Team:BNU-China/Model4
Tracing Generations
Introduction
In our project, we coupled the expression of Cas9 with cell division. To prove that our design can effectively extend the tracing time when barcode diversity reaches saturation, we consider estimating how long will barcodes reach saturation after coupling.
Models and Results
We first obtained data which is about the mutant fraction from the #22hgRNA (the hgRNA selected in Barcode Diversity model) in different time under the expression of Cas9 protein composition in the literature [1].
Figure 1. : Original mutant fraction of 22hgRNA during the developmental stage
It takes about 34 times of division to reach the 12 billion cells of adult mice, starting with fertilized eggs. And different cells in mice have different time of cell cycle and division at different times. So we consider to obtain specific data for the first 6 cell cycles from the literature [2] and estimate later divisions according to the general conclusion of mammalian cells for simplicity [3].
The specific data is shown below:
Parameters:
We reclassified the x-coordinate in Figure 1. into different cell generations according to the cell cycle in the above table. Since the final observation day in Figure 1. is E16.5 (Embryonic day16.5), it is calculated that it is the 19th generation corresponding to cell division. Therefore, N = 19.
In this model, we assumed that the rate of producing mutants at different periods is only related to the current cell generation. Therefore, we should have following equations:
By substituting the above expressions and the data in Figure 1. into Matlab, the result showed that at the time of E16.5 (i.e. the 19th generation of cell division), the mutation fraction in the coupling condition was only 30%. The graph below shows the comparison between the mutant fraction in the coupling condition and the original case.
Figure 2. : Comparison between original and coupling mutant fraction
We wanted to estimate at least how many generations of mutants
were left to reach saturation. Considering the fact that major zygotic genome activation in
the mouse occurs at the two-cell stage we choose 
as the growth rates for the 70% mutants
left. The calculation showed that it takes 258h (about 10.75 generations) to reach
saturation. It also indicated that the mutant saturation time is extended to about 1.5 times
as much as the original.
Discussion
The simulation results show that our design can indeed extend the cells generations could be traced. Therefore, the practical application advantages of the system have been proved to a certain extent.
References
[1] Kalhor, R., Kalhor, K., Mejia, L., Leeper, K., Graveline, A., Mali, P., & Church, G. M. (2018). Developmental barcoding of whole mouse via homing CRISPR. Science (New York, N.Y.), 361(6405), eaat9804.
[2] Artus, J., & Cohen-Tannoudji, M. (2008). Cell cycle regulation during early mouse embryogenesis. Molecular and cellular endocrinology, 282(1-2), 78–86.
[3] Masnadi-Shirazi, M., Maurya, M. R., Pao, G., Ke, E., Verma, I. M., & Subramaniam, S. (2019). Time varying causal network reconstruction of a mouse cell cycle. BMC bioinformatics, 20(1), 294.
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