Modeling the effect of deregulated proliferation and apoptosis on the growth dynamics of epithelial cell populations in vitro

We present a three-dimensional individual cell-based, biophysical model to study the effect of normal and malfunctioning growth regulation and control on the spatial-temporal organization of growing cell populations in vitro. The model includes explicit representations of typical epithelial cell growth regulation and control mechanisms, namely 1), a cell-cell contact-mediated form of growth inhibition; 2), a cell-substrate contact-dependent cell-cycle arrest; and 3), a cell-substrate contact-dependent programmed cell death (anoikis). The model cells are characterized by experimentally accessible biomechanical and cell-biological parameters. First, we study by variation of these cell-specific parameters which of them affect the macroscopic morphology and growth kinetics of a cell population within the initial expanding phase. Second, we apply selective knockouts of growth regulation and control mechanisms to investigate how the different mechanisms collectively act together. Thereby our simulation studies cover the growth behavior of epithelial cell populations ranging from undifferentiated stem cell populations via transformed variants up to tumor cell lines in vitro. We find that the cell-specific parameters, and in particular the strength of the cell-substrate anchorage, have a significant impact on the population morphology. Furthermore, they control the efficacy of the growth regulation and control mechanisms, and consequently tune the transition from controlled to uncontrolled growth that is induced by the failures of these mechanisms. Interestingly, however, we find the qualitative and quantitative growth kinetics to be remarkably robust against variations of cell-specific parameters. We compare our simulation results with experimental findings on a number of epithelial and tumor cell populations and suggest in vitro experiments to test our model predictions.     

Evolution of RNA virus in spatially structured heterogeneous environments

A hallmark of the infectious cycle for many RNA viruses parasitizing multicellular hosts is the need to invade and successfully replicate in tissues that comprise a variety of cell types. Thus, multicellular hosts represent a heterogeneous environment to evolving viral populations. To understand viral adaptation to multicellular hosts, we took a double approach. First, we developed a mathematical model that served to make predictions concerning the dynamics of viral populations evolving in heterogeneous environments. Second, the predictions were tested by evolving vesicular stomatitis virus in vitro on a spatially structured environment formed by three different cell types. In the absence of gene flow, adaptation was tissue-specific, but fitness in all tissues decreased with migration rate. The performance in a given tissue was negatively correlated with its distance to the tissue hosting the population. This correlation decreased with migration rate.     

BIO-LGCA: A cellular automaton modelling class for analysing collective cell migration

Collective dynamics in multicellular systems such as biological organs and tissues plays a key role in biological development, regeneration, and pathological conditions. Collective tissue dynamics—understood as population behaviour arising from the interplay of the constituting discrete cells—can be studied with on- and off-lattice agent-based models. However, classical on-lattice agent-based models, also known as cellular automata, fail to replicate key aspects of collective migration, which is a central instance of collective behaviour in multicellular systems. To overcome drawbacks of classical on-lattice models, we introduce an on-lattice, agent-based modelling class for collective cell migration, which we call biological lattice-gas cellular automaton (BIO-LGCA). The BIO-LGCA is characterised by synchronous time updates, and the explicit consideration of individual cell velocities. While rules in classical cellular automata are typically chosen ad hoc, rules for cell-cell and cell-environment interactions in the BIO-LGCA can also be derived from experimental cell migration data or biophysical laws for individual cell migration. We introduce elementary BIO-LGCA models of fundamental cell interactions, which may be combined in a modular fashion to model complex multicellular phenomena. We exemplify the mathematical mean-field analysis of specific BIO-LGCA models, which allows to explain collective behaviour. The first example predicts the formation of clusters in adhesively interacting cells. The second example is based on a novel BIO-LGCA combining adhesive interactions and alignment. For this model, our analysis clarifies the nature of the recently discovered invasion plasticity of breast cancer cells in heterogeneous environments.     

Individual-based and continuum models of growing cell populations: a comparison

In this paper we compare two alternative theoretical approaches for simulating the growth of cell aggregates in vitro: individual cell (agent)-based models and continuum models. We show by a quantitative analysis of both a biophysical agent-based and a continuum mechanical model that for densely packed aggregates the expansion of the cell population is dominated by cell proliferation controlled by mechanical stress. The biophysical agent-based model introduced earlier (Drasdo and Hoehme in Phys Biol 2:133-147, 2005) approximates each cell as an isotropic, homogeneous, elastic, spherical object parameterised by measurable biophysical and cell-biological quantities and has been shown by comparison to experimental findings to explain the growth patterns of dense monolayers and multicellular spheroids. Both models exhibit the same growth kinetics, with initial exponential growth of the population size and aggregate diameter followed by linear growth of the diameter and power-law growth of the cell population size. Very sparse monolayers can be explained by a very small or absent cell-cell adhesion and large random cell migration. In this case the expansion speed is not controlled by mechanical stress but by random cell migration and can be modelled by the Fisher-Kolmogorov-Petrovskii-Piskounov (FKPP) reaction-diffusion equation. The growth kinetics differs from that of densely packed aggregates in that the initial spread, as quantified by the radius of gyration, is diffusive. Since simulations of the lattice-free agent-based model in the case of very large random migration are too long to be practical, lattice-based cellular automaton (CA) models have to be used for a quantitative analysis of sparse monolayers. Analysis of these dense monolayers leads to the identification of a critical parameter of the CA model so that eventually a hierarchy of three model types (a detailed biophysical lattice-free model, a rule-based cellular automaton and a continuum approach) emerge which yield the same growth pattern for dense and sparse cell aggregates.     

Stochastic Models of Lymphocyte Proliferation and Death

Quantitative understanding of the kinetics of lymphocyte proliferation and death upon activation with an antigen is crucial for elucidating factors determining the magnitude, duration and efficiency of the immune response. Recent advances in quantitative experimental techniques, in particular intracellular labeling and multi-channel flow cytometry, allow one to measure the population structure of proliferating and dying lymphocytes for several generations with high precision. These new experimental techniques require novel quantitative methods of analysis. We review several recent mathematical approaches used to describe and analyze cell proliferation data. Using a rigorous mathematical framework, we show that two commonly used models that are based on the theories of age-structured cell populations and of branching processes, are mathematically identical. We provide several simple analytical solutions for a model in which the distribution of inter-division times follows a gamma distribution and show that this model can fit both simulated and experimental data. We also show that the estimates of some critical kinetic parameters, such as the average inter-division time, obtained by fitting models to data may depend on the assumed distribution of inter-division times, highlighting the challenges in quantitative understanding of cell kinetics.     

Aggregative cycles evolve as a solution to conflicts in social investment

Multicellular organization is particularly vulnerable to conflicts between different cell types when the body forms from initially isolated cells, as in aggregative multicellular microbes. Like other functions of the multicellular phase, coordinated collective movement can be undermined by conflicts between cells that spend energy in fuelling motion and ‘cheaters’ that get carried along. The evolutionary stability of collective behaviours against such conflicts is typically addressed in populations that undergo extrinsically imposed phases of aggregation and dispersal. Here, via a shift in perspective, we propose that aggregative multicellular cycles may have emerged as a way to temporally compartmentalize social conflicts. Through an eco-evolutionary mathematical model that accounts for individual and collective strategies of resource acquisition, we address regimes where different motility types coexist. Particularly interesting is the oscillatory regime that, similarly to life cycles of aggregative multicellular organisms, alternates on the timescale of several cell generations phases of prevalent solitary living and starvation-triggered aggregation. Crucially, such self-organized oscillations emerge as a result of evolution of cell traits associated to conflict escalation within multicellular aggregates.     

Large-scale in silico modeling of metabolic interactions between cell types in the human brain

Metabolic interactions between multiple cell types are difficult to model using existing approaches. Here we present a workflow that integrates gene expression data, proteomics data and literature-based manual curation to model human metabolism within and between different types of cells. Transport reactions are used to account for the transfer of metabolites between models of different cell types via the interstitial fluid. We apply the method to create models of brain energy metabolism that recapitulate metabolic interactions between astrocytes and various neuron types relevant to Alzheimer's disease. Analysis of the models identifies genes and pathways that may explain observed experimental phenomena, including the differential effects of the disease on cell types and regions of the brain. Constraint-based modeling can thus contribute to the study and analysis of multicellular metabolic processes in the human tissue microenvironment and provide detailed mechanistic insight into high-throughput data analysis.     

Multilevel complexity of calcium signaling: Modeling angiogenesis

Intracellular calcium signaling is a universal,evolutionary conserved and versatile regulator of cell biochemistry.The complexity of calcium signaling and related cell machinery can be investigated by the use of experimental strategies,as well as by computational approaches.Vascular endothelium is a fascinating model to study the specific properties and roles of calcium signals at multiple biological levels.During the past 20 years,live cell imaging,patch clamp and other techniques have allowed us to detect and interfere with calcium signaling in endothelial cells(ECs),providing a huge amount of information on the regulation of vascularization(angiogenesis) in normal and tumoral tissues.These data range from the spatiotemporal dynamics of calcium within different cell microcompartments to those in entire multicellular and organized EC networks.Beside experimental strategies,in silico endothelial models,specifically designed for simulating calcium signaling,are contributing to our knowledge of vascular physiol-ogy and pathology.They help to investigate and predict the quantitative features of proangiogenic events moving through subcellular,cellular and supracellular levels.This review focuses on some recent developments of computational approaches for proangiogenic endothelial calcium signaling.In particular,we discuss the creation of hybrid simulation environments,which combine and integrate discrete Cellular Potts Models.They are able to capture the phenomenological mechanisms of cell morphological reorganization,migration,and intercellular adhesion,with single-cell spatiotemporal models,based on reaction-diffusion equations that describe the agonist-induced intracellular calcium events.     

Modeling the effects of biologically incorporated radionuclides and chronic low-dose ionizing radiation exposure on both cancer and chronic non-cancer diseases

Efforts to model the health effects of low-dose ionizing radiation (IR) have often focused on cancer. Meanwhile, significant evidence links IR and age-associated non-cancer diseases. Modeling of such complex processes, which are not currently well understood, is a challenging problem. In this paper we briefly overview recent successful attempts to model cancer on a population level and propose how those models may be adapted to include the impact of IR and to describe complex non-cancer diseases. We propose three classes of models which we believe are well suited for the analysis of the health effects in human populations exposed to low-dose IR. These models use biostatistical/epidemiological techniques and mathematical formulas describing the biological mechanisms of the impact of IR on human health. They can combine data from multiple sources and from distinct levels of biological/population organization. The proposed models are intrinsically multivariate and non-linear and capture the dynamic aspects of health change.     

Proteomics - The key to understanding systems biology of Arabidopsis trichomes

Every multicellular organism consists of numerous organs, tissues and specific cell types. To gain detailed knowledge about the morphogenesis of these complex structures, it is inevitable to advance biochemical analyses to ultimate spatial and temporal resolution since individual cell types contribute differently to the overall performance of living objects. Single cell sampling combined with systems biological approaches was recently applied to investigations of Arabidopsis thaliana trichomes (leaf hairs). These are single celled structures that provide ideal model systems to address various aspects of plant cell development and differentiation at the level of individual cells. A previously suggested function of trichomes in plant stress responses could thus be confirmed. Furthermore, trichome-specific “omics” data collected in several laboratories are mutually conclusive which demonstrates the applicability of systems biological approaches at the single cell level.     

Quantification of cell turnover kinetics using 5-bromo-2'-deoxyuridine

5-Bromo-2'-deoxyuridine (BrdU) is frequently used to measure the turnover of cell populations in vivo. However, due to a lack of detailed mathematical models that describe the uptake and loss of BrdU in dividing cell populations, assessments of cell turnover kinetics have been largely qualitative rather than quantitative. In this study, we develop a mathematical framework for the analysis of BrdU-labeling experiments. We derive analytical expressions for the fraction of labeled cells within cell populations that are growing, declining, or at equilibrium. Fitting the analytical functions to data allows us to quantify the rates of cell proliferation and cell loss, as well as the rate of cell input from a source. We illustrate this for the BrdU labeling of T lymphocytes of uninfected and SIV-infected rhesus macaques.     

Functional genomics and proteomics approaches to study the ERBB network in cancer

Substantial progress in functional genomic and proteomic technologies has opened new perspectives in biomedical research. The sequence of the human genome has been mostly determined and opened new visions on its complexity and regulation. New technologies, like RNAi and protein arrays, allow gathering knowledge beyond single gene analysis. Increasingly, biological processes are studied with systems biological approaches, where qualitative and quantitative data of the components are utilized to model the respective processes, to predict effects of perturbations, and to then refine these models after experimental testing. Here, we describe the potential of applying functional genomics and proteomics, taking the ERBB family of growth-factor receptors as an example to study the signaling network and its impact on cancer.     

The systems biology of signaling pathways

Signaling networks play the central role in the regulation of processes in a single cell and in the entire body. A recent breakthrough in technologies for systems biology, which combine experimental and mathematical methods, permits scientists to model signaling pathways in an individual cell and in cell populations. This approach provides new information on mechanisms that regulate a variety of biological processes. Here we discuss the mathematical formalisms that are applied to signaling pathway modeling and relevant experimental methods.     

Mapping of mechanical strains and stresses around quiescent engineered three-dimensional epithelial tissues

Understanding how physical signals guide biological processes requires qualitative and quantitative knowledge of the mechanical forces generated and sensed by cells in a physiologically realistic three-dimensional (3D) context. Here, we used computational modeling and engineered epithelial tissues of precise geometry to define the experimental parameters that are required to measure directly the mechanical stress profile of 3D tissues embedded within native type I collagen. We found that to calculate the stresses accurately in these settings, we had to account for mechanical heterogeneities within the matrix, which we visualized and quantified using confocal reflectance and atomic force microscopy. Using this technique, we were able to obtain traction forces at the epithelium-matrix interface, and to resolve and quantify patterns of mechanical stress throughout the surrounding matrix. We discovered that whereas single cells generate tension by contracting and pulling on the matrix, the contraction of multicellular tissues can also push against the matrix, causing emergent compression. Furthermore, tissue geometry defines the spatial distribution of mechanical stress across the epithelium, which communicates mechanically over distances spanning hundreds of micrometers. Spatially resolved mechanical maps can provide insight into the types and magnitudes of physical parameters that are sensed and interpreted by multicellular tissues during normal and pathological processes.     

Mechanistic systems models of cell signaling networks: a case study of myocyte adrenergic regulation

Signal transduction networks coordinate a wide variety of cellular functions, including gene expression, metabolism, and cell fate processes. Understanding biological networks quantitatively is a major challenge to post-genomic biology, and mechanistic systems models will be crucial for this task. Here, we review approaches towards developing mechanistic systems models of established cell signaling networks. The ability of mechanistic system models to generate testable biological hypotheses and experimental strategies is discussed. As a case study of model development and analysis, we examined the functional roles of phospholamban, the L-type calcium channel, the ryanodine receptor, and troponin I phosphorylation upon β-adrenergic stimulation in the rat ventricular myocyte. Model analysis revealed that while protein kinase A-mediated phosphorylation of the ryanodine receptor greatly increases its calcium sensitivity, calcium autoregulation may adapt quickly by negating potential increases in contractility. Systematic combinations of in silico perturbations supported the conclusion that phospholamban phosphoregulation is the primary mechanism for increased sarcoplasmic reticulum load and calcium relaxation rate during β-adrenergic stimulation, while both phospholamban and the L-type calcium channel contribute to increased systolic calcium. Combined with detailed experimental studies, mechanistic systems models will be valuable for developing a quantitative understanding of cell signaling networks.