Learning the rules of collective cell migration using deep attention networks

Learning dynamical models of single and collective cell migration: a review

Single and collective cell migration are fundamental processes critical for physiological phenomena ranging from embryonic development and immune response to wound healing and cancer metastasis. To understand cell migration from a physical perspective, a broad variety of models for the underlying physical mechanisms that govern cell motility have been developed. A key challenge in the development of such models is how to connect them to experimental observations, which often exhibit complex stochastic behaviours. In this review, we discuss recent advances in data-driven theoretical approaches that directly connect with experimental data to infer dynamical models of stochastic cell migration. Leveraging advances in nanofabrication, image analysis, and tracking technology, experimental studies now provide unprecedented large datasets on cellular dynamics. In parallel, theoretical efforts have been directed towards integrating such datasets into physical models from the single cell to the tissue scale with the aim of conceptualising the emergent behaviour of cells. We first review how this inference problem has been addressed in both freely migrating and confined cells. Next, we discuss why these dynamics typically take the form of underdamped stochastic equations of motion, and how such equations can be inferred from data. We then review applications of data-driven inference and machine learning approaches to heterogeneity in cell behaviour, subcellular degrees of freedom, and to the collective dynamics of multicellular systems. Across these applications, we emphasise how data-driven methods can be integrated with physical active matter models of migrating cells, and help reveal how underlying molecular mechanisms control cell behaviour. Together, these data-driven approaches are a promising avenue for building physical models of cell migration directly from experimental data, and for providing conceptual links between different length-scales of description.

Structure formation induced by non-reciprocal cell-cell interactions in a multicellular system

Collective cellular behavior plays a crucial role in various biological processes, ranging from developmental morphogenesis to pathological processes such as cancer metastasis. Our previous research has revealed that a mutant cell of Dictyostelium discoideum exhibits collective cell migration, including chain migration and traveling band formation, driven by a unique tail-following behavior at contact sites, which we term "contact following locomotion" (CFL). Here, we uncover an imbalance of forces between the front and rear cells within cell chains, leading to an additional propulsion force in the rear cells. Drawing inspiration from this observation, we introduce a theoretical model that incorporates non-reciprocal cell-cell interactions. Our findings highlight that the non-reciprocal interaction, in conjunction with self-alignment interactions, significantly contributes to the emergence of the observed collective cell migrations. Furthermore, we present a comprehensive phase diagram, showing distinct phases at both low and intermediate cell densities. This phase diagram elucidates a specific regime that corresponds to the experimental system.

Learning Dynamics from Multicellular Graphs with Deep Neural Networks

The inference of multicellular self-assembly is the central quest of understanding morphogenesis, including embryos, organoids, tumors, and many others. However, it has been tremendously difficult to identify structural features that can indicate multicellular dynamics. Here we propose to harness the predictive power of graph-based deep neural networks (GNN) to discover important graph features that can predict dynamics. To demonstrate, we apply a physically informed GNN (piGNN) to predict the motility of multi-cellular collectives from a snapshot of their positions both in experiments and simulations. We demonstrate that piGNN is capable of navigating through complex graph features of multicellular living systems, which otherwise can not be achieved by classical mechanistic models. With increasing amounts of multicellular data, we propose that collaborative efforts can be made to create a multicellular data bank (MDB) from which it is possible to construct a large multicellular graph model (LMGM) for general-purposed predictions of multicellular organization.

Migrate3D: Software for simplified post-tracking analysis of 3D and 2D cell migration data

Migrate3D is a cell migration analysis tool whose purpose is to computationally process positional cell tracking data generated via other image acquisition/analysis software and generate biologically meaningful results. The functionalities of Migrate3D include step-based calculations of each cell track, single-cell-level summary statistics, mean squared displacement analysis, and machine learning-based evaluation of the entire dataset and subpopulations of cells found within it. The parameters calculated within Migrate3D have been previously developed and validated by other groups, and were selected to facilitate extraction of the maximum depth of information possible from input datasets. Variables are user-adjustable to enable customized analyses of diverse motility patterns and cell types, both in three-and two-dimensional timelapse data. Independent of any particular upstream image analysis or cell tracking software, Migrate3D only needs positional data over time to execute the suite of calculations. This presents a unique opportunity to standardize and streamline cell migration analysis.

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.

Connecting theory and experiment in cell and tissue mechanics

Understanding complex living systems, which are fundamentally constrained by physical phenomena, requires combining experimental data with theoretical physical and mathematical models. To develop such models, collaborations between experimental cell biologists and theoreticians are increasingly important but these two groups often face challenges achieving mutual understanding. To help navigate these challenges, this Perspective discusses different modelling approaches, including bottom-up hypothesis-driven and top-down data-driven models, and highlights their strengths and applications. Using cell mechanics as an example, we explore the integration of specific physical models with experimental data from the molecular, cellular and tissue level up to multiscale input. We also emphasize the importance of constraining model complexity and outline strategies for crosstalk between experimental design and model development. Furthermore, we highlight how physical models can provide conceptual insights and produce unifying and generalizable frameworks for biological phenomena. Overall, this Perspective aims to promote fruitful collaborations that advance our understanding of complex biological systems.

Self-extinguishing relay waves enable homeostatic control of human neutrophil swarming

Neutrophils exhibit self-amplified swarming to sites of injury and infection. How swarming is controlled to ensure the proper level of neutrophil recruitment is unknown. Using an ex vivo model of infection, we find that human neutrophils use active relay to generate multiple pulsatile waves of swarming signals. Unlike classic active relay systems such as action potentials, neutrophil swarming relay waves are self-extinguishing, limiting the spatial range of cell recruitment. We identify an NADPH-oxidase-based negative feedback loop that is needed for this self-extinguishing behavior. Through this circuit, neutrophils adjust the number and size of swarming waves for homeostatic levels of cell recruitment over a wide range of initial cell densities. We link a broken homeostat to neutrophil over-recruitment in the context of human chronic granulomatous disease.