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.     

Individual‐based and stochastic modeling of cell population dynamics considering substrate dependency

In this article, we propose an individual‐based and stochastic modeling approach that is capable of describing the bacterial cell population dynamics during a batch culture. All stochastic nature inherent in intracellular molecular level reactions and cell division processes were considered in a single model framework by embedding a sub‐model describing individual cell's growth kinetics in a discrete event simulation algorithm. The resultant unique feature of the model is that the effects of the stochasticities on the cell population dynamics can be investigated for different substrate‐dependent cell growth kinetics. When Monod kinetics was used as the sub‐model, the stochasticities only slightly affected the cell mass increase and substrate consumption profiles during the batch culture although they were still important in describing the changes of cell population distributions. When Andrews substrate inhibition kinetics was used, however, it was revealed that the overall cell population dynamics could be seriously influenced by the stochasticities. Under a critical initial substrate level, the cell population could proliferate against the substrate inhibition only when the stochasticities were considered. Biotechnol. Bioeng. 2009;103: 891–899. © 2009 Wiley Periodicals, Inc.     

A structured model and likelihood approach to estimate yeast prion propagon replication rates and their asymmetric transmission

Prion proteins cause a variety of fatal neurodegenerative diseases in mammals but are generally harmless to Baker’s yeast (Saccharomyces cerevisiae). This makes yeast an ideal model organism for investigating the protein dynamics associated with these diseases. The rate of disease onset is related to both the replication and transmission kinetics of propagons, the transmissible agents of prion diseases. Determining the kinetic parameters of propagon replication in yeast is complicated because the number of propagons in an individual cell depends on the intracellular replication dynamics and the asymmetric division of yeast cells within a growing yeast cell colony. We present a structured population model describing the distribution and replication of prion propagons in an actively dividing population of yeast cells. We then develop a likelihood approach for estimating the propagon replication rate and their transmission bias during cell division. We first demonstrate our ability to correctly recover known kinetic parameters from simulated data, then we apply our likelihood approach to estimate the kinetic parameters for six yeast prion variants using propagon recovery data. We find that, under our modeling framework, all variants are best described by a model with an asymmetric transmission bias. This demonstrates the strength of our framework over previous formulations assuming equal partitioning of intracellular constituents during cell division.     

Effect of hydration on the water content of human erythrocytes.

An ideal, hydrated, nondilute pseudobinary salt-protein-water solution model of the RBC intracellular solution has been developed to describe the osmotic behavior of human erythrocytes during freezing and thawing. Because of the hydration of intracellular solutes (mostly cell proteins), our analytical results predict that at least 16.65% of the isotonic cell water content will be retained within RBCs placed in hypertonic solutions. These findings are consistent not only with the experimental measurements of the amount of isotonic cell water retained within RBCs subjected to nonisotonic extracellular solutions (20-32%) but also with the experimental evidence that all of the water within RBCs is solvent water. By modeling the RBC intracellular solution as a hydrated salt-protein-water solution, no anomalous osmotic behavior is apparent.     

Transition to quorum sensing in an Agrobacterium population: A stochastic model

Understanding of the intracellular molecular machinery that is responsible for the complex collective behavior of multicellular populations is an exigent problem of modern biology. Quorum sensing, which allows bacteria to activate genetic programs cooperatively, provides an instructive and tractable example illuminating the causal relationships between the molecular organization of gene networks and the complex phenotypes they control. In this work we—to our knowledge for the first time—present a detailed model of the population-wide transition to quorum sensing using the example of Agrobacterium tumefaciens. We construct a model describing the Ti plasmid quorum-sensing gene network and demonstrate that it behaves as an “on–off” gene expression switch that is robust to molecular noise and that activates the plasmid conjugation program in response to the increase in autoinducer concentration. This intracellular model is then incorporated into an agent-based stochastic population model that also describes bacterial motion, cell division, and chemical communication. Simulating the transition to quorum sensing in a liquid medium and biofilm, we explain the experimentally observed gradual manifestation of the quorum-sensing phenotype by showing that the transition of individual model cells into the “on” state is spread stochastically over a broad range of autoinducer concentrations. At the same time, the population-averaged values of critical autoinducer concentration and the threshold population density are shown to be robust to variability between individual cells, predictable and specific to particular growth conditions. Our modeling approach connects intracellular and population scales of the quorum-sensing phenomenon and provides plausible answers to the long-standing questions regarding the ecological and evolutionary significance of the phenomenon. Thus, we demonstrate that the transition to quorum sensing requires a much higher threshold cell density in liquid medium than in biofilm, and on this basis we hypothesize that in Agrobacterium quorum sensing serves as the detector of biofilm formation.     

Translating Biomaterial Properties to Intracellular Signaling

Bioactive materials present important micro-environmental cues that induce specific intracellular signaling responses which ultimately determine cell behavior. For example, vascular endothelial cells on a normal vessel wall resist inflammation and thrombosis, but the same cells seeded on an artificial vascular graft or stent do not. What makes these cells behave so differently when they are adhered to different materials? Intracellular signaling from integrins and other cell-surface receptors is an important part of the answer, but these signaling responses constitute a highly-branched, interconnected network of molecules. In order to perform rational design of biomaterials, one must understand how altering the properties of the material (micro-environment) causes changes in cell behavior, and this in turn requires understanding the complex signaling response. Systems biology and mathematical modeling aid analysis of the connectivity of this network. This review summarizes applicable systems biology and mathematical modeling techniques including ordinary differential equations-based models, principal component analysis, and Bayesian networks. Next covered is biomaterials research which studies the intracellular signaling responses generated by variation of biomaterial properties. Finally, the review details ways in which modeling has been or could be applied to better understand the link between biomaterial properties and intracellular signaling.     

Impact of Dimensionality and Network Disruption on Microrheology of Cancer Cells in 3D Environments

Dimensionality is a fundamental component that can have profound implications on the characteristics of physical systems. In cell biology, however, the majority of studies on cell physical properties, from rheology to force generation to migration, have been performed on 2D substrates, and it is not clear how a more realistic 3D environment influences cell properties. Here, we develop an integrated approach and demonstrate the combination of mitochondria-tracking microrheology, microfluidics, and Brownian dynamics simulations to explore the impact of dimensionality on intracellular mechanics and on the effects of intracellular disruption. Additionally, we consider both passive thermal and active motor-driven processes within the cell and demonstrate through modeling how active internal fluctuations are modulated via dimensionality. Our results demonstrate that metastatic breast cancer cells (MDA-MB-231) exhibit more solid-like internal motions in 3D compared to 2D, and actin network disruption via Cytochalasin D has a more pronounced effect on internal cell fluctuations in 2D. Our computational results and modeling show that motor-induced active stress fluctuations are enhanced in 2D, leading to increased local intracellular particle fluctuations and apparent fluid-like behavior.     

Overview of Mathematical Approaches Used to Model Bacterial Chemotaxis I: The Single Cell

Mathematical modeling of bacterial chemotaxis systems has been influential and insightful in helping to understand experimental observations. We provide here a comprehensive overview of the range of mathematical approaches used for modeling, within a single bacterium, chemotactic processes caused by changes to external gradients in its environment. Specific areas of the bacterial system which have been studied and modeled are discussed in detail, including the modeling of adaptation in response to attractant gradients, the intracellular phosphorylation cascade, membrane receptor clustering, and spatial modeling of intracellular protein signal transduction. The importance of producing robust models that address adaptation, gain, and sensitivity are also discussed. This review highlights that while mathematical modeling has aided in understanding bacterial chemotaxis on the individual cell scale and guiding experimental design, no single model succeeds in robustly describing all of the basic elements of the cell. We conclude by discussing the importance of this and the future of modeling in this area.     

Do Pioneer Cells Exist?

Most mathematical models of collective cell spreading make the standard assumption that the cell diffusivity and cell proliferation rate are constants that do not vary across the cell population. Here we present a combined experimental and mathematical modeling study which aims to investigate how differences in the cell diffusivity and cell proliferation rate amongst a population of cells can impact the collective behavior of the population. We present data from a three-dimensional transwell migration assay that suggests that the cell diffusivity of some groups of cells within the population can be as much as three times higher than the cell diffusivity of other groups of cells within the population. Using this information, we explore the consequences of explicitly representing this variability in a mathematical model of a scratch assay where we treat the total population of cells as two, possibly distinct, subpopulations. Our results show that when we make the standard assumption that all cells within the population behave identically we observe the formation of moving fronts of cells where both subpopulations are well-mixed and indistinguishable. In contrast, when we consider the same system where the two subpopulations are distinct, we observe a very different outcome where the spreading population becomes spatially organized with the more motile subpopulation dominating at the leading edge while the less motile subpopulation is practically absent from the leading edge. These modeling predictions are consistent with previous experimental observations and suggest that standard mathematical approaches, where we treat the cell diffusivity and cell proliferation rate as constants, might not be appropriate.     

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.     

A mathematical model of the nutrient dynamics of phytoplankton in a nitrate-limited environment

Insofar as saturation kinetics are applicable to the growth of phytoplankton in laboratory experiments and to growth in nature, the computer modeling of intracellular nutrient partitioning in populations of cells can lead to better understanding of the dynamics of natural populations. A three-compartment mathematical model was developed to represent a phytoplankton population having the capability to store nitrogen in a nitrate-limited environment. Parameters were estimated by fitting the model to data from two chemostat experiments reported by Caperon (1968). The model was used to simulate growth dynamics observed in chemostat and batch experiments. The model demonstrated the changes which may occur in the nitrogenous constituents of a phytoplankton population with time and environmental conditions. The model also demonstrates three phenomena which have been observed in field and laboratory experiments but which are not represented by the customary Monod model: (1) uptake rates may significantly exceed not growth rates, (2) high growth rates may be encountered at very low environmental nitrate concentrations, and (3) the ratio of internal nitrogen to population size may change significantly during a study period. It is suggested that the amount of nitorgen in storage may be used as an indicator of the physiological state of a monospecific population. Parameters for the one-compartment Monod model were estimated by customary methods form data generated by the three-compartment model. It was shown that difficulties encountered in estimating the yield coefficient and the decay coefficient may be attributed to the intracellular storage phenomenon. It was also demonstrated that the one-compartment Monod model was inadequate to accurately represent population growth in chemostat experiments when intracellular storage is a significant factor.     

Cellware--a multi-algorithmic software for computational systems biology

The intracellular environment of a cell hosts a wide variety of enzymatic reactions, diffusion events, molecular binding, polymerization and metabolic channeling. To transform these biological events into a computational framework, distinct modeling strategies are required. While currently no tool is capable of capturing all these events, progress is being made to create an integrated environment for the modeling community. To address this niche requirement, Cellware has been developed to offer a multi-algorithmic environment for modeling and simulating both deterministic and stochastic events in the cell. AVAILABILITY: The software is available for free and can be downloaded from http://www.bii.a-star.edu.sg/sbg/cellware     

Importance of intracellular water apparent diffusion to the measurement of membrane permeability

The exchange of water across biological membranes is of fundamental significance to both animal and plant physiology. Diffusional membrane permeability (P(d)) for the Xenopus oocyte, an important model system for water channel investigation, is typically calculated from intracellular water pre-exchange lifetime, cell volume, and cell surface area. There is debate, however, whether intracellular water motion affects water lifetime, and thereby P(d). Mathematical modeling of water transport is problematic because the intracellular water diffusion rate constant (D) for cells is usually unknown. The measured permeability may be referred to as the apparent diffusional permeability, P, to acknowledge this potential error. Herein, we show that magnetic resonance (MR) spectroscopy can be used to measure oocyte water exchange with greater temporal resolution and higher signal-to-noise ratio than other methods. MR imaging can be used to assess both oocyte geometry and intracellular water diffusion for the same single cells. MR imaging is used to confirm the dependence of intracellular water lifetime on intracellular diffusion. A model is presented to relate intracellular lifetime to true membrane diffusional permeability. True water diffusional permeability (2.7 +/- 0.4 microm/s) is shown to be 39 +/- 6% greater than apparent diffusional permeability for 8 oocytes. This discrepancy increases with cell size and permeability (such as after water channel expression) and decreases with increasing intracellular water D.     

OPP Labeling Enables Total Protein Synthesis Quantification in CHO Production Cell Lines at the Single‐Cell Level

Accurate measurement of global and specific protein synthesis rates is becoming increasingly important, especially in the context of biotechnological applications such as process modeling or selection of production cell clones. While quantification of total protein translation across whole cell populations is easily achieved, methods that are capable of tracking population dynamics at the single‐cell level are still lacking. To address this need, we apply O‐propargyl‐puromycin (OPP) labeling to assess total protein synthesis in single recombinant Chinese hamster ovary (CHO) cells by flow cytometry. Thereby we demonstrate that global protein translation rates slightly increase with progression through the cell cycle during exponential growth. Stable CHO cell lines producing recombinant protein display similar levels of total protein synthesis as their parental CHO host cell line. Global protein translation does not correlate with intracellular product content of three model proteins, but the host cell line with high transient productivity has a higher OPP signal. This indicates that production cell lines with increased overall protein synthesis capacity can be identified by our method at the single‐cell level. In conclusion, OPP‐labeling allows rapid and reproducible assessment of global protein synthesis in single CHO cells, and can be multiplexed with DNA staining or any type of immunolabeling of specific proteins or markers for organelles.     

Branching stochastic processes with immigration in analysis of renewing cell populations

This paper considers the utility of a new class of stochastic branching processes with non-homogeneous immigration in modeling complex renewing cell systems. Such systems typically include the population of stem cells that provides an inexhaustible supply of cells necessary for maintaining the cellular composition of a tissue. A stem cell may be induced to transform (differentiate) into a progenitor cell. Progenitor cells retain the ability to proliferate and their function is believed to provide a quick proliferative response to an increased demand for cells in the population. There may be several sub-types of progenitor cells. Terminally differentiated cells do not divide under normal conditions; they are responsible for maintaining tissue-specific functions. Recent advancements in experimental techniques offer considerable scope for quantitative studies of in vivo cell kinetics based on stochastic modeling of renewing cell populations. However, no ready-made theory is currently available to take full advantage of these advancements. This paper introduces such a theory with a special focus on its feasibility in biological applications.     

A novel assay based on fluorescence microscopy and image processing for determining phenotypic distributions of rod-shaped bacteria

Cell population balance (CPB) models can account for the phenotypic heterogeneity that characterizes isogenic cell populations. To utilize the predictive power of these models, however, we must determine the single-cell reaction and division rates as well as the partition probability density function of the cell population. These functions can be obtained through the Collins-Richmond inverse CPB modeling methodology, if we know the phenotypic distributions of (a) the overall cell population, (b) the dividing cell subpopulation, and (c) the newborn cell subpopulation. This study presents the development of a novel assay that combines fluorescence microscopy and image processing to determine these distributions. The method is generally applicable to rod-shaped cells dividing through the formation of a characteristic constriction. Morphological criteria were developed for the automatic identification of dividing cells and validated through direct comparison with manually obtained measurements. The newborn cell subpopulation was obtained from the corresponding dividing cell subpopulation by collecting information from the two compartments separated by the constriction. The method was applied to E. coli cells carrying the genetic toggle network with a green fluorescent marker. Our measurements for the overall cell population were in excellent agreement with the distributions obtained via flow cytometry. The new assay constitutes a powerful tool that can be used in conjunction with inverse CPB modeling to rigorously quantify single-cell behavior from data collected from highly heterogeneous cell populations.     

Functional Study of NIPA2 Mutations Identified from the Patients with Childhood Absence Epilepsy

Recently many genetic mutations that are associated with epilepsy have been identified. The protein NIPA2 (non-imprinted in Prader-Willi/Angelman syndrome region protein 2) is a highly selective magnesium transporter encoded by the gene NIPA2 in which we have found three mutations (p.I178F, p.N244S and p.N334_E335insD) within a population of patients with childhood absence epilepsy (CAE). In this study, immunofluorescence labeling, inductively coupled plasma-optical emission spectroscopy (ICP-OES), MTT metabolic rate detection and computational modeling were utilized to elucidate how these mutations result in CAE. We found in cultured neurons that NIPA2 (wild-type) proteins were localized to the cell periphery, whereas mutant proteins were not effectively trafficked to the cell membrane. Furthermore, we found a decrease in intracellular magnesium concentration in the neurons transfected with mutant NIPA2, but no effect on the survival of neurons. To understand how low intracellular magnesium resulted in hyperexcitability, we built and analyzed a computational model to simulate the effects of mutations. The model suggested that lower intracellular magnesium concentration enhanced synaptic N-methyl-D-aspartate receptor (NMDAR) currents. This study primarily reveals that a selective magnesium transporter NIPA2 may play a role in the pathogenesis of CAE.     

Examples of Mathematical Modeling: Tales from the Crypt

Mathematical modeling is being increasingly recognized within the biomedical sciences as an important tool that can aid the understanding of biological systems. The heavily regulated cell renewal cycle in the colonic crypt provides a good example of how modeling can be used to find out key features of the system kinetics, and help to explain both the breakdown of homeostasis and the initiation of tumorigenesis.We use the cell population model by Johnston et al. (2007) Proc. Natl. Acad. Sci. USA 104, 4008-4013, to illustrate the power of mathematical modeling by considering two key questions about the cell population dynamics in the colonic crypt. We ask: how can a model describe both homeostasis and unregulated growth in tumorigenesis; and to which parameters in the system is the model most sensitive? In order to address these questions, we discuss what type of modeling approach is most appropriate in the crypt.We use the model to argue why tumorigenesis is observed to occur in stages with long lag phases between periods of rapid growth, and we identify the key parameters.