Casimir forces are of fundamental interest because they originate from quantum fluctuations of the electromagnetic field 1 . Apart from controlling the Casimir force via the optical properties of the materials 2-11 , a number of novel geometries have been proposed to generate repulsive and/or non-monotonic Casimir forces between bodies separated by vacuum gaps 12-14 . Experimental realization of these geometries, however, is hindered by the difficulties in alignment when the bodies are brought into close proximity. Here, using an on-chip platform with integrated force sensors and actuators 15 , we circumvent the alignment problem and measure the Casimir force between two surfaces with nanoscale protrusions. We demonstrate that the Casimir force depends non-monotonically on the displacement. At some displacements, the Casimir force leads to an effective stiffening of the nanomechanical spring. Our findings pave the way for exploiting the Casimir force in nanomechanical systems using structures of complex and non-conventional shapes.The prediction of the attraction between two neutral perfect conductors by Casimir 1 was obtained by considering the boundary conditions imposed by two planar surfaces on the quantum fluctuations of the electromagnetic field. Alternatively, the Casimir force is sometimes considered as an extension of the van der Waals force between fluctuating dipoles to solid bodies and in the regime of retardation. This attractive force increases monotonically when the distance between the two planes decreases. As the Casimir force becomes the dominant interaction between electrically neutral surfaces separated by nanoscale gaps, they are of practical importance in nanomechanical devices 16,17 . In experiments, one of the flat surfaces is often replaced by a spherical body 4-11 due to the difficulty in maintaining parallelism at small separations 18 . By introducing corrugations to one of the surfaces, recent experiments 19,20 have demonstrated the non-trivial geometry dependence of the Casimir force. Measuring the Casimir Device fabrication Supplementary Figure S1 | The fabrication procedure of the device (not to scale). a, A cross-sectional view of the silicon-on-insulator wafer. The silicon device layer, the buried oxide layer and the substrate are shown in blue, yellow and grey respectively. b, The silicon oxide etch mask (red) is created using the resist pattern from lithography. c, Silicon in the regions not protected by silicon oxide is removed by DRIE. d, HF selectively etches the silicon oxide isotropically, undercutting of the top silicon structure by ~ 2.7 µm. The middle silicon piece is thin enough to be suspended. The other two pieces have oxide underneath and therefore are anchored to the substrate.

How migrating cells differentially adapt and respond to extracellular track geometries remains unknown. Using intravital imaging, we demonstrate that invading cells exhibit dorsoventral (top-to-bottom) polarity in vivo. To investigate the impact of dorsoventral polarity on cell locomotion through different confining geometries, we fabricated microchannels of fixed cross-sectional area, albeit with distinct aspect ratios. Vertical confinement, exerted along the dorsoventral polarity axis, induces myosin II–dependent nuclear stiffening, which results in RhoA hyperactivation at the cell poles and slow bleb-based migration. In lateral confinement, directed perpendicularly to the dorsoventral polarity axis, the absence of perinuclear myosin II fails to increase nuclear stiffness. Hence, cells maintain basal RhoA activity and display faster mesenchymal migration. In summary, by integrating microfabrication, imaging techniques, and intravital microscopy, we demonstrate that dorsoventral polarity, observed in vivo and in vitro, directs cell responses in confinement by spatially tuning RhoA activity, which controls bleb-based versus mesenchymal migration.

The mechanical properties of the cellular nucleus are extensively studied as they play a critical role in important processes, such as cell migration, gene transcription, and stem cell differentiation. While the mechanical properties of the isolated nucleus have been tested, there is a lack of measurements about the mechanical behavior of the nucleus within intact cells and specifically about the interplay of internal nuclear components with the intracellular microenvironment, because current testing methods are based on contact and only allow studying the nucleus after isolation from a cell or disruption of cytoskeleton. Here, all‐optical Brillouin microscopy and 3D chemomechanical modeling are used to investigate the regulation of nuclear mechanics in physiological conditions. It is observed that the nuclear modulus can be modulated by epigenetic regulation targeting internal nuclear nanostructures such as lamin A/C and chromatin. It is also found that nuclear modulus is strongly regulated by cytoskeletal behavior through a robust mechanism conserved in different culturing conditions. Given the active role of cytoskeletal modulation in nearly all cell functions, this work will enable to reveal highly relevant mechanisms of nuclear mechanical regulations in physiological and pathological conditions.

In Brillouin microscopy, absorption-induced photodamage of incident light is the primary limitation on signal-to-noise ratio in many practical scenarios. Here we show that 660 nm may represent an optimal wavelength for Brillouin microscopy as it offers minimal absorption-mediated photodamage at high Brillouin scattering efficiency and the possibility to use a pure and narrow laser line from solid-state lasing medium. We demonstrate that live cells are ~80 times less susceptible to the 660 nm incident light compared to 532 nm light, which overall allows Brillouin imaging of up to more than 30 times higher SNR. We show that this improvement enables Brillouin imaging of live biological samples with improved accuracy, higher speed and/or larger fields of views with denser sampling.

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