A mechanical atlas for ascidian gastrulation

The intricate three-dimensional (3D) structures of multicellular organisms emerge through genetically encoded spatio-temporal patterns of mechanical stress. Cell atlases of gene expression during embryogenesis are now available for many organisms, but connecting these to the mechanical drivers of embryonic shape requires a corresponding mechanical atlas. That is, it requires physical models of multicellular tissues that identify the relevant mechanical and geometric constraints, and an ability to measure mechanical stresses at single-cell resolution over time. Taking significant steps towards both these goals, we develop a new mathematical theory for the mechanics of 3D multicellular aggregates involving the quasi-static balance of cellular pressures, surface tensions, and line tensions. Our theory yields a quantitatively accurate low-dimensional description for the time-varying geometric dynamics of 3D multicellular aggregates and, through the solution of a mechanical inverse problem, an image-based strategy for constructing spatio-temporal maps of the mechanical stresses driving morphogenesis in 3D. Using synthetic image data, we confirm the accuracy and robustness of our geometric and mechanical approaches. We then apply our approach to segmented light sheet data, representing cellular membranes with isotropic resolution, to construct a 3D mechanical atlas for ascidian gastrulation. The atlas captures a surprisingly accurate low-dimensional description of ascidian gastrulation, revealing the adiabatic nature of the underlying mechanical dynamics. Mapping the inferred forces onto the invariant embryonic lineage reveals a rich correspondence between dynamically evolving cell states, patterns of cell division, and local regulation of cellular pressure and contractile stress. Thus, our mechanical atlas reveals a new view of ascidian gastrulation in which lineage-specific control over a complex heterogenous pattern of cellular pressure and contractile stress, integrated globally, governs the emergent dynamics of ascidian gastrulation.

多细胞生物复杂的三维（3D）结构，经由基因编码的机械应力时空模式逐步涌现形成。目前已有多种生物的胚胎发生时期基因表达细胞图谱，但要将这些图谱与胚胎形态形成的力学驱动因素关联起来，还需要对应的力学图谱（mechanical atlas）。具体而言，这需要构建能够识别相关力学与几何约束的多细胞组织物理模型，同时具备在时间维度上以单细胞分辨率（single-cell resolution）测量机械应力的能力。为朝着这两大目标取得实质性进展，我们针对3D多细胞聚集体的力学特性提出了一套全新的数学理论，该理论涵盖细胞压力、表面张力与线张力的准静态平衡。我们的理论可对3D多细胞聚集体随时间变化的几何动力学给出定量准确的低维描述；同时，通过求解力学逆问题（mechanical inverse problem），还能得到一种基于图像的策略，用于构建驱动3D形态发生的机械应力时空图谱。我们通过合成图像数据验证了所提出的几何与力学方法的准确性与鲁棒性。随后我们将该方法应用于以各向同性分辨率（isotropic resolution）标记细胞膜的分割光片显微镜数据（segmented light sheet data），为被囊动物（ascidian）原肠胚形成构建了3D力学图谱。该力学图谱可给出被囊动物原肠胚形成过程出人意料准确的低维描述，揭示了其背后力学动力学的绝热特性。将推断得到的力映射至保守胚胎谱系（invariant embryonic lineage）后，可发现动态变化的细胞状态、细胞分裂模式与细胞压力及收缩应力的局部调控之间存在丰富的对应关系。综上，我们的力学图谱为被囊动物原肠胚形成提供了全新视角：通过全局整合的谱系特异性调控，作用于复杂非均一的细胞压力与收缩应力模式，最终主导了被囊动物原肠胚形成的涌现动力学过程。