Seeing around corners: Cells solve mazes and respond at a distance using attractant breakdown

Tweedy, Luke; Thomason, Peter A.; Paschke, Peggy; Martin, Kirsty J.; Machesky, Laura M.; Zagnoni, Michele; Insall, Robert H.

doi:10.1126/science.aay9792

Cited by 127 publications

(103 citation statements)

References 39 publications

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“…We also made a quasi-steady state approximation for the TAF dynamics, which simplified our analysis by making the TAF field linear. TAF dynamics may be more complicated in reality, however, and can play a more significant role in the migratory dynamics: cell-induced gradients, for instance, can provide time-dependent guidance cues for tip cells, and will generate spatial heterogeneities in the TAF gradient that were not considered here (Tweedy et al 2020).…”

Section: Discussionmentioning

confidence: 99%

Comparative analysis of continuum angiogenesis models

2021

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Although discrete approaches are increasingly employed to model biological phenomena, it remains unclear how complex, population-level behaviours in such frameworks arise from the rules used to represent interactions between individuals. Discrete-to-continuum approaches, which are used to derive systems of coarse-grained equations describing the mean-field dynamics of a microscopic model, can provide insight into such emergent behaviour. Coarse-grained models often contain nonlinear terms that depend on the microscopic rules of the discrete framework, however, and such nonlinearities can make a model difficult to mathematically analyse. By contrast, models developed using phenomenological approaches are typically easier to investigate but have a more obscure connection to the underlying microscopic system. To our knowledge, there has been little work done to compare solutions of phenomenological and coarse-grained models. Here we address this problem in the context of angiogenesis (the creation of new blood vessels from existing vasculature). We compare asymptotic solutions of a classical, phenomenological “snail-trail” model for angiogenesis to solutions of a nonlinear system of partial differential equations (PDEs) derived via a systematic coarse-graining procedure (Pillay et al. in Phys Rev E 95(1):012410, 2017. https://doi.org/10.1103/PhysRevE.95.012410). For distinguished parameter regimes corresponding to chemotaxis-dominated cell movement and low branching rates, both continuum models reduce at leading order to identical PDEs within the domain interior. Numerical and analytical results confirm that pointwise differences between solutions to the two continuum models are small if these conditions hold, and demonstrate how perturbation methods can be used to determine when a phenomenological model provides a good approximation to a more detailed coarse-grained system for the same biological process.

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Section: Discussionmentioning

confidence: 99%

Comparative analysis of continuum angiogenesis models

2021

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“…Furthermore, we analyzed tip and stalk cell dynamics in an idealized condition where the TAF concentration was at steady state. In more biologically relevant scenarios, however, the TAF field is unlikely to match the profiles investigated in Table II and its dynamics will likely be more complex: for example, cells may degrade the chemoattractant and create cell-induced gradients [57]. It may therefore be necessary to include such dynamics in the snail-trail modeling framework when it is used to analyze experimental results.…”

Section: Discussionmentioning

confidence: 99%

“…Additionally, we assume that the system contains a generic chemoattractant (a TAF) whose concentration is denoted by c(x, y, t ). In general, the value of c is governed by a differential equation that may include terms corresponding to diffusion and/or uptake by tip and stalk cells [46,56,57]. However, in this article we are most interested in determining appropriate equations for describing cell movement and proliferation.…”

Section: Snail-trail Model Development In 2dmentioning

confidence: 99%

Evaluating snail-trail frameworks for leader-follower behavior with agent-based modeling

Byrne

Maini

2020

Phys. Rev. E

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Branched networks constitute a ubiquitous structure in biology, arising in plants, lungs, and the circulatory system; however, the mechanisms behind their creation are not well understood. A commonly used model for network morphogenesis proposes that sprouts develop through interactions between leader (tip) cells and follower (stalk) cells. In this description, tip cells emerge from existing structures, travel up chemoattractant gradients, and form new networks by guiding the movement of stalk cells. Such dynamics have been mathematically represented by continuum "snail-trail" models in which the tip cell flux contributes to the stalk cell proliferation rate. Although snail-trail models constitute a classical depiction of leader-follower behavior, their accuracy has yet to be evaluated in a rigorous quantitative setting. Here, we extend the snail-trail modeling framework to two spatial dimensions by introducing a novel multiplicative factor to the stalk cell rate equation, which corrects for neglected network creation in directions other than that of the migrating front. Our derivation of this factor demonstrates that snail-trail models are valid descriptions of cell dynamics when chemotaxis dominates cell movement. We confirm that our snail-trail model accurately predicts the dynamics of tip and stalk cells in an existing agent-based model (ABM) for network formation [Pillay et al., Phys. Rev. E 95, 012410 (2017)]. We also derive conditions for which it is appropriate to use a reduced, one-dimensional snail-trail model to analyze ABM results. Our analysis identifies key metrics for cell migration that may be used to anticipate when simple snail-trail models will accurately describe experimentally observed cell dynamics in network formation.

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“…Another emerging aspect of tumor invasion is the decision-making ability of cancer cells when they are faced with branching tracks. The ECM is like a maze for cancer cells migrating inside, and a recent study demonstrated a surprising ability of pancreatic cancer cells to navigate efficiently inside a microfluidic-based maze (Tweedy et al, 2020). Another recent study on immune cells also unveiled that the cell nucleus and microtubule-organizing center can act as a gauge to efficiently navigate neutrophil transmigration in matrices with differently sized pores (Renkawitz et al, 2019).…”

Section: Microfluidic Channelmentioning

confidence: 99%

Engineering confining microenvironment for studying cancer metastasis

2021

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The physical microenvironment of cells plays a fundamental role in regulating cellular behavior and cell fate, especially in the context of cancer metastasis. For example, capillary deformation can destroy arrested circulating tumor cells while the dense extracellular matrix can form a physical barrier for invading cancer cells. Understanding how metastatic cancer cells overcome the challenges brought forth by physical confinement can help in developing better therapeutics that can put a stop to this migratory stage of the metastatic cascade. Numerous in vivo and in vitro assays have been developed to recapitulate the metastatic processes and study cancer cell migration in a confining microenvironment. In this review, we summarize some of the representative techniques and the exciting new findings. We critically review the advantages, as well as challenges associated with these tools and methodologies, and provide a guide on the applications that they are most suited for. We hope future efforts that push forward our current understanding on metastasis under confinement can lead to novel and more effective diagnostic and therapeutic strategies against this dreaded disease.

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Seeing around corners: Cells solve mazes and respond at a distance using attractant breakdown

Cited by 127 publications

References 39 publications

Comparative analysis of continuum angiogenesis models

Comparative analysis of continuum angiogenesis models

Evaluating snail-trail frameworks for leader-follower behavior with agent-based modeling

Engineering confining microenvironment for studying cancer metastasis

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