Tethered surfaces: Statics and dynamics

Kantor, Yacov; Kardar, Mehran; Nelson, David R.

doi:10.1103/physreva.35.3056

Cited by 249 publications

(186 citation statements)

References 45 publications

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“…The number of folded layers N is then related to the compaction degree through N ∼ V /V f , where V f is the average volume occupied by the sheet. For high compactions, it is known that V f ∼ R d f g where R g is the radius of gyration and d f is the fractal dimension [23]. Thus we find F ∝ N ∼ φ β , with β = d f 2.5 [23,24].…”

mentioning

confidence: 82%

Comparative Study of Crumpling and Folding of Thin Sheets

et al. 2013

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Crumpling and folding of paper are at first sight very different ways of confining thin sheets in a small volume: the former one is random and stochastic whereas the latest one is regular and deterministic. Nevertheless, certain similarities exist. Crumpling is surprisingly inefficient: a typical crumpled paper ball in a waste-bin consists of as much as 80% air. Similarly, if one folds a sheet of paper repeatedly in two, the necessary force becomes so large that it is impossible to fold it more than 6 or 7 times. Here we show that the stiffness that builds up in the two processes is of the same nature, and therefore simple folding models allow to capture also the main features of crumpling. An original geometrical approach shows that crumpling is hierarchical, just as the repeated folding. For both processes the number of layers increases with the degree of compaction. We find that for both processes the crumpling force increases as a power law with the number of folded layers, and that the dimensionality of the compaction process (crumpling or folding) controls the exponent of the scaling law between the force and the compaction ratio.

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confidence: 82%

Comparative Study of Crumpling and Folding of Thin Sheets

et al. 2013

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“…It is appropriate to inteject here that the observation that a critical wall Reynolds stress must be exceeded for drag reduction to result is closely related to the time criterion expressed by Equation (1)(2)(3)(4)(5)(6)(7)(8)(9). This is easily seen by noting that for wall flows, the maximal eddy shearing rate is which defines a critical wall Reynolds stress varying inversely with R and which is independent of solvent density, viscosity and pipe radius.…”

Section: Elementary Facts About Polymersmentioning

confidence: 99%

“…It is possible to synthesize branched polymers, for example, whose connectivity is illustrated in Figure 1-2. There is currently considerable interest in the other novel architecture shown in Figure 1-2, that of polymerized membranes [9]. These flexible "tethered surfaces" assume configurations in a solvent not unlike crumpled pieces of paper.…”

Section: 3 Branched Polymers and Polymerized Membranesmentioning

confidence: 99%

“…Rg Pe AM; (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14) here n is the number of nodes in a branched polymer or tethered surface, and a' is proportional to m 3 '/ where m is the average number of monomers per nodes (inn ; N). The exponent, v, is approximately, 0.5 for branched polymers [10], and 0.4 for polymerized surfaces [9].…”

Section: 3 Branched Polymers and Polymerized Membranesmentioning

confidence: 99%

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Drag Reduction by Polymer Additives

Diamond¹,

Harvey²,

Katz³

et al. 1992

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“…In the continuum limit, the minimum-energy protein arrangement in Eq. (1) satisfying ρ o > ρ i then yields [16,25] the stretching modulus…”

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Symmetry and Size of Membrane Protein Polyhedral Nanoparticles

Kahraman

Haselwandter

2016

Phys. Rev. Lett.

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In recent experiments [T. Basta et al., Proc. Natl. Acad. Sci. U.S. A. 111, 670 (2014)] lipids and membrane proteins were observed to self-assemble into membrane protein polyhedral nanoparticles (MPPNs) with a well-defined polyhedral protein arrangement and characteristic size. We develop a model of MPPN self-assembly in which the preferred symmetry and size of MPPNs emerge from the interplay of protein-induced lipid bilayer deformations, topological defects in protein packing, and thermal effects. With all model parameters determined directly from experiments, our model correctly predicts the observed symmetry and size of MPPNs. Our model suggests how key lipid and protein properties can be modified to produce a range of MPPN symmetries and sizes in experiments. Utilization of MPPNs for high-resolution structural studies requires [4] control over the symmetry and size of MPPNs. In this Letter we develop a physical description of MPPNs which establishes a quantitative link between the shape of MPPNs and key molecular properties of their constituents. We first describe a simple meanfield model of MPPNs inspired by previous work on membrane budding [9-11] and viral capsid self-assembly [12]. Our mean-field model of MPPNs accounts for the lipid bilayer bending deformations induced by MscS [3,5,6] and the MscS packing defects resulting from the spherical topology of MPPNs, and yields the MPPN energy as a function of the number of MscS per MPPN without any free parameters. We confirm some of the key assumptions underlying our mean-field model by carrying out Monte Carlo simulations of a minimal molecular model of MPPN organization, which we formulate following previous work on viral capsid symmetry [13]. Finally, we use our mean-field model of MPPNs to calculate [12,14,15] the MPPN self-assembly phase diagram as a function of protein concentration, bilayer-protein contact angle, and protein size. We show that our model correctly predicts, with all model parameters determined directly from experiments, the observed [4] symmetry and size of MPPNs formed from MscS. Our results suggest that the preferred symmetry and size of MPPNs emerge from the interplay of protein-induced lipid bilayer deformations, topological defects in protein packing, and thermal effects.Mean-field model.-The membrane-spanning region of MscS [5,6] has an approximately conical shape [3,16] with radius ρ i ≈ 3.2 nm in the lipid bilayer midplane and bilayer-protein contact angle α ≈ 0.46-0.54 rad, yielding [3] protein-induced lipid bilayer bending deformations [see Fig. 1(b)]. The preferred MscS arrangement minimizing bilayer bending energy is expected [9-11] to be a uniform hexagonal lattice. Our simple mean-field model of MPPNs therefore considers, on the one hand, contri-

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Tethered surfaces: Statics and dynamics

Cited by 249 publications

References 45 publications

Comparative Study of Crumpling and Folding of Thin Sheets

Comparative Study of Crumpling and Folding of Thin Sheets

Drag Reduction by Polymer Additives

Symmetry and Size of Membrane Protein Polyhedral Nanoparticles

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