Self-organized shape dynamics of active surfaces

Mietke, Alexander; Jülicher, Frank; Sbalzarini, Ivo F.

doi:10.1073/pnas.1810896115

Cited by 119 publications

(154 citation statements)

References 34 publications

(75 reference statements)

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“…In case active contractile stresses are stronger in the lateral direction than perpendicular to the substrate, we observe an instability leading to a local increase in gel density. This is similar to the dynamics when neglecting the gel thickness [36,39]. However, the states emerging in our system differ fundamentally from those reported in these works: we find periodic stationary states and states that are apparently chaotic.…”

Section: Introductionsupporting

confidence: 83%

“…Furthermore, we impose periodic boundary conditions in the x-direction with period L. In the z-direction, the system extends to infinity and r  0 for  ¥ z . If we ignore the z-direction in equations (1)-(3), we arrive at a dynamic system similar to others that have been used before in the analysis of the actin cortex or other thin active gel layers [36,39]. For high enough activity, these systems typically generate contracted stationary states with a single region of high gel density unless nonlinear assembly terms are considered [40].…”

Section: Dynamics Of the Actin Cortexmentioning

confidence: 99%

“…Its thickness, which has been reported to be of a few hundred nanometers [27,28], is determined by the actin polymerization velocity and its disassembly rate [29]. Due to the large aspect ratio, in theoretical analysis, the cortex is typically considered as a two-dimensional surface [26,[30][31][32][33][34][35][36]. Such an approach has notably been used to measure physical properties of the cortex [37,38].…”

Section: Introductionmentioning

confidence: 99%

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Spontaneous formation of chaotic protrusions in a polymerizing active gel layer

Levernier

Kruse

2020

New J. Phys.

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The actin cortex is a thin layer of actin filaments and myosin motors beneath the outer membrane of animal cells. It determines the cells' mechanical properties and forms important morphological structures. Physical descriptions of the cortex as a contractile active gel suggest that these structures can result from dynamic instabilities. However, in these analyses the cortex is described as a twodimensional layer. Here, we show that the dynamics of the cortex is qualitatively different when gel fluxes in the direction perpendicular to the membrane are taken into account. In particular, an isotropic cortex is then stable for arbitrarily large active stresses. If lateral contractility exceeds vertical contractility, the system can either from protrusions with an apparently chaotic dynamics or a periodic static pattern of protrusions.

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Section: Introductionsupporting

confidence: 83%

Section: Dynamics Of the Actin Cortexmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Spontaneous formation of chaotic protrusions in a polymerizing active gel layer

Levernier

Kruse

2020

New J. Phys.

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“…intercellular pili-mediated forces is incorporated via binding and detachment kinetics. Force generation similar to pili-induced active stresses is common in many biological systems, not only interacting cells but for example also in active gels [23,53]. The remodeling of the active force gives rise to time dependent or permanent (if the active force persists) rheological responses.…”

Section: F Coalescence Of Coloniesmentioning

confidence: 99%

Continuum theory of active phase separation in cellular aggregates

Kuan

Pönisch

Jülicher

et al. 2020

Preprint

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Dense cellular aggregates are common in many biological settings, ranging from bacterial biofilms to organoids, cell spheroids and tumors. Motivated by Neisseria gonorrhoeae biofilms as a model system, we present a hydrodynamic theory to study dense, active, viscoelastic cellular aggregates.The dynamics of these aggregates, driven by forces generated by individual cells, is intrinsically out-of-equilibrium. Starting from the force balance at the level of individual cells, we arrive at the dynamic equations for the macroscopic cell number density via a systematic coarse-graining procedure taking into account a nematic tensor of intracellular force dipoles. We describe the basic process of aggregate formation as an active phase separation phenomenon. Our theory furthermore captures how two cellular aggregates coalesce. Merging of aggregates is a complex process exhibiting several time scales and heterogeneous cell behaviors as observed in experiments.In our theory, it emerges as a coalescence of active viscoelastic droplets where the key timescales are linked to the turnover of the active force generation. Our theory provides a general framework to study the rheology and dynamics of dense cellular aggregates out of thermal equilibrium. * vasily.zaburdaev@fau.de

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“…Often patterns emerge in finite areas or volumes. While most patterns occur in systems of fixed domain shapes, the action of nonlinear patterns on deformable domains they 'live on' has attracted increasing attention only recently [15][16][17]. Here, we hence address the following fundamental question: how do nonlinear stripe patterns affect in a generic manner the shape of a domain with deformable boundaries on which they form?…”

Section: Introductionmentioning

confidence: 99%

Nonlinear patterns shaping the domain on which they live

2020

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Nonlinear stripe patterns in two spatial dimensions break the rotational symmetry and generically show a preferred orientation near domain boundaries, as described by the famous Newell-Whitehead-Segel (NWS) equation. We first demonstrate that, as a consequence, stripes favour rectangular over quadratic domains. We then investigate the effects of patterns 'living' in deformable domains by introducing a model coupling a generalized Swift-Hohenberg model to a generic phase field model describing the domain boundaries. If either the control parameter inside the domain (and therefore the pattern amplitude) or the coupling strength ('anchoring energy' at the boundary) are increased, the stripe pattern self-organizes the domain on which it 'lives' into anisotropic shapes. For smooth phase field variations at the domain boundaries, we simultaneously find a selection of the domain shape and the wave number of the stripe pattern. This selection shows further interesting dynamical behavior for rather steep variations of the phase field across the domain boundaries. The here-discovered feedback between the anisotropy of a pattern and its orientation at boundaries is relevant e.g. for shaken drops or biological pattern formation during development.

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Self-organized shape dynamics of active surfaces

Cited by 119 publications

References 34 publications

Spontaneous formation of chaotic protrusions in a polymerizing active gel layer

Spontaneous formation of chaotic protrusions in a polymerizing active gel layer

Continuum theory of active phase separation in cellular aggregates

Nonlinear patterns shaping the domain on which they live

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