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Three-dimensional (3D) collective cell migration in a collagen-based extracellular matrix (ECM) is among one of the most significant topics in developmental biology, cancer progression, tissue regeneration, and immune response. Recent studies have suggested that collagen-fiber mediated force transmission in cellularized ECM plays an important role in stress homeostasis and regulation of collective cellular behaviors. Motivated by the recent in vitro observation that oriented collagen can significantly enhance the penetration of migrating breast cancer cells into dense Matrigel which mimics the intravasation process in vivo [Han et al. Proc. Natl. Acad. Sci. USA 113, 11208 (2016)PNASA60027-842410.1073/pnas.1610347113], we devise a procedure for generating realizations of highly heterogeneous 3D collagen networks with prescribed microstructural statistics via stochastic optimization. Specifically, a collagen network is represented via the graph (node-bond) model and the microstructural statistics considered include the cross-link (node) density, valence distribution, fiber (bond) length distribution, as well as fiber orientation distribution. An optimization problem is formulated in which the objective function is defined as the squared difference between a set of target microstructural statistics and the corresponding statistics for the simulated network. Simulated annealing is employed to solve the optimization problem by evolving an initial network via random perturbations to generate realizations of homogeneous networks with randomly oriented fibers, homogeneous networks with aligned fibers, heterogeneous networks with a continuous variation of fiber orientation along a prescribed direction, as well as a binary system containing a collagen region with aligned fibers and a dense Matrigel region with randomly oriented fibers. The generation and propagation of active forces in the simulated networks due to polarized contraction of an embedded ellipsoidal cell and a small group of cells are analyzed by considering a nonlinear fiber model incorporating strain hardening upon large stretching and buckling upon compression. Our analysis shows that oriented fibers can significantly enhance long-range force transmission in the network. Moreover, in the oriented-collagen-Matrigel system, the forces generated by a polarized cell in collagen can penetrate deeply into the Matrigel region. The stressed Matrigel fibers could provide contact guidance for the migrating cell cells, and thus enhance their penetration into Matrigel. This suggests a possible mechanism for the observed enhanced intravasation by oriented collagen.

Disordered hyperuniformity (DHU) is a recently proposed new state of matter, which has been observed in a variety of classical and quantum many-body systems. DHU systems are characterized by vanishing infinite-wavelength density fluctuations and are endowed with unique novel physical properties. Here we report the first discovery of disordered hyperuniformity in atomic-scale 2D materials, i.e., amorphous silica composed of a single layer of atoms, based on spectral-density analysis of high-resolution transmission electron microscope images. Subsequent simulations suggest that the observed DHU is closely related to the strong topological and geometrical constraints induced by the local chemical order in the system. Moreover, we show via large-scale density functional theory calculations that DHU leads to almost complete closure of the electronic band gap compared to the crystalline counterpart, making the material effectively a metal. This is in contrast to the conventional wisdom that disorder generally diminishes electronic transport and is due to the unique electron wave localization induced by the topological defects in the DHU state.Disorder hyperuniform (DHU) systems are a unique class of disordered systems which suppress large-scale density fluctuations like crystals and yet possess no Bragg peaks [1, 2]. For a point configuration (e.g., a collection of particle centers of a many-body system), hyperuniformity is manifested as the vanishing structure factor in the infinite-wavelength (or zero-wavenumber) limit, i.e., lim k→0 S(k) = 0, where k = 2π/λ is the wavenumber. In this case of a random field, the hyperuniform condition is given by lim k→0ψ (k) = 0, whereψ(k) is the spectral density [2]. It has been suggested that hyperuniformity can be considered as a new state of matter [1], which possesses a hidden order in between of that of a perfect crystal and a totally disordered system (e.g. a Poisson distribution of points).Recently, a wide spectrum of physical and biological systems have been identified to possess the remarkable property of hyperuniformity, which include the density fluctuations in early universe [3], disordered jammed packing of hard particles [4][5][6][7], certain exotic classical ground states of many-particle systems [8][9][10][11][12][13][14][15], jammed colloidal systems [16][17][18][19], driven non-equilibrium systems [20][21][22][23], certain quantum ground states [24,25], avian photoreceptor patterns [26], organization of adapted im- * These authors contributed equally to this work. † correspondence sent to: xwxfat@gmail.com ‡ correspondence sent to: mohanchen@pku.edu.cn § correspondence sent to: yang.jiao.2@asu.edu ¶ correspondence sent to: hzhuang7@asu.edu mune systems [27], amorphous silicon [28, 29], a wide class of disordered cellular materials [30], dynamic random organizating systems [31-35], and even the distribution of primes on the number axis [36]. In addition, it has been shown that hyperuniform materials can be designed to possess superior physical properties including ...

Cell migration in fibreous extracellular matrix (ECM) is crucial to many physiological and pathological processes such as tissue regeneration, immune response and cancer progression. During migration, individual cells can generate active pulling forces via actin filament contraction, which are transmitted to the ECM fibers through focal adhesion complexes, remodel the ECM, and eventually propagate to and can be sensed by other cells in the system. The microstructure and physical properties of the ECM can also significantly influence cell migration, e.g., via durotaxis and contact guidance. Here, we develop a computational model for cell migration regulated by cell-ECM micro-mechanical coupling. Our model explicitly takes into account a variety of cellular level processes including focal adhesion formation and disassembly, active traction force generation and cell locomotion due to actin filament contraction, transmission and propagation of tensile forces in the ECM, as well as the resulting ECM remodeling. We validate our model by accurately reproducing single-cell dynamics of MCF-10A breast cancer cells migrating on collagen gels and show that the durotaxis and contact guidance effects naturally arise as a consequence of the cell-ECM micromechanical interactions considered in the model. Moreover, our model predicts strongly correlated multi-cellular migration dynamics, which are resulted from the ECM-mediated mechanical coupling among the migrating cell and are subsequently verified in in vitro experiments using MCF-10A cells. Our computational model provides a robust tool to investigate emergent collective dynamics of multi-cellular systems in complex in vivo micro-environment and can be utilized to design in vitro micro-environments to guide collective behaviors and self-organization of cells.

Metastasis of mesenchymal tumor cells is traditionally considered as a single-cell process. Here, we report an emergent collective phenomenon in which the dissemination rate of mesenchymal breast cancer cells from three-dimensional tumors depends on the tumor geometry. Combining experimental measurements and computational modeling, we demonstrate that the collective dynamics is coordinated by the mechanical feedback between individual cells and their surrounding extracellular matrix (ECM). We find the tissue-like fibrous ECM supports long-range physical interactions between cells, which turn geometric cues into regulated cell dissemination dynamics. Our results suggest that migrating cells in three-dimensional ECM represent a distinct class of an active particle system in which the collective dynamics is governed by the remodeling of the environment rather than direct particle-particle interactions.To study the collective invasion of solid tumors, we use in vitro tumor models in three-dimensional (3D) cultures, which offer more physiologically relevant insights compared with two-dimensional assays (7). We