Zhang Lei/Tang Chao's team builds a computational model of the early developmental morphology of nematode embryos

Essay topic:

Computable early Caenorhabditis elegans embryo with a phase field model

Paper address:

https://doi.
org/10.
1371/journal.
pcbi.
1009755

Cells are the smallest moving units of life
.
Cells of different species, organs, and tissues have different morphologies, and morphologies characterize the mechanical properties and functions of cells
.
What kind of mathematical and physical equations can accurately describe the dynamic characteristics of cell morphology is an important issue for biomechanics, cell biology and developmental biology
.
On January 14, 2022, Zhang Lei's research group from Peking University Quantitative Biology Center/Beijing International Mathematical Research Center and Tang Chao's research group from Quantitative Biology Center/Life Science Joint Center/School of Physics published a paper entitled "PLoS Computational Biology".
Article on Computable early Caenorhabditis elegans embryo with a phase field model
.
This article uses the morphological data of nematode embryos to construct a simplest phase field model, which can accurately calculate the morphological changes of real embryos and inverse the underlying cellular mechanical properties, and use this model to analyze the early development process of nematode embryos (Figure 1) [ 1]
.

Figure 1.
Simulated (top) and experimentally photographed (bottom) nematode embryo structures
.

Caenorhabditis elegans has the developmental precision of a single cell, that is, the division time, division direction, movement path, fate identity and other attributes of each cell are highly consistent among different individuals [2]
.
Due to the low noise and repeatability of the system, some scholars have been trying to establish different mechanical models (such as multi-particle model and coarse-grained model) from 20 years ago to the present to reconstruct its morphological evolution process by computer [3,4]
.
However, the previous models had the limitation of too many parameters or too low precision, and the detailed information of cell morphology and movement (such as the contact area between cells) could not be completely and accurately calculated [5]
.

The research team established a set of phase field models considering cell surface tension, repulsive and attractive forces between cells, cell volume constraints, and the confinement effect of eggshells on cells
.
The phase field model describes the cell as a constrained diffusible field that characterizes its morphology (Figure 2)
.
Subsequently, the team used the morphological map of nematode embryos drawn the previous year to simply determine the system parameters of the model, and used it as a reference to test the accuracy of the model[6]
.
Entering the experimentally measured cell division order, direction, and volume ratio, the model-predicted embryo morphology and motion at the 1-8-cell stage were highly consistent with the experimental observations (Fig.
1), and reproduced the complete cell contact network
.
By comparing the simulated structure with the experimental structure, the model inferred that the EMS-P2 cell pair at the 4-cell stage and the ABpl-E cell pair at the 8-cell stage had significantly lower viscosity, which was recently confirmed by experiments (Fig.
3) [7,8]
.

Figure 2.
Phase field model depicting cellular morphology and mechanics
.

Figure 3.
Theoretical prediction of uneven distribution of 4-cell-phase viscosity (σ is global viscosity, σEMS, P2 is EMS-P2 viscosity)
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Left: fitting global viscosity; middle: fitting EMS-P2 cell pair viscosity; right: the viscous protein HMR-1 is less distributed at the EMS-P2 interface
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Based on the above phase field model, the research team focused on how the cell division direction, division time, and viscosity relationship affect the embryonic morphological evolution path
.
Among them, the orientation of reality-encoded splits (including the orientation of asymmetric splits) is critical for morphological evolution
.
Timely cell division improves the embryo's ability to withstand pressure and effectively prevents the collapse of the cell contact network and the embryo's structure; the theoretical prediction that the embryo tends to "flatten" under pressure has been verified by experiments of artificially interrupting cell division
.
In addition, the viscosity relationship effectively provides multiple possible paths for morphological evolution, and the low viscosity of ABpl-E observed in reality is the only additional regulation in the simulation that produces a stable, three-dimensional, and normal embryonic structure
.
The above simulations show that, over the long evolutionary process, nematodes have developed a variety of ingenious genetic programs to ensure their developmental robustness
.

Figure 4.
A tree of developmental pathways determined by cell division timing and a single regulator of viscosity
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Left: Triggering cell division at different time points, there are multiple outcomes for embryo morphology at the 6-8 cell stage
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Right: Adhesion regulation of a single cell pair, there are multiple pathways for morphological evolution at the 8-cell stage (ABpl-E regulation is the only stable and stress-resistant pathway)
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The phase field model proposed in this work has been carefully experimentally verified.
On the one hand, it provides an effective computational tool for the accurate simulation of cell morphology and mechanics; an accurate model can not only help us understand the coding logic of real life systems, but also apply to engineering applications, such as the optimal design of multicellular robots
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On the other hand, using the simplest model to successfully calculate the evolution of the actual embryo morphology and inverse the underlying mechanical information, by finding suitable mathematical and physical equations, gradually build the model and prevent parameter overfitting, so as to more accurately understand the biological development process
.

Associate Professor Zhang Lei of Peking University Center for Quantitative Biology/Beijing International Mathematical Research Center and Professor Tang Chao from Center for Quantitative Biology/Life Science Joint Center/School of Physics are the co-corresponding authors of the article; Ph.
D students Kuang Xiangyu and Guan Guoye of Peking University Center for Quantitative Biology are the article Co-first authors; Prof.
Zhongying Zhao, Dr.
Mingjian Wang and Lu-Yan Chan from the Department of Biology, Hong Kong Baptist University provided experimental support
.
This work was supported by the National Natural Science Foundation of China and the Ministry of Science and Technology's key research and development projects
.
The research team is working on developing new data collection methods, constructing mathematical and physical models, and analyzing the basic principles of the development of model organisms such as nematodes
.

references:

[1] Kuang & Guan, et al.
PLoS Comput.

[2] Sulston, et al.

[3] Kajita, et al.

[4] Fickentscher et al.

[5] Guan, et al.

[6] Cao & Guan & Ho, et al.

[7] Yamamoto, et al.

[8] Dutta, et al.