Force exertion is an integral part of cellular behavior. Traction force microscopy (TFM) has been instrumental for studying such forces, providing spatial force measurements at subcellular resolution. However, the applications of classical TFM are restricted by the typical planar geometry. Here, we develop a particle-based force sensing strategy for studying cellular interactions. We establish a straightforward batch approach for synthesizing uniform, deformable and tuneable hydrogel particles, which can also be easily derivatized. The 3D shape of such particles can be resolved with superresolution (<50 nm) accuracy using conventional confocal microscopy. We introduce a reference-free computational method allowing inference of traction forces with high sensitivity directly from the particle shape. We illustrate the potential of this approach by revealing subcellular force patterns throughout phagocytic engulfment and force dynamics in the cytotoxic T-cell immunological synapse. This strategy can readily be adapted for studying cellular forces in a wide range of applications.

Phagocytosis requires rapid actin reorganization and spatially controlled force generation to ingest targets ranging from pathogens to apoptotic cells. How actomyosin activity directs membrane extensions to engulf such diverse targets remains unclear. Here, we combine lattice light-sheet microscopy (LLSM) with microparticle traction force microscopy (MP-TFM) to quantify actin dynamics and subcellular forces during macrophage phagocytosis. We show that spatially localized forces leading to target constriction are prominent during phagocytosis of antibody-opsonized targets. This constriction is largely driven by Arp2/3-mediated assembly of discrete actin protrusions containing myosin 1e and 1f (‘teeth’) that appear to be interconnected in a ring-like organization. Contractile myosin-II activity contributes to late-stage phagocytic force generation and progression, supporting a specific role in phagocytic cup closure. Observations of partial target eating attempts and sudden target release via a popping mechanism suggest that constriction may be critical for resolving complex in vivo target encounters. Overall, our findings present a phagocytic cup shaping mechanism that is distinct from cytoskeletal remodeling in 2D cell motility and may contribute to mechanosensing and phagocytic plasticity.

We develop an efficient numerical method for calculating the image stress field induced by spherical voids in materials, and applied the method to dislocation-void interactions. The method is constructed based on a complete set of basis functions for the displacement potential of the elastic boundary value problem for a spherical hole, as well as the corresponding displacement, stress, and traction fields, all in terms of linear combinations of spherical harmonics. Using the fast transformation between the real and sphericalharmonics spaces provided by the SHTOOLS package, the method is more efficient than other image stress solvers such as the finite-element method. This method can be readily extended for solving elasticity problems involving inclusions and inhomogeneities, as well as contact between spheres. The tools developed here can also be useful for fast solution of differential equations with spherical boundaries beyond elasticity.

Nanoprecipitates play a significant role in the strength, ductility, and damage tolerance of metallic alloys through their interaction with crystalline defects, especially dislocations. However, the difficulty of observing the action of individual precipitates during plastic deformation has made it challenging to conclusively determine the mechanisms of the precipitate-defect interaction for a given alloy system and presents a major bottleneck in the rational design of nanostructured alloys. Here, we demonstrate the in situ compression of core–shell nanocubes as a promising platform to determine the precise role of individual precipitates. Each nanocube with a dimension of ∼85 nm contains a single spherical precipitate of ∼25 nm diameter. The Au-core/Ag-shell nanocubes show a yield strength of 495 MPa with no strain hardening. The deformation mechanism is determined to be surface nucleation of dislocations which easily traverses through the coherent Au–Ag interface. On the other hand, the Au-core/Cu-shell nanocubes show a yield strength of 829 MPa with a pronounced strain hardening rate. Molecular dynamics and dislocation dynamics simulations, in conjunction with TEM analysis, have demonstrated the yield mechanism to be the motion of threading dislocations extending from the semicoherent Au–Cu interface to the surface, and strain hardening to be caused by a single-armed Orowan looping mechanism. Nanocube compression offers an exciting opportunity to directly compare computational models of defect dynamics with in situ deformation measurements to elucidate the precise mechanisms of precipitate hardening.

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Force exertion is an integral part of cellular behavior. Traction force microscopy (TFM) has been instrumental for studying such forces, providing both spatial and directional force measurements at subcellular resolution. However, the applications of classical TFM are restricted by the typical planar geometry. Here, we develop a particle-based force sensing strategy, specifically designed for studying ligand-dependent cellular interactions. We establish a straightforward batch approach for synthesizing highly uniform, deformable and tunable hydrogel particles, which can also be easily derivatized to trigger specific cellular behavior. The 3D shape of such particles can be resolved with superresolution (<50 nm) accuracy using conventional confocal microscopy. We introduce a computational method that allows inference of surface traction forces with high sensitivity (~10 Pa) directly from the particle shape. We illustrate the potential and flexibility of this approach by revealing surprising subcellular force patterns throughout phagocytic engulfment and measuring dynamics of cytotoxic T cell force exertion in the immunological synapse. This strategy can readily be adapted for studying cellular forces in a wide range of applications. <50 nm precision. Finally, we solve the inverse problem of inferring the displacement field and traction forces from the measured particle shape and traction-free regions. This is accomplished by iteratively minimizing a cost function consisting of contributions from shape mismatch, residual tractions, and the elastic energy, and is enabled by a fast spherical harmonics-based method 17 . We illustrate the potential of this MP-TFM method by revealing subcellular details of the mechanical interaction of macrophages with their targets during phagocytosis, as well as the dynamics of force exertion in the T cell immunological synapse.

Cross-slip of screw dislocations in crystalline solids is a stress-driven thermally activated process essential to many phenomena during plastic deformation, including dislocation pattern formation, strain hardening, and dynamic recovery. Molecular dynamics (MD) simulation has played an important role in determining the microscopic mechanisms of cross-slip. However, due to its limited timescale, MD can only predict cross-slip rates in high-stress or high-temperature conditions. The transition state theory can predict the cross-slip rate over a broad range of stress and temperature conditions, but its predictions have been found to be several orders of magnitude too low in comparison to MD results. This discrepancy can be expressed as an anomalously large activation entropy whose physical origin remains unclear. Here, we resolve this discrepancy by showing that the large activation entropy results from anharmonic effects, including thermal softening, thermal expansion, and soft vibrational modes of the dislocation. We expect these anharmonic effects to be significant in a wide range of stress-driven thermally activated processes in solids.

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