Multi-scale analysis and modelling of collective migration in biological systems

Collective phases and long-term dynamics in a fish school model with burst-and-coast swimming

Intermittent and asynchronous burst-and-coast swimming is widely adopted by various species of fish as an energy-efficient mode of locomotion. This swimming mode significantly influences how fish integrate information and make decisions in a social context. Here, we introduce a simplified fish school model in which individuals have an asynchronous burst-and-coast swimming mode and selectively interact only with one or two neighbours that exert the largest influence on their behaviour over a limited spatial range. The interactions consist of a fish that is attracted to and aligned with these neighbours. We show that, by adjusting the interactions between individuals above a sufficiently high level, depending on the relative strength of attraction and alignment, the model can produce a cohesive fish school that replicates the main collective phases observed in nature: schooling, milling and swarming when each individual interacts with only one neighbour; and schooling and swarming when each individual interacts with two neighbours. Moreover, the model showed that these patterns can be maintained over long simulations. However, with the exception of swarming, these patterns do not persist indefinitely, and fish lose cohesion and progressively disperse. We further identified the mechanisms that lead to group dispersion.

The self-organized structure of glioma oncostreams and the disruptive role of passive cells

Oncostreams are self-organized structures formed by spindle-like, elongated, self-propelled cells recently described in glioblastomas and especially in gliosarcomas. Cells within these structures either move as large clusters in one main direction, flocks, or as linear, intermingling collections of cells advancing in opposite directions, streams. Round, passive cells are also observed, either inside or segregated from the oncostreams. Here we generalize a recently formulated particle-field approach to investigate the genesis and evolution of these structures, first showing that, in systems consisting only of identical self-propelled cells, both flocks and streams emerge as self-organized dynamic configurations. Flocks are the more stable configurations, while streams are transient and usually originate in collisions between flocks. Stream degradation is easier at low self-propulsion speeds. In systems consisting of both motile and passive cells, the latter block stream formation and accelerate their degradation and flock stabilization. Since the flock appears to be the most effective invasive structure, we thus argue that a phenotype mixture (motile and passive cells) may favor glioblastoma invasion. hlBy relating cellular properties to the observed outcome, our model shows that oncostreams are self-organized structures that result from the interplay between speed, shape, and steric repulsion.

Impact of diffusion on synchronization pattern of epidemics in non-identical meta-population networks

In epidemic networks, it has been demonstrated that implementing any intervention strategy on nodes with specific characteristics (such as a high degree or node betweenness) substantially diminishes the outbreak size. We extend this finding with a disease-spreading meta-population model using testkits to explore the influence of migration on infection dynamics within the distinct communities of the network. Notably, we observe that nodes equipped with testkits and no testkits tend to segregate into two separate clusters when migration is low, but above a critical migration rate, they coalesce into one single cluster. Based on this clustering phenomenon, we develop a reduced model and validate the emergent clustering behavior through comprehensive simulations. We observe this property in both homogeneous and heterogeneous networks.

Dynamics of multicellular swirling on micropatterned substrates

Chirality plays a crucial role in biology, as it is highly conserved and fundamentally important in the developmental process. To better understand the relationship between the chirality of individual cells and that of tissues and organisms, we develop a generalized mechanics model of chiral polarized particles to investigate the swirling dynamics of cell populations on substrates. Our analysis reveals that cells with the same chirality can form distinct chiral patterns on ring-shaped or rectangular substrates. Interestingly, our studies indicate that an excessively strong or weak individual cellular chirality hinders the formation of such chiral patterns. Our studies also indicate that there exists the influence distance of substrate boundaries in chiral patterns. Smaller influence distances are observed when cell-cell interactions are weaker. Conversely, when cell-cell interactions are too strong, multiple cells tend to be stacked together, preventing the formation of chiral patterns on substrates in our analysis. Additionally, we demonstrate that the interaction between cells and substrate boundaries effectively controls the chiral distribution of cellular orientations on ring-shaped substrates. This research highlights the significance of coordinating boundary features, individual cellular chirality, and cell-cell interactions in governing the chiral movement of cell populations and provides valuable mechanics insights into comprehending the intricate connection between the chirality of single cells and that of tissues and organisms.

Predicting the long-term collective behaviour of fish pairs with deep learning

Modern computing has enhanced our understanding of how social interactions shape collective behaviour in animal societies. Although analytical models dominate in studying collective behaviour, this study introduces a deep learning model to assess social interactions in the fish species Hemigrammus rhodostomus. We compare the results of our deep learning approach with experiments and with the results of a state-of-the-art analytical model. To that end, we propose a systematic methodology to assess the faithfulness of a collective motion model, exploiting a set of stringent individual and collective spatio-temporal observables. We demonstrate that machine learning (ML) models of social interactions can directly compete with their analytical counterparts in reproducing subtle experimental observables. Moreover, this work emphasizes the need for consistent validation across different timescales, and identifies key design aspects that enable our deep learning approach to capture both short- and long-term dynamics. We also show that our approach can be extended to larger groups without any retraining, and to other fish species, while retaining the same architecture of the deep learning network. Finally, we discuss the added value of ML in the context of the study of collective motion in animal groups and its potential as a complementary approach to analytical models.

Intrinsic statistical separation of subpopulations in heterogeneous collective motion via dimensionality reduction

Collective motion of locally interacting agents is found ubiquitously throughout nature. The inability to probe individuals has driven longstanding interest in the development of methods for inferring the underlying interactions. In the context of heterogeneous collectives, where the population consists of individuals driven by different interactions, existing approaches require some knowledge about the heterogeneities or underlying interactions. Here, we investigate the feasibility of identifying the identities in a heterogeneous collective without such prior knowledge. We numerically explore the behavior of a heterogeneous Vicsek model and find sufficiently long trajectories intrinsically cluster in a principal component analysis-based dimensionally reduced model-agnostic description of the data. We identify how heterogeneities in each parameter in the model (interaction radius, noise, population proportions) dictate this clustering. Finally, we show the generality of this phenomenon by finding similar behavior in a heterogeneous D'Orsogna model. Altogether, our results establish and quantify the intrinsic model-agnostic statistical disentanglement of identities in heterogeneous collectives.

Motility-Induced Phase Separation Mediated by Bacterial Quorum Sensing

We study motility-induced phase separation (MIPS) in living active matter, in which cells interact through chemical signaling, or quorum sensing. In contrast to previous theories of MIPS, our multiscale continuum model accounts explicitly for genetic regulation of signal production and motility. Through analysis and simulations, we derive a new criterion for the onset of MIPS that depends on features of the genetic network. Furthermore, we identify and characterize a new type of oscillatory instability that occurs when gene regulation inside cells promotes motility in higher signal concentrations.

Tuning social interactions' strength drives collective response to light intensity in schooling fish

Schooling fish heavily rely on visual cues to interact with neighbors and avoid obstacles. The availability of sensory information is influenced by environmental conditions and changes in the physical environment that can alter the sensory environment of the fish, which in turn affects individual and group movements. In this study, we combine experiments and data-driven modeling to investigate the impact of varying levels of light intensity on social interactions and collective behavior in rummy-nose tetra fish. The trajectories of single fish and groups of fish swimming in a tank under different lighting conditions were analyzed to quantify their movements and spatial distribution. Interaction functions between two individuals and the fish interaction with the tank wall were reconstructed and modeled for each light condition. Our results demonstrate that light intensity strongly modulates social interactions between fish and their reactions to obstacles, which then impact collective motion patterns that emerge at the group level.

Modelling Keloids Dynamics: A Brief Review and New Mathematical Perspectives

Keloids are fibroproliferative disorders described by excessive growth of fibrotic tissue, which also invades adjacent areas (beyond the original wound borders). Since these disorders are specific to humans (no other animal species naturally develop keloid-like tissue), experimental in vivo/in vitro research has not led to significant advances in this field. One possible approach could be to combine in vitro human models with calibrated in silico mathematical approaches (i.e., models and simulations) to generate new testable biological hypotheses related to biological mechanisms and improved treatments. Because these combined approaches do not really exist for keloid disorders, in this brief review we start by summarising the biology of these disorders, then present various types of mathematical and computational approaches used for related disorders (i.e., wound healing and solid tumours), followed by a discussion of the very few mathematical and computational models published so far to study various inflammatory and mechanical aspects of keloids. We conclude this review by discussing some open problems and mathematical opportunities offered in the context of keloid disorders by such combined in vitro/in silico approaches, and the need for multi-disciplinary research to enable clinical progress.

Data-driven discovery of stochastic dynamical equations of collective motion

Coarse-grained descriptions of collective motion of flocking systems are often derived for the macroscopic or the thermodynamic limit. However, the size of many real flocks falls within 'mesoscopic' scales (10 to 100 individuals), where stochasticity arising from the finite flock sizes is important. Previous studies on mesoscopic models have typically focused on non-spatial models. Developing mesoscopic scale equations, typically in the form of stochastic differential equations, can be challenging even for the simplest of the collective motion models that explicitly account for space. To address this gap, here, we take a novel data-driven equation learning approach to construct the stochastic mesoscopic descriptions of a simple, spatial, self-propelled particle (SPP) model of collective motion. In the spatial model, a focal individual can interact withkrandomly chosen neighbours within an interaction radius. We considerk = 1 (called stochastic pairwise interactions),k = 2 (stochastic ternary interactions), andkequalling all available neighbours within the interaction radius (equivalent to Vicsek-like local averaging). For the stochastic pairwise interaction model, the data-driven mesoscopic equations reveal that the collective order is driven by a multiplicative noise term (hence termed, noise-induced flocking). In contrast, for higher order interactions (k > 1), including Vicsek-like averaging interactions, models yield collective order driven by a combination of deterministic and stochastic forces. We find that the relation between the parameters of the mesoscopic equations describing the dynamics and the population size are sensitive to the density and to the interaction radius, exhibiting deviations from mean-field theoretical expectations. We provide semi-analytic arguments potentially explaining these observed deviations. In summary, our study emphasises the importance of mesoscopic descriptions of flocking systems and demonstrates the potential of the data-driven equation discovery methods for complex systems studies.

Coordination of non-professional efferocytosis and actomyosin contractility during epithelial tissue morphogenesis

In developing embryos, specific cell populations are often removed to remodel tissue architecture for organogenesis. During urinary tract development, an epithelial duct called the common nephric duct (CND) gets shortened and eventually eliminated to remodel the entry point of the ureter into the bladder. Here we show that non-professional efferocytosis (the process in which epithelial cells engulf apoptotic bodies) is the main mechanism that contributes to CND shortening. Combining biological metrics and computational modeling, we show that efferocytosis with actomyosin contractility are essential factors that drive the CND shortening without compromising the ureter-bladder structural connection. The disruption of either apoptosis, non-professional efferocytosis, or actomyosin results in contractile tension reduction and deficient CND shortening. Actomyosin activity helps to maintain tissue architecture while non-professional efferocytosis removes cellular volume. Together our results demonstrate that non-professional efferocytosis with actomyosin contractility are important morphogenetic factors controlling CND morphogenesis.

Direct tool for quantitative analysis of cell/object dynamic behavior - metastasis and far beyond

INTRODUCTION

The dynamics and depth of invasion as well as the ability of cancer cells to penetrate the walls of  lymphatic or blood vessels represent critical survival-influencing factors in cancer patients. Depending on the cell type and tissue environment, cancer cell invasion differ in terms of motility mechanism and migration modes. Thus, there is the need of effective models allowing not only for single cell invasion potential assessment but also for collective migration and expansive growth evaluation in 3D microenvironment e.g. basement membranes. To meet this task, the specimens should be compared and analyzed in terms of the dynamics of movement and the evolution of the shape.

OBJECTIVES

Our main objective was development of the mathematical method that enables fast and credible calculation of parameters of shape and position, namely standard deviations (σ_X, σ_Y), centroid position (μ_X, μ_Y) and correlation coefficient ρ, based only on the contour of the aggregate.

METHODS

In order to accomplish this goal we measured geometrical properties of aggregates of RGM1 cells seeded in 3D Geltrex basement membrane. Referential microscopic images were taken 24 and 48 h after seeding and cell group dynamics was registered over 8 h periods using time lapse microscopy.

RESULTS

Based on gathered data, we managed to develop and fully test universal numerical tool allowing for estimation of statistical parameters of cell groups and aggregates which then allows for the precise evaluation of their behavior within microenvironment with time.

CONCLUSION

We conclude, that our tool is suitable for any research on the metastatic potential and motility of cancer cells in a given microenvironment, regardless of the migration mechanism, which together with the advanced analysis like cell single-cell transcriptomic, proteomic, and chromatin accessibility data may allow to identify precise targets for anti-cancer therapies, to predict the degree of malignancy of neoplastic lesions as well as it can be useful during architecting therapeutic strategies. Moreover, the developed tool seems to be broadly applicable for assessment of behavioural dynamics of any population.

Multilevel Mesoscale Complexities in Mesoregimes: Challenges in Chemical and Biochemical Engineering

This review discusses the complex behaviors in diverse chemical and biochemical systems to elucidate their commonalities and thus help develop a mesoscience methodology to address the complexities in even broader topics. This could possibly build a new scientific paradigm for different disciplines and could meanwhile provide effective tools to tackle the big challenges in various fields, thus paving a path toward combining the paradigm shift in science with the breakthrough in technique developments. Starting with our relatively fruitful understanding of chemical systems, the discussion focuses on the relatively pristine but very intriguing biochemical systems. It is recognized that diverse complexities are multilevel in nature, with each level being multiscale and the complexity emerging always at mesoscales in mesoregimes. Relevant advances in theoretical understandings and mathematical tools are summarized as well based on case studies, and the convergence between physics and mathematics is highlighted. Expected final online publication date for the Annual Review of Chemical and Biomolecular Engineering, Volume 13 is October 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Computational modelling of cell motility modes emerging from cell-matrix adhesion dynamics

Lymphocytes have been described to perform different motility patterns such as Brownian random walks, persistent random walks, and Lévy walks. Depending on the conditions, such as confinement or the distribution of target cells, either Brownian or Lévy walks lead to more efficient interaction with the targets. The diversity of these motility patterns may be explained by an adaptive response to the surrounding extracellular matrix (ECM). Indeed, depending on the ECM composition, lymphocytes either display a floating motility without attaching to the ECM, or sliding and stepping motility with respectively continuous or discontinuous attachment to the ECM, or pivoting behaviour with sustained attachment to the ECM. Moreover, on the long term, lymphocytes either perform a persistent random walk or a Brownian-like movement depending on the ECM composition. How the ECM affects cell motility is still incompletely understood. Here, we integrate essential mechanistic details of the lymphocyte-matrix adhesions and lymphocyte intrinsic cytoskeletal induced cell propulsion into a Cellular Potts model (CPM). We show that the combination of de novo cell-matrix adhesion formation, adhesion growth and shrinkage, adhesion rupture, and feedback of adhesions onto cell propulsion recapitulates multiple lymphocyte behaviours, for different lymphocyte subsets and various substrates. With an increasing attachment area and increased adhesion strength, the cells’ speed and persistence decreases. Additionally, the model predicts random walks with short-term persistent but long-term subdiffusive properties resulting in a pivoting type of motility. For small adhesion areas, the spatial distribution of adhesions emerges as a key factor influencing cell motility. Small adhesions at the front allow for more persistent motility than larger clusters at the back, despite a similar total adhesion area. In conclusion, we present an integrated framework to simulate the effects of ECM proteins on cell-matrix adhesion dynamics. The model reveals a sufficient set of principles explaining the plasticity of lymphocyte motility.

During immunosurveillance, lymphocytes patrol through tissues to interact with cancer cells, other immune cells, and pathogens. The efficiency of this process depends on the kinds of trajectories taken, ranging from simple Brownian walks to Lévy walks. The composition of the extracellular matrix (ECM), a network of macromolecules, affects the formation of cell-matrix adhesions, thus strongly influencing the way lymphocytes move. Here, we present a model of lymphocyte motility driven by adhesions that grow, shrink and rupture in response to the ECM and cellular forces. Compared to other models, our model is computationally light making it suitable for generating long term cell track data, while still capturing actin dynamics and adhesion turnover. Our model suggests that cell motility is affected by the force required to break adhesions and the rate at which new adhesions form. Adhesions can promote cell protrusion by inhibiting retrograde actin flow. After introducing this effect into the model, we found that it reduces the cellular diffusivity and that it promotes stick-slip behaviour. Furthermore, location and size of adhesion clusters determined cell persistence. Overall, our model explains the plasticity of lymphocyte behaviour in response to the ECM.

Mathematical modeling of therapeutic neural stem cell migration in mouse brain with and without brain tumors

Neural stem cells (NSCs) offer a potential solution to treating brain tumors. This is because NSCs can circumvent the blood-brain barrier and migrate to areas of damage in the central nervous system, including tumors, stroke, and wound injuries. However, for successful clinical application of NSC treatment, a sufficient number of viable cells must reach the diseased or damaged area(s) in the brain, and evidence suggests that it may be affected by the paths the NSCs take through the brain, as well as the locations of tumors. To study the NSC migration in brain, we develop a mathematical model of therapeutic NSC migration towards brain tumor, that provides a low cost platform to investigate NSC treatment efficacy. Our model is an extension of the model developed in Rockne et al. (PLoS ONE 13, e0199967, 2018) that considers NSC migration in non-tumor bearing naive mouse brain. Here we modify the model in Rockne et al. in three ways: (i) we consider three-dimensional mouse brain geometry, (ii) we add chemotaxis to model the tumor-tropic nature of NSCs into tumor sites, and (iii) we model stochasticity of migration speed and chemosensitivity. The proposed model is used to study migration patterns of NSCs to sites of tumors for different injection strategies, in particular, intranasal and intracerebral delivery. We observe that intracerebral injection results in more NSCs arriving at the tumor site(s), but the relative fraction of NSCs depends on the location of injection relative to the target site(s). On the other hand, intranasal injection results in fewer NSCs at the tumor site, but yields a more even distribution of NSCs within and around the target tumor site(s).

Spatio-temporal analysis of collective migrationin vivoby particle image velocimetry

Collective cell migration drives the formation of complex organ systems as well as certain tumour invasions and wound healing processes. A characteristic feature of many migrating collectives is tissue-scale polarity, whereby 'leader' cells at the tissue edge guide 'followers' cells that become assembled into polarized epithelial tissues. In this study, we employed particle image velocimetry (PIV) as a tool to quantitate local dynamics underlying the migration of the posterior lateral line primordium (pLLP) in zebrafish at a short time scale. Epithelial cadherin-EGFP was the fluorescent tracer in time-lapse images for PIV analysis. At the tissue level, global speed and directionality of the primordium were extracted from spatially averaged velocity fields. Interestingly, fluctuating velocity patterns evolve at the mesoscale level, which distinguishes the pseudo-mesenchymal leading front from the epithelialized trailing edge, and superimpose to the global deceleration of the whole primordium during the separation of a protoneuromast. Local velocity fields obtained by PIV proved sensitive to estimate the migration speed and directionality of the pLLP in zebrafish, predicting protoneuromast separation at short time scales. Finally, the PIV approach may be suitable for analysing the dynamics of otherin vivomodels of collective migration.

Cellular sociology regulates the hierarchical spatial patterning and organization of cells in organisms

Advances in single-cell biotechnology have increasingly revealed interactions of cells with their surroundings, suggesting a cellular society at the microscale. Similarities between cells and humans across multiple hierarchical levels have quantitative inference potential for reaching insights about phenotypic interactions that lead to morphological forms across multiple scales of cellular organization, namely cells, tissues and organs. Here, the functional and structural comparisons between how cells and individuals fundamentally socialize to give rise to the spatial organization are investigated. Integrative experimental cell interaction assays and computational predictive methods shape the understanding of societal perspective in the determination of the cellular interactions that create spatially coordinated forms in biological systems. Emerging quantifiable models from a simpler biological microworld such as bacterial interactions and single-cell organisms are explored, providing a route to model spatio-temporal patterning of morphological structures in humans. This analogical reasoning framework sheds light on structural patterning principles as a result of biological interactions across the cellular scale and up.