Paper List

期刊: ArXiv Preprint
发布日期: 2026-03-16
BiophysicsDevelopmental Biology

A mechanical bifurcation constrains the evolution of cell sheet folding in the family Volvocaceae

Département de Physique, École Normale Supérieure, Paris, France | Max Planck Institute for the Physics of Complex Systems, Dresden, Germany | Center for Systems Biology Dresden, Germany | Max Planck Institute of Molecular Cell Biology and Genetics, Dresden, Germany

Valens Tribet, Pierre A. Haas
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30秒速读

IN SHORT: This paper addresses the core problem of why there is an evolutionary gap in species with intermediate cell numbers (e.g., 256 cells) in Volvocaceae, linking it to a mechanical bifurcation that prevents simple inversion strategies beyond a critical size.

核心创新

  • Methodology Developed a novel continuum elastic sheet model for cell sheet inversion, parameterizing cell shape changes as intrinsic curvature variations.
  • Biology Identified and quantified a mechanical bifurcation (critical intrinsic curvature k1) that acts as a constraint, making inversion impossible for parameter sets extrapolated to 256+ cells.
  • Theory Proposed that the evolution of complex inversion programs in Volvox (e.g., type-A/B) was a necessary adaptation to circumvent this fundamental physical constraint, linking developmental mechanics to evolutionary trajectories.

主要结论

  • A mechanical bifurcation in the elastic sheet model defines a critical intrinsic curvature (k1); inversion is only possible for k > k1. Parameters for P. californica (k ≈ 2.5 ± 0.4) satisfy this.
  • Allometric scaling (h ∝ N^{-1/4}, ξ ≈ 1.14 ± 0.06) and geometric extrapolation predict that for N ≥ 256 cells, the required parameters fall outside the inversion-possible regime (k < k1).
  • The absence of species with ~256 cells and the evolution of complex inversion in Volvox are direct consequences of this bifurcation, demonstrating how physics can constrain evolutionary possibilities.
研究空白： The field lacks a mechanistic explanation for the observed evolutionary gap in species with intermediate cell numbers (e.g., 256 cells) within Volvocaceae, and how physical constraints can directly shape the evolution of developmental programs.

摘要: The processes of morphogenesis that give rise to the shapes of organs and organisms during development are often driven by mechanical instabilities. Can such mechanical bifurcations also drive or constrain the evolution of these processes in the first place? We discover an instance of these constraints in the green algae of the family Volvocaceae. During their development, their bowl-shaped embryonic cell sheet turns itself inside out. This inversion is driven by a simple wave of cell wedging in the genus Pleodorina (16–128 cells) and more complex programmes of cell shape changes in Volvox (∼400–50 000 cells). However, no species with intermediate cell numbers (256 cells) have been described. Here, we relate this gap to a mechanical bifurcation: Focusing on the inversion of Pleodorina californica (64 cells), we develop a continuum model, in which the cell shape changes driving inversion appear as changes of the intrinsic curvature of an elastic surface. A mechanical bifurcation in this model predicts that inversion is only possible in a subset of its parameter space. Strikingly, parameters estimated for P. californica fall into this possible subset, but those that we extrapolate to 256 or more cells using allometric observations and a model of cell cleavage in Volvocaceae do not. Our work thus suggests that the more complex inversion strategies of Volvox are an evolutionary necessity to obviate this bifurcation and indicates more broadly how mechanical bifurcations can drive the evolution of morphogenesis.