Inference of the drivers of collective movement in two cell types: Dictyostelium and melanoma

Modelling dynamics between free-living amoebae and bacteria

Free-living amoebae (FLA) serve as hosts for a variety of endosymbionts, which are microorganisms that reside and multiply within the FLA. Some of these endosymbionts pose a pathogenic threat to humans, animals, or both. The symbiotic relationship with FLA not only offers these microorganisms protection but also enhances their survival outside their hosts and assists in their dispersal across diverse habitats, thereby escalating disease transmission. This review is intended to offer an exhaustive overview of the existing mathematical models that have been applied to understand the dynamics of FLA, especially concerning their interactions with bacteria. An extensive literature review was conducted across Google Scholar, PubMed, and Scopus databases to identify mathematical models that describe the dynamics of interactions between FLA and bacteria, as published in peer-reviewed scientific journals. The literature search revealed several FLA-bacteria model systems, including Pseudomonas aeruginosa, Pasteurella multocida, and Legionella spp. Although the published mathematical models account for significant system dynamics such as predator-prey relationships and non-linear growth rates, they generally overlook spatial and temporal heterogeneity in environmental conditions, such as temperature, and population diversity. Future mathematical models will need to incorporate these factors to enhance our understanding of FLA-bacteria dynamics and to provide valuable insights for future risk assessment and disease control measures.

Bat Motion can be Described by Leap Frogging

We present models of bat motion derived from radio-tracking data collected over 14 nights. The data presents an initial dispersal period and a return to roost period. Although a simple diffusion model fits the initial dispersal motion we show that simple convection cannot provide a description of the bats returning to their roost. By extending our model to include non-autonomous parameters, or a leap frogging form of motion, where bats on the exterior move back first, we find we are able to accurately capture the bat's motion. We discuss ways of distinguishing between the two movement descriptions and, finally, consider how the different motion descriptions would impact a bat's hunting strategy.

Leveraging the model-experiment loop: Examples from cellular slime mold chemotaxis

Interplay between models and experimental data advances discovery and understanding in biology, particularly when models generate predictions that allow well-designed experiments to distinguish between alternative mechanisms. To illustrate how this feedback between models and experiments can lead to key insights into biological mechanisms, we explore three examples from cellular slime mold chemotaxis. These examples include studies that identified chemotaxis as the primary mechanism behind slime mold aggregation, discovered that cells likely measure chemoattractant gradients by sensing concentration differences across cell length, and tested the role of cell-associated chemoattractant degradation in shaping chemotactic fields. Although each study used a different model class appropriate to their hypotheses - qualitative, mathematical, or simulation-based - these examples all highlight the utility of modeling to formalize assumptions and generate testable predictions. A central element of this framework is the iterative use of models and experiments, specifically: matching experimental designs to the models, revising models based on mismatches with experimental data, and validating critical model assumptions and predictions with experiments. We advocate for continued use of this interplay between models and experiments to advance biological discovery.

Social information use and collective foraging in a pursuit diving seabird

Individuals of many species utilise social information whilst making decisions. While many studies have examined social information in making large scale decisions, there is increasing interest in the use of fine scale social cues in groups. By examining the use of these cues and how they alter behaviour, we can gain insights into the adaptive value of group behaviours. We investigated the role of social information in choosing when and where to dive in groups of socially foraging European shags. From this we aimed to determine the importance of social information in the formation of these groups. We extracted individuals' surface trajectories and dive locations from video footage of collective foraging and used computational Bayesian methods to infer how social interactions influence diving. Examination of group spatial structure shows birds form structured aggregations with higher densities of conspecifics directly in front of and behind focal individuals. Analysis of diving behaviour reveals two distinct rates of diving, with birds over twice as likely to dive if a conspecific dived within their visual field in the immediate past. These results suggest that shag group foraging behaviour allows individuals to sense and respond to their environment more effectively by making use of social cues.

Optimal estimation of drift and diffusion coefficients in the presence of static localization error

We consider the inference of the drift velocity and the diffusion coefficient of a particle undergoing a directed random walk in the presence of static localization error. A weighted least-squares fit to mean-square displacement (MSD) data is used to infer the parameters of the assumed drift-diffusion model. For experiments which cannot be repeated we show that the quality of the inferred parameters depends on the number of MSD points used in the fitting. An optimal number of fitting points p_{opt} is shown to exist which depends on the time interval between frames Δt and the unknown parameters. We therefore also present a simple iterative algorithm which converges rapidly toward p_{opt}. For repeatable experiments the quality depends crucially on the measurement time interval over which measurements are made, reflecting the different timescales associated with drift and diffusion. An optimal measurement time interval T_{opt} exists, which depends on the number of measurement points and the unknown parameters, and so again we present an iterative algorithm which converges quickly toward T_{opt} and is shown to be robust to initial parameter guesses.

Inferring the rules of social interaction in migrating caribou

Social interactions are a significant factor that influence the decision-making of species ranging from humans to bacteria. In the context of animal migration, social interactions may lead to improved decision-making, greater ability to respond to environmental cues, and the cultural transmission of optimal routes. Despite their significance, the precise nature of social interactions in migrating species remains largely unknown. Here we deploy unmanned aerial systems to collect aerial footage of caribou as they undertake their migration from Victoria Island to mainland Canada. Through a Bayesian analysis of trajectories we reveal the fine-scale interaction rules of migrating caribou and show they are attracted to one another and copy directional choices of neighbours, but do not interact through clearly defined metric or topological interaction ranges. By explicitly considering the role of social information on movement decisions we construct a map of near neighbour influence that quantifies the nature of information flow in these herds. These results will inform more realistic, mechanism-based models of migration in caribou and other social ungulates, leading to better predictions of spatial use patterns and responses to changing environmental conditions. Moreover, we anticipate that the protocol we developed here will be broadly applicable to study social behaviour in a wide range of migratory and non-migratory taxa.

This article is part of the theme issue ‘Collective movement ecology’.

Mechanical positioning of multiple nuclei in muscle cells

Many types of large cells have multiple nuclei. In skeletal muscle fibers, the nuclei are distributed along the cell to maximize their internuclear distances. This myonuclear positioning is crucial for cell function. Although microtubules, microtubule associated proteins, and motors have been implicated, mechanisms responsible for myonuclear positioning remain unclear. We used a combination of rough interacting particle and detailed agent-based modeling to examine computationally the hypothesis that a force balance generated by microtubules positions the muscle nuclei. Rather than assuming the nature and identity of the forces, we simulated various types of forces between the pairs of nuclei and between the nuclei and cell boundary to position the myonuclei according to the laws of mechanics. We started with a large number of potential interacting particle models and computationally screened these models for their ability to fit biological data on nuclear positions in hundreds of Drosophila larval muscle cells. This reverse engineering approach resulted in a small number of feasible models, the one with the best fit suggests that the nuclei repel each other and the cell boundary with forces that decrease with distance. The model makes nontrivial predictions about the increased nuclear density near the cell poles, the zigzag patterns of the nuclear positions in wider cells, and about correlations between the cell width and elongated nuclear shapes, all of which we confirm by image analysis of the biological data. We support the predictions of the interacting particle model with simulations of an agent-based mechanical model. Taken together, our data suggest that microtubules growing from nuclear envelopes push on the neighboring nuclei and the cell boundaries, which is sufficient to establish the nearly-uniform nuclear spreading observed in muscle fibers.

How the cell organizes its interior is one of the fundamental biological questions, but the principles of organelles’ positioning remains largely unclear. In this study we use computational modeling and image analysis to elucidate mechanisms of positioning of multiple nuclei in muscle cells. We start with the general hypothesis, supported by published data, that a force balance generated by microtubule asters growing from the nuclei envelopes are responsible for pushing or pulling neighboring nuclei and cell boundaries, and that these forces position the nuclei. Instead of assuming what these forces are, we computationally screen all possible forces by comparing predictions of hundreds simple mechanical models to experimentally measured nuclear positions and shapes in hundreds of Drosophila muscle cells. This screening results in the model, according to which microtubules from one nucleus push away both neighboring nuclei and cell boundaries. We also perform detailed stochastic simulations of the only surviving model with individual growing, pushing and bending microtubules. This model predicts subtle features of nuclear patterns, all of which we confirm experimentally. Our study sheds light on general principles of organelle positioning.

Modeling factors that regulate cell cooperativity in the zebrafish posterior lateral line primordium

Collective cell migration is an integral part of organismal development. We consider migration of the zebrafish primordium during development of the posterior lateral line, a sensory system that detects water movement patterns. Experiments have shown that the chemokine ligand CXCL12a and its receptors CXCR4b and CXCR7b are key players for driving migration of the primordium, while FGF signaling helps maintain cohesion. In this work, we formulate a mathematical model of a laser ablated primordium separated into two smaller cell collectives: a leading collective that responds to local CXCL12a levels and a trailing collective that migrates up a local FGF gradient. Our model replicates recent experimental results, while also predicting a "runaway" behavior when FGF gradient response is inhibited. We also use our model to estimate diffusion coefficients of CXCL12a and FGF in the lateral line.

Leaders in collective migration: are front cells really endowed with a particular set of skills?

Collective cell migration is the coordinated movement emerging from the interaction of at least two cells. In multicellular organisms, collective cell migration is ubiquitous. During development, embryonic cells often travel in numbers, whereas in adults, epithelial cells close wounds collectively. There is often a division of labour and two categories of cells have been proposed: leaders and followers. These two terms imply that followers are subordinated to leaders whose proposed broad range of actions significantly biases the direction of the group of cells towards a specific target. These two terms are also tied to topology. Leaders are at the front while followers are located behind them. Here, we review recent work on some of the main experimental models for collective cell migration, concluding that leader-follower terminology may not be the most appropriate. It appears that not all collectively migrating groups are driven by cells located at the front. Moreover, the qualities that define leaders (pathfinding, traction forces and matrix remodelling) are not specific to front cells. These observations indicate that the terms leaders and followers are not suited to every case. We think that it would be more accurate to dissociate the function of a cell from its position in the group. The position of cells can be precisely defined with respect to the direction of movement by purely topological terms such as "front" or "rear" cells. In addition, we propose the more ample and strictly functional definition of "steering cells" which are able to determine the directionality of movement for the entire group. In this context, a leader cell represents only a specific case in which a steering cell is positioned at the front of the group.