Curvature in Biological Systems: Its Quantification, Emergence, and Implications across the Scales

Abstract

Surface curvature both emerges from, and influences the behavior of, living objects at length scales ranging from cell membranes to single cells to tissues and organs. The relevance of surface curvature in biology has been supported by numerous recent experimental and theoretical investigations in recent years. In this review, we first give a brief introduction to the key ideas of surface curvature in the context of biological systems and discuss the challenges that arise when measuring surface curvature. Giving an overview of the emergence of curvature in biological systems, its significance at different length scales becomes apparent. On the other hand, summarizing current findings also shows that both single cells and entire cell sheets, tissues or organisms respond to curvature by modulating their shape and their migration behavior. Finally, we address the interplay between the distribution of morphogens or micro-organisms and the emergence of curvature across length scales with examples demonstrating these key mechanistic principles of morphogenesis. Overall, this review highlights that curved interfaces are not merely a passive by-product of the chemical, biological and mechanical processes but that curvature acts also as a signal that co-determines these processes.

Shape‐Morphing Photoresponsive Hydrogels Reveal Dynamic Topographical Conditioning of Fibroblasts

“…The applied topography (90 μm wide anisotropic grooves, 𝜅 = 3 mm −1 ) can be found in vivo as small vasculature (e.g., alveoli have d = 75-300 μm), gut villi, but also in the shape of small wounds (nano to millimeter scale) and the anisotropic organization of ECM protein fibers. [8,28] After two rounds of topographical actuation, fibroblasts displayed a smaller spread area on dynamic topographies than on the flat substrates, in accordance with previous literature using static topographies. [1,65] Surprisingly, we did not observe alignment of cells with the introduced anisotropic topography or an increase in cell elongation after one and two rounds of topography change.…”

Effect of Porous Substrate Topographies on Cell Dynamics: A Computational Study

“…The simulation is tightly convergent without the membrane tension term at any of these element sizes. However, the inclusion of curvature is known to be sensitive to spatial discretization . In the case of the phase-field model, this is further complicated by the need to define the lattice points that are associated with the membrane.…”

Drying of bio-colloidal sessile droplets: Advances, applications, and perspectives

“…The particles at the air-liquid interface prefer to move from the apex (higher curvature) to the periphery (lower curvature), and the particles accumulate near the periphery [52]. Differential curvatures can have significant implications in biological systems [53]; however, their role in drying bio-colloidal droplets remains to be explored. Another interesting study argues that the diffusion (here, non-directional bulk flow for mass transport), advection (here, horizontal mass transport towards the periphery), and capillary attraction (the ordered arrangement of the particles mainly induced by the capillary forces near the three-phase interface) are responsible for the emerging patterns in the drying droplets that are partially-wet to the substrate [54].…”