### Model

Cyclebow Hybrid-Color Model

The Cyclebow Hybrid-Color Model with the parameter we choose are able to fulfill our purpose of extending the cell-cycle color to 7 generations. **Figure 1A** indicates the proportion of color we use to represent each RGB color, and the color keeps changing under every cell division. **Figure 1B** is the cell cycle color change indicator, where each circle represent one specific cell going through its cell division process and express different colors. The Cyclebow Hybrid-Color Model can distinguish up to 7 generations of HSC cells, which equals to about 4.6 years on average, so that it will be qualified for a 5-year clinical research purpose.

HSC Cell Survival Model

Deterministic Model

First we didn't take emigration rate into consider and plot the cell survival curve. Figure 2 shows the cell survival curve (repopulation curve) after one time transplantation of 400 HSCs. It reaches the HSCs maximum number at about 150 week, after which the HSC will divide but only one of the two sub-cells will survive.

If we take into consideration the emigration rate, then the HSC cell growth will be slowed down. The HSC cell reserve reaches K = 11,000 at the week around 890 (figure 3). The blue vertical line shows five years, which is normally the concern after transplantation surgery.

When we take a closer look at the 5 years of concern in our HSC reserve cell survival model (figure 4), the HSCs in the reserve are in their steady increasing pace and reach twice the amount of the transplantation on the 5th generation.

**Remark**: The plot is just for average Cyclebow Hybrid-Color change process whereas some clone groups may go through a cell cycle faster than the others.

Within 5 year of concern, the immigrated HSC serves as repairing cells to the recipient body and exhausts after a certain period of time. Figure 5 shows the model where we are concerned about the HSCs differentiation and the number of active differentiation clones of human HSC within 5 years of notice. There is a strong turning point at Week 21, where the number of differentiating cells are 67, then the differentiating cell growth goes into a linear growing period. We combine the Cyclebow Hybrid-Color Model with the HSC differentiating clones curve to show how the active differentiating cells change their colors within 5 years of concern.

**Remark**: The plot is just for average Cyclebow Hybrid-Color change process whereas some clone groups may go through a cell cycle faster than the others.

Stochastic Model

Figure 6 shows the stochastic result of our cell survival model. Bold blue line represents the number of HSCs in the HSC reserve (reaching maximum capacity at about 900 weeks). The stochastic model resembles the deterministic one, both in curve shape and in the end point. The blue vertical line indicates the end of fifth year.

Figure 7 shows the cumulative cell count curve for one general and three separate cell behaviors. The bold blue line represents the general cumulative cell count after one time transplantation of 400 HSCs, and reaches its capacity at 11,000 cells, afterwards each HSC will divide but only one the two sub-cells will survive. The green one is the cumulative cell count for HSCs that divide along this time of period, while yellow and red account for the cumulative cell emigration and cell death, respectively.

for HSCs that divide along this time of period, while yellow and red account for the cumulative cell emigration and cell death, respectively.