182,473 research outputs found
Curvature-Induced Instabilities of Shells
Induced by proteins within the cell membrane or by differential growth,
heating, or swelling, spontaneous curvatures can drastically affect the
morphology of thin bodies and induce mechanical instabilities. Yet, the
interaction of spontaneous curvature and geometric frustration in curved shells
remains still poorly understood. Via a combination of precision experiments on
elastomeric spherical bilayer shells, simulations, and theory, we show a
spontaneous curvature-induced rotational symmetry-breaking as well as a
snapping instability reminiscent of the Venus fly trap closure mechanism. The
instabilities and their dependence on geometry are rationalized by reducing the
spontaneous curvature to an effective mechanical load. This formulation reveals
a combined pressurelike bulk term and a torquelike boundary term, allowing
scaling predictions for the instabilities in excellent agreement with
experiments and simulations. Moreover, the effective pressure analogy suggests
a curvature-induced buckling in closed shells. We determine the critical
buckling curvature via a linear stability analysis that accounts for the
combination of residual membrane and bending stresses. The prominent role of
geometry in our findings suggests the applicability of the results over a wide
range of scales.Comment: 12 pages, 9 figures (including Supporting Information
TopologyNet: Topology based deep convolutional neural networks for biomolecular property predictions
Although deep learning approaches have had tremendous success in image, video
and audio processing, computer vision, and speech recognition, their
applications to three-dimensional (3D) biomolecular structural data sets have
been hindered by the entangled geometric complexity and biological complexity.
We introduce topology, i.e., element specific persistent homology (ESPH), to
untangle geometric complexity and biological complexity. ESPH represents 3D
complex geometry by one-dimensional (1D) topological invariants and retains
crucial biological information via a multichannel image representation. It is
able to reveal hidden structure-function relationships in biomolecules. We
further integrate ESPH and convolutional neural networks to construct a
multichannel topological neural network (TopologyNet) for the predictions of
protein-ligand binding affinities and protein stability changes upon mutation.
To overcome the limitations to deep learning arising from small and noisy
training sets, we present a multitask topological convolutional neural network
(MT-TCNN). We demonstrate that the present TopologyNet architectures outperform
other state-of-the-art methods in the predictions of protein-ligand binding
affinities, globular protein mutation impacts, and membrane protein mutation
impacts.Comment: 20 pages, 8 figures, 5 table
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