Persistence and Adaptation in Immunity: T Cells Balance the Extent and Thoroughness of Search

More Is Faster: Why Population Size Matters in Biological Search

Many biological scenarios have multiple cooperating searchers, and the timing of the initial first contact between any one of those searchers and its target is critically important. However, we are unaware of biological models that predict how long it takes for the first of many searchers to discover a target. We present a novel mathematical model that predicts initial first contact times between searchers and targets distributed at random in a volume. We compare this model with the extreme first passage time approach in physics that assumes an infinite number of searchers all initially positioned at the same location. We explore how the number of searchers, the distribution of searchers and targets, and the initial distances between searchers and targets affect initial first contact times. Given a constant density of uniformly distributed searchers and targets, the initial first contact time decreases linearly with both search volume and the number of searchers. However, given only a single target and searchers placed at the same starting location, the relationship between the initial first contact time and the number of searchers shifts from a linear decrease to a logarithmic decrease as the number of searchers grows very large. More generally, we show that initial first contact times can be dramatically faster than the average first contact times and that the initial first contact times decrease with the number of searchers, while the average search times are independent of the number of searchers. We suggest that this is an underappreciated phenomenon in biology and other collective search problems.

Decoding Immuno-Competence: A Novel Analysis of Complete Blood Cell Count Data in COVID-19 Outcomes

BACKGROUND

While 'immuno-competence' is a well-known term, it lacks an operational definition. To address this omission, this study explored whether the temporal and structured data of the complete blood cell count (CBC) can rapidly estimate immuno-competence. To this end, one or more ratios that included data on all monocytes, lymphocytes and neutrophils were investigated.

MATERIALS AND METHODS

Longitudinal CBC data collected from 101 COVID-19 patients (291 observations) were analyzed. Dynamics were estimated with several approaches, which included non-structured (the classic CBC format) and structured data. Structured data were assessed as complex ratios that capture multicellular interactions among leukocytes. In comparing survivors with non-survivors, the hypothesis that immuno-competence may exhibit feedback-like (oscillatory or cyclic) responses was tested.

RESULTS

While non-structured data did not distinguish survivors from non-survivors, structured data revealed immunological and statistical differences between outcomes: while survivors exhibited oscillatory data patterns, non-survivors did not. In survivors, many variables (including IL-6, hemoglobin and several complex indicators) showed values above or below the levels observed on day 1 of the hospitalization period, displaying L-shaped data distributions (positive kurtosis). In contrast, non-survivors did not exhibit kurtosis. Three immunologically defined data subsets included only survivors. Because information was based on visual patterns generated in real time, this method can, potentially, provide information rapidly.

DISCUSSION

The hypothesis that immuno-competence expresses feedback-like loops when immunological data are structured was not rejected. This function seemed to be impaired in immuno-suppressed individuals. While this method rapidly informs, it is only a guide that, to be confirmed, requires additional tests. Despite this limitation, the fact that three protective (survival-associated) immunological data subsets were observed since day 1 supports many clinical decisions, including the early and personalized prognosis and identification of targets that immunomodulatory therapies could pursue. Because it extracts more information from the same data, structured data may replace the century-old format of the CBC.

Heterogeneous anomalous transport in cellular and molecular biology

It is well established that a wide variety of phenomena in cellular and molecular biology involve anomalous transport e.g. the statistics for the motility of cells and molecules are fractional and do not conform to the archetypes of simple diffusion or ballistic transport. Recent research demonstrates that anomalous transport is in many cases heterogeneous in both time and space. Thus single anomalous exponents and single generalised diffusion coefficients are unable to satisfactorily describe many crucial phenomena in cellular and molecular biology. We consider advances in the field ofheterogeneous anomalous transport(HAT) highlighting: experimental techniques (single molecule methods, microscopy, image analysis, fluorescence correlation spectroscopy, inelastic neutron scattering, and nuclear magnetic resonance), theoretical tools for data analysis (robust statistical methods such as first passage probabilities, survival analysis, different varieties of mean square displacements, etc), analytic theory and generative theoretical models based on simulations. Special emphasis is made on high throughput analysis techniques based on machine learning and neural networks. Furthermore, we consider anomalous transport in the context of microrheology and the heterogeneous viscoelasticity of complex fluids. HAT in the wavefronts of reaction-diffusion systems is also considered since it plays an important role in morphogenesis and signalling. In addition, we present specific examples from cellular biology including embryonic cells, leucocytes, cancer cells, bacterial cells, bacterial biofilms, and eukaryotic microorganisms. Case studies from molecular biology include DNA, membranes, endosomal transport, endoplasmic reticula, mucins, globular proteins, and amyloids.

Quantitative analyses of T cell motion in tissue reveals factors driving T cell search in tissues

T cells are required to clear infection, and T cell motion plays a role in how quickly a T cell finds its target, from initial naive T cell activation by a dendritic cell to interaction with target cells in infected tissue. To better understand how different tissue environments affect T cell motility, we compared multiple features of T cell motion including speed, persistence, turning angle, directionality, and confinement of T cells moving in multiple murine tissues using microscopy. We quantitatively analyzed naive T cell motility within the lymph node and compared motility parameters with activated CD8 T cells moving within the villi of small intestine and lung under different activation conditions. Our motility analysis found that while the speeds and the overall displacement of T cells vary within all tissues analyzed, T cells in all tissues tended to persist at the same speed. Interestingly, we found that T cells in the lung show a marked population of T cells turning at close to 180o, while T cells in lymph nodes and villi do not exhibit this "reversing" movement. T cells in the lung also showed significantly decreased meandering ratios and increased confinement compared to T cells in lymph nodes and villi. These differences in motility patterns led to a decrease in the total volume scanned by T cells in lung compared to T cells in lymph node and villi. These results suggest that the tissue environment in which T cells move can impact the type of motility and ultimately, the efficiency of T cell search for target cells within specialized tissues such as the lung.

Alcohol-sourced acetate impairs T cell function by promoting cortactin acetylation

Alcohol is among the most widely consumed dietary substances. Excessive alcohol consumption damages the liver, heart, and brain. Alcohol also has strong immunoregulatory properties. Here, we report how alcohol impairs T cell function via acetylation of cortactin, a protein that binds filamentous actin and facilitates branching. Upon alcohol consumption, acetate, the metabolite of alcohol, accumulates in lymphoid organs. T cells exposed to acetate, exhibit increased acetylation of cortactin. Acetylation of cortactin inhibits filamentous actin binding and hence reduces T cell migration, immune synapse formation and activation. While mutated, acetylation-resistant cortactin rescues the acetate-induced inhibition of T cell migration, primary mouse cortactin knockout T cells exhibited impaired migration. Acetate-induced cytoskeletal changes effectively inhibited activation, proliferation, and immune synapse formation in T cells in vitro and in vivo in an influenza infection model in mice. Together these findings reveal cortactin as a possible target for mitigation of T cell driven autoimmune diseases.

Random walk informed heterogeneity detection reveals how the lymph node conduit network influences T cells collective exploration behavior

Random walks on networks are widely used to model stochastic processes such as search strategies, transportation problems or disease propagation. A prominent example of such process is the dynamics of naive T cells within the lymph node while they are scanning for antigens. The observed T cells trajectories in small sub-volumes of the lymph node are well modeled as a random walk and they have been shown to follow the lymphatic conduit network as substrate for migration. One can then ask how does the connectivity patterns of the lymph node conduit network affect the T cells collective exploration behavior. In particular, does the network display properties that are uniform across the whole volume of the lymph node or can we distinguish some heterogeneities? We propose a workflow to accurately and efficiently define and compute these quantities on large networks, which enables us to characterize heterogeneities within a very large published dataset of Lymph Node Conduit Network. To establish the significance of our results, we compared the results obtained on the lymph node to null models of varying complexity. We identified significantly heterogeneous regions characterized as "remote regions" at the poles and next to the medulla, while a large portion of the network promotes uniform exploration by T cells.

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.

Protocol and Software for Automated Detection of Lysosome Active "Runs" and "Flights" with Wavelet Transform Approach

Lysosomes are highly dynamic degradation/recycling organelles that harbor sophisticated molecular sensors and signal transduction machinery through which they control cell adaptation to environmental cues and nutrients. The movements of these signaling hubs comprise persistent, directional runs-active, ATP-dependent transport along the microtubule tracks-interspersed by short, passive movements and pauses imposed by cytoplasmic constraints. The trajectories of individual lysosomes are usually obtained by time-lapse imaging of the acidic organelles labeled with LysoTracker dyes or fluorescently-tagged lysosomal-associated membrane proteins LAMP1 and LAMP2. Subsequent particle tracking generates large data sets comprising thousands of lysosome trajectories and hundreds of thousands of data points. Analyzing such data sets requires unbiased, automated methods to handle large data sets while capturing the temporal heterogeneity of lysosome trajectory data. This chapter describes integrated and largely automated workflow from live cell imaging to lysosome trajectories to computing the parameters of lysosome dynamics. We describe an open-source code for implementing the continuous wavelet transform (CWT) to distinguish trajectory segments corresponding to active transport (i.e., "runs" and "flights") versus passive lysosome movements. Complementary cumulative distribution functions (CDFs) of the "runs/flights" are generated, and Akaike weight comparisons with several competing models (lognormal, power law, truncated power law, stretched exponential, exponential) are performed automatically. Such high-throughput analyses yield useful aggregate/ensemble metrics for lysosome active transport.

New definitions of human lymphoid and follicular cell entities in lymphatic tissue by machine learning

Histological sections of the lymphatic system are usually the basis of static (2D) morphological investigations. Here, we performed a dynamic (4D) analysis of human reactive lymphoid tissue using confocal fluorescent laser microscopy in combination with machine learning. Based on tracks for T-cells (CD3), B-cells (CD20), follicular T-helper cells (PD1) and optical flow of follicular dendritic cells (CD35), we put forward the first quantitative analysis of movement-related and morphological parameters within human lymphoid tissue. We identified correlations of follicular dendritic cell movement and the behavior of lymphocytes in the microenvironment. In addition, we investigated the value of movement and/or morphological parameters for a precise definition of cell types (CD clusters). CD-clusters could be determined based on movement and/or morphology. Differentiating between CD3- and CD20 positive cells is most challenging and long term-movement characteristics are indispensable. We propose morphological and movement-related prototypes of cell entities applying machine learning models. Finally, we define beyond CD clusters new subgroups within lymphocyte entities based on long term movement characteristics. In conclusion, we showed that the combination of 4D imaging and machine learning is able to define characteristics of lymphocytes not visible in 2D histology.

Heterogeneous run-and-tumble motion accounts for transient non-Gaussian super-diffusion in haematopoietic multi-potent progenitor cells

Multi-potent progenitor (MPP) cells act as a key intermediary step between haematopoietic stem cells and the entirety of the mature blood cell system. Their eventual fate determination is thought to be achieved through migration in and out of spatially distinct niches. Here we first analyze statistically MPP cell trajectory data obtained from a series of long time-course 3D in vivo imaging experiments on irradiated mouse calvaria, and report that MPPs display transient super-diffusion with apparent non-Gaussian displacement distributions. Second, we explain these experimental findings using a run-and-tumble model of cell motion which incorporates the observed dynamical heterogeneity of the MPPs. Third, we use our model to extrapolate the dynamics to time-periods currently inaccessible experimentally, which enables us to quantitatively estimate the time and length scales at which super-diffusion transitions to Fickian diffusion. Our work sheds light on the potential importance of motility in early haematopoietic progenitor function.

High resolution microfluidic assay and probabilistic modeling reveal cooperation between T cells in tumor killing

Cytotoxic T cells are important components of natural anti-tumor immunity and are harnessed in tumor immunotherapies. Immune responses to tumors and immune therapy outcomes largely vary among individuals, but very few studies examine the contribution of intrinsic behavior of the T cells to this heterogeneity. Here we show the development of a microfluidic-based in vitro method to track the outcome of antigen-specific T cell activity on many individual cancer spheroids simultaneously at high spatiotemporal resolution, which we call Multiscale Immuno-Oncology on-Chip System (MIOCS). By combining parallel measurements of T cell behaviors and tumor fates with probabilistic modeling, we establish that the first recruited T cells initiate a positive feedback loop to accelerate further recruitment to the spheroid. We also provide evidence that cooperation between T cells on the spheroid during the killing phase facilitates tumor destruction. Thus, we propose that both T cell accumulation and killing function rely on collective behaviors rather than simply reflecting the sum of individual T cell activities, and the possibility to track many replicates of immune cell-tumor interactions with the level of detail our system provides may contribute to our understanding of immune response heterogeneity.

Anti-cancer cytotoxic T cell responses largely vary among individuals. Here authors show, by stochastic modeling on high throughput T cell behavior and matched tumor spheroid fate data generated by a microfluidics system, that tumor killing is dependent on T cell cooperativity, which might contribute to the heterogeneity of T cell responses.

From Antibody Repertoires to Cell-Cell Interactions to Molecular Networks: Bridging Scales in the Germinal Center

Antibody-mediated adaptive immunity must provide effective long-term protection with minimal adverse effects, against rapidly mutating pathogens, in a human population with diverse ages, genetics, and immune histories. In order to grasp and leverage the complexities of the antibody response, we advocate for a mechanistic understanding of the multiscale germinal center (GC) reaction - the process by which precursor B-cells evolve high-affinity antigen-specific antibodies, forming an effector repertoire of plasma and memory cells for decades-long protection. The regulatory dynamics of B-cells within the GC are complex, and unfold across multiple interacting spatial and temporal scales. At the organism scale, over weeks to years, the antibody sequence repertoire formed by various B-cell clonal lineages modulates antibody quantity and quality over time. At the tissue and cellular scale, over hours to weeks, B-cells undergo selection via spatially distributed interactions with local stroma, antigen, and helper T-cells. At the molecular scale, over seconds to days, intracellular signaling, transcriptional, and epigenetic networks modulate B-cell fates and shape their clonal lineages. We summarize our current understanding within each of these scales, and identify missing links in connecting them. We suggest that quantitative multi-scale mathematical models of B-cell and GC reaction dynamics provide predictive frameworks that can apply basic immunological knowledge to practical challenges such as rational vaccine design.

Zebrafish airinemes optimize their shape between ballistic and diffusive search

In addition to diffusive signals, cells in tissue also communicate via long, thin cellular protrusions, such as airinemes in zebrafish. Before establishing communication, cellular protrusions must find their target cell. Here we demonstrate that the shapes of airinemes in zebrafish are consistent with a finite persistent random walk model. The probability of contacting the target cell is maximized for a balance between ballistic search (straight) and diffusive search (highly curved, random). We find that the curvature of airinemes in zebrafish, extracted from live cell microscopy, is approximately the same value as the optimum in the simple persistent random walk model. We also explore the ability of the target cell to infer direction of the airineme's source, finding that there is a theoretical trade-off between search optimality and directional information. This provides a framework to characterize the shape, and performance objectives, of non-canonical cellular protrusions in general.

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.

Large-Scale, Wavelet-Based Analysis of Lysosomal Trajectories and Co-Movements of Lysosomes with Nanoparticle Cargos

Lysosomes—that is, acidic organelles known for degradation/recycling—move through the cytoplasm alternating between bursts of active transport and short, diffusive motions or even pauses. While their mobility is essential for lysosomes’ fusogenic and non-fusogenic interactions with target organelles, their movements have not been characterized in adequate detail. Here, large-scale statistical analysis of lysosomal movement trajectories reveals that lysosome trajectories in all examined cell types—both cancer and noncancerous ones—are superdiffusive and characterized by heavy-tailed distributions of run and flight lengths. Consideration of Akaike weights for various potential models (lognormal, power law, truncated power law, stretched exponential, and exponential) indicates that the experimental data are best described by the lognormal distribution, which, in turn, can be related to one of the space-search strategies particularly effective when “thorough” search needs to balance search for rare target(s) (organelles). In addition, automated, wavelet-based analysis allows for co-tracking the motions of lysosomes and the cargos they carry—particularly the nanoparticle aggregates known to cause selective lysosome disruption in cancerous cells. The methods we describe here could help study nanoparticle assemblies, viruses, and other objects transported inside various vesicle types, as well as coordinated movements of organelles/particles in the cytoplasm. Custom-written code that includes integrated workflow for our analyses is made available for academic use.

The Critical Importance of Spatial and Temporal Scales in Designing and Interpreting Immune Cell Migration Assays

Intravital microscopy and other direct-imaging techniques have allowed for a characterisation of leukocyte migration that has revolutionised the field of immunology, resulting in an unprecedented understanding of the mechanisms of immune response and adaptive immunity. However, there is an assumption within the field that modern imaging techniques permit imaging parameters where the resulting cell track accurately captures a cell's motion. This notion is almost entirely untested, and the relationship between what could be observed at a given scale and the underlying cell behaviour is undefined. Insufficient spatial and temporal resolutions within migration assays can result in misrepresentation of important physiologic processes or cause subtle changes in critical cell behaviour to be missed. In this review, we contextualise how scale can affect the perceived migratory behaviour of cells, summarise the limited approaches to mitigate this effect, and establish the need for a widely implemented framework to account for scale and correct observations of cell motion. We then extend the concept of scale to new approaches that seek to bridge the current "black box" between single-cell behaviour and systemic response.

Single-cell tracking reveals super-spreading brain cancer cells with high persistence

Cell migration is a fundamental characteristic of vital processes such as tissue morphogenesis, wound healing and immune cell homing to lymph nodes and inflamed or infected sites. Therefore, various brain defect diseases, chronic inflammatory diseases as well as tumor formation and metastasis are associated with aberrant or absent cell migration. We embedded multicellular brain cancer spheroids in Matrigel™ and utilized single-particle tracking to extract the paths of cells migrating away from the spheroids. We found that - in contrast to local invasion - single cell migration is independent of Matrigel™ concentration and is characterized by high directionality and persistence. Furthermore, we identified a subpopulation of super-spreading cells with >200-fold longer persistence times than the majority of cells. These results highlight yet another aspect of cell heterogeneity in tumors.

Spatially distributed infection increases viral load in a computational model of SARS-CoV-2 lung infection

A key question in SARS-CoV-2 infection is why viral loads and patient outcomes vary dramatically across individuals. Because spatial-temporal dynamics of viral spread and immune response are challenging to study in vivo, we developed Spatial Immune Model of Coronavirus (SIMCoV), a scalable computational model that simulates hundreds of millions of lung cells, including respiratory epithelial cells and T cells. SIMCoV replicates viral growth dynamics observed in patients and shows how spatially dispersed infections can lead to increased viral loads. The model also shows how the timing and strength of the T cell response can affect viral persistence, oscillations, and control. By incorporating spatial interactions, SIMCoV provides a parsimonious explanation for the dramatically different viral load trajectories among patients by varying only the number of initial sites of infection and the magnitude and timing of the T cell immune response. When the branching airway structure of the lung is explicitly represented, we find that virus spreads faster than in a 2D layer of epithelial cells, but much more slowly than in an undifferentiated 3D grid or in a well-mixed differential equation model. These results illustrate how realistic, spatially explicit computational models can improve understanding of within-host dynamics of SARS-CoV-2 infection.

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.

Amoebic Foraging Model of Metastatic Cancer Cells

The Lévy walk is a pattern that is often seen in the movement of living organisms; it has both ballistic and random features and is a behavior that has been recognized in various animals and unicellular organisms, such as amoebae, in recent years. We proposed an amoeba locomotion model that implements Bayesian and inverse Bayesian inference as a Lévy walk algorithm that balances exploration and exploitation, and through a comparison with general random walks, we confirmed its effectiveness. While Bayesian inference is expressed only by P(h) = P(h|d), we introduce inverse Bayesian inference expressed as P(d|h) = P(d) in a symmetry fashion. That symmetry contributes to balancing contracting and expanding the probability space. Additionally, the conditions of various environments were set, and experimental results were obtained that corresponded to changes in gait patterns with respect to changes in the conditions of actual metastatic cancer cells.

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.

Characterization of immune cell migration using microfabrication

The immune system provides our defense against pathogens and aberrant cells, including tumorigenic and infected cells. Motility is one of the fundamental characteristics that enable immune cells to find invading pathogens, control tissue damage, and eliminate primary developing tumors, even in the absence of external treatments. These processes are termed "immune surveillance." Migration disorders of immune cells are related to autoimmune diseases, chronic inflammation, and tumor evasion. It is therefore essential to characterize immune cell motility in different physiologically and pathologically relevant scenarios to understand the regulatory mechanisms of functionality of immune responses. This review is focused on immune cell migration, to define the underlying mechanisms and the corresponding investigative approaches. We highlight the challenges that immune cells encounter in vivo, and the microfabrication methods to mimic particular aspects of their microenvironment. We discuss the advantages and disadvantages of the proposed tools, and provide information on how to access them. Furthermore, we summarize the directional cues that regulate individual immune cell migration, and discuss the behavior of immune cells in a complex environment composed of multiple directional cues.

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.

γδ T cell migration: Separating trafficking from surveillance behaviors at barrier surfaces

γδ T cells are found in highest numbers at barrier surfaces throughout the body, including the skin, intestine, lung, gingiva, and uterus. Under homeostatic conditions, γδ T cells provide immune surveillance of the epidermis, intestinal, and oral mucosa, whereas the presence of pathogenic microorganisms in the dermis or lungs elicits a robust γδ17 response to clear the infection. Although T cell migration is most frequently defined in the context of trafficking, analysis of specific migratory behaviors of lymphocytes within the tissue microenvironment can provide valuable insight into their function. Intravital imaging and computational analyses have been used to define "search" behavior associated with conventional αβ T cells; however, based on the known role of γδ T cells as immune sentinels at barrier surfaces and their TCR-independent functions, we put forth the need to classify distinct migratory patterns that reflect the surveillance capacity of these unconventional lymphocytes. This review will focus on how γδ T cells traffic to various barrier surfaces and how recent investigation into their migratory behavior has provided unique insight into the contribution of γδ T cells to barrier immunity.

Intravital Imaging Reveals Motility of Adult Hematopoietic Stem Cells in the Bone Marrow Niche

Adult mammalian hematopoietic stem cells (HSCs) reside in the bone marrow (BM) but can be mobilized into blood for use in transplantation. HSCs interact with BM niche cells that produce growth factor c-Kit ligand (Kitl/SCF) and chemokine CXCL12, and were thought to be static and sessile. We used two-photon laser scanning microscopy to visualize genetically labeled HSCs in the BM of live mice for several hours. The majority of HSCs showed a dynamic non-spherical morphology and significant motility, undergoing slow processive motion interrupted by short stretches of confined motion. HSCs moved in the perivascular space and showed intermittent close contacts with SCF-expressing perivascular stromal cells. In contrast, mobilization-inducing blockade of CXCL12 receptor CXCR4 and integrins rapidly abrogated HSC motility and shape dynamics in real time. Our results reveal an unexpectedly dynamic nature of HSC residence in the BM and interaction with the SCF⁺ stromal niche, which is disrupted during HSC mobilization.

Tissue-resident T cell-derived cytokines eliminate herpes simplex virus-2-infected cells

The mechanisms underlying rapid elimination of herpes simplex virus-2 (HSV-2) in the human genital tract despite low CD8+ and CD4+ tissue-resident T cell (Trm cell) density are unknown. We analyzed shedding episodes during chronic HSV-2 infection; viral clearance always predominated within 24 hours of detection even when viral load exceeded 1 × 107 HSV DNA copies, and surges in granzyme B and IFN-γ occurred within the early hours after reactivation and correlated with local viral load. We next developed an agent-based mathematical model of an HSV-2 genital ulcer to integrate mechanistic observations of Trm cells in in situ proliferation, trafficking, cytolytic effects, and cytokine alarm signaling from murine studies with viral kinetics, histopathology, and lesion size data from humans. A sufficiently high density of HSV-2-specific Trm cells predicted rapid elimination of infected cells, but our data suggest that such Trm cell densities are relatively uncommon in infected tissues. At lower, more commonly observed Trm cell densities, Trm cells must initiate a rapidly diffusing, polyfunctional cytokine response with activation of bystander T cells in order to eliminate a majority of infected cells and eradicate briskly spreading HSV-2 infection.

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.

Stochastic and Heterogeneous Cancer Cell Migration: Experiment and Theory

Cell migration, an essential process for normal cell development and cancer metastasis, differs from a simple random walk: the mean-square displacement (〈(Δr)²(t)〉) of cells sometimes shows non-Fickian behavior, and the spatiotemporal correlation function (G(r, t)) of cells is often non-Gaussian. We find that this intriguing cell migration should be attributed to heterogeneity in a cell population, even one with a homogeneous genetic background. There are two limiting types of heterogeneity in a cell population: cellular heterogeneity and temporal heterogeneity. Cellular heterogeneity accounts for the cell-to-cell variation in migration capacity, while temporal heterogeneity arises from the temporal noise in the migration capacity of single cells. We illustrate that both cellular and temporal heterogeneity need to be taken into account simultaneously to elucidate cell migration. We investigate the two-dimensional migration of A549 lung cancer cells using time-lapse microscopy and find that the migration of A549 cells is Fickian but has a non-Gaussian spatiotemporal correlation. We find that when a theoretical model considers both cellular and temporal heterogeneity, the model reproduces all of the anomalous behaviors of cancer cell migration.

Distributed Adaptive Search in T Cells: Lessons From Ants

There are striking similarities between the strategies ant colonies use to forage for food and immune systems use to search for pathogens. Searchers (ants and cells) use the appropriate combination of random and directed motion, direct and indirect agent-agent interactions, and traversal of physical structures to solve search problems in a variety of environments. An effective immune response requires immune cells to search efficiently and effectively for diverse types of pathogens in different tissues and organs, just as different species of ants have evolved diverse search strategies to forage effectively for a variety of resources in a variety of habitats. Successful T cell search is required to initiate the adaptive immune response in lymph nodes and to eradicate pathogens at sites of infection in peripheral tissue. Ant search strategies suggest novel predictions about T cell search. In both systems, the distribution of targets in time and space determines the most effective search strategy. We hypothesize that the ability of searchers to sense and adapt to dynamic targets and environmental conditions enhances search effectiveness through adjustments to movement and communication patterns. We also suggest that random motion is a more important component of search strategies than is generally recognized. The behavior we observe in ants reveals general design principles and constraints that govern distributed adaptive search in a wide variety of complex systems, particularly the immune system.

How does mobility help distributed systems compute?

Brains are composed of connected neurons that compute by transmitting signals. The neurons are generally fixed in space, but the communication patterns that enable information processing change rapidly. By contrast, other biological systems, such as ant colonies, bacterial colonies, slime moulds and immune systems, process information using agents that communicate locally while moving through physical space. We refer to systems in which agents are strongly connected and immobile as solid, and to systems in which agents are not hardwired to each other and can move freely as liquid. We ask how collective computation depends on agent movement. A liquid cellular automaton (LCA) demonstrates the effect of movement and communication locality on consensus problems. A simple mathematical model predicts how these properties of the LCA affect how quickly information propagates through the system. While solid brains allow complex network structures to move information over long distances, mobility provides an alternative way for agents to transport information when long-range connectivity is expensive or infeasible. Our results show how simple mobile agents solve global information processing tasks more effectively than similar systems that are stationary. This article is part of the theme issue 'Liquid brains, solid brains: How distributed cognitive architectures process information'.

Lévy-like movement patterns of metastatic cancer cells revealed in microfabricated systems and implicated in vivo

Metastatic cancer cells differ from their non-metastatic counterparts not only in terms of molecular composition and genetics, but also by the very strategy they employ for locomotion. Here, we analyzed large-scale statistics for cells migrating on linear microtracks to show that metastatic cancer cells follow a qualitatively different movement strategy than their non-invasive counterparts. The trajectories of metastatic cells display clusters of small steps that are interspersed with long "flights". Such movements are characterized by heavy-tailed, truncated power law distributions of persistence times and are consistent with the Lévy walks that are also often employed by animal predators searching for scarce prey or food sources. In contrast, non-metastatic cancerous cells perform simple diffusive movements. These findings are supported by preliminary experiments with cancer cells migrating away from primary tumors in vivo. The use of chemical inhibitors targeting actin-binding proteins allows for "reprogramming" the Lévy walks into either diffusive or ballistic movements.

Integrative Computational Modeling of the Lymph Node Stromal Cell Landscape

Adaptive immune responses develop in secondary lymphoid organs such as lymph nodes (LNs) in a well-coordinated series of interactions between migrating immune cells and resident stromal cells. Although many processes that occur in LNs are well understood from an immunological point of view, our understanding of the fundamental organization and mechanisms that drive these processes is still incomplete. The aim of systems biology approaches is to unravel the complexity of biological systems and describe emergent properties that arise from interactions between individual constituents of the system. The immune system is greater than the sum of its parts, as is the case with any sufficiently complex system. Here, we review recent work and developments of computational LN models with focus on the structure and organization of the stromal cells. We explore various mathematical studies of intranodal T cell motility and migration, their interactions with the LN-resident stromal cells, and computational models of functional chemokine gradient fields and lymph flow dynamics. Lastly, we discuss briefly the importance of hybrid and multi-scale modeling approaches in immunology and the technical challenges involved.

Quantitative Measurement of Naïve T Cell Association With Dendritic Cells, FRCs, and Blood Vessels in Lymph Nodes

T cells play a vital role in eliminating pathogenic infections. To activate, naïve T cells search lymph nodes (LNs) for dendritic cells (DCs). Positioning and movement of T cells in LNs is influenced by chemokines including CCL21 as well as multiple cell types and structures in the LNs. Previous studies have suggested that T cell positioning facilitates DC colocalization leading to T:DC interaction. Despite the influence chemical signals, cells, and structures can have on naïve T cell positioning, relatively few studies have used quantitative measures to directly compare T cell interactions with key cell types. Here, we use Pearson correlation coefficient (PCC) and normalized mutual information (NMI) to quantify the extent to which naïve T cells spatially associate with DCs, fibroblastic reticular cells (FRCs), and blood vessels in LNs. We measure spatial associations in physiologically relevant regions. We find that T cells are more spatially associated with FRCs than with their ultimate targets, DCs. We also investigated the role of a key motility chemokine receptor, CCR7, on T cell colocalization with DCs. We find that CCR7 deficiency does not decrease naïve T cell association with DCs, in fact, CCR7-/- T cells show slightly higher DC association compared with wild type T cells. By revealing these associations, we gain insights into factors that drive T cell localization, potentially affecting the timing of productive T:DC interactions and T cell activation.

Purinergic P2X4 receptors and mitochondrial ATP production regulate T cell migration

T cells must migrate in order to encounter antigen-presenting cells (APCs) and to execute their varied functions in immune defense and inflammation. ATP release and autocrine signaling through purinergic receptors contribute to T cell activation at the immune synapse that T cells form with APCs. Here, we show that T cells also require ATP release and purinergic signaling for their migration to APCs. We found that the chemokine stromal-derived factor-1α (SDF-1α) triggered mitochondrial ATP production, rapid bursts of ATP release, and increased migration of primary human CD4+ T cells. This process depended on pannexin-1 ATP release channels and autocrine stimulation of P2X4 receptors. SDF-1α stimulation caused localized accumulation of mitochondria with P2X4 receptors near the front of cells, resulting in a feed-forward signaling mechanism that promotes cellular Ca2+ influx and sustains mitochondrial ATP synthesis at levels needed for pseudopod protrusion, T cell polarization, and cell migration. Inhibition of P2X4 receptors blocked the activation and migration of T cells in vitro. In a mouse lung transplant model, P2X4 receptor antagonist treatment prevented the recruitment of T cells into allograft tissue and the rejection of lung transplants. Our findings suggest that P2X4 receptors are therapeutic targets for immunomodulation in transplantation and inflammatory diseases.

Switching between individual and collective motility in B lymphocytes is controlled by cell-matrix adhesion and inter-cellular interactions

Lymphocytes alternate between phases of individual migration across tissues and phases of clustering during activation and function. The range of lymphocyte motility behaviors and the identity of the factors that govern them remain elusive. To explore this point, we here collected unprecedented statistics pertaining to cell displacements, cell:matrix and cell:cell interactions using a model B cell line as well as primary human B lymphocytes. At low cell density, individual B lymphocytes displayed a high heterogeneity in their speed and diffusivity. Beyond this intrinsic variability, B lymphocytes adapted their motility to the composition of extra-cellular matrix, adopting slow persistent walks over collagen IV and quick Brownian walks over fibronectin. At high cell density, collagen IV favored the self-assembly of B lymphocytes into clusters endowed with collective coordination, while fibronectin stimulated individual motility. We show that this behavioral plasticity is controlled by acto-myosin dependent adhesive and Arp2/3-dependent protrusive actin pools, respectively. Our study reveals the adaptive nature of B lymphocyte motility and group dynamics, which are shaped by an interplay between and cell:matrix and cell:cell interactions.

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.

Current status and future directions of Lévy walk research

Lévy walks are a mathematical construction useful for describing random patterns of movement with bizarre fractal properties that seem to have no place in biology. Nonetheless, movement patterns resembling Lévy walks have been observed at scales ranging from the microscopic to the ecological. They have been seen in the molecular machinery operating within cells during intracellular trafficking, in the movement patterns of T cells within the brain, in DNA, in some molluscs, insects, fish, birds and mammals, in the airborne flights of spores and seeds, and in the collective movements of some animal groups. Lévy walks are also evident in trace fossils (ichnofossils) – the preserved form of tracks made by organisms that occupied ancient sea beds about 252-66 million years ago. And they are utilised by algae that originated around two billion years ago, and still exist today. In September of 2017, leading researchers from across the life sciences, along with mathematicians and physicists, got together at a Company of Biologists' Workshop to discuss the origins and biological significance of these movement patterns. In this Review the essence of the technical and sometimes heated discussions is distilled and made accessible for all. In just a few pages, the reader is taken from a gentle introduction to the frontiers of a very active field of scientific enquiry. What emerges is a fascinating story of a truly inter-disciplinary scientific endeavour that is seeking to better understand movement patterns occurring across all biological scales.

Summary: Movement patterns resembling Lévy walks are found in a wide variety of organisms, from cells to humans. In this Review the latest research into their origins and biological significance is discussed.

ROCK regulates the intermittent mode of interstitial T cell migration in inflamed lungs

Effector T cell migration through tissues can enable control of infection or mediate inflammatory damage. Nevertheless, the molecular mechanisms that regulate migration of effector T cells within the interstitial space of inflamed lungs are incompletely understood. Here, we show T cell migration in a mouse model of acute lung injury with two-photon imaging of intact lung tissue. Computational analysis indicates that T cells migrate with an intermittent mode, switching between confined and almost straight migration, guided by lung-associated vasculature. Rho-associated protein kinase (ROCK) is required for both high-speed migration and straight motion. By contrast, inhibition of Gα_i signaling with pertussis toxin affects speed but not the intermittent migration of lung-infiltrating T cells. Computational modeling shows that an intermittent migration pattern balances both search area and the duration of contacts between T cells and target cells. These data identify that ROCK-dependent intermittent T cell migration regulates tissue-sampling during acute lung injury.

ROCK is associated with T cell movement in lymph nodes. Here the authors use an LPS lung damage model and two-photon imaging to show that CD8⁺ T cells in lung tissue engage in ROCK-dependent fast linear migration alternating with bursts of slower confined migration that together optimize contact with target cells.

Hybrid approach to model the spatial regulation of T cell responses

BACKGROUND

Moving from the molecular and cellular level to a multi-scale systems understanding of immune responses requires the development of novel approaches to integrate knowledge and data from different biological levels into mechanism-based integrative mathematical models. The aim of our study is to present a methodology for a hybrid modelling of immunological processes in their spatial context.

METHODS

A two-level hybrid mathematical model of immune cell migration and interaction integrating cellular and organ levels of regulation for a 2D spatial consideration of idealized secondary lymphoid organs is developed. It considers the population dynamics of antigen-presenting cells, CD4 + and CD8 + T lymphocytes in naive-, proliferation- and differentiated states. Cell division is assumed to be asymmetric and regulated by the extracellular concentration of interleukin-2 (IL-2) and type I interferon (IFN), together controlling the balance between proliferation and differentiation. The cytokine dynamics is described by reaction-diffusion PDEs whereas the intracellular regulation is modelled with a system of ODEs.

RESULTS

The mathematical model has been developed, calibrated and numerically implemented to study various scenarios in the regulation of T cell immune responses to infection, in particular the change in the diffusion coefficient of type I IFN as compared to IL-2. We have shown that a hybrid modelling approach provides an efficient tool to describe and analyze the interplay between spatio-temporal processes in the emergence of abnormal immune response dynamics.

DISCUSSION

Virus persistence in humans is often associated with an exhaustion of T lymphocytes. Many factors can contribute to the development of exhaustion. One of them is associated with a shift from a normal clonal expansion pathway to an altered one characterized by an early terminal differentiation of T cells. We propose that an altered T cell differentiation and proliferation sequence can naturally result from a spatial separation of the signaling events delivered via TCR, IL-2 and type I IFN receptors. Indeed, the spatial overlap of the concentration fields of extracellular IL-2 and IFN in lymph nodes changes dynamically due to different migration patterns of APCs and CD4 + T cells secreting them.

CONCLUSIONS

The proposed hybrid mathematical model of the immune response represents a novel analytical tool to examine challenging issues in the spatio-temporal regulation of cell growth and differentiation, in particular the effect of timing and location of activation signals.

Immune-inspired search strategies for robot swarms

Detection of targets distributed randomly in space is a task common to both robotic and biological systems. Lévy search has previously been used to characterize T cell search in the immune system. We use a robot swarm to evaluate the effectiveness of a Lévy search strategy and map the relationship between search parameters and target configurations. We show that the fractal dimension of the Lévy search which optimizes search efficiency depends strongly on the distribution of targets but only weakly on the number of agents involved in search. Lévy search can therefore be tuned to the target configuration while also being scalable. Implementing search behaviors observed in T cells in a robot swarm provides an effective, adaptable, and scalable swarm robotic search strategy. Additionally, the adaptability and scalability of Lévy search may explain why Lévy-like movement has been observed in T cells in multiple immunological contexts.