Emergence and Persistence of Collective Cell Migration on Small Circular Micropatterns

Segerer, Felix J.; Thüroff, Florian; Alberola, Alicia Piera; Frey, Erwin; Rädler, Joachim O.

doi:10.1103/physrevlett.114.228102

Cited by 120 publications

(144 citation statements)

References 42 publications

(57 reference statements)

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“…(21), and (22) around homogeneous polar state, or disordered phase. For this purpose, we write the fields W and ρ as W ( r, t) = W 0êx + δ W ( r, t), ρ( r, t) = ρ 0 + δρ( r, t) (24) where ρ 0 , and W 0 are homogeneous steady solution of density and polarization respectively,ê x is the unit vector along x direction, and δ W and δρ are spatio-temporal perturbations. We linearize Eq.…”

Section: Linear Stabilitymentioning

confidence: 99%

“…There are many examples, such as birds flocks [11][12][13][14][15], schools of fishes [16][17][18], herds of animals [19,20], bacteria colonies [21][22][23], clusters of cells [24], and vibrated granular particles [25,26]. One of the fundamental and pioneer works in active matter is the introduction of a dynamical microscopic model, known as Vicsek model, to study the emergence of collective behavior [27].…”

Section: Introductionmentioning

confidence: 99%

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Gaussian theory for spatially distributed self-propelled particles

2016

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Obtaining a reduced description with particle and momentum flux densities outgoing from the microscopic equations of motion of the particles requires approximations. The usual method, we refer to as truncation method, is to zero Fourier modes of the orientation distribution starting from a given number. Here we propose another method to derive continuum equations for interacting selfpropelled particles. The derivation is based on a Gaussian approximation (GA) of the distribution of the direction of particles. First, by means of simulation of the microscopic model we justify that the distribution of individual directions fits well to a wrapped Gaussian distribution. Second, we numerically integrate the continuum equations derived in the GA in order to compare with results of simulations. We obtain that the global polarization in the GA exhibits a hysteresis in dependence on the noise intensity. It shows qualitatively the same behavior as we find in particles simulations. Moreover, both global polarizations agree perfectly for low noise intensities. The spatio-temporal structures of the GA are also in agreement with simulations. We conclude that the GA shows qualitative agreement for a wide range of noise intensities. In particular, for low noise intensities the agreement with simulations is better as other approximations, making the GA to an acceptable candidates of describing spatially distributed self-propelled particles.

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Section: Linear Stabilitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Gaussian theory for spatially distributed self-propelled particles

2016

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“…However, the scaling of the rotational diffusion coefficient with cluster size is not obvious, and will depend on the model. Rotational diffusion could arise from clusters that undergo collectively-driven rotation, but occasionally switch between moving in different directions over a timescale τ switch -this is observed in small clusters of cells on micropatterns [48]. If this is the case, the effective rotational diffusion coefficient is just D r ∼ Ω 2 τ switch -so D r ∼ v 2 max τ switch /R 2 .…”

Section: Si Appendixmentioning

confidence: 99%

Cell-to-cell variation sets a tissue-rheology–dependent bound on collective gradient sensing

Camley

Rappel

2017

Proc. Natl. Acad. Sci. U.S.A.

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When a single cell senses a chemical gradient and chemotaxes, stochastic receptor-ligand binding can be a fundamental limit to the cell's accuracy. For clusters of cells responding to gradients, however, there is a critical difference: even genetically identical cells have differing responses to chemical signals. With theory and simulation, we show collective chemotaxis is limited by cell-to-cell variation in signaling. We find that when different cells cooperate the resulting bias can be much larger than the effects of ligand-receptor binding. Specifically, when a strongly-responding cell is at one end of a cell cluster, cluster motion is biased toward that cell. These errors are mitigated if clusters average measurements over times long enough for cells to rearrange. In consequence, fluid clusters are better able to sense gradients: we derive a link between cluster accuracy, cellto-cell variation, and the cluster rheology. Because of this connection, increasing the noisiness of individual cell motion can actually increase the collective accuracy of a cluster by improving fluidity.Many cells follow signal gradients to survive or perform their functions, including white blood cells finding a wound, cells crossing a developing embryo, and cancerous cells migrating from tumors. Chemotaxis, sensing and responding to chemical gradients, is crucial in all of these examples [1,2]. Chemotaxis is traditionally studied by exposing single cells to gradients -but cells often travel in groups, not singly [3,4]. Collective cell migration is essential to development and metastasis [5], and can have remarkable effects on chemotaxis. Even when single cells cannot sense a gradient, a cluster of cells may cooperate to sense it. While collective chemotaxis is our primary focus, this "emergent" gradient sensing is found in response to many signals, including soluble chemical gradients (chemotaxis) [6][7][8], conditioned substrates (haptotaxis) [9], substrate stiffness gradients (durotaxis) [10] and electrical potential (galvanotaxis) [11,12].Cells can cooperate to sense gradients -but the physical principles limiting a cluster's sensing accuracy are not settled. For single cells, the fundamental bounds on sensing chemical concentrations and gradients are well-studied [13][14][15][16][17][18][19][20][21][22], showing unavoidable stochasticity in receptor-ligand binding limits chemotactic accuracy. Is this true for cell clusters? Is a cell cluster simply equivalent to a larger cell? No! There is an essential difference between many clustered cells and a single large cell: even clonal populations of cells can have highly variable responses to signals, due to many factors, including intrinsic variations in regulatory protein concentrations [23][24][25]. These cell-to-cell variations (CCV) can be persistent over timescales much larger than the typical motility timescale of the cell [25]. CCV has not been addressed in models of collective chemotaxis and it is not clear whether collective gradient sensing is limited by CCV or by stochasti...

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“…In the L/R asymmetry field, this amounts to multi-scale biophysical models that quantitatively explain the integration of chiral cell behaviours towards whole body axes. Recent work has begun this task [20,23,[29][30][31], and the contribution by Martinez et al [32] extends the effort to patterns of plant leaf asymmetry. Analysis of several mutants with spiral phyllotaxis found the mirrored patterns of L/R leaflet displacement as predicted by the model, as were the results of analysis of leaf pair shapes in plants with distichous phyllotaxis.…”

Section: Synopsis Of Laterality Chaptersmentioning

confidence: 99%

Introduction to provocative questions in left–right asymmetry

Levin

Klar

Ramsdell

2016

Phil. Trans. R. Soc. B

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Left–right asymmetry is a phenomenon that has a broad appeal—to anatomists, developmental biologists and evolutionary biologists—because it is a morphological feature of organisms that spans scales of size and levels of organization, from unicellular protists, to vertebrate organs, to social behaviour. Here, we highlight a number of important aspects of asymmetry that encompass several areas of biology—cell-level, physiological, genetic, anatomical and evolutionary components—and that are based on research conducted in diverse model systems, ranging from single cells to invertebrates to human developmental disorders. Together, the contributions in this issue reveal a heretofore-unsuspected variety in asymmetry mechanisms, including ancient chirality elements that could underlie a much more universal basis to asymmetry development, and provide much fodder for thought with far reaching implications in biomedical, developmental, evolutionary and synthetic biology. The new emerging theme of binary cell-fate choice, promoted by asymmetric cell division of a deterministic cell, has focused on investigating asymmetry mechanisms functioning at the single cell level. These include cytoskeleton and DNA chain asymmetry—mechanisms that are amplified and coordinated with those employed for the determination of the anterior–posterior and dorsal–ventral axes of the embryo. This article is part of the themed issue ‘Provocative questions in left–right asymmetry’.

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Emergence and Persistence of Collective Cell Migration on Small Circular Micropatterns

Cited by 120 publications

References 42 publications

Gaussian theory for spatially distributed self-propelled particles

Gaussian theory for spatially distributed self-propelled particles

Cell-to-cell variation sets a tissue-rheology–dependent bound on collective gradient sensing

Introduction to provocative questions in left–right asymmetry

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