Imposed deformations play an important role in morphogenesis and tissue homeostasis, both in normal and pathological conditions 1-5. To perceive mechanical perturbations of different types and magnitudes, tissues need a range of appropriate detectors 6-8 , with a compliance that has to match the perturbation amplitude. As a proxy of biological tissues, we use multicellular aggregates, a composite material made of cells, extracellular matrix and permeating fluid. We compare the effect of a selective compression of cells within the aggregate, leaving the extracellular matrix unstrained, to a global compression of the whole aggregate. We show that the global compression strongly reduces the aggregate volume 9-13 , while the same amount of selective compression on cells has almost no effect 14,15. We support this finding with a theoretical model of an actively pre-stressed composite material, made of incompressible and impermeable cells and a poroelastic interstitial space. This description correctly predicts the emergent bulk modulus of the aggregate as well as the hydrodynamic diffusion coefficient of the percolating interstitial fluid under compression. We further show that, on a longer timescale, the extracellular matrix serves as a sensor that regulates cell proliferation and migration in a 3D environment through its permanent deformation and dehydration following the global compression.