Interpreting two-photon imaging data of lymphocyte motility

A Multiscale Spatial Modeling Framework for the Germinal Center Response

The germinal center response or reaction (GCR) is a hallmark event of adaptive humoral immunity. Unfolding in the B cell follicles of the secondary lymph organs, a GC culminates in the production of high-affinity antibody-secreting plasma cells along with memory B cells. By interacting with follicular dendritic cells (FDC) and T follicular helper (Tfh) cells, GC B cells exhibit complex spatiotemporal dynamics. Driving the B cell dynamics are the intracellular signal transduction and gene regulatory network that responds to cell surface signaling molecules, cytokines, and chemokines. As our knowledge of the GC continues to expand in depth and in scope, mathematical modeling has become an important tool to help disentangle the intricacy of the GCR and inform novel mechanistic and clinical insights. While the GC has been modeled at different granularities, a multiscale spatial simulation framework - integrating molecular, cellular, and tissue-level responses - is still rare. Here, we report our recent progress toward this end with a hybrid stochastic GC framework developed on the Cellular Potts Model-based CompuCell3D platform. Tellurium is used to simulate the B cell intracellular molecular network comprising NF-κB, FOXO1, MYC, AP4, CXCR4, and BLIMP1 that responds to B cell receptor (BCR) and CD40-mediated signaling. The molecular outputs of the network drive the spatiotemporal behaviors of B cells, including cyclic migration between the dark zone (DZ) and light zone (LZ) via chemotaxis; clonal proliferative bursts, somatic hypermutation, and DNA damage-induced apoptosis in the DZ; and positive selection, apoptosis via a death timer, and emergence of plasma cells in the LZ. Our simulations are able to recapitulate key molecular, cellular, and morphological GC events including B cell population growth, affinity maturation, and clonal dominance. This novel modeling framework provides an open-source, customizable, and multiscale virtual GC simulation platform that enables qualitative and quantitative in silico investigations of a range of mechanic and applied research questions in future.

The role of geometric features in a germinal center

The germinal center (GC) is a self-organizing structure produced in the lymphoid follicle during the T-dependent immune response and is an important component of the humoral immune system. However, the impact of the special structure of GC on antibody production is not clear. According to the latest biological experiments, we establish a spatiotemporal stochastic model to simulate the whole self-organization process of the GC including the appearance of two specific zones: the dark zone (DZ) and the light zone (LZ), the development of which serves to maintain an effective competition among different cells and promote affinity maturation. A phase transition is discovered in this process, which determines the critical GC volume for a successful growth in both the stochastic and the deterministic model. Further increase of the volume does not make much improvement on the performance. It is found that the critical volume is determined by the distance between the activated B cell receptor (BCR) and the target epitope of the antigen in the shape space. The observation is confirmed in both 2D and 3D simulations and explains partly the variability of the observed GC size.

B Cell Speed and B-FDC Contacts in Germinal Centers Determine Plasma Cell Output via Swiprosin-1/EFhd2

Plasma cells secreting affinity-matured antibodies develop in germinal centers (GCs), where B cells migrate persistently and directionally over defined periods of time. How modes of GC B cell migration influence plasma cell development remained unclear. Through genetic deletion of the F-actin bundling protein Swiprosin-1/EF-hand domain family member 2 (EFhd2) and by two-photon microscopy, we show that EFhd2 restrains B cell speed in GCs and hapten-specific plasma cell output. Modeling the GC reaction reveals that increasing GC B cell speed promotes plasma cell generation. Lack of EFhd2 also reduces contacts of GC B cells with follicular dendritic cells in vivo. Computational modeling uncovers that both GC output and antibody affinity depend quantitatively on contacts of GC B cells with follicular dendritic cells when B cells migrate more persistently. Collectively, our data explain how GC B cells integrate speed and persistence of cell migration with B cell receptor affinity.

Physiological factors leading to a successful vaccination: A computational approach

The immune system mounts a response to an infection by activating T cells. T cell activation occurs when dendritic cells, which have already interacted with the pathogen, scan a T cell that is cognate for (responsive to) the pathogen. This often occurs inside lymph nodes. The time it takes for this scanning event to occur, indeed the probability that it will occur at all, depends on many factors, including the rate that T cells and dendritic cells enter and leave the lymph node as well as the geometry of the lymph node and of course other cellular and molecular parameters. In this paper, we develop a hybrid stochastic-deterministic mathematical model at the tissue scale of the lymph node and simulate dendritic cells and cognate T cells to investigate the most important physiological factors leading to a successful and timely immune response after a vaccination. We use an agent-based model to describe the small population of cognate naive T cells and a partial differential equation description for the concentration of mature dendritic cells. We estimate the model parameters based on the known literature and measurements previously taken in our lab. We perform a parameter sensitivity analysis to quantify the sensitivity of the model results to the parameters. The results show that increasing T cell inflow through high endothelial venules, restricting cellular egress via the efferent lymph and increasing the total dendritic cell count by improving vaccinations are the among the most important physiological factors leading to an improved immune response. We also find that increasing the physical size of lymph nodes improves the overall likelihood that an immune response will take place but has a fairly weak effect on the response rate. The nature of dendritic cell trafficking through the LN (either passive or active transport) seems to have little effect on the overall immune response except if a change in overall egress time is observed.

Cell Cycle-Associated CXCR4 Expression in Germinal Center B Cells and Its Implications on Affinity Maturation

Adaptation of antibody-mediated immunity occurs in germinal centers (GC). It is where affinity maturation, class switching, memory and plasma cell differentiation synergize to generate specific high-affinity antibodies that aid both to clear and protect against reinfection of invading pathogens. Within GCs, light and dark zone are two compartments instrumental in regulating this process, by segregating T cell-dependent selection and differentiation from generation of GC B cells bearing hypermutated antigen receptors. Spatial segregation of GC B cells into the two zones relies on the chemokine receptor CXCR4, with textbooks attributing high and low expression to a dark and light zone phenotype. Interestingly, this bipolarity is not reflected in the CXCR4 expression profile of GC B cells, which is highly variable and unimodal, indicating a continuum of intermediate CXCR4 levels rather than a binary dark or light zone phenotype. Here, analysis of published BrdU pulse-chase data reveals that throughout cell cycle, average CXCR4 expression in GC B cells steadily increases close to twofold, scaling with cell surface area. CXCR4 expression in recently divided GC B cells in G0/G1 or early S phase shows intermediate levels compared to cells in G2M phase, consistent with their smaller size. The lowest number of CXCR4 receptors are displayed by relatively aged GC B cells in G0/G1 or early S phase. The latter, upon progressing through S phase, however, ramp up relative CXCR4 expression twice as much as recently divided cells. Twelve hours after the BrdU pulse, labeled GC B cells, while initially in S phase, are desynchronized in terms of cell cycle and match the CXCR4 profile of unlabeled cells. A model is discussed in which CXCR4 expression in GC B cell increases with cell cycle and cell surface area, with highest levels in G2 and M phase, coinciding with GC B cell receptor signaling in G2 and immediately preceding activation-induced cytidine deaminase (AID) activity in early G1. In the model, GC B cells compete for CXCL12 expression on the basis of their CXCR4 expression, gaining a relative advantage as they progress in cell cycle, but loosing the advantage at the moment they divide.

How to Simulate a Germinal Center

Germinal centers host a mini-evolutionary environment where B cells can mutate their receptor and be selected depending on its affinity to target antigens in a process called affinity maturation. Starting from founder cells with a weak B cell receptor affinity, germinal centers release output cells as antibody-secreting cells or memory cells with a very high affinity, a property which is essential for pathogen clearance and immune memory. Therapeutic interventions on the germinal centers are tantalizing approaches to improve vaccines or to support rejection of chronic pathogens such as HIV. However, the complexity of the selection processes makes it very hard to make reliable predictions. Here, we present in detail how to build an agent-based model (hyphasma), accounting for the dynamics of the germinal center. It encompasses the core quantitative traits of affinity maturation, and allowed to make reliable predictions in previous studies.

Leukocyte Motility Models Assessed through Simulation and Multi-objective Optimization-Based Model Selection

The advent of two-photon microscopy now reveals unprecedented, detailed spatio-temporal data on cellular motility and interactions in vivo. Understanding cellular motility patterns is key to gaining insight into the development and possible manipulation of the immune response. Computational simulation has become an established technique for understanding immune processes and evaluating hypotheses in the context of experimental data, and there is clear scope to integrate microscopy-informed motility dynamics. However, determining which motility model best reflects in vivo motility is non-trivial: 3D motility is an intricate process requiring several metrics to characterize. This complicates model selection and parameterization, which must be performed against several metrics simultaneously. Here we evaluate Brownian motion, Lévy walk and several correlated random walks (CRWs) against the motility dynamics of neutrophils and lymph node T cells under inflammatory conditions by simultaneously considering cellular translational and turn speeds, and meandering indices. Heterogeneous cells exhibiting a continuum of inherent translational speeds and directionalities comprise both datasets, a feature significantly improving capture of in vivo motility when simulated as a CRW. Furthermore, translational and turn speeds are inversely correlated, and the corresponding CRW simulation again improves capture of our in vivo data, albeit to a lesser extent. In contrast, Brownian motion poorly reflects our data. Lévy walk is competitive in capturing some aspects of neutrophil motility, but T cell directional persistence only, therein highlighting the importance of evaluating models against several motility metrics simultaneously. This we achieve through novel application of multi-objective optimization, wherein each model is independently implemented and then parameterized to identify optimal trade-offs in performance against each metric. The resultant Pareto fronts of optimal solutions are directly contrasted to identify models best capturing in vivo dynamics, a technique that can aid model selection more generally. Our technique robustly determines our cell populations’ motility strategies, and paves the way for simulations that incorporate accurate immune cell motility dynamics.

Advances in imaging technology allow investigators to monitor the movements and interactions of immune cells in a live animal, processes essential to understanding and manipulating how an immune response is generated. T cells in the brains of Toxoplasma gondii-infected mice have previously been described as performing a Lévy walk, an optimal strategy for locating sparsely, randomly distributed targets. Determining which motility model best characterizes a population of cells is problematic; multiple metrics are required to specify as intricate and nuanced a process as 3D motility, and the tools to evaluate model-parameter combinations have been lacking. We have developed a novel framework to perform this model evaluation through simulation, a popular tool for exploring complex immune system phenomena. We find that Lévy walk offers an inferior capture of our data to another class of motility model, the correlated random walk, and this determination was possible because we are able to explicitly evaluate several motility metrics simultaneously. Further, we find evidence that leukocytes differ in their inherent translational and rotational speeds. These findings facilitate more accurate immune system simulations aimed at unravelling the processes underpinning this critical biological function.

A Stochastic Model of the Germinal Center Integrating Local Antigen Competition, Individualistic T-B Interactions, and B Cell Receptor Signaling

The germinal center (GC) reaction underlies productive humoral immunity by orchestrating competition-based affinity maturation to produce plasma cells and memory B cells. T cells are limiting in this process. How B cells integrate signals from T cells and BCRs to make fate decisions while subjected to a cyclic selection process is not clear. In this article, we present a spatiotemporally resolved stochastic model that describes cell behaviors as rate-limited stochastic reactions. We hypothesize a signal integrator protein integrates follicular helper T (Tfh)- and Ag-derived signals to drive different B cell fates in a probabilistic manner and a dedicated module of Tfh interaction promoting factors control the efficiency of contact-dependent Tfh help delivery to B cells. Without assuming deterministic affinity-based decisions or temporal event sequence, this model recapitulates GC characteristics, highlights the importance of efficient T cell help delivery during individual contacts with B cells and intercellular positive feedback for affinity maturation, reveals the possibility that antagonism between BCR signaling and T cell help accelerates affinity maturation, and suggests that the dichotomy between affinity and magnitude of GC reaction can be avoided by tuning the efficiency of contact-dependent help delivery during reiterative T-B interactions.

Computational immuno-biology for organ transplantation and regenerative medicine

Organ transplantation and regenerative medicine are adopted platforms that provide replacement tissues and organs from natural or engineered sources. Acceptance, tolerance and rejection depend greatly on the proper control of the immune response against graft antigens, motivating the development of immunological and genetical therapies that prevent organ failure. They rely on a complete, or partial, understanding of the immune system. Ultimately, they are innovative technologies that ensure permanent graft tolerance and indefinite graft survival through the modulation of the immune system. Computational immunology has arisen as a tool towards a mechanistic understanding of the biological and physicochemical processes surrounding an immune response. It comprehends theoretical and computational frameworks that simulate immuno-biological systems. The challenge is centered on the multi-scale character of the immune system that spans from atomistic scales, during peptide-epitope and protein interactions, to macroscopic scales, for lymph transport and organ-organ reactions. In this paper, we discuss, from an engineering perspective, the biological processes that are involved during the immune response of organ transplantation. Previous computational efforts, including their characteristics and visible limitations, are described. Finally, future perspectives and challenges are listed to motivate further developments.

Mathematics in modern immunology

Mathematical and statistical methods enable multidisciplinary approaches that catalyse discovery. Together with experimental methods, they identify key hypotheses, define measurable observables and reconcile disparate results. We collect a representative sample of studies in T-cell biology that illustrate the benefits of modelling–experimental collaborations and that have proven valuable or even groundbreaking. We conclude that it is possible to find excellent examples of synergy between mathematical modelling and experiment in immunology, which have brought significant insight that would not be available without these collaborations, but that much remains to be discovered.

T cell and reticular network co-dependence in HIV infection

Fibroblastic reticular cells (FRC) are arranged on a network in the T cell zone of lymph nodes, forming a scaffold for T cell migration, and providing survival factors, especially interleukin-7 (IL-7). Conversely, CD4(+) T cells are the major producers of lymphotoxin-β (LT-β), necessary for the construction and maintenance of the FRC network. This interdependence creates the possibility of a vicious cycle, perpetuating loss of both FRC and T cells. Furthermore, evidence that HIV infection is responsible for collagenation of the network suggests that long term loss of network function might be responsible for the attenuated recovery in T cell count seen in HIV patients undergoing antiretroviral therapy (ART). We present computational and mathematical models of this interaction mechanism and subsequent naive CD4(+) T-cell depletion in which (1) collagen deposition impedes access of naive T cells to IL-7 on the FRC and loss of IL-7 production by loss of FRC network itself, leading to the depletion of naive T cells through increased apoptosis; and (2) depletion of naive T cells as the source of LT-β on which the FRC depend for survival leads to loss of the network, thereby amplifying and perpetuating the cycle of depletion of both naive T cells and stromal cells. Our computational model explicitly includes an FRC network and its cytokine exchange with a heterogeneous T-cell population. We also derive lumped models, in terms of partial differential equations and reduced to ordinary differential equations, that provide additional insight into the mechanisms at work. The central conclusions are that (1) damage to the reticular network, caused by HIV infection is a plausible mechanism for attenuated recovery post-ART; (2) within this, the production of T cell survival factors by FRCs may be the key rate-limiting step; and (3) the methods of model reduction and analysis presented are useful for both immunological studies and other contexts in which agent-based models are severely limited by computational cost.

Heterogeneous CD8+ T cell migration in the lymph node in the absence of inflammation revealed by quantitative migration analysis

The three-dimensional positions of immune cells can be tracked in live tissues precisely as a function of time using two-photon microscopy. However, standard methods of analysis used in the field and experimental artifacts can bias interpretations and obscure important aspects of cell migration such as directional migration and non-Brownian walk statistics. Therefore, methods were developed for minimizing drift artifacts, identifying directional and anisotropic (asymmetric) migration, and classifying cell migration statistics. These methods were applied to describe the migration statistics of CD8+ T cells in uninflamed lymph nodes. Contrary to current models, CD8+ T cell statistics are not well described by a straightforward persistent random walk model. Instead, a model in which one population of cells moves via Brownian-like motion and another population follows variable persistent random walks with noise reproduces multiple statistical measures of CD8+ T cell migration in the lymph node in the absence of inflammation.

Migration is fundamental to immune cell function, and accurate quantitative methods are crucial for analyzing and interpreting migration statistics. However, existing methods of analysis cannot uniquely describe cell behavior and suffer from various limitations. This complicates efforts to address questions such as to what extent chemotactic signals direct cellular behaviors and how random migration of many cells leads to coordinated immune response. We therefore develop methods that provide a complete description of migration with a minimum of assumptions and describe specific quantities for characterizing directional motion. Using numerical simulations and experimental data, we evaluate these measures and discuss methods to minimize the effects of experimental artifacts. These methodologies may be applied to various migrating cells or organisms. We apply our approach to an important model system, T cells migrating in lymph node. Surprisingly, we find that the canonical Brownian-walker-like model does not accurately describe migration. Instead, we find that T cells move heterogeneously and are described by a two-population model of persistent and diffusive random walkers. This model is completely different from the generalized Lévy walk model that describes activated T cells in brains infected with Toxoplasma gondii, indicating that T cells exhibit distinct migration statistics in different tissues.

Multiphoton microscopy: An introduction to gastroenterologists

Multiphoton microscopy, relying on the simultaneous absorption of two or more photons by a fluorophore, has come to occupy a prominent place in modern biomedical research with its ability to allow real-time observation of a single cell and molecules in intact tissues. Multiphoton microscopy exhibits nonlinear optical contrast properties, which can make it possible to provide an exceptionally large depth penetration with less phototoxicity. This system becomes more and more an inspiring tool for a non-invasive imaging system to realize “optical biopsy” and to examine the functions of living cells. In this review, we briefly present the physical principles and properties of multiphoton microscopy as well as the current applications in biological fields. In addition, we address what we see as the future potential of multiphoton microscopy for gastroenterologic research.

Systems biology approaches for understanding cellular mechanisms of immunity in lymph nodes during infection

Adaptive immunity is initiated in secondary lymphoid tissues when naive T cells recognize foreign antigen presented as MHC-bound peptide on the surface of dendritic cells. Only a small fraction of T cells in the naive repertoire will express T cell receptors specific for a given epitope, but antigen recognition triggers T cell activation and proliferation, thus greatly expanding antigen-specific clones. Expanded T cells can serve a helper function for B cell responses or traffic to sites of infection to secrete cytokines or kill infected cells. Over the past decade, two-photon microscopy of lymphoid tissues has shed important light on T cell development, antigen recognition, cell trafficking and effector functions. These data have enabled the development of sophisticated quantitative and computational models that, in turn, have been used to test hypotheses in silico that would otherwise be impossible or difficult to explore experimentally. Here, we review these models and their principal findings and highlight remaining questions where modeling approaches are poised to advance our understanding of complex immunological systems.

T cell responses in lymph nodes

Activation of T cells by antigen-presenting cells (APCs) in lymph nodes (LNs) is a key initiating event in many immune responses. Our understanding of this process has been both improved and complicated in recent years by evidence from techniques such as intravital microscopy that has revealed new levels of dynamism in the interaction of T cells and APCs. In particular, the complex motility of T cells within LNs, and their serial interactions with many APCs, imply that earlier static models of T cell activation need to be updated. Here we review the first attempts to model T cell interactions with APCs in LNs that incorporate simulations of T cell motility, based on experimental observations. We show that lattice-based modeling approaches are the dominant trend in these models, and then chart a possible course for development of these models toward spatially-resolved models of immune responses within LNs.

Agent-based simulation of T-cell activation and proliferation within a lymph node

Recent intravital microscopy experiments have revealed the complex behavior of T cells within lymph nodes. Modeling T-cell responses in lymph nodes now requires integration of cell trafficking and motility with the molecular processes involved in T-cell activation. We describe an agent-based model that allows such integration, in which T cells undertake a random walk through a three-dimensional representation of the lymph node paracortex, integrating signals from dendritic cells (DCs), and proliferating in response. The model accommodates simulation of a large number of T cells packed at realistic densities, and includes dynamic cell trafficking that allows the lymph nodes to swell and shrink as the immune response progresses. The results from the model, including the kinetics of cognate T-cell proliferation and release, and the changes in their avidity profile, are similar to those observed in vivo. We therefore propose that this modeling framework is capable of successfully simulating T-cell activation while also accounting for new spatiotemporal knowledge of how T cells and DCs interact. Although some of the parameters used to drive the model are not yet experimentally validated, the model is capable of testing the effects of alternative values for any parameter on the T-cell response. We intend to refine each aspect of the model in collaboration with both theoreticians and experimentalists.

Agent-based modeling of host-pathogen systems: The successes and challenges

Agent-based models have been employed to describe numerous processes in immunology. Simulations based on these types of models have been used to enhance our understanding of immunology and disease pathology. We review various agent-based models relevant to host–pathogen systems and discuss their contributions to our understanding of biological processes. We then point out some limitations and challenges of agent-based models and encourage efforts towards reproducibility and model validation.

T cell migration dynamics within lymph nodes during steady state: an overview of extracellular and intracellular factors influencing the basal intranodal T cell motility

Naive T lymphocytes continuously recirculate through secondary lymphoid organs such as lymph nodes until they are eventually activated by recognizing cognate peptide/MHC-complexes on the surface of antigen-protecting cells. The intranodal T cell migration behavior leading to these crucial--and potentially rare--encounters during the induction of an adaptive immune response could not be directly addressed until, in 2002, the use of two-photon microscopy also allowed the visualization of cellular dynamics deep within intact lymph nodes. Since then, numerous studies have confirmed that, by default, naive T cells are extremely motile, scanning the paracortical T cell zone for cognate antigen by means of an apparent random walk. This review attempts to summarize the current knowledge of factors influencing the basal migration behavior of naive T lymphocytes within lymph nodes during steady state. Extracellular cues, such as the motility-promoting influence of CCR7 ligands and the role of integrins during interstitial migration, as well as intracellular signaling pathways involved in T cell motility, will be discussed. Particular emphasis is placed on structural features of the lymph node environment orchestrating T cell migration, namely the framework of fibroblastic reticular cells serving as migration "highways." Finally, new approaches to simulate the cellular dynamics within lymph nodes in silico by means of mathematical modeling will be reviewed.

Deriving a germinal center lymphocyte migration model from two-photon data

Recently, two-photon imaging has allowed intravital tracking of lymphocyte migration and cellular interactions during germinal center (GC) reactions. The implications of two-photon measurements obtained by several investigators are currently the subject of controversy. With the help of two mathematical approaches, we reanalyze these data. It is shown that the measured lymphocyte migration frequency between the dark and the light zone is quantitatively explained by persistent random walk of lymphocytes. The cell motility data imply a fast intermixture of cells within the whole GC in approximately 3 h, and this does not allow for maintenance of dark and light zones. The model predicts that chemotaxis is active in GCs to maintain GC zoning and demonstrates that chemotaxis is consistent with two-photon lymphocyte motility data. However, the model also predicts that the chemokine sensitivity is quickly down-regulated. On the basis of these findings, we formulate a novel GC lymphocyte migration model and propose its verification by new two-photon experiments that combine the measurement of B cell migration with that of specific chemokine receptor expression levels. In addition, we discuss some statistical limitations for the interpretation of two-photon cell motility measurements in general.

Scaling aspects of lymphocyte trafficking

We consider the long lived pool of B and T cells that recirculate through blood, tissues and the lymphatic system of an animal with body mass M. We derive scaling rules (allometric relations) for: (1) the rate of production of mature lymphocytes, (2) the accumulation of lymphocytes in the tissues, (3) the flux of lymphocytes through the lymphatic system, (4) the number of lymph nodes, (5) the number of lymphocytes per clone within a lymph node, and (6) the total number of lymphocytes within a lymph node. Mass-dependent aspects of immune learning and of the immunological self are shown to be not very significant. Our treatment is somewhat heuristic and aims at combining immunological data with recent progress in biological scaling.

Grid-free models of multicellular systems, with an application to large-scale vortices accompanying primitive streak formation

This paper is comprised of two parts. In the first we provide a brief overview of grid-free methods for modeling multicellular systems. We focus on an approach based on Langevin equations, in which inertia is ignored, and stochastic effects on cell motion are included. The discussion starts with simpler models, in which cells are modeled as adhesive spheres. We then turn to more sophisticated approaches in which nontrivial cell shape is accommodated, including the recently introduced Subcellular Element Model, in which each cell is described as a cluster of adhesively coupled over-damped subcellular elements, representing patches of cytoskeleton. In the second part of the paper we illustrate the use of a standard grid-free cell-based model to computationally probe interesting new features associated with primitive streak formation in the chick embryo. Streak formation is a key developmental step in amniotes (i.e., birds, reptiles, and mammals), and can be observed in detail in the chick embryo, where the streak extends across a tightly-packed two-dimensional sheet (the epiblast) comprised of about 50,000 cells. The Weijer group [Cui, Yang, Chuai, Glazier, and Weijer, Dev. Biol. 284 (2005) 37-47] recently observed that streak formation is accompanied by coordinated cell movement lateral to the streak, resulting in two large counter-rotating vortices. We study a mechanism based on cell polarity (in the plane of the epiblast) that provides an explanation for these vortices, and test it successfully using computer simulations. This mechanism is robust, since the emergent vortex formation depends only on the gross features of the initial spatial distribution of planar polarity in the epiblast.

The molecular makeup and function of regulatory and effector synapses

Physical interactions between T cells and antigen-presenting cells (APCs) form the basis of any specific immune response. Upon cognate contacts, a multimolecular assembly of receptors and adhesion molecules on both cells is created, termed the immunological synapse (IS). Very diverse structures of ISs have been described, yet the functional importance for T-cell differentiation is largely unclear. Here we discuss the principal structure and function of ISs. We then focus on two characteristic T-cell-APC pairs, namely T cells contacting dendritic cells (DCs) or naive B cells, for which extremely different patterns of the IS have been observed as well as fundamentally different effects on the function of the activated T cells. We provide a model on how differences in signaling and the involvement of adhesion molecules might lead to diverse interaction kinetics and, eventually, diverse T-cell differentiation. We hypothesize that the preferred activation of the adhesion molecule leukocyte function-associated antigen-1 (LFA-1) and of the negative regulator for T-cell activation, cytotoxic T-lymphocyte antigen-4 (CTLA-4), through contact with naive B cells, lead to prolonged cell-cell contacts and the generation of T cells with regulatory capacity. In contrast, DCs might have evolved mechanisms to avoid LFA-1 overactivation and CTLA-4 triggering, thereby promoting more dynamic contacts that lead to the preferential generation of effector cells.

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.

Characterizing T cell movement within lymph nodes in the absence of antigen

The recent application of two-photon microscopy to the visualization of T cell movement has presented trajectories of individual T cells within lymphoid organs both in the presence and in the absence of Ag-loaded dendritic cells. Remarkably, even though T cells largely move along conduits of the fibroblastic reticular cell network, they appear to execute random walks in lymphoid organs rather than chemotaxis. In this study, we analyze experimental trajectories of T cells using computer simulations of idealized random walks. Comparisons of simulations with experimental data provide estimates of key parameters that characterize T cell motion in vivo. For example, we find that the distance moved before turning is about twice the distance between intersections in the fibroblastic reticular cell network, suggesting that at an intersection a T cell will turn onto a new fiber approximately 50% of the time. Although the calibrated model appears to offer an accurate representation of T cell movement, it has also uncovered inconsistencies across different experimental data sets.

Spatial modelling of brief and long interactions between T cells and dendritic cells

In the early phases of an immune response, T cells of appropriate antigen specificity become activated by antigen-presenting cells in secondary lymphoid organs. Two-photon microscopy imaging experiments have shown that this stimulation occurs in distinct stages during which T cells exhibit different motilities and interactions with dendritic cells (DCs). In this paper, we utilize the Cellular Potts Model, a model formalism that takes cell shapes and cellular interactions explicitly into account, to simulate the dynamics of, and interactions between, T cells and DCs in the lymph node paracortex. Our three-dimensional simulations suggest that the initial decrease in T-cell motility after antigen appearance is due to "stop signals" transmitted by activated DCs to T cells. The long-lived interactions that occur at a later stage can only be explained by the presence of both stop signals and a high adhesion between specific T cells and antigen-bearing DCs. Furthermore, our results indicate that long-lasting contacts with T cells are promoted when DCs retract dendrites that detect a specific contact at lower velocities than other dendrites. Finally, by performing long simulations (after prior fitting to short time scale data) we are able to provide an estimate of the average contact duration between T cells and DCs.

A modelling approach towards epidermal homoeostasis control

In order to grasp the features arising from cellular discreteness and individuality, in large parts of cell tissue modelling agent-based models are favoured. The subclass of off-lattice models allows for a physical motivation of the intercellular interaction rules. We apply an improved version of a previously introduced off-lattice agent-based model to the steady-state flow equilibrium of skin. The dynamics of cells is determined by conservative and drag forces, supplemented with delta-correlated random forces. Cellular adjacency is detected by a weighted Delaunay triangulation. The cell cycle time of keratinocytes is controlled by a diffusible substance provided by the dermis. Its concentration is calculated from a diffusion equation with time-dependent boundary conditions and varying diffusion coefficients. The dynamics of a nutrient is also taken into account by a reaction-diffusion equation. It turns out that the analysed control mechanism suffices to explain several characteristics of epidermal homoeostasis formation. In addition, we examine the question of how in silico melanoma with decreased basal adhesion manage to persist within the steady-state flow equilibrium of the skin. Interestingly, even for melanocyte cell cycle times being substantially shorter than for keratinocytes, tiny stochastic effects can lead to completely different outcomes. The results demonstrate that the understanding of initial states of tumour growth can profit significantly from the application of off-lattice agent-based models in computer simulations.

Dynamics of in silico leukocyte rolling, activation, and adhesion

Background

We present a multilevel, agent based, in silico model that represents the dynamics of rolling, activation, and adhesion of individual leukocytes in vitro. Object-oriented software components were designed, verified, plugged together, and then operated in ways that represent the molecular and cellular mechanisms believed responsible for leukocyte rolling and adhesion. The result is an in silico analogue of an experimental in vitro system. The experimentally measured, phenotypic attributes of the analogue were compared and contrasted to those of leukocytes in vitro from three different experimental conditions.

Results

The individual in silico dynamics of "rolling" on simulated P-selectin, and separately on simulated VCAM-1, were an acceptable match to individual in vitro distance-time and velocity-time measurements. The analogues are also able to represent the transition from rolling to adhesion on P-selectin and VCAM-1 in the presence of GRO-α chemokine. The individual in silico and in vitro behavioral similarities translated successfully to population level measures. These behavioral similarities were enabled in part by subdividing the functionality of the analogue's surface into 600 independent, "cell"-controlled, equally capable modules of comparable functionality.

Conclusion

The overlap in phenotypic attributes of our analogue with those of leukocytes in vitro confirm the considerable potential of our model for studying the key events that determine the behavioral outcome of individual leukocytes during rolling, activation, and adhesion. Our results provide an important foundation and framework for future in silico research into plausible causal links between well-documented, subcellular molecular level events and the variety of systemic phenotypic attributes that distinguish normal leukocyte adhesion from abnormal disease-associated adhesion.