Colloquium: Mechanical formalisms for tissue dynamics

The understanding of morphogenesis in living organisms has been renewed by tremendous progressin experimental techniques that provide access to cell-scale, quantitative information both on theshapes of cells within tissues and on the genes being expressed. This information suggests that ourunderstanding of the respective contributions of gene expression and mechanics, and of their crucialentanglement, will soon leap forward. Biomechanics increasingly benefits from models, which assistthe design and interpretation of experiments, point out the main ingredients and assumptions, andultimately lead to predictions. The newly accessible local information thus calls for a reflectionon how to select suitable classes of mechanical models. We review both mechanical ingredientssuggested by the current knowledge of tissue behaviour, and modelling methods that can helpgenerate a rheological diagram or a constitutive equation. We distinguish cell scale ("intra-cell")and tissue scale ("inter-cell") contributions. We recall the mathematical framework developpedfor continuum materials and explain how to transform a constitutive equation into a set of partialdifferential equations amenable to numerical resolution. We show that when plastic behaviour isrelevant, the dissipation function formalism appears appropriate to generate constitutive equations;its variational nature facilitates numerical implementation, and we discuss adaptations needed in thecase of large deformations. The present article gathers theoretical methods that can readily enhancethe significance of the data to be extracted from recent or future high throughput biomechanicalexperiments.Comment: 33 pages, 20 figures. This version (26 Sept. 2015) contains a few corrections to the published version, all in Appendix D.2 devoted to large deformation

Multi-scaled confinement of cells by gradients of rigidity

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The role of fluctuations and stress on the effective viscosity of cell aggregates

Cell aggregates are a tool for in vitro studies of morphogenesis, cancer invasion, and tissue engineering. They respond to mechanical forces as a complex rather than simple liquid. To change an aggregate's shape, cells have to overcome energy barriers. If cell shape fluctuations are active enough, the aggregate spontaneously relaxes stresses (“fluctuation-induced flow”). If not, changing the aggregate's shape requires a sufficiently large applied stress (“stress-induced flow”). To capture this distinction, we develop a mechanical model of aggregates based on their cellular structure. At stress lower than a characteristic stress τ*, the aggregate as a whole flows with an apparent viscosity η*, and at higher stress it is a shear-thinning fluid. An increasing cell–cell tension results in a higher η* (and thus a slower stress relaxation time tc). Our constitutive equation fits experiments of aggregate shape relaxation after compression or decompression in which irreversibility can be measured; we find tc of the order of 5 h for F9 cell lines. Predictions also match numerical simulations of cell geometry and fluctuations. We discuss the deviations from liquid behavior, the possible overestimation of surface tension in parallel-plate compression measurements, and the role of measurement duration

Soluble VE-cadherin in metastatic breast cancer: an independent prognostic factor for both progression-free survival and overall survival

International audiencePatients with metastatic breast cancer (MBC) represent a heterogeneous group, with large differences in outcomes from individual patients. VE-cadherin, an endothelial-specific cadherin, was shown to promote tumour proliferation and angiogenesis. Soluble VE-cadherin has been recently associated to breast cancer progression. This study was designed to investigate the prognosis significance of soluble VE-cadherin in hormone-refractory MBC

The tyrosine-kinase inhibitor sunitinib targets vascular endothelial (VE)-cadherin: a marker of response to antitumoural treatment in metastatic renal cell carcinoma

International audienceVascular endothelial (VE)-cadherin is an endothelial cell-specific protein responsible for endothelium integrity. Its adhesive properties are regulated by post-translational processing, such as tyrosine phosphorylation at site Y685 in its cytoplasmic domain, and cleavage of its extracellular domain (sVE). In hormone-refractory metastatic breast cancer, we recently demonstrated that sVE levels correlate to poor survival. In the present study, we determine whether kidney cancer therapies had an effect on VE-cadherin structural modifications and their clinical interest to monitor patient outcome