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Quantifying pre-inversion denting in Volvox globator embryos

BackgroundVolvocine algae2 serve as powerful model

organisms in the study of embryonic development.

Volvox is a genus of green algae in the family of

Volvocaceae that has been used to research

the mechanics of cell sheet movements3

in order to provide insight into the process of

morphogenesis in more complex organisms.

Volvox embryos consist of a spherical monolayer

of cells (Figure 1A). Seemingly random dents

appear across the embryo’s surface (Figure

1B), followed by a circular invagination called

the bend region (Figure 1D) at its equator.

The embryo eventually turns itself inside-out

in a process called inversion (Figure 1C - H)4 5.

To investigate whether the denting correlates with

the bend region position, it is necessary to quantify

the spatio-temporal dynamics of the embryonic

shape changes.

Rashid’s experience in fluorescence microscopy

and computational image analysis helped him

carry out the proposed microscopical analysis

of embryonic development in the green micro-

algae Volvox and other members of the family

Volvocaceae. Embryonic morphogenesis is a

fundamental aspect of development that requires

emergence of chemical and mechanical patterns

from initially homogeneous groups of cells1. The

exact mechanisms of this pattern formation

are still elusive, in part, due to the difficulty in

quantitatively correlating chemical and mechanical

changes during embryogenesis. This work is

aimed at developing a method for quantifying the

3-dimensional morphological changes that occur

during pre-inversion denting in Volvox globator

captured using light-sheet microscopy.

This report is the result of the work of one of our Summer Studentship recipients. Rashid Khashiev is a second year student in Natural Sciences (NST) at the University of Cambridge and undertook his project with Dr Stephanie Höhn at DAMTP Cambridge.

Materials & Methods

Acquisition of images. Volvox globator parent spheroids containing embryos were imaged

using OpenSPIM software6 running a custom-

built selective plane illumination microscope

(SPIM) with a 637nm laser stimulating chlorophyll

autofluorescence. The imaging involved taking

stacks of images every 60s over 8-12 hours.

Segmenting images. After cropping out the embryos from the original raw data using Fiji

(ImageJ)7, the images of each embryo still contained

parts of other embryos and the parent. LimeSeg8

plugin for Fiji was used to segment the embryos,

producing about 5000 points (XYZ coordinates) to

represent the shape of each embryo at each time

point.

Converting coordinates. The coordinates are translated into a spherical coordinate system (XYZ

into rθφ).

Fitting spherical harmonics. Spherical harmonic functions of up to 8th degree were fitted

to the spherical coordinates in order to determine

spherical harmonic coefficients that enable the best

fit to data.

Aligning embryos. The spherical harmonic coefficients were then rotated by Euler angles α,β,γ9

to minimize the difference between coefficients

of different embryos and hence align all embryos

together to eliminate orientation differences in

further analysis. Alignment in time dimension was

carried out manually to have all embryos form the

bend region simultaneously.

Results

The here presented workflow serves to

characterize dynamic morphogenetic changes in

space and time. This lays the groundwork for future

comparative studies of morphogenetic changes. As

proof-of-concept, the workflow has been applied

to V.globator embryos in order to quantify how the

major morphological features vary with time before

bend region formation.

A B C D

E F G H

Figure 1. Each image is a false-colour maximum-intensity z-projection of a stack of 2D images of a V.globator embryo recorded using light-sheet microscopy to capture chlorophyll autofluorescence:• A,B: embryo undergoing pre-inversion denting (notice the dent highlighted in B being absent in A). • C-H: the process of inversion.

Figure 2. Simplified workflow for one embryo at one point in time: (notice how the morphological feature highlighted is preserved throughout the process):A: Acquisition of images – z-projection given here instead of a stack of separate images.B: Pre-processing of images – z-projection given here instead of a stack of separate images.C: Segmenting images – colour reflects distance from centre of mass of the embryo.D: Converting coordinates – colour reflects the value of Radius at each point.E,F: Fitting spherical harmonics – only large to medium morphological features are retained (hence the surface here looks smoother than the original in C,D).G,H: Aligning embryos – all embryos are rotated in the spherical harmonic space to have similar orientations in that space. This also aligns their morphologies in 3D space.

A B C D

E F G H

36 ISSUE 52 DECEMBER 2018 37

Further ANOVA-SCA10 analysis on the spherical

harmonic coefficients has shown that approximately

63% of variation over time can be explained by

just two principal components, allowing them

to be plotted against time to represent those

morphological changes (see Figure 3). Mean

spherical harmonic coefficients at any given time

point can be translated back into 3D coordinates

to show the average embryo morphology at that

time point, revealing a common pre-inversion

morphology at that developmental age (see

Figure 4, central embryo). Similarly, it is possible

to generate synthetic embryo morphologies by

choosing new spherical harmonic coefficients that

are a standard deviation away from the average

in the principal component space (see Figure 4,

surrounding embryos).

The first few principal components (PCs) from PCA

of individual embryos explain a significantly greater

percentage of variation in the data compared to

PCs from ANOVA-SCA on all embryos together

(e.g. 86% vs 46% for the first PC). Since ANOVA-

SCA relies on the alignment of embryos in space,

this shows that pre-inversion dents do not align in

space across embryos. On the other hand, denting

events in different embryos do approximately align

in time with respect to bend region formation (see

Figure 5). For both PCA and ANOVA-SCA, the

Figure 4. New embryo morphologies generated based on collected data:Central embryo: Mean embryo morphology at the time of the denting event pointed out in Figure 3. Notice that there is no denting in the average morphology, since the locations of dents in individual embryos differ, but there is still some morphology common to all embryos as seen in this image. Surrounding embryos: New morphologies generated at the specified number of standard deviations away from the mean in the first and second principal component dimensions (corresponding to the standard deviation lines from Figure 3A&B). This reflects the variation in embryo morphologies.

Figure 3. Results of ANOVA-SCA applied to the spherical harmonic coefficients of all embryos:A,B: Plots of the first two principal components (PCs) from ANOVA-SCA in black against time before bend region formation. PC1 is responsible for 46% of variation in values of spherical harmonic coefficients across time, while PC2 reflects 17% of the variation. The coloured lines represent standard deviations at each time point. Rapid changes in PC1 and PC2 (such as the one pointed out by arrows) represent simultaneous pre-inversion denting events in all embryos.C-E: Morphological changes of an embryo over a period of 6 minutes – before (C), during (D) and after (E) the peak highlighted in A&B. Notice the denting in D corresponding to the peaks highlighted in A&B.

A B

C D E

Figure 5. First principal component (PC1) from PCA show that pre-inversion denting roughly aligns in time with respect to bend region formation, i.e. peaks in PC1 signifying rapid morphological changes align when looking at embryos individually (A) and when averaging across embryos (B).A: Plot of PC1 of separate embryos (from PCA) against time before bend region formation.B: Plot of PC1 of all embryos (from ANOVA-SCA) against time before bend region formation. This is the same plot as Figure 3A without the standard deviation lines.

A B

38 ISSUE 52 DECEMBER 2018 39

principal components are orthogonal to each other,

enabling the use of other statistical techniques to

study embryo morphology in the future.

Further work focusing on applying this workflow

to images of embryos with fluorescently labelled

putative morphogens is needed. Morphogen

concentrations can be quantified using a similar

method, and together with morphology information,

they can shed light on mechanochemical signalling

during embryogenesis.

Rashid Khashiev University of Cambridge

References

1. Miller, C. J. & Davidson, L. (2013). The interplay between cell signaling and mechanics in developmental processes. Nature Reviews. Genetics, 14(10), 733–744. http://doi.org/10.1038/nrg3513

2. Herron, M. D. & Hackett, J. D. & Aylward, F. O. & Michod, R. E. (2009). Triassic origin and early radiation of multicellular volvocine algae. Proceedings of the National Academy of Sciences of the United States of America, 106(9), 3254–3258. http://doi.org/10.1073/pnas.0811205106

3. Haas, P. A. & Höhn, S. & Honerkamp-Smith, A. R. & Kirkegaard, J. B. & Goldstein, R. E. (2018). The noisy basis of morphogenesis: Mechanisms and mechanics of cell sheet folding inferred from developmental variability. PLOS Biology 16, e2005536

4. Höhn, S. & Hallmann A. (2011). “There is more than one way to turn a spherical cellular monolayer inside out: type B embryo inversion in Volvox globator”, BMC Biology 9, 89

5. Höhn, S. & Honerkamp-Smith, A. R. & Haas, P. A. & Khuc Trong, P. & Goldstein, R. E. (2015). “Dynamics of a Volvox Embryo Turning Itself Inside Out,” Phys. Rev. Lett. 114, 178101

6. Pitrone, P. G. & Schindelin, J. & Stuyvenberg, L. & Preibisch, S. & Weber, M. & Eliceiri, K. W. & Huisken J. & Tomancak, P. (2013). OpenSPIM: an open access light sheet microscopy platform

7. Schindelin, J. & Arganda-Carreras, I. & Frise, E. et al. (2012). Fiji: an open-source platform for biological-image analysis, Nature methods 9(7): 676-682, PMID 22743772, doi:10.1038/nmeth.2019

8. Machado, S. & Mercier, V. & Chiaruttini, N. (2018). LimeSeg: A coarsed-grained lipid membrane simulation for 3D image segmentation, bioRxiv 267534; doi: https://doi.org/10.1101/267534

9. Huang, H. & Shen, L. & Zhang, R. & Makedon, F. & Hettleman, B. & Pearlman, J. (2005). Surface Alignment of 3D Spherical Harmonic Models: Application to Cardiac MRI Analysis; doi:10.1007/11566465_9

10. Smilde, A. K. & Jansen, J. J. & Hoefsloot, H. C. J. & Lamers, R. A. N. & Greef, J. & Timmerman, M. E. (2005). ANOVA-simultaneous component analysis (ASCA): a new tool for analyzing designed metabolomics data, Bioinformatics, Volume 21, Issue 13, 1 July 2005, Pages 3043-3048, https://doi.org/10.1093/bioinformatics/bti476

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