Mechanics of morphological instabilities and surface wrinkling in soft materials: a review

Li, Bo; Cao, Yanping; Feng, Xi‐Qiao; Gao, Huajian

doi:10.1039/c2sm00011c

Cited by 688 publications

(578 citation statements)

References 231 publications

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“…Leonhard Euler derived the celebrated Euler buckling formula for slender columns in the mid-18th century and the buckling of plates and shells was analyzed in the early 20th century (20). In the last few decades, buckling instabilities have been used to model and understand the force-deformation response of a wide variety of biological structures including DNA (32), cytoskeletal filaments (33)(34)(35)(36), membranes (37)(38)(39)(40)(41), white blood cells (42), viruses (43), and tissues (44)(45)(46)(47). Here we present an example in which the buckling of curved membranes can explain the ultradonut topology of the nuclear envelope.…”

Section: Discussionmentioning

confidence: 99%

Ultradonut topology of the nuclear envelope

Torbati

Lele

Agrawal

2016

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

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The nuclear envelope is a unique topological structure formed by lipid membranes in eukaryotic cells. Unlike other membrane structures, the nuclear envelope comprises two concentric membrane shells fused at numerous sites with toroid-shaped pores that impart a "geometric" genus on the order of thousands. Despite the intriguing architecture and vital biological functions of the nuclear membranes, how they achieve and maintain such a unique arrangement remains unknown. Here, we used the theory of elasticity and differential geometry to analyze the equilibrium shape and stability of this structure. Our results show that modest inand out-of-plane stresses present in the membranes not only can define the pore geometry, but also provide a mechanism for destabilizing membranes beyond a critical size and set the stage for the formation of new pores. Our results suggest a mechanism wherein nanoscale buckling instabilities can define the global topology of a nuclear envelope-like structure.nuclear envelope | lipid membranes | topology | buckling instability T he cell nucleus is bounded by two lipid bilayers arranged in a unique geometry called the nuclear envelope. These two bilayers are shaped into concentric spheres that are maintained at a remarkably uniform spacing of ∼ 30−50 nm (1), and yet are fused together at thousands of pores (holes) at an average spacing of ∼ 250−500 nm from each other [based on areal density measurements (2-4)]. At these pores, the membranes locally take on a toroid shape with a radius of curvature on the order of ∼ 20 nm ( Fig. 1). Lipid structures such as vesicles, spherocylinders (bacterial membranes), and biconcave discoids (red blood cell membranes) are all closed structures with no holes, and hence possess a zero genus (5) (Fig. 1). A donut, on the other hand, is also a closed structure but has one hole, and as a result has a genus of 1 (Fig. 1). If we fuse two donuts, we get a shape with a genus of 2, and if we fuse thousands of donuts and bend them to form a sphere, we obtain a nucleus-membrane-like structure ( Fig. 1). This structure, therefore, can be thought of as an "ultradonut" with a genus on the order of thousands. How the two membranes assemble in a unique arrangement with such a large number of local fusions is a fundamental question in both physics and biology that is still unresolved (6-10). To seek an answer to this puzzle, we ask three natural questions based on the common notions in the field of membrane physics.First, can membrane curvature-mediated interactions determine optimal pore number and interpore separation? This principle has been successfully used to predict the interactions of membraneembedded proteins and nanoparticles (11-13). However, in the case of nuclear envelope, Fig. 1C (14) shows that the curved shapes of the membranes at the pores do not persist over interpore length scales; The "curvature memory" of the membranes is lost beyond ∼ 100 nm and they remain essentially flat in between the pores. As a result, a pore does not sense the presence of other p...

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Section: Discussionmentioning

confidence: 99%

Ultradonut topology of the nuclear envelope

Torbati

Lele

Agrawal

2016

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

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“…Hydrogels, either as unsupported entities or integrated as a part of layered structures with different mechanical properties, are reported to display formation of creases or buckling patterns. 9,[38][39][40] In the present modeling approach, such effects have not been included. Our approach is thus limited to cases where uniform deformation of the coupled layer is achieved, and the selection of molecular parameters for the ionic hydrogel core offers a range of final properties that can be explored in such a context.…”

Section: Discussionmentioning

confidence: 99%

Swelling of a hemi-ellipsoidal ionic hydrogel for determination of material properties of deposited thin polymer films: an inverse finite element approach

et al. 2013

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Selective deposition of polymers at the surface of an ionic hydrogel is conventionally used to tailor properties of the composite material for application within for instance drug release and cell encapsulation. Here we describe a method for determination of the mechanical properties of a thin polymer film deposited on an ionic hydrogel core. The ionic strength-dependent hydrogel swelling is affected by the crosslink density and thickness of the deposited polymer layer. A hemi-ellipsoidal geometry of the hydrogel, corresponding to that employed in proof-of-concept experiments, is used to enforce biaxial deformation of the deposited layer when the ionic hydrogel core is equilibrated at various ionic strengths. The ionic strength dependent equilibrium swelling ratio of the hydrogel with deposited polymer film is modeled using a finite element approach. The free energy of the hydrogel core includes contributions accounting for the polymer mixing, the elastic deformation of the network and the Donnan equilibrium. The latter type of contribution is not included in the neutral thin layer in the present study. Adding the polymer multilayer/shell at the surface reveals that the ionic strength-dependent swelling constraint is more pronounced the thicker and stiffer the film is. Combining thickness measurements of the polymer film with high resolution interferometric determination of reduction in swelling capacity of ionic hydrogels, an equivalent elastic property of the polymer layer is obtained using inverse finite element analysis. In the proof-of-concept experiments, analysis of data obtained for chitosan-alginate multilayers composed of four and eight polymer bilayers deposited on anionic acrylamide-based hydrogel core suggest that these bilayers show an elastic stiffness one order of magnitude larger than the one of the hydrogel core.

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“…Most living systems are very complex and soft, usually with multi-field coupling, and hence ongoing continuum mechanics approaches will manifest themselves in biology in terms of efficiency and accuracy. There are a lot of challenges (Volokh, 2013), which also indicate a great chance and brilliant future for mechanicians (Kim et al, 2011;Shi et al, 2011;Li et al, 2012).…”

Section: Discussionmentioning

confidence: 99%

The renaissance of continuum mechanics

Chen

2014

J. Zheijang Univ.-Sci.

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Continuum mechanics, just as the name implies, deals with the mechanics problems of all continua, whose physical (or mechanical) properties are assumed to vary continuously in the spaces they occupy. Continuum mechanics may be seen as the symbol of modern mechanics, which differs greatly from current physics, the two often being mixed up by people and even scientists. In this short paper, I will first try to give an illustration on the differences between (modern) mechanics and physics, in my personal view, and then focus on some important current research activities in continuum mechanics, attempting to identify its path to the near future. We can see that continuum mechanics, while having a dominating impact on engineering design in the 20th century, also plays a pivotal role in modern science, and is much closer to physics, chemistry, biology, etc. than ever before.

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Mechanics of morphological instabilities and surface wrinkling in soft materials: a review

Cited by 688 publications

References 231 publications

Ultradonut topology of the nuclear envelope

Ultradonut topology of the nuclear envelope

Swelling of a hemi-ellipsoidal ionic hydrogel for determination of material properties of deposited thin polymer films: an inverse finite element approach

The renaissance of continuum mechanics

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