Negative interactions and feedback regulations are required for transient cellular response.

Signal transduction is a process required to conduct information from a receptor to the nucleus. This process is vital for the control of cellular function and fate. The dynamics of signaling activation and inhibition determine processes such as apoptosis, proliferation, and differentiation. Thus, it is important to understand the factors modulating transient and sustained response. To address this question, by applying mathematical approach we have studied the factors which can alter the activation nature of downstream signaling molecules. The factors which we have investigated are loops (feed forward and feedback loops), cross-talk of signal transduction pathways, and the change in the concentration of the signaling molecules. Based on our results we conclude that among these factors feedback loop and the cross-talks which directly inhibit the target protein dominantly controls the transient cellular response.

Discrete, qualitative models of interaction networks.

Logical models for cellular signaling networks are recently attracting wide interest: Their ability to integrate qualitative information at different biological levels, from receptor-ligand interactions to gene-regulatory networks, is becoming essential for understanding complex signaling behavior. We present an overview of Boolean modeling paradigms and discuss in detail an approach based on causal logical interactions that yields descriptive and predictive signaling network models. Our approach offers a mathematically well-defined concept, improving the efficiency of analytical tools to meet the demand of large-scale data sets, and can be extended into various directions to include timing information as well as multiple discrete values for components.

Simulated evolution of signal transduction networks.

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.

Integrating signals from the T-cell receptor and the interleukin-2 receptor.

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.

Multiscale modeling of cell mechanics and tissue organization.

Nowadays, experimental biology gathers a large number of molecular and genetic data to understand the processes in living systems. Many of these data are evaluated on the level of cells, resulting in a changed phenotype of cells. Tools are required to translate the information on the cellular scale to the whole tissue, where multiple interacting cell types are involved. Agent-based modeling allows the investigation of properties emerging from the collective behavior of individual units. A typical agent in biology is a single cell that transports information from the intracellular level to larger scales. Mainly, two scales are relevant: changes in the dynamics of the cell, e.g. surface properties, and secreted molecules that can have effects at a distance larger than the cell diameter.

Cell transmembrane receptors determine tissue pattern stability.

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.

Mechanisms of organogenesis of primary lymphoid follicles.

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.

Modeling emergent tissue organization involving high-speed migrating cells in a flow equilibrium.

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 the purposes 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 type of seeder cells determines the efficiency of germinal center reactions.

During humoral immune responses some germinal centers (GCs) develop very well and give rise to a large number of high affinity antibody producing plasma cells. Other GC reactions develop poorly, somatic mutation is reduced, and the output production is practically absent. This led to the hypothesis that two classes of GCs exist, and that GCs show an all-or-none behaviour. We investigate the role of the seeder B cells affinity to the antigen in this context. It is shown in the framework of a space-time simulation of GC reactions that, indeed, the seeder cell affinity is a critical parameter that determines the fate of the GC reaction. Starting from a homogeneous distributions of seeder cell affinities in an ensemble of GC reactions, we demonstrate that an all-or-none behaviour of GCs has to be expected. Possible implications are discussed.

A possible role of chemotaxis in germinal center formation.

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.

Conclusions from two model concepts on germinal center dynamics and morphology.

Germinal centers (GC) are an essential part of the humoral immune response. They develop a clear structure during maturation: Centroblasts and centrocytes are separated into two zones, the dark and the light zone. The mechanisms leading to this specific morphology as well as the reason for zone-depletion during a later phase of the GC reaction have not clearly been revealed in experiment. We discuss and weigh possible mechanisms of dark and light zone development in the framework of two mathematical models. In a comparative approach we formulate constraints on typical lymphocyte velocities in GCs which are characteristic for the different proposed mechanisms.