Computational approaches of multicellular assemblies have reached a stage where they may contribute to unveil the processes that underlie the organization of tissues and multicellular aggregates. In this article, we briefly review and present some new results on a number of 3D lattice free individual cell-based mathematical models of epithelial cell populations. The models we consider here are parameterized by bio-physical and cell-biological quantities on the level of an individual cell. Eventually, they aim at predicting the dynamics of the biological processes on the tissue level. We focus on a number of systems, the growth of cell populations in vitro, and the spatial-temporal organization of regenerative tissues. However, many processes on the sub-cellular scale do act cooperatively together and have a summary effect on a limited number of effective parameters on the cellular or the multicellular level. To unveil these hierarchies is one of the major issues of current research in systems biology (3). The parameters on the cellular scale are functions of characteristic quantities on the molecular scale, which are actively regulated by the cell (4,5). For example, although cells have a complex cytoskeleton they essentially behave as a viscoelastic, or on short time scales, as isotropic elastic body (6). Their biomechanical properties, therefore, may be characterized by a small number of material parameters, e.g. the Young modulus and the Poisson number. Further parameters are, for example, cell doubling time, cell mobility, and the cell-cell and cell-substrate adhesion.Because of recent advances in cell biophysics and cellbiology (7-10), the possibilities to collect new information on these parameters of cells and tissues are strongly improving. Nevertheless, an unique experimental identification of how the parameters on the cellular and subcellular level affect the organization on the multicellular level is often difficult. Many of the parameters cannot be directly modified and modifications of one property very often result in the modifications of other properties at the same time. This asks for new complementary methods that can deal with this complexity.Individual cell-based models (ICBM's, also called agentbased models) represent a recent trend in this context. These computer models use explicit representations of individual cells to model the organization of multicellular aggregates. One can distinguish two classes of them. In one class, the cellular automaton models, each cell is rep-

There is increasing interest in the analysis of biological tissue, its organization and its dynamics with the help of mathematical models. In the ideal case emergent properties on the tissue scale can be derived from the cellular scale. However, this has been achieved in rare examples only, in particular, when involving high-speed migration of cells. One major difficulty is the lack of a suitable multiscale simulation platform, which embeds reaction-diffusion of soluble substances, fast cell migration and mechanics, and, being of great importance in several tissue types, cell flow homeostasis. In this paper a step into this direction is presented by developing an agent-based mathematical model specifically designed to incorporate these features with special emphasis on high speed cell migration. Cells are represented as elastic spheres migrating on a substrate in lattice-free space. Their movement is regulated and guided by chemoattractants that can be derived from the substrate. The diffusion of chemoattractants is considered to be slower than cell migration and, thus, to be far from equilibrium. Tissue homeostasis is not achieved by the balance of growth and death but by a flow equilibrium of cells migrating in and out of the tissue under consideration. In this sense the number and the distribution of the cells in the tissue is a result of the model and not part of the assumptions. For purpose of demonstration of the model properties and functioning, the model is applied to a prominent example of tissue in a cellular flow equilibrium, the secondary lymphoid tissue. The experimental data on cell speed distributions in these tissues can be reproduced using reasonable mechanical parameters for the simulated cell migration in dense tissue.

The analysis of biological systems requires mathematical tools that represent their complexity from the molecular scale up to the tissue level. The formation of cell aggregates by chemotaxis is investigated using Delaunay object dynamics. It is found that when cells migrate fast such that the chemokine distribution is far from equilibrium, the details of the chemokine receptor dynamics can induce an internalization driven instability of cell aggregates. The instability occurs in a parameter regime relevant for lymphoid tissue and is similar to ectopic lymphoid structures.

Signal transduction is the process of routing information inside cells when receiving stimuli from their environment that modulate the behavior and function. In such biological processes, the receptors, after receiving the corresponding signals, activate a number of biomolecules which eventually transduce the signal to the nucleus. The main objective of our work is to develop a theoretical approach which will help to better understand the behavior of signal transduction networks due to changes in kinetic parameters and network topology. By using an evolutionary algorithm, we designed a mathematical model which performs basic signaling tasks similar to the signaling process of living cells. We use a simple dynamical model of signaling networks of interacting proteins and their complexes. We study the evolution of signaling networks described by mass-action kinetics. The fitness of the networks is determined by the number of signals detected out of a series of signals with varying strength. The mutations include changes in the reaction rate and network topology. We found that stronger interactions and addition of new nodes lead to improved evolved responses. The strength of the signal does not play any role in determining the response type. This model will help to understand the dynamic behavior of the proteins involved in signaling pathways. It will also help to understand the robustness of the kinetics of the output response upon changes in the rate of reactions and the topology of the network.

T cells orchestrate the adaptive immune response, making them targets for immunotherapy. Although immunosuppressive therapies prevent disease progression, they also leave patients susceptible to opportunistic infections. To identify novel drug targets, we established a logical model describing T-cell receptor (TCR) signaling. However, to have a model that is able to predict new therapeutic approaches, the current drug targets must be included. Therefore, as a next step we generated the interleukin-2 receptor (IL-2R) signaling network and developed a tool to merge logical models. For IL-2R signaling, we show that STAT activation is independent of both Src- and PI3-kinases, while ERK activation depends upon both kinases and additionally requires novel PKCs. In addition, our merged model correctly predicted TCR-induced STAT activation. The combined network also allows information transfer from one receptor to add detail to another, thereby predicting that LAT mediates JNK activation in IL-2R signaling. In summary, the merged model not only enables us to unravel potential cross-talk, but it also suggests new experimental designs and provides a critical step towards designing strategies to reprogram T cells.

No abstract

During the germinal center (GC) reaction a characteristic morphology is developed. In the framework of a recently developed space-time model for the GC, a mechanism for the formation of dark and light zones has been proposed. There, the mechanism is based on a diffusing differentiation signal which is distinguished by follicular dendritic cells (FDC). Here, we investigate a possible influence of recently found chemoattractants on GC formation in the framework of a single cell-based stochastic and discrete three-dimensional model. This necessitates a more detailed spatial description. The model is enlarged by a detailed prescription of cell motility and it is introduced as a consistent volume concept. We consider various possible chemotactic pathways that may play a role for the development of both zones. Our results suggest that the centrocyte motility resulting from a FDC-derived chemoattractant has to exceed a lower limit to allow the separation of centroblasts and centrocytes. In contrast to light microscopy, the dark zone is ring shaped. This suggests that FDC-derived chemoattractants alone cannot explain the typical GC morphology.

Primary lymphoid follicles (PLFs) in secondary lymphoid tissue (SLT) of mammals are the backbone for the formation of follicular dendritic cell (FDC) networks. These are important for germinal center reactions during which affinity maturation creates optimized antibodies in adaptive immune responses. In the context of organogenesis, molecular requirements for the formation of follicles have been identified. The present study complements these findings with a simulation of the dynamics of the PLF formation, and a critical analysis of the relevant molecular interactions. In contrast to other problems of pattern formation, the homeostasis of cell populations in SLTs is not governed by a growth-death balance but by a flow equilibrium of migrating cells. The influx of cells into these tissues has been extensively studied. However, less information is available about the efflux of lymphocytes from SLTs. This study formulates the minimal requirements for cell efflux that guarantee a flow equilibrium and, thus, a stable PLF. The model predicts that in addition to already identified regulatory mechanisms, a negative regulation of the generation of FDCs is required. Furthermore, a comparison with data concerning the microanatomy of SLTs yields the conclusion that dynamical changes of the lymphatic endothelium during the formation of FDC networks are necessary to understand the genesis and maintenance of follicles.