Peristaltic instability of cylindrical gels

Barrière, Benoı̂t; Sekimoto, Ken; Leibler, Ludwik

doi:10.1063/1.472544

Cited by 44 publications

(37 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The neurite is unstable above a critical tension σ c = 2 , thus initially the dynamics is governed by the gel compression modes, which is qualitatively similar to the result in [8]. Above a second critical tension σ c2 = 6µR c , the instability grows with the much faster rate ω ∼ 1/ √ τ S τ C .…”

Section: (I)supporting

confidence: 65%

“…In stretch injuries, tension in the axon is responsible for beading. In the other examples, disruption of cytoskeletal integrity appears to be a common feature.Peristaltic modes have been studied in tubular membranes and gels under tension [6,7,8]. This "pearling instability" is driven by surface tension, as in the Rayleigh-Plateau instability of liquid columns [9].…”

mentioning

confidence: 99%

See 1 more Smart Citation

Osmotically Driven Shape Transformations in Axons

et al. 2006

View full text Add to dashboard Cite

We report a cylindrical-peristaltic shape transformation in axons exposed to a controlled osmotic perturbation. The peristaltic shape relaxes and the axon recovers its original geometry within minutes. We show that the shape instability depends critically on swelling rate and that volume and membrane area regulation are responsible for the shape relaxation. We propose that volume regulation occurs via leakage of ions driven by elastic pressure, and analyse the peristaltic shape dynamics taking into account the internal structure of the axon. The results obtained provide a framework for understanding peristaltic shape dynamics in nerve fibers occurring in vivo. PACS numbers: 47.20.Dr, 87.19.La Axons and dendrites, collectively known as neurites, are thin, tubular extensions produced by neuronal cells [1]. Structurally, they consist of an outer lipid membrane sheath bound to a core made up of an elastic network of highly cross-linked biopolymers known as the cytoskeleton. Neurites are known to lose their normal cylindrical geometry and become peristaltically modulated-a process commonly known as beading-under a wide range of situations. These include neuro-degenerative diseases like Alzheimer's [2], brain trauma [3], stretch injuries to nerves [4] and in vitro as well as in vivo application of neurotoxins or drugs [5], among others. In stretch injuries, tension in the axon is responsible for beading. In the other examples, disruption of cytoskeletal integrity appears to be a common feature.Peristaltic modes have been studied in tubular membranes and gels under tension [6,7,8]. This "pearling instability" is driven by surface tension, as in the Rayleigh-Plateau instability of liquid columns [9]. In liquid columns, peristaltic perturbations with wavelengths larger than the circumference grow as they reduce surface area at constant volume. Unlike liquid columns, cylindrical vesicles/gels are unstable only beyond a critical tension, when the gain in surface energy due to a reduction in area overcomes the elastic energy for deforming the membrane/gel. Similar arguments can explain peristaltic modes observed in stretched nerves [10] and cell protrusions exposed to toxins [11]. In all the above mentioned biological examples the beaded state persists and no recovery has been observed.We report a novel, reversible, peristaltic instability observed in chick-embryo axons and in PC12 neurites [12] after a sudden dilution of the external medium, as shown in Fig. 1. The transition to the peristaltic state occurs at a threshold membrane tension, induced by osmotic swelling. However, unlike previous reports on beading, the osmotically induced instability relaxes and the neurite recovers its original shape within minutes. We show that the relaxation is due both to cell volume and membrane surface regulation. Remarkably, the shape stability depends critically on the swelling rate. We model the pearling/beading instability taking into account the gel-like dynamics of the cytoskeleton and the membranecytoskeleton coupling, and fin...

show abstract

Section: (I)supporting

confidence: 65%

mentioning

confidence: 99%

Osmotically Driven Shape Transformations in Axons

et al. 2006

View full text Add to dashboard Cite

show abstract

“…Focusing on the particular case of soft elastic cylinders with a superficial energy, Barrière et al (1996) proved that capillarity may drive the onset of a long-wavelength peristaltic pattern without the application of any external strain, differently from the short-wavelength buckling arising in compressed cylinders with negligible surface effects (Vaughan, 1971). More recently, Mora et al (2010) proposed a linear stability analysis for this elastocapillary problem, validating their theoretical predictions with experiments made on soft gel fibres.…”

mentioning

confidence: 98%

Beading instability in soft cylindrical gels with capillary energy: Weakly non-linear analysis and numerical simulations

Taffetani

Ciarletta

2015

Journal of the Mechanics and Physics of Solids

View full text Add to dashboard Cite

a b s t r a c tSoft cylindrical gels can develop a long-wavelength peristaltic pattern driven by a competition between surface tension and bulk elastic energy. In contrast to the RayleighPlateau instability for viscous fluids, the macroscopic shape in soft solids evolves toward a stable beading, which strongly differs from the buckling arising in compressed elastic cylinders.This work proposes a novel theoretical and numerical approach for studying the onset and the non-linear development of the elasto-capillary beading in soft cylinders, made of neo-Hookean hyperelastic material with capillary energy at the free surface, subjected to axial stretch. Both a theoretical study, deriving the linear and the weakly non-linear stability analyses for the problem, and numerical simulations, investigating the fully nonlinear evolution of the beaded morphology, are performed. The theoretical results prove that an axial elongation can not only favour the onset of beading, but also determine the nature of the elastic bifurcation. The fully non-linear phase diagrams of the beading are also derived from finite element numerical simulations, showing two peculiar morphological transitions when varying either the axial stretch or the material properties of the gel. Since the bifurcation is found to be subcritical for very slender cylinders, an imperfection sensitivity analysis is finally performed. In this case, it is shown that a surface sinusoidal imperfection can resonate with the corresponding marginally stable solution, thus selecting the emerging beading wavelength.In conclusion, the results of this study provide novel guidelines for controlling the beaded morphology in different experimental conditions, with important applications in micro-fabrication techniques, such as electrospun fibres.

show abstract

“…These can be formed when water and NaCl molecules squeezed out of the interior are stored in the surface due to the relatively large friction near the surface. These can be induced by peristaltic instability due to the strong surface tension (13). The necessary conditions in both of the cases were that the density of the chains in the binding state near the surface was larger than that in the interior.…”

Section: Discussionmentioning

confidence: 98%