Center for Soft and Living Matter

A model of epithelial tissues with edge tensions

Learning modifies a physical learning network. a) Input forces (black) are applied to the physical degrees of freedom (green, e.g. node positions) of a physical network (e.g. mechanical spring network), whose interactions correspond to learning degrees of freedom (blue, e.g. spring constants). b) In the physical configuration space, this input force causes the system to respond, equilibrating in a free state (red dot). To train the system, a further `output force’ is applied, nudging the system to a clamped state (green dot). The blue arrows describe the inherent physical coordinate system, with direction corresponding to eigenmodes v of the physical Hessian H, and lengths correspond to the associated inverse eigenvalues. c) A local learning rule is applied, modifying the learning degrees of freedom. On top of improving the system free state response, learning tends to rotate the Hessian coordinate system such that the eigenmode corresponding to the lower eigenvalues align with the free state response, and decrease these eigenvalues. d) Training results in a physical system whose lower eigenvalues are reduced, and eigenmodes aligned with the trained task(s). The system responds considerably more strongly to random forces, shown by the area spanned by the trained inverse eigenvalues (blue ellipse) compared to the untrained ones (red ellipse). Training makes the physical system more conductive and lower dimensional.

Cryo-electron tomography unveils the intricate molecular structural details in situ at the tip of a frozen parasite cell.

Cooperative clusters of immune cells (pink) form when engulfing cancer cells (green).By Dr. Larry Dooling, Discher Lab (Nature Biomed Eng’g 2023)

Fat droplets (yellow) within cells collide with the nucleus (white) and rupture it (red), and droplet roundness indicates high interfacial tension. By Dr. Irena Ivanovska and Michael Tobin, Discher Lab (J Cell Biology 2023).

Cellular communities of the protist Spirostomum ambiguum use hydrodynamic trigger waves to communicate with each other. Spirostomum can contract its body length by 60% within milliseconds, creating accelerations that can reach forces of 14g and generating long-ranged vortex flows that trigger neighboring Spirostomum cells to contract. The connecting lines and colors indicate which cells triggered which other cells.

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A paramagnetic Co^II₄ capsule binds xenon, which is stably encapsulated in the solid state through hydrogen-bonding interactions of the capsule with guanidinium cations. Rapid exchange of xenon in solution enables ultrasensitive ¹²⁹Xe NMR sensing applications.

In this image, a biomimetic lotus is gradually blooming, which is made from stimuli-responsive soft materials with folding properties from 2D to 3D, leading to a variety of potential applications including biomimetic machines, wearable electronics, drug delivery and soft robotics. Different types of responsive materials with folding properties are summarized in the review article by J. Liu,Y. Gao, Y-J. Lee, S. Yang*, Trends Chem.2, 107–122 (2020).

A biopolymer network with stiff inclusions responds to uniaxial compression. Compressed network fibers are colored orange and stretched network fibers are colored blue. Under small compressions, the network fibers bend and the sample first softens then stiffens with increasing compression (right). Further increasing compression leads to rearrangement of the stiff inclusions, driving stretching of fibers (middle) and leading to a crossover from bending-dominated to stretching-dominated mechanics and increasing stiffness. With sufficiently large compression the inclusions jam (left), increasing the stiffness still further.

Cytoskeletal filaments inside the leading edge of a frozen-hydrated human cell imaged by cryo-electron tomography.

Image taken by Dr. Longsheng Lai from the Yi-Wei Chang lab in the Department of Biochemistry and Biophysics, Perelman School of Medicine, University of Pennsylvania

Morphological transition in growing adaptive flow networks such as the vascular networks of leaves. Line width is proportional to the quarter root of the conductance, color indicates the pressure p. (top left) Initially the network is disordered and not hierarchically organized, with many long branches connecting directly to the source. (top right) Hierarchical organization begins to appear. (lower left) The network is hierarchically organized and efficient. Few long branches are visible (compare with (top left)). (lower right) Optimal network when the source is at the boundary, showing leaf-like main and secondary veins.

As liquids are cooled towards their glass transitions, they exhibit dramatically more sluggish and heterogeneous dynamics. One notorious stumbling block in understanding this behavior has been the inability to identify structural features corresponding to the dynamics. We use machine learning methods to construct a structural quantity that correlates strongly with dynamics. We call this quantity “softness”—particles with high softness are highly vulnerable to rearrangement, while those with low softness are resistant. Here we show results from a simulation of a liquid near the glass transition, in which particles with high softness (and corresponding high dynamical mobility) are opaque and colored while particles with low softness are translucent and black. The image was constructed from a two-dimensional slab of the system rendered in POVRAY and then processed with a color gradient.

Characterizing structural inhomogeneity is an essential step in understanding the mechanical response of amorphous materials. We introduce a threshold-free measure based on the field of vectors pointing from the center of each particle to the centroid of the Voronoi cell in which the particle resides. These vectors tend to point in toward regions of high free volume and away from regions of low free volume, reminiscent of sinks and sources in a vector field. The divergence of this vector field correlates with rearrangements, as in the shear band pictured here for a 2d system of bidisperse grains.