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     

INSTAR,a discrete event model for simulating zooplankton population dynamics

In this paper we discuss the basic principles of discrete event, individual oriented, data based modelling in ecology, and we present an application of this modelling strategy. The strategy is contrasted with some more conventional modelling strategies with respect to its purpose, its basic units and its heuristic properties.INSTAR applies this modelling strategy to the simulation of the fluctuations of the population structure and density of microcrustaceans through the year. The model encompasses one microcrustacean species at a time, and its interface with the rest of the ecosystem; it has been applied to several Cladocera and Copepoda species in a shallow eutrophic lake in the Netherlands (Vijverberg & Richter 1982a, b). Possibilities for extending the model are discussed.     

Combining Gompertzian growth and cell population dynamics

A two-compartment model of cancer cells population dynamics proposed by Gyllenberg and Webb includes transition rates between proliferating and quiescent cells as non-specified functions of the total population, N. We define the net inter-compartmental transition rate function: Phi(N). We assume that the total cell population follows the Gompertz growth model, as it is most often empirically found and derive Phi(N). The Gyllenberg-Webb transition functions are shown to be characteristically related through Phi(N). Effectively, this leads to a hybrid model for which we find the explicit analytical solutions for proliferating and quiescent cell populations, and the relations among model parameters. Several classes of solutions are examined. Our model predicts that the number of proliferating cells may increase along with the total number of cells, but the proliferating fraction appears to be a continuously decreasing function. The net transition rate of cells is shown to retain direction from the proliferating into the quiescent compartment. The death rate parameter for quiescent cell population is shown to be a factor in determining the proliferation level for a particular Gompertz growth curve.     

Distributed modeling of human influenza a virus–host cell interactions during vaccine production

This contribution is concerned with population balance modeling of virus–host cell interactions during vaccine production. Replication of human influenza A virus in cultures of adherent Madin–Darby canine kidney (MDCK) cells is considered as a model system. The progress of infection can be characterized by the intracellular amount of viral nucleoprotein (NP) which is measured via flow cytometry. This allows the differentiation of the host cell population and gives rise to a distributed modeling approach. For this purpose a degree of fluorescence is introduced as an internal coordinate which is linearly linked to the intracellular amount of NP. Experimental results for different human influenza A subtypes reveal characteristic dynamic phenomena of the cell distribution like transient multimodality and reversal of propagation direction. The presented population balance model provides a reasonable explanation for these dynamic phenomena by the explicit consideration of different states of infection of individual cells. Kinetic parameters are determined from experimental data. To translate the emerging infinite dimensional parameter estimation problem to a finite dimension the parameters are assumed to depend linearly on the internal coordinate. As a result, the model is able to reproduce all characteristic dynamic phenomena of the considered process for the two examined virus strains and allows deeper insight into the underlying kinetic processes. Thus, the model is an important contribution to the understanding of the intracellular virus replication and virus spreading in cell cultures and can serve as a stepping stone for optimization in vaccine production. Biotechnol. Bioeng. 2013; 110: 2252–2266. © 2013 Wiley Periodicals, Inc.     

Computational modeling of combined cell population dynamics and oxygen transport in engineered tissue subject to interstitial perfusion

This work presents a computational model of tissue growth under interstitial perfusion inside a tissue engineering bioreactor. The model accounts both for the cell population dynamics, using a model based on cellular automata, and for the hydrodynamic microenvironment imposed by the bioreactor, using a model based on the Lattice–Boltzmann equation and the convection-diffusion equation. The conditions of static culture versus perfused culture were compared, by including the population dynamics along with oxygen diffusion, convective transport and consumption. The model is able to deal with arbitrary complex geometries of the spatial domain; in the present work, the domain modeled was the void space of a porous scaffold for tissue-engineered cartilage. The cell population dynamics algorithm provided results which qualitatively resembled population dynamics patterns observed in experimental studies, and these results were in good quantitative agreement with previous computational studies. Simulation of oxygen transport and consumption showed the fundamental contribution of convective transport in maintaining a high level of oxygen concentration in the whole spatial domain of the scaffold. The model was designed with the aim to be computationally efficient and easily expandable, i.e. to allow straightforward implementability of further models of complex biological phenomena of increasing scientific interest in tissue engineering, such as chemotaxis, extracellular matrix deposition and effect of mechanical stimulation.     

Integration of stochastic simulation with multivariate analysis: Short‐term facility fit prediction

This article describes a decision‐support tool to help pinpoint the potential root causes of sub‐optimal short‐term facility fit issues in biopharmaceutical facilities. This was achieved by creating a tool that integrated stochastic simulation with advanced multivariate statistical analysis. Process fluctuations in product titers in cell culture, step yields, and chromatography eluate volumes were mimicked using Monte Carlo simulation data derived using a stochastic discrete‐event simulation model. The resulting stochastic datasets, with the computed consequences on key metrics such as product mass loss and cost of goods, were examined using advanced multivariate statistical techniques. Principal component analysis combined with clustering algorithms was used to analyze the complex datasets from complete industrial batch processes for biopharmaceuticals. The challenge of visualizing the multidimensional nature of the dataset was addressed using hierarchical and k‐means clustering as well as stacked parallel co‐ordinate plots to help identify process fingerprints and characteristics of clusters leading to sub‐optimal facility fit issues. Industrially‐relevant case studies are presented that focus on technology transfer challenges for therapeutic antibodies moving from early phase to late phase clinical trials. The case study details how sub‐optimal facility fit can be alleviated by allocating alternative product pool tanks. The impact of this operational change is then assessed by reviewing an updated process fingerprint. © 2013 American Institute of Chemical Engineers Biotechnol. Prog., 29: 368–377, 2013     

An integrated modeling approach to estimating Gunnison sage‐grouse population dynamics: combining index and demographic data

Evaluation of population dynamics for rare and declining species is often limited to data that are sparse and/or of poor quality. Frequently, the best data available for rare bird species are based on large‐scale, population count data. These data are commonly based on sampling methods that lack consistent sampling effort, do not account for detectability, and are complicated by observer bias. For some species, short‐term studies of demographic rates have been conducted as well, but the data from such studies are typically analyzed separately. To utilize the strengths and minimize the weaknesses of these two data types, we developed a novel Bayesian integrated model that links population count data and population demographic data through population growth rate (λ) for Gunnison sage‐grouse (Centrocercus minimus). The long‐term population index data available for Gunnison sage‐grouse are annual (years 1953–2012) male lek counts. An intensive demographic study was also conducted from years 2005 to 2010. We were able to reduce the variability in expected population growth rates across time, while correcting for potential small sample size bias in the demographic data. We found the population of Gunnison sage‐grouse to be variable and slightly declining over the past 16 years.     

A population‐based temporal logic gate for timing and recording chemical events

Engineered bacterial sensors have potential applications in human health monitoring, environmental chemical detection, and materials biosynthesis. While such bacterial devices have long been engineered to differentiate between combinations of inputs, their potential to process signal timing and duration has been overlooked. In this work, we present a two‐input temporal logic gate that can sense and record the order of the inputs, the timing between inputs, and the duration of input pulses. Our temporal logic gate design relies on unidirectional DNA recombination mediated by bacteriophage integrases to detect and encode sequences of input events. For an E. coli strain engineered to contain our temporal logic gate, we compare predictions of Markov model simulations with laboratory measurements of final population distributions for both step and pulse inputs. Although single cells were engineered to have digital outputs, stochastic noise created heterogeneous single‐cell responses that translated into analog population responses. Furthermore, when single‐cell genetic states were aggregated into population‐level distributions, these distributions contained unique information not encoded in individual cells. Thus, final differentiated sub‐populations could be used to deduce order, timing, and duration of transient chemical events.     

A population balance equation model of aggregation dynamics in Taxus suspension cell cultures

The nature of plant cells to grow as multicellular aggregates in suspension culture has profound effects on bioprocess performance. Recent advances in the measurement of plant cell aggregate size allow for routine process monitoring of this property. We have exploited this capability to develop a conceptual model to describe changes in the aggregate size distribution that are observed over the course of a Taxus cell suspension batch culture. We utilized the population balance equation framework to describe plant cell aggregates as a particulate system, accounting for the relevant phenomenological processes underlying aggregation, such as growth and breakage. We compared model predictions to experimental data to select appropriate kernel functions, and found that larger aggregates had a higher breakage rate, biomass was partitioned asymmetrically following a breakage event, and aggregates grew exponentially. Our model was then validated against several datasets with different initial aggregate size distributions and was able to quantitatively predict changes in total biomass and mean aggregate size, as well as actual size distributions. We proposed a breakage mechanism where a fraction of biomass was lost upon each breakage event, and demonstrated that even though smaller aggregates have been shown to produce more paclitaxel, an optimum breakage rate was predicted for maximum paclitaxel accumulation. We believe this is the first model to use a segregated, corpuscular approach to describe changes in the size distribution of plant cell aggregates, and represents an important first step in the design of rational strategies to control aggregation and optimize process performance.     

Agent-based modeling of the context dependency in T cell recognition

Antigen recognition by T cells is a key event in the adaptive immune response. T cells scan the surface of antigen-presenting cells (APCs) or target cells for specific peptides bound to MHC molecules. In the physiological setting, a typical APC presents tens of thousands of diverse endogenous self-derived peptides complexed to MHC (pMHC complexes). When 'foreign' peptides are presented, they constitute a small fraction of the total surface peptide repertoire. As T cells seem to be capable of discerning minute amounts of 'foreign' peptides among a complex background of self-peptides, endogenous peptides are generally assumed to play no role in recognition. However, recent results suggest that these background peptides may alter the sensitivity of T cells to foreign peptides. Current experimental limitations preclude analysis of peptide mixtures approaching physiological complexity, making it difficult to further address the role of complex background peptides. In this paper, we present a computational model to test how complex, varied peptide populations on an APC could potentially modulate a T cell's ability to detect the presence of small numbers of agonist peptides among a diverse population. We use the model to investigate the notion that under physiological conditions, T cell recognition of foreign peptides is context dependent, that is, T cells process signals gathered from all pMHC interactions, not just from a few agonist peptides while ignoring all others.     

A stochastic discrete generation birth,continuous death population growth model and its approximate solution

This paper describes a single species growth model with a stochastic population size dependent number of births occurring at discrete generation times and a continuous population size dependent death rate. An integral equation for a suitable transformation of the limiting population size density function is not in general soluble, but a Gram-Charlier representation procedure, previously used in storage theory, is successfully extended to cover this problem. Examples of logistic and Gompertz type growth are used to illustrate the procedure, and to compare with growth models in random environments. Comments on the biological consequences of these models are also given.Currently at Department of Mathematics, University of MarylandWork partially supported by the Danish Natural Science Research Council and Monash University     

Individual‐based modelling of resource competition to predict density‐dependent population dynamics: a case study with white storks

Density regulation influences population dynamics through its effects on demographic rates and consequently constitutes a key mechanism explaining the response of organisms to environmental changes. Yet, it is difficult to establish the exact form of density dependence from empirical data. Here, we developed an individual‐based model to explore how resource limitation and behavioural processes determine the spatial structure of white stork Ciconia ciconia populations and regulate reproductive rates. We found that the form of density dependence differed considerably between landscapes with the same overall resource availability and between home range selection strategies, highlighting the importance of fine‐scale resource distribution in interaction with behaviour. In accordance with theories of density dependence, breeding output generally decreased with density but this effect was highly variable and strongly affected by optimal foraging strategy, resource detection probability and colonial behaviour. Moreover, our results uncovered an overlooked consequence of density dependence by showing that high early nestling mortality in storks, assumed to be the outcome of harsh weather, may actually result from density dependent effects on food provision. Our findings emphasize that accounting for interactive effects of individual behaviour and local environmental factors is crucial for understanding density‐dependent processes within spatially structured populations. Enhanced understanding of the ways animal populations are regulated in general, and how habitat conditions and behaviour may dictate spatial population structure and demographic rates is critically needed for predicting the dynamics of populations, communities and ecosystems under changing environmental conditions.     

Asymptotic behavior of some stochastic difference equation population models

We consider a general class of Markov population models formulated as stochastic difference equations. The population density is shown to converge either to 0, to +, or to a unique stationary distribution concentrated on (0, +), depending on the signs of the mean log growth rates near 0 and +. These results are applied to the Watkinson-MacDonald bottleneck model of annual plants with a seedbank, extended to allow for random environmental fluctuations and competition among co-occurring species. We obtain criteria for long-term persistence of single-species populations, and for coexistence of two competing species, and the biological significance of the criteria is discussed. The lamentably few applications to the problem at hand of classical limit-theory for Markov chains are surveyed.     

Progress toward forecasting product quality and quantity of mammalian cell culture processes by performance‐based modeling

The production of biopharmaceuticals requires highly sophisticated, complex cell based processes. Once a process has been developed, acceptable ranges for various control parameters are typically defined based on process characterization studies often comprising several dozens of small scale bioreactor cultivations. A lot of data is generated during these studies and usually only the information needed to define acceptable ranges is processed in more detail. Making use of the wealth of information contained in such data sets, we present here a methodology that uses performance data (such as metabolite profiles) to forecast the product quality and quantity of mammalian cell culture processes based on a toolbox of advanced statistical methods. With this performance based modeling (PBM) the final product concentration and 12 quality attributes (QAs) for two different biopharmaceutical products were predicted in daily intervals throughout the main stage process. The best forecast was achieved for product concentration in a very early phase of the process. Furthermore, some glycan isoforms were predicted with good accuracy several days before the bioreactor was harvested. Overall, PBM clearly demonstrated its capability of early process endpoint prediction by only using commonly available data, even though it was not possible to predict all QAs with the desired accuracy. Knowing the product quality prior to the harvest allows the manufacturer to take counter measures in case the forecasted quality or quantity deviates from what is expected. This would be a big step towards real‐time release, an important element of the FDA's PAT initiative. © 2015 American Institute of Chemical Engineers Biotechnol. Prog., 31:1119–1127, 2015     

A stochastic model of a cell population with quiescence

A cell population in which cells are allowed to enter a quiescent (nonproliferating) phase is analyzed using a stochastic approach. A general branching process is used to model the population which, under very mild conditions, exhibits balanced exponential growth. A formula is given for the asymptotic fraction of quiescent cells, and a numerical example illustrates how convergence toward the asymptotic fraction exhibits a typical oscillatory pattern. The model is compared with deterministic models based on semigroup analysis of systems of differential equations.     

The demographic impact of extreme events: stochastic weather drives survival and population dynamics in a long-lived seabird

1. Most scenarios for future climate change predict increased variability and thus increased frequency of extreme weather events. To predict impacts of climate change on wild populations, we need to understand whether this translates into increased variability in demographic parameters, which would lead to reduced population growth rates even without a change in mean parameter values. This requires robust estimates of temporal process variance, for example in survival, and identification of weather covariates linked to interannual variability. 2. The European shag Phalacrocorax aristotelis (L.) shows unusually large variability in population size, and large-scale mortality events have been linked to winter gales. We estimated first-year, second-year and adult survival based on 43 years of ringing and dead recovery data from the Isle of May, Scotland, using recent methods to quantify temporal process variance and identify aspects of winter weather linked to survival. 3. Survival was highly variable for all age groups, and for second-year and adult birds process variance declined strongly when the most extreme year was excluded. Survival in these age groups was low in winters with strong onshore winds and high rainfall. Variation in first-year survival was not related to winter weather, and process variance, although high, was less affected by extreme years. A stochastic population model showed that increasing process variance in survival would lead to reduced population growth rate and increasing probability of extinction. 4. As in other cormorants, shag plumage is only partially waterproof, presumably an adaptation to highly efficient underwater foraging. We speculate that this adaptation may make individuals vulnerable to rough winter weather, leading to boom-and-bust dynamics, where rapid population growth under favourable conditions allows recovery from periodic large-scale weather-related mortality. 5. Given that extreme weather events are predicted to become more frequent, species such as shags that are vulnerable to such events are likely to exhibit stronger reductions in population growth than would be expected from changes in mean climate. Vulnerability to extreme events thus needs to be accounted for when predicting the ecological impacts of climate change.     

Using stage‐based system dynamics modeling for demographic management of captive populations

Management of captive populations relies on a complex synthesis of genetic and demographic analyses to guide populations toward sustainability. Demographic analyses of captive populations currently utilize age‐based matrix projections to predict a population's trajectory. An alternate approach is to use a stage‐based, system dynamics model for captive systems. Such models can more easily incorporate complex captive systems in which population dynamics are dependent on a combination of management and a species' biology. By linking these two areas, population managers can gain a more accurate understanding of how management decisions impact captive populations and which aspects of a species' demography should be of special concern in the future. We present a general stage‐based system dynamics model that has been developed for use with captive populations. The utility of the model is then illustrated by applying it to three captive bear populations: spectacled bears (Tremarctos ornatus), sloth bears (Melursus ursinus), and sun bears (Helarctos malayanus). Zoo Biol 22:45–64, 2003. © 2003 Wiley‐Liss, Inc.