## 3 Results
### Behavior of DPCs from the Alginate Sphere  
To study the proliferation capacity of remained dormant cells in long-term alginate sphere, we cut every alginate sphere into pieces after the cultivation in alginate sphere. When we started to cultivate DPCs in alginate sphere, we usually used passage 3-4 DPCs _in vitro_ cultivation since they go into the senescent status in couple of more passages, in general passage 6 or more. We incubated dermal papilla for 10 days, 50 days and 80 days in alginate sphere, then we tried to cultivate the dormant cells by breaking the alginate sphere structures. We found that some of the spheres without breaking alginate sphere form had their own colonies beneath them like primary human DPC explants (Figure 4A). As shown in Figure 4B,C, their ability to grow and make colonies was similar as it was in normal in vivo dermal papillae. Considering that the cells in the alginate spheres were not proliferative, their ability to grow in the explants showed that the DPCs have trichogenic properties to induce hair follicle formation but the alginate spheres put the cells into a dormant state.  
To check the proliferative ability of the dormant state, we used the CMDil trace method. This chemical is diluted once the cell divides. The cells taken from the alginate spheres rapidly grew and divided in the 2D plate (Figure 4D). However, their CMDil level was extremely low compared to that of the cells inside the alginate sphere, which meant that the cells from the alginate sphere have a high potential to divide (Figure 4E).  
Next, every culture of the human DPCs in the alginate spheres showed the convergence phenomenon after day 70. We concluded that there was a certain rule for this convergence and that we could combine the parameters of cellular densities as well as size of sphere. In the cellular density experiment, every experiment showed convergence to a specific range of cell numbers no matter how many cells we put inside the alginate sphere (Figure 4F). At the same time, the sphere size experiment showed that the convergence was mainly dependent on the volume of the alginate sphere (Figure 4G). Considering that we controlled the alginate spheres so that they all had similar sizes in the experiment on cellular density, we could conclude that there is a certain rule for the convergence toward a specific cellular number in long-term cultivation.  
Reanalysis of our data after combining into single table and using the volume parameter as the candidate factor, we found the same convergence rate after 70 days (Figure 4H). As we expected, the number of live cells was significantly dependent on the volume of the alginate spheres.  
Figure 4: Cultivation of explants and cellular convergence rate of dermal papilla alginate spheres. (**A–C**) Colony forming properties of alginate spheres with human DPCs. (**D**,**E**) CMDil trace of cell culture from alginate sphere explants of human DPCs: light microscopy (**D**) and fluorescent microscopy (**E**). The subpanel of (**D**) is tone-modulated to show the diluted cells originated from CMDil retaining cells. The normalized live cell number with the volume of alginate spheres at different cellular densities (**F**) and different sizes (**H**). (**G**) The normalized live cell number with the volume of alginate sphere of different cellular densities at day 70, day 80 and day 90. (**I**) The normalized live cell number with the volume of alginate spheres under every experimental condition.  
The convergence density varied from 2235.05 cells/mm\({}^{3}\) to 3872.16 cells/mm\({}^{3}\). If we excluded the smallest size of alginate sphere, the range was between 2235.05 cells/mm\({}^{3}\) and 2628.80 cells/mm\({}^{3}\). Furthermore, these cells were highly dormant considering that they did not proliferate after being placed inside the alginate but simply remained static as they were in vivo.