Cell movement has essential functions in development, immunity, and cancer. Various cell migration patterns have been reported, but no general rule has emerged so far. Here, we show on the basis of experimental data in vitro and in vivo that cell persistence, which quantifies the straightness of trajectories, is robustly coupled to cell migration speed. We suggest that this universal coupling constitutes a generic law of cell migration, which originates in the advection of polarity cues by an actin cytoskeleton undergoing flows at the cellular scale. Our analysis relies on a theoretical model that we validate by measuring the persistence of cells upon modulation of actin flow speeds and upon optogenetic manipulation of the binding of an actin regulator to actin filaments. Beyond the quantitative prediction of the coupling, the model yields a generic phase diagram of cellular trajectories, which recapitulates the full range of observed migration patterns.

Summary An understanding of how animal size is controlled requires knowledge of how positive and negative growth regulatory signals are balanced and integrated within cells. Here we demonstrate that the activities of the conserved growth promoting transcription factor Myc and the tumor-suppressing Hippo pathway are co-dependent during growth of Drosophila imaginal discs. We find that Yorkie (Yki), the Drosophila homolog of the Hippo pathway transducer, Yap, regulates the transcription of Myc, and that Myc functions as a critical cellular growth effector of the pathway. We demonstrate that in turn, Myc regulates the expression of Yki as a function of its own cellular level, such that high levels of Myc repress Yki expression through both transcriptional and post-transcriptional mechanisms. We propose that the co-dependent regulatory relationship functionally coordinates the cellular activities of Yki and Myc and provides a mechanism of growth control that regulates organ size and has broad implications for cancer.

E-cadherin plays a key role at adherens junctions between epithelial cells, but the mechanisms controlling its assembly, maintenance, and dissociation from junctions remain poorly understood. In particular, it is not known to what extent the number of E-cadherins engaged at junctions is regulated by endocytosis, or by dissociation of adhesive bonds and redistribution within the membrane from a pool of diffusive cadherins. To determine whether cadherin levels at mature junctions are regulated by endocytosis or dissociation and membrane diffusion, the dynamics of E-cadherin were quantitatively analyzed by a new approach combining 2-photon fluorescence recovery after photobleaching (FRAP) and fast 3D wide-field fluorescence microscopy. Image analysis of fluorescence recovery indicates that most E-cadherin did not diffuse in the membrane along mature junctions, but followed a first order turn-over process that was rate-limited by endocytosis. In confluent cultures of MCF7 or MDCK cells, stably expressed EGFP-Ecadherin was rapidly recycled with spatially uniform kinetics (50 s in MCF7 and 4 min in MDCK). In addition, when endocytosis was pharmacologically blocked by dynasore or MiTMAB, no fluorescence recovery was observed, suggesting that no endocytosisindependent membrane redistribution was occurring. Our data show that membrane redistribution of E-cadherin molecules engaged in mature junctions requires endocytosis and subsequent exocytosis, and lead to the notion that E-cadherins engaged at junctions do not directly revert to free membrane diffusion. Our results point to the possibility that a direct mechanical coupling between endocytosis efficiency and cadherin-mediated forces at junctions could help to regulate intercellular adhesion and locally stabilize epithelia.diffusion ͉ fluorescence recovery after photobleaching E