This review encompasses the most important advances in liver functions and hepatotoxicity and analyzes which mechanisms can be studied in vitro. In a complex architecture of nested, zonated lobules, the liver consists of approximately 80 % hepatocytes and 20 % non-parenchymal cells, the latter being involved in a secondary phase that may dramatically aggravate the initial damage. Hepatotoxicity, as well as hepatic metabolism, is controlled by a set of nuclear receptors (including PXR, CAR, HNF-4α, FXR, LXR, SHP, VDR and PPAR) and signaling pathways. When isolating liver cells, some pathways are activated, e.g., the RAS/MEK/ERK pathway, whereas others are silenced (e.g. HNF-4α), resulting in up- and downregulation of hundreds of genes. An understanding of these changes is crucial for a correct interpretation of in vitro data. The possibilities and limitations of the most useful liver in vitro systems are summarized, including three-dimensional culture techniques, co-cultures with non-parenchymal cells, hepatospheres, precision cut liver slices and the isolated perfused liver. Also discussed is how closely hepatoma, stem cell and iPS cell–derived hepatocyte-like-cells resemble real hepatocytes. Finally, a summary is given of the state of the art of liver in vitro and mathematical modeling systems that are currently used in the pharmaceutical industry with an emphasis on drug metabolism, prediction of clearance, drug interaction, transporter studies and hepatotoxicity. One key message is that despite our enthusiasm for in vitro systems, we must never lose sight of the in vivo situation. Although hepatocytes have been isolated for decades, the hunt for relevant alternative systems has only just begun.Electronic supplementary materialThe online version of this article (doi:10.1007/s00204-013-1078-5) contains supplementary material, which is available to authorized users.

To what extent the growth dynamics of tumors is controlled by nutrients, biomechanical forces and other factors at different stages and in different environments is still largely unknown. Here we present a biophysical model to study the spatio-temporal growth dynamics of two-dimensional tumor monolayers and three-dimensional tumor spheroids as a complementary tool to in vitro experiments. Within our model each cell is represented as an individual object and parametrized by cell-biophysical and cell-kinetic parameters that can all be experimentally determined. Hence our modeling strategy allows us to study which mechanisms on the microscopic level of individual cells may affect the macroscopic properties of a growing tumor. We find the qualitative growth kinetics and patterns at early growth stages to be remarkably robust. Quantitative comparisons between computer simulations using our model and published experimental observations on monolayer cultures suggest a biomechanically-mediated form of growth inhibition during the experimentally observed transition from exponential to sub-exponential growth at sufficiently large tumor sizes. Our simulations show that the same transition during the growth of avascular tumor spheroids can be explained largely by the same mechanism. Glucose (or oxygen) depletion seems to determine mainly the size of the necrotic core but not the size of the tumor. We explore the consequences of the suggested biomechanical form of contact inhibition, in order to permit an experimental test of our model. Based on our findings we propose a phenomenological growth law in early expansion phases in which specific biological small-scale processes are subsumed in a small number of effective parameters.

Only little is known about how cells coordinately behave to establish functional tissue structure and restore microarchitecture during regeneration. Research in this field is hampered by a lack of techniques that allow quantification of tissue architecture and its development. To bridge this gap, we have established a procedure based on confocal laser scans, image processing, and three-dimensional tissue reconstruction, as well as quantitative mathematical modeling. As a proof of principle, we reconstructed and modeled liver regeneration in mice after damage by CCl 4 , a prototypical inducer of pericentral liver damage. We have chosen the regenerating liver as an example because of the tight link between liver architecture and function: the complex microarchitecture formed by hepatocytes and microvessels, i.e. sinusoids, ensures optimal exchange of metabolites between blood and hepatocytes. Our model captures all hepatocytes and sinusoids of a liver lobule during a 16 days regeneration process. The model unambiguously predicted a so-far unrecognized mechanism as essential for liver regeneration, whereby daughter hepatocytes align along the orientation of the closest sinusoid, a process which we named "hepatocyte-sinusoid alignment" (HSA). The simulated tissue architecture was only in agreement with the experimentally obtained data when HSA was included into the model and, moreover, no other likely mechanism could replace it. In order to experimentally validate the model of prediction of HSA, we analyzed the three-dimensional orientation of daughter hepatocytes in relation to the sinusoids. The results of this analysis clearly confirmed the model prediction. We believe our procedure is widely applicable in the systems biology of tissues.agent based model | image processing and analysis | mathematical tissue modeling | systems biology | morphogenesis T he liver is the main metabolic organ which removes drugs and toxins from the blood. One of the outstanding features of the liver is its capacity to regenerate hepatocyte loss of up to 70% of its mass within a relatively short period of time (1). Hepatic parenchyma is organized in repetitive functional units called liver lobules, which besides its main constituents, hepatocytes, consists of sinusoidal endothelial cells, Kupffer, stellate, and bile duct cells. Branches of the hepatic artery and portal vein guide blood to the periportal regions of the lobules (Fig. 1A). From there, it flows through microvessels, the sinusoids, along hepatocyte columns that are lined with endothelial cells (generally known as sinusoidal cells), and drains into the central vein. This complex lobule architecture ensures a maximal exchange area between blood and hepatocytes in healthy liver. In liver disease, such as hepatocellular cancer, the contact surface between hepatocytes and sinusoidal cells decreases and contributes to compromised liver function (Fig. 1F). Recent research on liver regeneration has focused on molecular pathways and the mechanisms involved (2). Little is known about...

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.

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.

In this paper we present an overview of agentbased models that are used to simulate mechanical and physiological phenomena in cells and tissues, and we discuss underlying concepts, limitations, and future perspectives of these models. As the interest in cell and tissue mechanics increase, agent-based models are becoming more common the modeling community. We overview the physical aspects, complexity, shortcomings, and capabilities of the major agent-based model categories: lattice-based models (cellular automata, lattice gas cellular automata, cellular Potts models), off-lattice models (center-based models, deformable cell models, vertex models), and hybrid discrete-continuum models. In this way, we hope to assist future researchers in choosing a model for the phenomenon they want to model and understand. The article also contains some novel results.

In this article, we show, using a mathematical multiscale model, how cell adhesion may be regulated by interactions between E-cadherin and beta-catenin and how the control of cell adhesion may be related to cell migration, to the epithelial-mesenchymal transition and to invasion in populations of eukaryotic cells. E-cadherin mediates cell-cell adhesion and plays a critical role in the formation and maintenance of junctional contacts between cells. Loss of E-cadherin-mediated adhesion is a key feature of the epithelial-mesenchymal transition. beta-catenin is an intracellular protein associated with the actin cytoskeleton of a cell. E-cadherins bind to beta-catenin to form a complex which can interact both with neighboring cells to form bonds, and with the cytoskeleton of the cell. When cells detach from one another, beta-catenin is released into the cytoplasm, targeted for degradation, and downregulated. In this process there are multiple protein-complexes involved which interact with beta-catenin and E-cadherin. Within a mathematical individual-based multiscale model, we are able to explain experimentally observed patterns solely by a variation of cell-cell adhesive interactions. Implications for cell migration and cancer invasion are also discussed.

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