Single-cell morphometrics reveals ancestral principles of notochord development

ABSTRACT Embryonic tissues are shaped by the dynamic behaviours of their constituent cells. To understand such cell behaviours and how they evolved, new approaches are needed to map out morphogenesis across different organisms. Here, we apply a quantitative approach to learn how the notochord forms during the development of amphioxus: a basally branching chordate. Using a single-cell morphometrics pipeline, we quantify the geometries of thousands of amphioxus notochord cells, and project them into a common mathematical space, termed morphospace. In morphospace, notochord cells disperse into branching trajectories of cell shape change, revealing a dynamic interplay between cell shape change and growth that collectively contributes to tissue elongation. By spatially mapping these trajectories, we identify conspicuous regional variation, both in developmental timing and trajectory topology. Finally, we show experimentally that, unlike ascidians but like vertebrates, posterior cell division is required in amphioxus to generate full notochord length, thereby suggesting this might be an ancestral chordate trait that is secondarily lost in ascidians. Altogether, our novel approach reveals that an unexpectedly complex scheme of notochord morphogenesis might have been present in the first chordates. This article has an associated ‘The people behind the papers’ interview.

. Image segmentation and morphospace embedding pipeline. Panels illustrate key steps in the single-cell morphometrics pipeline used to infer cell shape trajectories in amphioxus notochord cells. See Materials and Methods section for further explanation of procedures involved in each step.

Geometric modelling in single cells
The aim of the geometric modelling is to identify how individual geometric transformations affect cell and tissue length in the notochord.
To achieve this, we first need to define a set of measures that allow for a simplified characterisation of the cell shapes and shape changes. To this aim, we first create an object-oriented bounding box around the cell, corresponding to the three-dimensional cell shape, and find that the box aligns with the anteroposterior (AP) axis, the dorsoventral (DV) axis and mediolateral (ML) axis of the embryo (Fig. S10). The bounding box has the volume ("") and is defined by three lengths, ("") and () ("") (see Fig. 9B). We assume that the cells can be approximated as a two-dimensional shape that is oriented along the DV-ML plane and then projected along the AP axis for a length $% (*+,,) (see Fig. S10B and S10C). We find that bounding box length $% ("") is a good approximation for cell length $% (*+,,) , but convolution of the membrane on the transverse DV-ML plane generates a discrepancy between cell spreading area, defined by the bounding box area ("") , and real cell area ("") . In this case, we can assume We then define the spreading area which corresponds to the transverse area (the area in the − plane) of the bounding box, and estimate the transverse cross-sectional area of the cell, where (*+,,) is the cell volume. We also define the ratio which is a measure of how convoluted the transverse cell shape is in the DV-ML plane. For a small value of , the cell is characterised by one more long and thin elongations, generating a discrepancy between (*+,,) and ("") . For = 1 it fills the complete rectangle, such that (*+,,) approaches ("") (see Fig. 9C).
From these measurements for mean cells we can calculate the spreading area as   The raw measurements used to define the mean cell at each stage are shown in Table. S1. The positions of cells in morphospace with mean values for all geometric parameters used for PCA are also shown in Fig. S11, within the total point cloud for the corresponding stage, with segmentation data for cells representing the extremes of shape variation for each stage.  We can now measure the effects of change in cell volume, transverse cross-sectional area (affecting the level of AP anisotropy) and surface convolution on cell spreading area and AP length using the equations shown in Table. S2. Here, -defines the initial state of the cell, at 6ss. We find that the cell length along the AP axis only changes when the cell is elongated in this direction, grows anisotropically in this direction or isotropically in all directions. A convolution that does not affect the transverse cross-sectional area (*+,,) ( ) will also not affect the elongation.

Geometric modelling in cell groups
To compute how these geometric transformations in single cells affect the length of a group of cells undergoing intercalation, we define a measure of cell intercalation at each stage. To this aim, we assume that the length contribution of a group of cells (where we assume that is large) in the direction is given by (.) and the equation with the intercalation correction ( ). We calculate ( ) at each stage as a ratio of cell neighbourhood length, (.) ( ), to the maximal possible extension of a group of cells of the same number. The maximal elongation of a group of cells is defined when cells are stacked perfectly on the AP axis in a stack-ofcoins topology, and neighbourhood length equals $% (*+,,) ( ). (.) ( ) is manually measured in the notochord at each stage, as the AP length of groups of cells measured in the 40-60% region. For our calculations of ( ), = 10. Cell groups were defined by selecting a cell at random, and identifying its nearest 9 cells in AP position. Where n is large, groups identified with this method include cells from all DV layers of the notochord, regardless of intercalation state. AP length of the group was then measured between the most anterior and posterior phalloidin signal using a straight line tool in FIJI. For = 1, cells are perfectly stacked on the AP axis, whereas when ≳ 0, many layers of cells are present on the DV plane (see Fig. S12).
We now start with a group of cells, each of volume (*+,,) ( ), area (*+,,) ( ) and ratio ( ), and an intercalation level of ( ), and calculate neighbourhood length as With this, we can study the effect of each geometric transformation in single cells, with and without intercalation, on neighbourhood length (.) ( ), using the equations shown in Table. S3.  Development: doi:10.1242/dev.199430: Supplementary information Development: doi:10.1242/dev.199430: Supplementary information