Finite element formulation and analysis for an arterial wall with residual and active stresses

An energy landscape approach to understanding variety and robustness in tissue morphogenesis

During morphogenesis in development, multicellular tissues deform by mechanical forces induced by spatiotemporally regulated cellular activities, such as cell proliferation and constriction. Various morphologies are formed because of various spatiotemporal combinations and sequences of multicellular activities. Despite its potential to variations, morphogenesis is a surprisingly robust process, in which qualitatively similar morphologies are reproducibly formed even under spatiotemporal fluctuation of multicellular activities. To understand these essential characteristics of tissue morphogenesis, which involves the coexistence of various morphologies and robustness of the morphogenetic process, in this study, we propose a novel approach to capture the overall view of morphogenesis from mechanical viewpoints. This approach will enable visualization of the energy landscape, which includes morphogenetic processes induced by admissible histories of cellular activities. This approach was applied to investigate the morphogenesis of a sheet-like tissue with curvature, where it deformed to a concave or convex morphology depending on the history of growth and constriction. Qualitatively different morphologies were produced by bifurcation of the valley in the energy landscape. The depth and steepness of the valley near the stable states represented the degree of robustness to fluctuations of multicellular activities. Furthermore, as a realistic example, we showed an application of this approach to luminal folding observed in the initial stage of intestinal villus formation. This approach will be helpful to understand the mechanism of how various morphologies are formed and how tissues reproducibly achieve specific morphologies.