An effective method for quantification, visualization, and analysis of 3D cell shape during early embryogenesis

Abstract

Embryogenesis is the most basic process in developmental biology. Effectively and simply quantifying cell shape is challenging for the complex and dynamic 3D embryonic cells. Traditional descriptors such as volume, surface area, and mean curvature often fall short, providing only a global view and lacking in local detail and reconstruction capability. Addressing this, we introduce an effective integrated method, 3D Cell Shape Quantification (3DCSQ), for transforming digitized 3D cell shapes into analytical feature vectors, named eigengrid (proposed grid descriptor like eigen value), eigenharmonic, and eigenspectrum. We uniquely combine spherical grids, spherical harmonics, and principal component analysis for cell shape quantification. We demonstrate 3DCSQ’s effectiveness in recognizing cellular morphological phenotypes and clustering cells. Applied to Caenorhabditis elegans embryos of 29 living embryos from 4- to 350-cell stages, 3DCSQ identifies and quantifies biologically reproducible cellular patterns including distinct skin cell deformations. We also provide automatically cell shape lineaging analysis program. This method not only systematizes cell shape description and evaluation but also monitors cell differentiation through shape changes, presenting an advancement in biological imaging and analysis.

Keywords

Caenorhabditis elegans ( C. elegans) / cell shape quantification / eigen features (eigengrid / eigenharmonic & eigenspectrum) / lineage analysis / morphological reproducibility / spherical harmonics (SPHARM)

References

[1] Fickentscher R , Struntz P , Weiss M . Setting the clock for fail-safe early embryogenesis. Phys Rev Lett. 2016; 117 (18): 188101.

[2] Guan G , Wong MK , Zhao Z , Tang LH , Tang C . Volume segregation programming in a nematode's early embryogenesis. Phys Rev E. 2021; 104 (5): 054409.

[3] Guan G , Zhao Z , Tang C . Delineating mechanisms and design principles of Caenorhabditis elegans embryogenesis using in toto high-resolution imaging data and computational modeling. Comput Struct Biotechnol J. 2022; 20: 5500- 15.

[4] Guignard L , Fiúza U-M , Leggio B , Laussu J , Faure E , Michelin G , et al. Contact area-dependent cell communication and the morphological invariance of ascidian embryogenesis. Science. 2020; 369: eaar5663.

[5] Shah P , Bao Z , Zaidel-Bar R . Visualizing and quantifying molecular and cellular processes in Caenorhabditis elegans using light microscopy. Genetics. 2022; 221 (4): iyac068.

[6] Pintard L , Bowerman B . Mitotic cell division in Caenorhabditis elegans. Genetics. 2019; 211 (1): 35- 73.

[7] Guan G , Kuang X , Tang C , Zhang L . Comparison between phase-field model and coarse-grained model for characterizing cell-resolved morphological and mechanical properties in a multicellular system. Commun Nonlinear Sci Numer Simulat. 2023; 117: 106966.

[8] Guan G , Li Z , Ma Y , Cao J , Wong M-K , Chan L-Y , et al. Quantitative cell morphology in C. elegans embryos reveals regulations of cell volume asymmetry. 2023. Preprint at bioRxiv: 2023.11.20.567849

[9] Cao J , Guan G , Ho VWS , Wong M-K , Chan L-Y , Tang C , et al. Establishment of a morphological atlas of the Caenorhabditis elegans embryo using deep-learning-based 4D segmentation. Nat Commun. 2020; 11: 6254.

[10] Lejeune E , Linder C . Quantifying the relationship between cell division angle and morphogenesis through computational modeling. J Theor Biol. 2017; 418: 1- 7.

[11] Wang Z , Wang D , Li C , Xu Y , Li H , Bao Z . Deep reinforcement learning of cell movement in the early stage of C.elegans embryogenesis. Bioinformatics. 2018; 34 (18): 3169- 77.

[12] Wang Z , Xu Y , Wang D , Yang J , Bao Z . Hierarchical deep reinforcement learning reveals a modular mechanism of cell movement. Nat Mach Intell. 2022; 4 (1): 73- 83.

[13] Xiong R , Sugioka K . Improved 3D cellular morphometry of Caenorhabditis elegans embryos using a refractive index matching medium. PLoS One. 2020; 15 (9): e0238955.

[14] Jelier R , Kruger A , Swoger J , Zimmermann T , Lehner B . Compensatory cell movements confer robustness to mechanical deformation during embryonic development. Cell Systems. 2016; 3 (2): 160- 71.

[15] Mendonca T , Jones AA , Pozo JM , Baxendale S , Whitfield TT , Frangi AF . Origami: single-cell 3D shape dynamics oriented along the apico-basal axis of folding epithelia from fluorescence microscopy data. PLoS Comput Biol. 2021; 17 (11): e1009063.

[16] Ichbiah S , Delbary F , Mcdougall A , Dumollard R , Turlier H . Embryo mechanics cartography: inference of 3D force atlases from fluorescence microscopy. Nat Methods. 2023; 20: 1989- 99.

[17] Sulston JE , Schierenberg E , White JG , Thomson JN . The embryonic cell lineage of the nematode Caenorhabditis elegans. Dev Biol. 1983; 100 (1): 64- 119.

[18] Long F , Peng H , Liu X , Kim SK , Myers E . A 3D digital atlas of C. elegans and its application to single-cell analyses. Nat. Methods. 2009; 6: 667- 72.

[19] Pillai EK , Franze K . Mechanics in the nervous system: from development to disease. Neuron. 2023; 112 (3): 342- 61.

[20] Azuma Y , Okada H , Onami S . Systematic analysis of cell morphodynamics in C. elegans early embryogenesis. Front. Bioinform. 2023; 3: 1082531.

[21] Du CJ , Hawkins PT , Stephens LR , Bretschneider T . 3D time series analysis of cell shape using Laplacian approaches. BMC Bioinform. 2013; 14: 296.

[22] Ducroz C , Olivo-Marin JC , Dufour A . Characterization of cell shape and deformation in 3D using Spherical Harmonics. In: 2012 9th IEEE international Symposium on biomedical imaging (ISBI). IEEE. 2012; 848- 51.

[23] Xu M , Wu Y , Shroff H , Xu M , Mani M . A scheme for 3-dimensional morphological reconstruction and force inference in the early C. elegans embryo. PLoS One. 2018; 13 (7): e0199151.

[24] Thiels W , Smeets B , Cuvelier M , Caroti F , Jelier R . spheresDT/Mpacts-PiCS: cell tracking and shape retrieval in membrane-labeled embryos. Bioinformatics. 2021; 37 (24): 4851- 6.

[25] Yuan Z , Li F , Zhang P , Chen B . Description of shape characteristics through Fourier and wavelet analysis. Chin J Aeronaut. 2014; 27 (1): 160- 8.

[26] Ruan X , Murphy RF . Evaluation of methods for generative modeling of cell and nuclear shape. Bioinformatics. 2019; 35 (14): 2475- 85.

[27] Shen L , Farid H , Mcpeek MA . Modeling three-dimensional morphological structures using spherical harmonics. Evolution. 2009; 63 (4): 1003- 16.

[28] Larsen ABL , Vestergaard JS , Larsen R . HEp-2 cell classification using shape index histograms with donut-shaped spatial pooling. IEEE Trans Med Imag. 2014; 33 (7): 1573- 80.

[29] Li X , Zhao Z , Xu W , Fan R , Xiao L , Ma X , et al. Systems properties and spatiotemporal regulation of cell position variability during embryogenesis. Cell Rep. 2019; 26 (2): 313- 21.e7.

[30] Driscoll JR , Healy DM . Computing Fourier transforms and convolutions on the 2-sphere. Adv Appl Math. 1994; 15 (2): 202- 50.

[31] Wieczorek MA , Meschede M . SHTools: tools for working with spherical harmonics. Geochemistry, Geophysics, Geosystems. 2018; 19 (8): 2574- 92.

RIGHTS & PERMISSIONS

The Author(s). Quantitative Biology published by John Wiley & Sons Australia, Ltd on behalf of Higher Education Press.