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

Modeling three-dimensional T-cell motility using clustering and hidden Markov models

Recent advances in imaging technologies now allow for real-time tracking of fast-moving immune cells as they search for targets such as pathogens and tumor cells through complex three-dimensional tissues. Cytotoxic T cells are specialized immune cells that continually scan tissues for such targets to engage and kill, and have emerged as the principle mediators of breakthrough immunotherapies against cancers. Modeling the way these T cells move is of great value in furthering our understanding of their collective search efficiency. T-cell motility is characterized by heterogeneity at two levels: (a) Individual cells display different distributions of translational speeds and turning angles, and (b) each cell can during a given track, its motility, switch between local search and directional motion. Despite a likely considerable influence on a motile population's search performance, statistical models that accurately capture both such heterogeneities in a distinguishing manner are lacking. Here, we model three-dimensional T-cell trajectories through a spherical representation of their incremental steps and compare model outputs to real-world motility data from primary T cells navigating physiological environments. T cells in a population are clustered based on their directional persistence and characteristic "step lengths" therein capturing between-cell heterogeneity. The motility dynamics of cells within each cluster are individually modeled through hidden Markov model to capture within-cell transitions between local and more extensive search patterns. We explore the importance of explicitly capturing altered motility patterns when cells lie in close proximity to one another, through a non-homogenous hidden Markov model.

New tools for immunologists: models of lymph node function from cells to tissues

The lymph node is a highly structured organ that mediates the body's adaptive immune response to antigens and other foreign particles. Central to its function is the distinct spatial assortment of lymphocytes and stromal cells, as well as chemokines that drive the signaling cascades which underpin immune responses. Investigations of lymph node biology were historically explored in vivo in animal models, using technologies that were breakthroughs in their time such as immunofluorescence with monoclonal antibodies, genetic reporters, in vivo two-photon imaging, and, more recently spatial biology techniques. However, new approaches are needed to enable tests of cell behavior and spatiotemporal dynamics under well controlled experimental perturbation, particularly for human immunity. This review presents a suite of technologies, comprising in vitro, ex vivo and in silico models, developed to study the lymph node or its components. We discuss the use of these tools to model cell behaviors in increasing order of complexity, from cell motility, to cell-cell interactions, to organ-level functions such as vaccination. Next, we identify current challenges regarding cell sourcing and culture, real time measurements of lymph node behavior in vivo and tool development for analysis and control of engineered cultures. Finally, we propose new research directions and offer our perspective on the future of this rapidly growing field. We anticipate that this review will be especially beneficial to immunologists looking to expand their toolkit for probing lymph node structure and function.

Interpreting T-cell search "strategies" in the light of evolution under constraints

Two decades of in vivo imaging have revealed how diverse T-cell motion patterns can be. Such recordings have sparked the notion of search "strategies": T cells may have evolved ways to search for antigen efficiently depending on the task at hand. Mathematical models have indeed confirmed that several observed T-cell migration patterns resemble a theoretical optimum; for example, frequent turning, stop-and-go motion, or alternating short and long motile runs have all been interpreted as deliberately tuned behaviours, optimising the cell's chance of finding antigen. But the same behaviours could also arise simply because T cells cannot follow a straight, regular path through the tight spaces they navigate. Even if T cells do follow a theoretically optimal pattern, the question remains: which parts of that pattern have truly been evolved for search, and which merely reflect constraints from the cell's migration machinery and surroundings? We here employ an approach from the field of evolutionary biology to examine how cells might evolve search strategies under realistic constraints. Using a cellular Potts model (CPM), where motion arises from intracellular dynamics interacting with cell shape and a constraining environment, we simulate evolutionary optimization of a simple task: explore as much area as possible. We find that our simulated cells indeed evolve their motility patterns. But the evolved behaviors are not shaped solely by what is functionally optimal; importantly, they also reflect mechanistic constraints. Cells in our model evolve several motility characteristics previously attributed to search optimisation-even though these features are not beneficial for the task given here. Our results stress that search patterns may evolve for other reasons than being "optimal". In part, they may be the inevitable side effects of interactions between cell shape, intracellular dynamics, and the diverse environments T cells face in vivo.

A tessellated lymphoid network provides whole-body T cell surveillance in zebrafish

Homeostatic trafficking to lymph nodes allows T cells to efficiently survey the host for cognate antigen. Non-mammalian jawed vertebrates lack lymph nodes but maintain similarly diverse T cell pools. Here, we exploit in vivo imaging of transparent zebrafish to investigate how T cells organize and survey for antigen in an animal devoid of lymph nodes. We find that naïve-like T cells in zebrafish organize into a previously undescribed whole-body lymphoid network that supports streaming migration and coordinated trafficking through the host. This network has the cellular hallmarks of a mammalian lymph node, including naïve T cells and CCR7-ligand expressing non-hematopoietic cells, and facilitates rapid collective migration. During infection, T cells transition to a random walk that supports antigen presenting cell interactions and subsequent activation. Our results reveal that T cells can toggle between collective migration and individual random walks to prioritize either large-scale trafficking or antigen search in situ . This novel lymphoid network thus facilitates whole-body T cell trafficking and antigen surveillance in the absence of a lymph node system.

Significance Statement

In mammals, lymph nodes play a critical role in the initiation of adaptive immune responses by providing a dedicated place for T cells to scan antigen-presenting cells. Birds, reptiles, amphibians, and fish all maintain diverse repertoires of T cells but lack lymph nodes, raising questions about how adaptive immunity functions in lower jawed vertebrates. Here, we describe a novel network of lymphocytes in zebrafish that supports whole-body T cell trafficking and provides a site for antigen search, mirroring the function of mammalian lymph nodes. Within this network, T cells can prioritize large-scale trafficking or antigen scanning by toggling between two distinct modes of migration. This network provides valuable insights into the evolution of adaptive immunity.

Integrative lymph node-mimicking models created with biomaterials and computational tools to study the immune system

The lymph node (LN) is a vital organ of the lymphatic and immune system that enables timely detection, response, and clearance of harmful substances from the body. Each LN comprises of distinct substructures, which host a plethora of immune cell types working in tandem to coordinate complex innate and adaptive immune responses. An improved understanding of LN biology could facilitate treatment in LN-associated pathologies and immunotherapeutic interventions, yet at present, animal models, which often have poor physiological relevance, are the most popular experimental platforms. Emerging biomaterial engineering offers powerful alternatives, with the potential to circumvent limitations of animal models, for in-depth characterization and engineering of the lymphatic and adaptive immune system. In addition, mathematical and computational approaches, particularly in the current age of big data research, are reliable tools to verify and complement biomaterial works. In this review, we first discuss the importance of lymph node in immunity protection followed by recent advances using biomaterials to create in vitro/vivo LN-mimicking models to recreate the lymphoid tissue microstructure and microenvironment, as well as to describe the related immuno-functionality for biological investigation. We also explore the great potential of mathematical and computational models to serve as in silico supports. Furthermore, we suggest how both in vitro/vivo and in silico approaches can be integrated to strengthen basic patho-biological research, translational drug screening and clinical personalized therapies. We hope that this review will promote synergistic collaborations to accelerate progress of LN-mimicking systems to enhance understanding of immuno-complexity.

CelltrackR: An R package for fast and flexible analysis of immune cell migration data

Visualization of cell migration via time-lapse microscopy has greatly advanced our understanding of the immune system. However, subtle differences in migration dynamics are easily obscured by biases and imaging artifacts. While several analysis methods have been suggested to address these issues, an integrated tool implementing them is currently lacking. Here, we present celltrackR, an R package containing a diverse set of state-of-the-art analysis methods for (immune) cell tracks. CelltrackR supports the complete pipeline for track analysis by providing methods for data management, quality control, extracting and visualizing migration statistics, clustering tracks, and simulating cell migration. CelltrackR supports the analysis of both 2D and 3D cell tracks. CelltrackR is an open-source package released under the GPL-2 license, and is freely available on both GitHub and CRAN. Although the package was designed specifically for immune cell migration data, many of its methods will also be of use in other research areas dealing with moving objects.

Local actin dynamics couple speed and persistence in a cellular Potts model of cell migration

Cell migration is astoundingly diverse. Molecular signatures, cell-cell interactions, and environmental structures each play their part in shaping cell motion, yielding numerous morphologies and migration modes. Nevertheless, in recent years, a simple unifying law was found to describe cell migration across many different cell types and contexts: faster cells turn less frequently. This universal coupling between speed and persistence (UCSP) was explained by retrograde actin flow from front to back, but it remains unclear how this mechanism generalizes to cells with complex shapes and cells migrating in structured environments, which may not have a well-defined front-to-back orientation. Here, we present an in-depth characterization of an existing cellular Potts model, in which cells polarize dynamically from a combination of local actin dynamics (stimulating protrusions) and global membrane tension along the perimeter (inhibiting protrusions). We first show that the UCSP emerges spontaneously in this model through a cross talk of intracellular mechanisms, cell shape, and environmental constraints, resembling the dynamic nature of cell migration in vivo. Importantly, we find that local protrusion dynamics suffice to reproduce the UCSP-even in cases in which no clear global, front-to-back polarity exists. We then harness the spatial nature of the cellular Potts model to show how cell shape dynamics limit both the speed and persistence a cell can reach and how a rigid environment such as the skin can restrict cell motility even further. Our results broaden the range of potential mechanisms underlying the speed-persistence coupling that has emerged as a fundamental property of migrating cells.

Enhanced segmentation of label-free cells for automated migration and interaction tracking

In biomedical research, the migration behavior of cells and interactions between various cell types are frequently studied subjects. An automated and quantitative analysis of time-lapse microscopy data is an essential component of these studies, especially when characteristic migration patterns need to be identified. Plenty of software tools have been developed to serve this need. However, the majority of algorithms is designed for fluorescently labeled cells, even though it is well-known that fluorescent labels can substantially interfere with the physiological behavior of interacting cells. We here present a fully revised version of our algorithm for migration and interaction tracking (AMIT), which includes a novel segmentation approach. This approach allows segmenting label-free cells with high accuracy and also enables detecting almost all cells within the field of view. With regard to cell tracking, we designed and implemented a new method for cluster detection and splitting. This method does not rely on any geometrical characteristics of individual objects inside a cluster but relies on monitoring the events of cell-cell fusion from and cluster fission into single cells forward and backward in time. We demonstrate that focusing on these events provides accurate splitting of transient clusters. Furthermore, the substantially improved quantitative analysis of cell migration by the revised version of AMIT is more than two orders of magnitude faster than the previous implementation, which makes it feasible to process video data at higher spatial and temporal resolutions.

Evaluation of CD8 T cell killing models with computer simulations of 2-photon imaging experiments

In vivo imaging of cytotoxic T lymphocyte (CTL) killing activity revealed that infected cells have a higher observed probability of dying after multiple contacts with CTLs. We developed a three-dimensional agent-based model to discriminate different hypotheses about how infected cells get killed based on quantitative 2-photon in vivo observations. We compared a constant CTL killing probability with mechanisms of signal integration in CTL or infected cells. The most likely scenario implied increased susceptibility of infected cells with increasing number of CTL contacts where the total number of contacts was a critical factor. However, when allowing in silico T cells to initiate new interactions with apoptotic target cells (zombie contacts), a contact history independent killing mechanism was also in agreement with experimental datasets. The comparison of observed datasets to simulation results, revealed limitations in interpreting 2-photon data, and provided readouts to distinguish CTL killing models.

Migration of Cytotoxic T Lymphocytes in 3D Collagen Matrices

CD8+ cytotoxic T lymphocytes (CTL) and natural killer cells are the main cytotoxic killer cells of the human body to eliminate pathogen-infected or tumorigenic cells (also known as target cells). To find their targets, they have to navigate and migrate through complex biological microenvironments, a key component of which is the extracellular matrix (ECM). The mechanisms underlying killer cell's navigation are not well understood. To mimic an ECM, we use a matrix formed by different collagen concentrations and analyze migration trajectories of primary human CTLs. Different migration patterns are observed and can be grouped into three motility types: slow, fast, and mixed. The dynamics are well described by a two-state persistent random walk model, which allows cells to switch between slow motion with low persistence and fast motion with high persistence. We hypothesize that the slow motility mode describes CTLs creating channels through the collagen matrix by deforming and tearing apart collagen fibers and that the fast motility mode describes CTLs moving within these channels. Experimental evidence supporting this scenario is presented by visualizing migrating T cells following each other on exactly the same track and showing cells moving quickly in channel-like cavities within the surrounding collagen matrix. Consequently, the efficiency of the stochastic search process of CTLs in the ECM should strongly be influenced by a dynamically changing channel network produced by the killer cells themselves.

Heterogeneous T cell motility behaviors emerge from a coupling between speed and turning in vivo

T cells in vivo migrate primarily via undirected random walks, but it remains unresolved how these random walks generate an efficient search. Here, we use light sheet microscopy of T cells in the larval zebrafish as a model system to study motility across large populations of cells over hours in their native context. We show that cells do not perform Levy flight; rather, there is substantial cell-to-cell variability in speed, which persists over timespans of a few hours. This variability is amplified by a correlation between speed and directional persistence, generating a characteristic cell behavioral manifold that is preserved under a perturbation to cell speeds, and seen in Mouse T cells and Dictyostelium. Together, these effects generate a broad range of length scales over which cells explore in vivo.

Spatial Lymphocyte Dynamics in Lymph Nodes Predicts the Cytotoxic T Cell Frequency Needed for HIV Infection Control

The surveillance of host body tissues by immune cells is central for mediating their defense function. In vivo imaging technologies have been used to quantitatively characterize target cell scanning and migration of lymphocytes within lymph nodes (LNs). The translation of these quantitative insights into a predictive understanding of immune system functioning in response to various perturbations critically depends on computational tools linking the individual immune cell properties with the emergent behavior of the immune system. By choosing the Newtonian second law for the governing equations, we developed a broadly applicable mathematical model linking individual and coordinated T-cell behaviors. The spatial cell dynamics is described by a superposition of autonomous locomotion, intercellular interaction, and viscous damping processes. The model is calibrated using in vivo data on T-cell motility metrics in LNs such as the translational speeds, turning angle speeds, and meandering indices. The model is applied to predict the impact of T-cell motility on protection against HIV infection, i.e., to estimate the threshold frequency of HIV-specific cytotoxic T cells (CTLs) that is required to detect productively infected cells before the release of viral particles starts. With this, it provides guidance for HIV vaccine studies allowing for the migration of cells in fibrotic LNs.

Integration of in vitro and in silico Models Using Bayesian Optimization With an Application to Stochastic Modeling of Mesenchymal 3D Cell Migration

Cellular migration plays a crucial role in many aspects of life and development. In this paper, we propose a computational model of 3D migration that is solved by means of the tau-leaping algorithm and whose parameters have been calibrated using Bayesian optimization. Our main focus is two-fold: to optimize the numerical performance of the mechano-chemical model as well as to automate the calibration process of in silico models using Bayesian optimization. The presented mechano-chemical model allows us to simulate the stochastic behavior of our chemically reacting system in combination with mechanical constraints due to the surrounding collagen-based matrix. This numerical model has been used to simulate fibroblast migration. Moreover, we have performed in vitro analysis of migrating fibroblasts embedded in 3D collagen-based fibrous matrices (2 mg/ml). These in vitro experiments have been performed with the main objective of calibrating our model. Nine model parameters have been calibrated testing 300 different parametrizations using a completely automatic approach. Two competing evaluation metrics based on the Bhattacharyya coefficient have been defined in order to fit the model parameters. These metrics evaluate how accurately the in silico model is replicating in vitro measurements regarding the two main variables quantified in the experimental data (number of protrusions and the length of the longest protrusion). The selection of an optimal parametrization is based on the balance between the defined evaluation metrics. Results show how the calibrated model is able to predict the main features observed in the in vitro experiments.

Search efficiency of biased migration towards stationary or moving targets in heterogeneously structured environments

Efficient search acts as a strong selective force in biological systems ranging from cellular populations to predator-prey systems. The search processes commonly involve finding a stationary or mobile target within a heterogeneously structured environment where obstacles limit migration. An open generic question is whether random or directionally biased motions or a combination of both provide an optimal search efficiency and how that depends on the motility and density of targets and obstacles. To address this question, we develop a simple model that involves a random walker searching for its targets in a heterogeneous medium of bond percolation square lattice and used mean first passage time (〈T〉) as an indication of average search time. Our analysis reveals a dual effect of directional bias on the minimum value of 〈T〉. For a homogeneous medium, directionality always decreases 〈T〉 and a pure directional migration (a ballistic motion) serves as the optimized strategy, while for a heterogeneous environment, we find that the optimized strategy involves a combination of directed and random migrations. The relative contribution of these modes is determined by the density of obstacles and motility of targets. Existence of randomness and motility of targets add to the efficiency of search. Our study reveals generic and simple rules that govern search efficiency. Our findings might find application in a number of areas including immunology, cell biology, ecology, and robotics.

Computational model of mesenchymal migration in 3D under chemotaxis

Cell chemotaxis is an important characteristic of cellular migration, which takes part in crucial aspects of life and development. In this work, we propose a novel in silico model of mesenchymal 3D migration with competing protrusions under a chemotactic gradient. Based on recent experimental observations, we identify three main stages that can regulate mesenchymal chemotaxis: chemosensing, dendritic protrusion dynamics and cell-matrix interactions. Therefore, each of these features is considered as a different module of the main regulatory computational algorithm. The numerical model was particularized for the case of fibroblast chemotaxis under a PDGF-bb gradient. Fibroblasts migration was simulated embedded in two different 3D matrices - collagen and fibrin - and under several PDGF-bb concentrations. Validation of the model results was provided through qualitative and quantitative comparison with in vitro studies. Our numerical predictions of cell trajectories and speeds were within the measured in vitro ranges in both collagen and fibrin matrices. Although in fibrin, the migration speed of fibroblasts is very low, because fibrin is a stiffer and more entangling matrix. Testing PDGF-bb concentrations, we noticed that an increment of this factor produces a speed increment. At 1 ng mL-1 a speed peak is reached after which the migration speed diminishes again. Moreover, we observed that fibrin exerts a dampening behavior on migration, significantly affecting the migration efficiency.

Mathematical Models for Immunology: Current State of the Art and Future Research Directions

The advances in genetics and biochemistry that have taken place over the last 10 years led to significant advances in experimental and clinical immunology. In turn, this has led to the development of new mathematical models to investigate qualitatively and quantitatively various open questions in immunology. In this study we present a review of some research areas in mathematical immunology that evolved over the last 10 years. To this end, we take a step-by-step approach in discussing a range of models derived to study the dynamics of both the innate and immune responses at the molecular, cellular and tissue scales. To emphasise the use of mathematics in modelling in this area, we also review some of the mathematical tools used to investigate these models. Finally, we discuss some future trends in both experimental immunology and mathematical immunology for the upcoming years.

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.

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.

T cell migration, search strategies and mechanisms

T cell migration is essential for T cell responses; it allows for the detection of cognate antigen at the surface of antigen-presenting cells and for interactions with other cells involved in the immune response. Although appearing random, growing evidence suggests that T cell motility patterns are strategic and governed by mechanisms that are optimized for both the activation stage of the cell and for environment-specific cues. In this Opinion article, we discuss how the combined effects of T cell-intrinsic and -extrinsic forces influence T cell motility patterns in the context of highly complex tissues that are filled with other cells involved in parallel motility. In particular, we examine how insights from 'search theory' can be used to describe T cell movement across an 'exploitation-exploration trade-off' in the context of activation versus effector function and lymph nodes versus peripheral tissues.

Zigzag Generalized Lévy Walk: the In Vivo Search Strategy of Immunocytes

Immune responses are based on the coordinated searching behaviors of immunocytes that are aimed at tracking down specific targets. The search efficiency of immunocytes significantly affects the speed of initiation and development of immune responses. Previous studies have shown that not only the intermittent walk but also the zigzag turning preference of immunocytes contributes to the search efficiency. However, among existing models describing immunocytes' search strategy, none has captured both features. Here we propose a zigzag generalized Lévy walk model to describe the search strategy of immunocytes more accurately and comprehensively by considering both the intermittent and the zigzag-turning walk features. Based on the analysis of the searching behaviors of typical immune cell types, dendritic cells and leukocytes, in their native physiological environment, we demonstrate that the model can describe the in vivo search strategy of immunocytes well. Furthermore, by analyzing the search efficiency, we find that this type of search strategy enables immunocytes to capture rare targets in approximately half the time than the previously proposed generalized Lévy walk. This study sheds new light on the fundamental mechanisms that drive the efficient initiation and development of immune responses and in turn may lead to the development of novel therapeutic approaches for diseases ranging from infection to cancer.

Changes in the flow-volume curve according to the degree of stenosis in patients with unilateral main bronchial stenosis

Objectives

The shape of the flow-volume (F-V) curve is known to change to showing a prominent plateau as stenosis progresses in patients with tracheal stenosis. However, no study has evaluated changes in the F-V curve according to the degree of bronchial stenosis in patients with unilateral main bronchial stenosis.

Methods

We performed an analysis of F-V curves in 29 patients with unilateral bronchial stenosis with the aid of a graphic digitizer between January 2005 and December 2011.

Results

The primary diseases causing unilateral main bronchial stenosis were endobronchial tuberculosis (86%), followed by benign bronchial tumor (10%), and carcinoid (3%). All unilateral main bronchial stenoses were classified into one of five grades (I, ≤25%; II, 26%-50%; III, 51%-75%; IV, 76%-90%; V, >90% to near-complete obstruction without ipsilateral lung collapse). A monophasic F-V curve was observed in patients with grade I stenosis and biphasic curves were observed for grade II-IV stenosis. Both monophasic (81%) and biphasic shapes (18%) were observed in grade V stenosis. After standardization of the biphasic shape of the F-V curve, the breakpoints of the biphasic curve moved in the direction of high volume (x-axis) and low flow (y-axis) according to the progression of stenosis.

Conclusion

In unilateral bronchial stenosis, a biphasic F-V curve appeared when bronchial stenosis was >25% and disappeared when obstruction was near complete. In addition, the breakpoint moved in the direction of high volume and low flow with the progression of stenosis.

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.

Detection of rare antigen-presenting cells through T cell-intrinsic meandering motility, mediated by Myo1g

To mount an immune response, T lymphocytes must successfully search for foreign material bound to the surface of antigen-presenting cells. How T cells optimize their chances of encountering and responding to these antigens is unknown. T cell motility in tissues resembles a random or Levy walk and is regulated in part by external factors including chemokines and lymph-node topology, but motility parameters such as speed and propensity to turn may also be cell intrinsic. Here we found that the unconventional myosin 1g (Myo1g) motor generates membrane tension, enforces cell-intrinsic meandering search, and enhances T-DC interactions during lymph-node surveillance. Increased turning and meandering motility, as opposed to ballistic motility, is enhanced by Myo1g. Myo1g acts as a "turning motor" and generates a form of cellular "flânerie." Modeling and antigen challenges show that these intrinsically programmed elements of motility search are critical for the detection of rare cognate antigen-presenting cells.

EGFR-blockade with erlotinib reduces EGF and TGF-β2 expression and the actin-cytoskeleton which influences different aspects of cellular migration in lens epithelial cells

INTRODUCTION

After cataract surgery, residual lens epithelial cells migrate and proliferate within the capsular bag resulting in posterior capsule opacification (PCO). The up-regulation of TGF-β2, EGF and FGF-2 has been identified as a key factor in PCO pathogenesis leading to actin fiber assembly and alterations in the migration pattern. In this in vitro study, the influence of Erlotinib as a selective EGFR inhibitor is investigated on the cellular features indicated, which might promote a future clinical application.

METHODS

Expression of EGF, FGF-2 and TGF-β2 was measured using RT-PCR and ELISA in human lens epithelial cells (HLEC). Computational data of an in vitro time lapse microscopy assay were used for statistical analysis of single cell migration with a particular focus on cell-cell interaction; cell velocity distribution; and displacement before, during and after mitosis. The effect of Erlotinib on the actin-cytoskeleton was evaluated using Alexa Fluor 488 Phalloidin and epifluorescence microscopy.

RESULTS

EGF and TGF-β2 mRNA expression and protein levels are reduced by Erlotinib, while FGF-2 expression remained stable. Overall fluidity of cell-cell interaction is less in the presence of Erlotinib compared to the control and the velocity distribution across all cells becomes less uniform within the cell cluster. After mitosis, HLEC move significantly faster without EGFR inhibition, which can be completely blocked by Erlotinib. Furthermore, Erlotinib diminishes the amount of actin stress fibers and the stress fiber diameter.

CONCLUSION

As a novel effect of Erlotinib on HLEC, we describe the down-regulation of EGF and TGF-β2 expression, both are crucial factors for PCO development. Cellular movement displays complex alterations under EGFR inhibition, which is partly explained by actin fiber depletion. These findings further underline the role of Erlotinib in pharmacologic PCO prophylaxis.

Analytical results on the Beauchemin model of lymphocyte migration

The Beauchemin model is a simple particle-based description of stochastic lymphocyte migration in tissue, which has been successfully applied to studying immunological questions. In addition to being easy to implement, the model is also to a large extent mathematically tractable. This article provides a comprehensive overview of both existing and new analytical results on the Beauchemin model within a common mathematical framework. Specifically, we derive the motility coefficient, the mean square displacement, and the confinement ratio, and discuss four different methods for simulating biased migration of pre-defined speed. The results provide new insight into published studies and a reference point for future research based on this simple and popular lymphocyte migration model.

A global "imaging'' view on systems approaches in immunology

The immune system exhibits an enormous complexity. High throughput methods such as the "-omic'' technologies generate vast amounts of data that facilitate dissection of immunological processes at ever finer resolution. Using high-resolution data-driven systems analysis, causal relationships between complex molecular processes and particular immunological phenotypes can be constructed. However, processes in tissues, organs, and the organism itself (so-called higher level processes) also control and regulate the molecular (lower level) processes. Reverse systems engineering approaches, which focus on the examination of the structure, dynamics and control of the immune system, can help to understand the construction principles of the immune system. Such integrative mechanistic models can properly describe, explain, and predict the behavior of the immune system in health and disease by combining both higher and lower level processes. Moving from molecular and cellular levels to a multiscale systems understanding requires the development of methodologies that integrate data from different biological levels into multiscale mechanistic models. In particular, 3D imaging techniques and 4D modeling of the spatiotemporal dynamics of immune processes within lymphoid tissues are central for such integrative approaches. Both dynamic and global organ imaging technologies will be instrumental in facilitating comprehensive multiscale systems immunology analyses as discussed in this review.

On-lattice simulation of T cell motility, chemotaxis, and trafficking in the lymph node paracortex

Agent-based simulation is a powerful method for investigating the complex interplay of the processes occurring in a lymph node during an adaptive immune response. We have previously established an agent-based modeling framework for the interactions between T cells and dendritic cells within the paracortex of lymph nodes. This model simulates in three dimensions the “random-walk” T cell motility observed in vivo, so that cells interact in space and time as they process signals and commit to action such as proliferation. On-lattice treatment of cell motility allows large numbers of densely packed cells to be simulated, so that the low frequency of T cells capable of responding to a single antigen can be dealt with realistically. In this paper we build on this model by incorporating new numerical methods to address the crucial processes of T cell ingress and egress, and chemotaxis, within the lymph node. These methods enable simulation of the dramatic expansion and contraction of the T cell population in the lymph node paracortex during an immune response. They also provide a novel probabilistic method to simulate chemotaxis that will be generally useful in simulating other biological processes in which chemotaxis is an important feature.

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.

Defining the quantitative limits of intravital two-photon lymphocyte tracking

Two-photon microscopy has substantially advanced our understanding of cellular dynamics in the immune system. Cell migration can now be imaged in real time in the living animal. Strikingly, the migration of naive lymphocytes in secondary lymphoid tissue appears predominantly random. It is unclear, however, whether directed migration may escape detection in this random background. Using a combination of mathematical modeling and experimental data, we investigate the extent to which modern two-photon imaging can rule out biologically relevant directed migration. For naive T cells migrating in uninfected lymph nodes (LNs) at average 3D speeds of around 18 μm/min, we rule out uniform directed migration of more than 1.7 μm/min at the 95% confidence level, confirming that T cell migration is indeed mostly random on a timescale of minutes. To investigate whether this finding still holds for longer timescales, we use a 3D simulation of the naive T cell LN transit. A pure random walk predicts a transit time of around 16 h, which is in good agreement with experimental results. A directional bias of only 0.5 μm/min-less than 3% of the cell speed-would already accelerate the transit twofold. These results jointly strengthen the random walk analogy for naive T cell migration in LNs, but they also emphasize that very small deviations from random migration can still be important. Our methods are applicable to cells of any type and can be used to reanalyze existing datasets.

B cells within germinal centers migrate preferentially from dark to light zone

One of the main questions in the field of imaging immune cell migration in living tissues is whether cells fulfill their functionality via random or nonrandom migration processes. For some applications, this issue has remained controversial even after publication of various imaging studies. A prime example is B-cell migration in germinal centers (GCs) where somatic hypermutation and clonal selection of B cells are thought to occur within morphologically distinct regions termed dark zone (DZ) and light zone (LZ). Here, we reanalyze a previously published dataset on GC B-cell migration, applying a sensitive analysis technique to detect directed migration and using a procedure to correct for a number of artifacts that frequently occur in time-lapse imaging experiments. Although B cells roughly perform a persistent random walk, we present evidence that they have a small preference (of on average about 0.2-0.3 μm min(-1)) to migrate from DZ to LZ, which is consistent with classical views of the GC reaction. This preference is most pronounced among a large subset of almost half of the B-cell population migrating along relatively straight tracks. Using a computational model to generate long-lasting B-cell tracks based on the experimental motility data (including the small directional preference), we predict a time course to travel from DZ to LZ of a few hours. This is consistent with experimental observations, and we show that at the observed cellular motility such a time course cannot be explained without the small preferential migration from DZ to LZ.

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.

Lymph node cortical sinus organization and relationship to lymphocyte egress dynamics and antigen exposure

Recent studies have identified cortical sinuses as sites of sphingosine-1-phosphate receptor-1 (S1P(1))-dependent T- and B-cell egress from the lymph node (LN) parenchyma. However, the distribution of cortical sinuses in the entire LN and the extent of lymph flow within them has been unclear. Using 3D reconstruction and intravital two-photon microscopy we describe the branched organization of the cortical sinus network within the inguinal LN and show that lymphocyte flow begins within blunt-ended sinuses. Many cortical sinuses are situated adjacent to high endothelial venules, and some lymphocytes access these sinuses within minutes of entering a LN. However, upon entry to inflamed LNs, lymphocytes rapidly up-regulate CD69 and are prevented from accessing cortical sinuses. Using the LN reconstruction data and knowledge of lymphocyte migration and cortical sinus entry dynamics, we developed a mathematical model of T-cell egress from LNs. The model suggests that random walk encounters with lymphatic sinuses are the major factor contributing to LN transit times. A slight discrepancy between predictions of the model and the measured transit times may be explained by lymphocytes undergoing a few rounds of migration between the parenchyma and sinuses before departing from the LN. Because large soluble antigens gain rapid access to cortical sinuses, such parenchyma-sinus shuttling may facilitate antibody responses.

Analysing immune cell migration

The visualization of the dynamic behaviour of and interactions between immune cells using time-lapse video microscopy has an important role in modern immunology. To draw robust conclusions, quantification of such cell migration is required. However, imaging experiments are associated with various artefacts that can affect the estimated positions of the immune cells under analysis, which form the basis of any subsequent analysis. Here, we describe potential artefacts that could affect the interpretation of data sets on immune cell migration. We propose how these errors can be recognized and corrected, and suggest ways to prevent the data analysis itself leading to biased results.

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.

Simulating T-cell motility in the lymph node paracortex with a packed lattice geometry

Agent-based simulation modelling of T-cell trafficking, activation and proliferation in the lymph node paracortex requires a model for cell motility. Such a model must be able to reproduce the observed random-walk behaviour of T cells, while accommodating large numbers of tightly packed cells, and must be computationally efficient. We report the development of a motility model, based on a three-dimensional lattice geometry, that meets these objectives. Cells make discrete jumps between neighbouring lattice sites in directions that are randomly determined from specified discrete probability distributions, which are defined by a small number of parameters. It is shown that the main characteristics of the random motion of T cells as typically observed in vivo can be reproduced by suitable specification of model parameters. The model is computationally highly efficient and provides a suitable engine for a model capable of simulating the full T-cell population of the paracortex.

How antigen quantity and quality determine T-cell decisions in lymphoid tissue

T lymphocytes (T cells) express T-cell receptor (TCR) molecules on their surface that can recognize peptides (p) derived from antigenic proteins bound to products of the major histocompatibility complex (MHC) genes. The pMHC molecules are expressed on the surface of antigen-presenting cells, such as dendritic cells (DCs). T cells first encounter antigen on DCs in lymph nodes (LN). Intravital microscopy experiments show that upon entering the LN containing antigen, CD8+ T cells first move rapidly. After a few hours, they stop and make extended contacts with DCs. The factors that determine when and how this transition occurs are not well understood. We report results from computer simulations that suggest that the duration of phase one is related to the low probability of productive interactions between T cells and DCs. This is demonstrated by our finding that the antigen dose and type determine when such a transition occurs. These results are in agreement with experimental observations. TCR-pMHC binding characteristics and the antigen dose determine the time required for a productive T-cell-DC encounter (resulting in sustained contact). We find that the ratio of this time scale and the half-life of the pMHC complex itself provide a consolidated measure of antigen quantity and type. Results obtained upon varying different measures of antigen quantity and type fall on one curve when graphed against this ratio of time scales. Thus, we provide a mechanism for how the effects of varying one set of parameters are influenced by other prevailing conditions. This understanding should help guide future experimentation.

A comparison of random vs. chemotaxis-driven contacts of T cells with dendritic cells during repertoire scanning

Generating adaptive immunity after infection or immunization requires physical interactions within a lymph node (LN) T-zone between antigen-bearing dendritic cells (DCs) that arrive from peripheral tissues and rare cognate T cells entering via high endothelial venules (HEVs). This interaction results in activation of cognate T cells, expansion of that T cell lineage and their exit from the LN T-zone via efferent lymphatics (ELs). How antigen-specific T cells locate DCs within this complex environment is controversial, and both random T cell migration and chemotaxis have been proposed. We developed an agent-based computational model of a LN that captures many features of T cell and DC dynamics observed by two-photon microscopy. Our simulations matched in vivo two-photon microscopy data regarding T cell speed, short-term directional persistence of motion and cell motility. We also obtained in vivo data regarding density of T cells and DCs within a LN and matched our model environment to measurements of the distance from HEVs to ELs. We used our model to compare chemotaxis with random motion and showed that chemotaxis increased total number of T cell DC contacts, but decreased unique contacts, producing fewer activated T cells. Our results suggest that, within a LN T-zone, a random search strategy is optimal for a rare cognate T cell to find its DC match and maximize production of activated T cells.

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.