TubULAR: Tracking in toto deformations of dynamic tissues via constrained maps

Abstract

A common motif in biology is the arrangement of cells into tube-like sheets, which further transform into more complex forms. Traditionally, analysis of tissues’ dynamic surfaces has relied on inspecting static snapshots, live imaging of cross-sections, or tracking isolated cells in 3D. However, capturing the interplay between in-plane and out-of-plane behaviors requires following the full surface as it deforms and integrating cell-scale motions into collective, tissue-scale deformations. Here, we introduce an approach to build in toto maps of surface deformation, following tissue parcels in the material frame of reference. The Tube-like sUrface Lagrangian Analysis Resource (‘TubULAR’) provides an open-source MATLAB implementation whose functionality is accessible either as a standalone toolkit or as an extension of the ImSAnE package used in the developmental biology community. TubULAR provides a framework for linking in-plane and out-of-plane behaviors and decomposing complex deformation maps into elementary contributions defining physically meaningful signatures of motion. We underscore the power of our approach by analyzing shape change in the embryonic Drosophila midgut and beating zebrafish heart. In the midgut, our results link asymmetric constrictions to the increasing organ length and to patterned vorticity in the organ chambers. We then extract the dynamics of the beating zebrafish heart, constructing a mode-based description for the organ’s beat cycle. The method naturally generalizes to in vitro and synthetic systems, such as stem cell models of tube development and deforming phase-separated interfaces.

Morphodynamic Atlas for Drosophila Development

“…5A [28][29][30]. This process is known to be stereotyped across embryos, but the quantification of its dynamics has until recently proven elusive, due to the complex shapes and inherently 3D deformations [30,31]. Variability of the morphogenetic program between embryos remains largely uncharacterized [32].…”

“… (A) The midgut envelops to the embryo’s yolk and folds into chambers ~ 13-15 hours post fertilization. Extracting the endodermal (inner) surface of the gut using TubULAR [31] yields collections of dynamic organ shapes. Scale bars are 100 μm.…”

“…To test this, we here extend our spatiotemporal registration and examination of velocity correlations during morphogenesis to the development of complex shapes in the midgut. We use level sets approaches of the TubU-LAR package [31, 33] to extract a surface that penetrates ~2.5 μm within the apical surface of the endoderm, along the surface that intersects endodermal nuclei. In contrast to the case of germ-band extension, these surfaces are highly dynamic, demanding additional steps for spatial registration.…”

Visceral organ morphogenesis via calcium-patterned muscle constrictions

“… Automatic segmentation of the apical (inner) surface of the endoderm minimizes a non-local Chan-Vese energy functional ( Chan and Vese, 2001 ; Márquez-Neila et al, 2014 ) to encapsulate yolk without enclosing midgut tissue, shown for four snapshots of mid-sagittal sections using TubULAR ( Mitchell and Cislo, 2022 ). Blue contours mark the surface intersection with the mid-sagittal plane.…”

“… We compute the centerline (brown curve) for extracted shapes (green with purple boundary for clarity) using the TubULAR package ( Mitchell and Cislo, 2022 ). The cumulative length of these curves defines the effective length of the organ reported in Figure 1 .…”