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

Abstract

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.

Cell proliferation and migration explain pore bridging dynamics in 3D printed scaffolds of different pore size

“…Several mathematical modelling strategies have been developed to explore the interplay between tissue growth and curvature effects, which is an important area of research toward the industrial implementation of scaffold design optimisation [11], see Callens et al [18] for a recent review. Mathematical models range from continuum mechanics growth laws [29][30][31]5], computational models based on the idea of mean curvature flow, that borrow ideas from fluid mechanics and the role of surface tension but that do not consider cells explicitly [13, 14, 21-23, 15, 16, 32, 17, 33, 34], to other modelling approaches that consider the effects of cell-level behaviour, such as particle-based models with mechanical interaction and contractile forces at tissue interfaces [35], and models including tissue crowding and spreading during surface growth, which lead to hyperbolic curvature flow models [36,27,37].…”

Computational mechanics simulations on epithelial folding (Strengths, insights, and future challenges)

“…Research by Takeda et al focused on the mechanical stability of tissues, visualizing the energy landscape of morphogenesis events to provide a new framework for understanding the mechanical forces driving morphogenesis (Takeda et al, 2020). Using simulations based on continuum mechanics, where the entire tissue uniformly grows in-plane under fixed boundary conditions, they constructed energy landscapes for tissue growth with a circular contraction pattern.…”

“…Epithelial folding manifests in various forms, including substantial invagination or evagination leading to three-dimensional large deformation and the formation of undulation patterns with relatively small out-of-plane displacement. For significant three-dimensional deformations, studies by Inoue et al and Takeda et al suggest that simulations reveal the potential control of invagination or evagination through the interplay of tissue growth and cellular contractile forces (Inoue et al, 2017;Takeda et al, 2020). Moreover, spatial distribution of contraction patterns and temporal histories of growth and contraction are proposed as mechanisms governing the regulation of invagination or evagination.…”

Continuum modeling for neuronal lamination during cerebral morphogenesis considering cell migration and tissue growth

“…This represents an influence of cellular processes on tissue formation. To obtain a conceptual understanding of the cellular and tissue interaction in morphogenesis, computational approaches are useful (Takeda et al 2020). (#1-1) A variety of computational models of 4 cell dynamics have been proposed in the fields of cell/tissue biology and tissue engineering to study cell movement based on cell-cell adhesion (Armstrong et al 2006), collective cell migration during wound healing (Buganza Tepole and Kuhl 2016), and scaffold-dependent cell migration (Elsayed et al 2019).…”