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Cells can sense the density and distribution of extracellular matrix (ECM) molecules by means of individual integrin proteins and larger, integrin-containing adhesion complexes within the cell membrane. This spatial sensing drives cellular activity in a variety of normal and pathological contexts. Previous studies of cells on rigid glass surfaces have shown that spatial sensing of ECM ligands takes place at the nanometre scale, with integrin clustering and subsequent formation of focal adhesions impaired when single integrin-ligand bonds are separated by more than a few tens of nanometres. It has thus been suggested that a crosslinking 'adaptor' protein of this size might connect integrins to the actin cytoskeleton, acting as a molecular ruler that senses ligand spacing directly. Here, we develop gels whose rigidity and nanometre-scale distribution of ECM ligands can be controlled and altered. We find that increasing the spacing between ligands promotes the growth of focal adhesions on low-rigidity substrates, but leads to adhesion collapse on more-rigid substrates. Furthermore, disordering the ligand distribution drastically increases adhesion growth, but reduces the rigidity threshold for adhesion collapse. The growth and collapse of focal adhesions are mirrored by, respectively, the nuclear or cytosolic localization of the transcriptional regulator protein YAP. We explain these findings not through direct sensing of ligand spacing, but by using an expanded computational molecular-clutch model, in which individual integrin-ECM bonds-the molecular clutches-respond to force loading by recruiting extra integrins, up to a maximum value. This generates more clutches, redistributing the overall force among them, and reducing the force loading per clutch. At high rigidity and high ligand spacing, maximum recruitment is reached, preventing further force redistribution and leading to adhesion collapse. Measurements of cellular traction forces and actin flow speeds support our model. Our results provide a general framework for how cells sense spatial and physical information at the nanoscale, precisely tuning the range of conditions at which they form adhesions and activate transcriptional regulation.

The $$\Lambda $$Λ-term in Einstein’s equations is a fundamental building block of the ‘concordance’ $$\Lambda $$ΛCDM model of cosmology. Even though the model is not free of fundamental problems, they have not been circumvented by any alternative dark energy proposal either. Here we stick to the $$\Lambda $$Λ-term, but we contend that it can be a ‘running quantity’ in quantum field theory (QFT) in curved space time. A plethora of phenomenological works have shown that this option can be highly competitive with the $$\Lambda $$ΛCDM with a rigid cosmological term. The, so-called, ‘running vacuum models’ (RVM’s) are characterized by the vacuum energy density, $$\rho _{vac}$$ρvac, being a series of (even) powers of the Hubble parameter and its time derivatives. Such theoretical form has been motivated by general renormalization group arguments, which look plausible. Here we dwell further upon the origin of the RVM structure within QFT in FLRW spacetime. We compute the renormalized energy-momentum tensor with the help of the adiabatic regularization procedure and find that it leads essentially to the RVM form. This means that $$\rho _{vac}(H)$$ρvac(H) evolves as a constant term plus dynamical components $${{\mathcal {O}}}(H^2)$$O(H2) and $$\mathcal{O}(H^4)$$O(H4), the latter being relevant for the early universe only. However, the renormalized $$\rho _{vac}(H)$$ρvac(H) does not carry dangerous terms proportional to the quartic power of the masses ($$\sim m^4$$∼m4) of the fields, these terms being a well-known source of exceedingly large contributions. At present, $$\rho _{vac}(H)$$ρvac(H) is dominated by the additive constant term accompanied by a mild dynamical component $$\sim \nu H^2$$∼νH2 ($$|\nu |\ll 1$$|ν|≪1), which mimics quintessence.

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The cosmological term, Λ, was introduced 104 years ago by Einstein in his gravitational field equations. Whether Λ is a rigid quantity or a dynamical variable in cosmology has been a matter of debate for many years, especially after the introduction of the general notion of dark energy (DE). Λ is associated to the vacuum energy density, , and one may expect that it evolves slowly with the cosmological expansion. Herein we present a devoted study testing this possibility using the promising class of running vacuum models (RVMs). We use a large string SNIa+BAO+H(z)+LSS+CMB of modern cosmological data, in which for the first time the CMB part involves the full Planck 2018 likelihood for these models. We test the dependence of the results on the threshold redshift at which the vacuum dynamics is activated in the recent past and find positive signals up to for . The RVMs prove very competitive against the standard ΛCDM model and give a handle for solving the tension and alleviating the H 0 one.