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 shapes. Traditionally, analysis of the dynamic surfaces of growing tissues 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. The advent of methods for whole-organ live imaging ushers the need for in toto analysis methods to understand these collective tissue dynamics. Here, we introduce an approach that builds in toto maps of surface deformation by following tissue parcels in the material frame of reference. Mapping the full 3D surface to 2D images such that the tissue motion in 2D is minimal enables the user to easily follow the tissue and discern its 3D motion. We then provide a computational framework for linking in-plane and out-of-plane behaviors and decomposing complex deformation maps into elementary contributions. 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. We underscore the power of our approach by analyzing shape change in the embryonic Drosophila midgut and beating zebrafish heart. Following deformations in the tissue/material frame reveals the signatures of tissue flow and a reduced-dimensional mode decomposition of the dynamics. The method naturally generalizes to in vitro and synthetic systems and provides ready access to the mechanical mechanisms relating genetic patterning to organ shape change.