Mammalian cells are surrounded by neighbouring cells and extracellular matrix (ECM), which provide cells with structural support and mechanical cues that influence diverse biological processes. The Hippo pathway effectors YAP (also known as YAP1) and TAZ (also known as WWTR1) are regulated by mechanical cues and mediate cellular responses to ECM stiffness. Here we identified the Ras-related GTPase RAP2 as a key intracellular signal transducer that relays ECM rigidity signals to control mechanosensitive cellular activities through YAP and TAZ. RAP2 is activated by low ECM stiffness, and deletion of RAP2 blocks the regulation of YAP and TAZ by stiffness signals and promotes aberrant cell growth. Mechanistically, matrix stiffness acts through phospholipase Cγ1 (PLCγ1) to influence levels of phosphatidylinositol 4,5-bisphosphate and phosphatidic acid, which activates RAP2 through PDZGEF1 and PDZGEF2 (also known as RAPGEF2 and RAPGEF6). At low stiffness, active RAP2 binds to and stimulates MAP4K4, MAP4K6, MAP4K7 and ARHGAP29, resulting in activation of LATS1 and LATS2 and inhibition of YAP and TAZ. RAP2, YAP and TAZ have pivotal roles in mechanoregulated transcription, as deletion of YAP and TAZ abolishes the ECM stiffness-responsive transcriptome. Our findings show that RAP2 is a molecular switch in mechanotransduction, thereby defining a mechanosignalling pathway from ECM stiffness to the nucleus.

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The standard theoretical treatment of collisional cascades derives a steadystate size distribution assuming a single constant velocity dispersion for all bodies regardless of size. Here we relax this assumption and solve self-consistently for the bodies' steady-state size and size-dependent velocity distributions. Specifically, we account for viscous stirring, dynamical friction, and collisional damping of the bodies' random velocities in addition to the mass conservation requirement typically applied to find the size distribution in a steady-state cascade. The resulting size distributions are significantly steeper than those derived without velocity evolution. For example, accounting self-consistently for the velocities can change the standard q = 3.5 power-law index of the Dohnanyi (1969) differential size spectrum to an index as large as q = 4. Similarly, for bodies held together by their own gravity, the corresponding power-law index range 2.88 < q < 3.14 of Pan & Sari (2005) can steepen to values as large as q = 3.26. Our velocity results allow quantitative predictions of the bodies' scale heights as a function of size. Together with our predictions, observations of the scale heights for different sized bodies for the Kuiper belt, the asteroid belt, and extrasolar debris disks may constrain the mass and number of large bodies stirring the cascade as well as the colliding bodies' internal strengths.

The vertical distribution of dust in debris disks is sensitive to the number and size of large planetesimals dynamically stirring the disk, and is therefore well-suited for constraining the prevalence of otherwise unobservable Uranus and Neptune analogs. Information regarding stirring bodies has previously been inferred from infrared and optical observations of debris disk vertical structure, but theoretical works predict that the small particles traced by short-wavelength observations will be 'puffed up' by radiation pressure, yielding only upper limits. The large grains that dominate the disk emission at millimeter wavelengths are much less sensitive to the effects of stellar radiation or stellar winds, and therefore trace the underlying mass distribution more directly. Here we present ALMA 1.3 mm dust continuum observations of the debris disk around the nearby M star AU Mic. The 3 au spatial resolution of the observations, combined with the favorable edge-on geometry of the system, allows us to measure the vertical thickness of the disk. We report a scale height-to-radius aspect ratio of h = 0.031 +0.005 −0.004 between radii of ∼ 23 au and ∼ 41 au. Comparing this aspect ratio to a theoretical model of size-dependent velocity distributions in the collisional cascade, we find that the perturbing bodies embedded in the local disk must be larger than about 400 km, and the largest perturbing body must be smaller than roughly 1.8 M ⊕ . These measurements rule out the presence of a gas giant or Neptune analog near the ∼ 40 au outer edge of the debris ring, but are suggestive of large planetesimals or an Earth-sized planet stirring the dust distribution.

We present ALMA mosaic observations at 1.3mm (223 GHz) of the Fomalhaut system with a sensitivity of 14μJy/beam. These observations provide the first millimeter map of the continuum dust emission from the complete outer debris disk with uniform sensitivity, enabling the first conclusive detection of apocenter glow. We adopt an MCMC modeling approach that accounts for the eccentric orbital parameters of a collection of particles within the disk. The outer belt is radially confined with an inner edge of 136.3±0.9au and width of 13.5±1.8au. We determine a best-fit eccentricity of 0.12±0.01. Assuming a size distribution power-law index of q=3.46±0.09, we constrain the dust absorptivity power-law index β to be 0.9<β<1.5. The geometry of the disk is robustly constrained with inclination 65°.6±0°. 3, position angle 337°.9±0°. 3, and argument of periastron 22°.5±4°.3. Our observations do not confirm any of the azimuthal features found in previous imaging studies of the disk with Hubble Space Telescope, SCUBA, and ALMA. However, we cannot rule out structures 10 au in size or that only affect smaller grains. The central star is clearly detected with a flux density of 0.75±0.02mJy, significantly lower than predicted by current photospheric models. We discuss the implications of these observations for the directly imaged Fomalhaut b and the inner dust belt detected at infrared wavelengths.