Scienific goals

In the last decades research in the life sciences had to face a rapidly increasing amount of data resulting from improved experimental methods. An example is the large amount of data from the high-throughput methods in molecular biology. However, these data were found to be insufficient to fully understand the behavior of complex biological systems such as multi-cellular tissues. Instead, a system level understanding was needed (Kitano, 2002), that permits insights in four major aspects: (1) the structure of the system which includes the physical properties of its intracellular and multi-cellular components together with the mechanisms that actively regulate them, (2) the system dynamics which summarizes the behavior of the system over time and under particular conditions, (3) the mechanisms that control the state of its functional building blocks such as the cell and thereby identify potential targets for therapeutic treatments of diseases and (4) strategies to modify and construct biological systems guided by predictive tools such a computer simulation models. Essentially, a system level understanding of biological entities in physiological and especially pathological states is required in order to deploy the full potential of modern life sciences. 
The extraordinary advances of computer science in combination with the ability to measure biological systems parameters on all spatial and temporal scales in the last two decades, however, is increasingly able to help mastering this complexity. Within systems biology mathematical modeling is being established as a complementary cornerstone to analyze biological systems in addition to biological experiments and clinical data acquisition. The main focus so far was on intracellular regulation and signal transduction pathways. However, for multi-cellular systems, experimental methods are now increasingly available to validate mechanisms on sub-cellular, cellular and also on multi-cellular scales, and current initiatives, often funded by national or international funding bodies fund large international networks of research groups from different disciplines to explore collaboratively disease-relevant multi-cellular growth and organization processes such as tumor development and growth, tissue regeneration, and cell re-programming. Hence, multi-cellular organization processes are increasingly becoming a main target of funding. One of the most important contributions of contemporary computer science are computational models that allow to test novel hypotheses by in silico simulations whose predictions can be validated by experiments in vitro and in vivo. The pluralism of causes requires the simultaneous measurements of system parameters across various scales. Computational models permit to stepwise integrate the different components on different scales into mathematical models and thereby gradually understand their role in the context of all other components. 

This EA

The collaborative projects presented in this proposal follow precisely this line. The projects pursued (T1) organ modelling: liver regeneration after drug intoxication and partial hepatectomy, cancerogenesis in liver, liver fibrosis, (T2) modelling of tumor growth and therapy in-vitro, in the animal model, and in patients, and (T3) modelling of cell differentiation and lineage specification are all embedded in large research consortia including various experimental and theoretical groups operating at different spatial and temporal scales spanning from the molecular to the centimetre scale of the whole organ.
The main methodical focus is on agent-based models in which each cell is represented as a single unit (agent). This facilitates the integration of the molecular building blocks such as signal-transduction and metabolic pathways. On the organ level, partly continuum models with be studied which do not resolve the individual cell anymore. 

State of art

Modeling: On the multi-cellular level, a number of mathematical individual-based model approaches have been studied: (i) Cellular automaton models on regular and irregular lattices, where a lattice site can be occupied by many cells (e.g. Radszuweit et. al., 2009), or by a single cell (Moreira and Deutsch, 2002 and refs. therein, Drasdo, 2005, Block et. al, 2007), or where a single cell can occupy many lattice sites (``Cellular Potts model´´, Graner and Glazier, 1992, 1993); (ii) Center-based models, where cells are mimicked as deformable, compressible spheres (Drasdo et. al., 2007 and refs therein, Galle et. al., 2006), or  ellipsoids (Palsson and Othmer, 2000, Palsson, 2003, Dallon and Othmer, 2004); (iii) Multi-center approaches, where a cell is mimicked by the hull of many spheres that are linked by effective forces (Newman, 2005). Center-based and multi-center models are lattice-free and usually parameterize the cell by directly measurable parameters.
Most models were applied to growing cell populations, cell sorting or to questions within developmental biology. While most models considered only one cell type, recently, the impact of oxygen tension on the differentiation of mesenchymal stem cells have been studied in spatial-temporal culture models both in-vitro and in-silico (Krinner et. al., 2009). For regenerative tissues, e.g. renewal of cells in intestinal crypts (Meineke et. al., 2001) and shape and length stability of crypts have been mimicked by mathematical models (Drasdo and Loeffler, 2001). Liver lobule regeneration has been mimicked by Hoehme et. al. in 2D models that represent a cross section of a liver lobule, and later in 3D models that include a detailed representation of the individual liver lobule. Also recently, the biophysical parameters in center-based models were linked to the intracellular and membrane concentration of β-catenin to mimic the epithelial-mesenchymal transition (EMT) (Ramis-Conde et. al., 2008) and intravasation (Ramis-Conde et. al., 2009). Both, the EMT and intravasation are fundamental processes in metastasis formation.
The link between liver architecture and function requires the investigation of the blood flow into the lobule from the periportal triads, through the sinusoids and how the blood drains into the central vein. The understanding of tumor growth beyond the millimetre scale requires an understanding of neo-vascularisation, the new formation of blood vessels gradually sprouting towards the tumor triggered by molecular (angiogenesis) factors released from the tumor cells. Models of blood flow have been extensively studied for vascularised tumours and angiogenesis (e.g. Mantzaris et. al., 2004, Lee and Rieger, 2006, Macklin et. al. 2009, Drasdo et. al. 2009). 
On the centimeter scale, a 3D tumor or densely packed tissue has about 109 cells. Agent-based systems at such population sizes are not feasible anymore. As a consequence, tissues may be modeled in two ways: A continuum mechanical model that is based on the mass, momentum and energy conservation equation complemented by a constitutive equation that describes the properties of the considered material. This approach considers locally averaged cell densities, the momentum and - in principle - energy density. Continuum models average over the fine structure of the tissue and therefore cannot resolve the precise position of cells or small multicellular substructures such as in liver the hepatocyte plates, sinusoidal networks or positions of other cell types and macrophages. 
For growing tumors, a number of continuous models have already been developed. 
In most cases deterministic models of the reaction-diffusion type or continuum mechanical models have been used (for comprehensive reviews see Adam and Belomo1997, Araujo, 2004, Mantzaris and Othmer, 2004, Preziosi, 2003, Roose et. al. 2007). Continuum models which have used to address tumor growth assume that growth is mechanically regulated (Ambrosi and Mollica, 2002, Byrne and Prezziosi, 2003), or nutrient-limited (Chaplain, 1996, Ward and King, 1997, Macklin, 2009).
These are well suited to the description of large scale phenomena where the cell and tissue properties vary smoothly over a length scale of several cell diameters.
However, only little work has been done so far to link individual-based with continuum models in such a way that both model types predict the same outcome. The reason for this is that only in rare cases continuous models can be obtained as a rigorous limit of the underlying stochastic multi-particle systems by hydrodynamic limiting or homogenization techniques, so one has to rely on direct comparisons rather than on rigorous derivations (e.g. Drasdo, 2005, Byrne and Drasdo, 2009).

Linking models to data:
 The development and validation of quantitative mathematical models on the tissue level require an objectified quantitative characterization of the underlying spatial-temporal processes. For this purpose, image processing and analysis has been shown to provide a perfect tool to extract quantitative information from the original bright field and confocal images (Hoehme et. al., 2009, PNAS, 2010) up to the millimetre scale. On larger spatial scales, MRI-images or ultrasound images have been shown to give useful inside into tissue shape and structure.

Both the IZBI team and the BANG team have a long-standing expertise in developing ``center-based´´ model approaches, in which each cell is mimicked as an individual agent interacting by central physical forces. Our most recent jointly submitted work on liver regeneration after drug intoxication is one of the very rare cases, where key processes in tissues could be successfully predicted and subsequently experimentally validated.  Following the same modeling strategy on modeling liver regeneration after drug intoxication (Hoehme et.al., 2010), that included several experimental partner groups, we will pursue the following projects:

T1: Liver

(i) Setting up an image processing and analysis chain and a mathematical model to analyze and predict liver regeneration after partial hepatectomy in mouse and human.
(ii) Setting up a multiscale-model that permit to mimic the effect of activation or de-activation of relevant pathways on the regeneration process. 
(iii) Studying how fibrosis can emerge from a healthy liver. 
(iv) Studying how activation or deactivation of pathways can initiate liver cancer in a multi-scale model that includes the molecular core modules within each cell and links it to the cellular function and behavior. 
(v) Explaining how zonation, a specialization of cells towards certain metabolic functions within liver can occur.
(vi) Predicting how the metabolism changes at the above disease states and during regeneration.

T2: Lung Cancer

Setting up a model to explain the growth pattern of lung cancer cells after administration of erythropoietin (used to protect blood cells from chemotherapeutic drugs, see below) in combination with chemotherapy in organotypic cultures, Xenografts of human lung cancer cells in the mouse model, and patients.

T3: Cell differentiation and specialization

Exporing optimized conditions to expand and differentiate mesenchymal stem cells in-vitro to permit reprogramming of cells for cell-based therapeutic strategies.