phenol, total biomass, and the biomass of each individual species. This study shows how serious discrepancies can arise in scale-up of biodegradation data if population dynamics are not taken into account. It also further confirms experimentally the theory of microbial competition in periodically forced bioreactors. (c) 1993 John Wiley & Sons, Inc.     

Process-induced cell cycle oscillations in CHO cultures: Online monitoring and model-based investigation

The influence of process strategies on the dynamics of cell population heterogeneities in mammalian cell culture is still not well understood. We recently found that the progression of cells through the cell cycle causes metabolic regulations with variable productivities in antibody-producing Chimese hamster ovary (CHO) cells. On the other hand, it is so far unknown how bulk cultivation conditions, for example, variable nutrient concentrations depending on process strategies, can influence cell cycle-derived population dynamics. In this study, process-induced cell cycle synchronization was assessed in repeated-batch and fed-batch cultures. An automated flow cytometry set-up was developed to measure the cell cycle distribution online, using antibody-producing CHO DP-12 cells transduced with the cell cycle-specific fluorescent ubiquitination-based cell cycle indicator (FUCCI) system. On the basis of the population-resolved model, feeding-induced partial self-synchronization was predicted and the results were evaluated experimentally. In the repeated-batch culture, stable cell cycle oscillations were confirmed with an oscillating G1 phase distribution between 41% and 72%. Furthermore, oscillations of the cell cycle distribution were simulated and determined in a (bolus) fed-batch process with up to cells/ml. The cell cycle synchronization arose with pulse feeding only and ceased with continuous feeding. Both simulated and observed oscillations occurred at higher frequencies than those observable based on regular (e.g., daily) sample analysis, thus demonstrating the need for high-frequency online cell cycle analysis. In summary, we showed how experimental methods combined with simulations enable the improved assessment of the effects of process strategies on the dynamics of cell cycle-dependent population heterogeneities. This provides a novel approach to understand cell cycle regulations, control cell population dynamics, avoid inadvertently induced oscillations of cell cycle distributions and thus to improve process stability and efficiency.     

Proteomic tracking and analysis of a bacterial mixed culture

To improve the understanding of microbial behaviors in communities, proteomic tracking, an approach for relative quantification of species-specific population dynamics of mixed cultures, was developed. Therefore, a bacterial mixed culture was analyzed during batch cultivations with and without addition of the antibiotic Ceftazidime. The community was composed of Burkholderia cepacia, Pseudomonas aeruginosa, and Staphylococcus aureus, pathogens causing infections in cystic fibrosis patients. Gel-based proteomics and mass spectrometry were used to obtain qualitative and quantitative proteomic data. During cultivation, P. aeruginosa became dominant within the mixed culture while S. aureus was inhibited in growth. Analysis of samples - taken along cultivation - revealed about 270 differentially expressed proteins. Some of those proteins are related to bacterial interactions, response to antibiotic treatment or metabolic shifts. For instance, the enzymes PhzS(flavin-containing monooxygenase), PhzD (phenazine biosynthesis protein), and PhzG2 (pyridoxamine 5'-phosphate oxidase) indicated the production of the antibiotic pigment pyocyanine by P. aeruginosa that is related to oxidative stress and therefore, might inhibit growth of S. aureus. Overall, the strategy applied not only allows species-specific tracking of the community composition but also provides valuable insights into the behavior of mixed cultures.     

Steady-State growth of budding yeast populations in well-mixed continous-flow microbial reactors

A population-balance mathematical model of microbial growth in a flow reactor is formulated which incorporates an asymmetric-division, budding-cycle model of coordinated cell and nuclear division cycles for the budding yeast Saccharomyces cerevisiae. Analytical solutions are obtained for limiting nutrient and cell-number concentrations in the reactor as functions of basic cell cycle parameters. Frequency functions for cell mass and DNA content in the resident yeast population are also derived under different assumptions concerning cell mass and DNA synthesis and bud scar accumulation. These results, which correspond to experimentally observable medium and population variables, provide new bases for evaluating budding-yeast-cell cycle models and for deducing kinetics of mass and DNA synthesis in single cells growing in steady-state, asynchronous populations.     

Coordinated Development of Yeast Colonies: Quantitative Modeling of Diffusion‐Limited Growth – Part 2

A mathematical model was developed which described the growth of yeast colonies based on the assumptions that (i) these populations were built up of single cells whose proliferation was (ii) exclusively controlled by nutrient availability in the environment. The model was of a hybrid cellular automaton type and described discrete cells residing on a one‐dimensional lattice as well as on continuously distributed nutrients. Experimental results and numerical calculations were compared to elucidate under which cultivation conditions the diffusion‐limited growth (DLG) was the major construction principle in yeast colonies. Simulations were scaled to the growth of Yarrowia lipolytica and Candida boidinii colonies under carbon and nitrogen limitation. They showed that nutrient‐controlled growth of the individual cells resulted in DLG of the population. Quantitative predictions for the spatio‐temporal development of the cell‐density profile inside a growing yeast mycelium were compared to the growth characteristics of the model yeast mycelia. Only for the carbon‐limited growth of C. boidinii colonies on glucose as the limiting nutrient resource did the DLG model reproduce the cell‐density profile estimated at the end of the cultivation. Under all other cultivation conditions, strong discrepancies between calculations and experimental results were evident precluding DLG as the ruling regulatory mechanism. Thus, whether or not the development of a yeast population could be described by a DLG scenario, was strongly dependent on the particular cultivation conditions and the applied yeast species. In those cases for which the DLG hypothesis failed to explain the observed growth patterns, the underlying assumptions, i.e., the complete absence of nutrient translocation between the individual cells inside the yeast mycelia as well as the exclusively nutrient‐controlled proliferation of the cells, have to be reevaluated. The presented study demonstrated how the mathematical analysis of growth processes in yeast populations could assist the experimental identification of potential regulatory mechanisms.     

Analytical Quantile Solution for the S‐distribution,Random Number Generation and Statistical Data Modeling

The selection of a specific statistical distribution as a model for describing the population behavior of a given variable is seldom a simple problem. One strategy consists in testing different distributions (normal, lognormal, Weibull, etc.), and selecting the one providing the best fit to the observed data and being the most parsimonious. Alternatively, one can make a choice based on theoretical arguments and simply fit the corresponding parameters to the observed data. In either case, different distributions can give similar results and provide almost equivalent models for a given data set. Model selection can be more complicated when the goal is to describe a trend in the distribution of a given variable. In those cases, changes in shape and skewness are difficult to represent by a single distributional form. As an alternative to the use of complicated families of distributions as models for data, the S‐distribution [Voit, E. O. (1992) Biom. J. 7 , 855–878] provides a highly flexible mathematical form in which the density is defined as a function of the cumulative. S‐distributions can accurately approximate many known continuous and unimodal distributions, preserving the well known limit relationships between them. Besides representing well‐known distributions, S‐distributions provide an infinity of new possibilities that do not correspond with known classical distributions. Although the utility and performance of this general form has been clearly proved in different applications, its definition as a differential equation is a potential drawback for some problems. In this paper we obtain an analytical solution for the quantile equation that highly simplifies the use of S‐distributions. We show the utility of this solution in different applications. After classifying the different qualitative behaviors of the S‐distribution in parameter space, we show how to obtain different S‐distributions that accomplish specific constraints. One of the most interesting cases is the possibility of obtaining distributions that acomplish P(X ≤ X_c) = 0. Then, we demonstrate that the quantile solution facilitates the use of S‐distributions in Monte‐Carlo experiments through the generation of random samples. Finally, we show how to fit an S‐distribution to actual data, so that the resulting distribution can be used as a statistical model for them.