Importance of a diffusion-dominant small volume to activate cell-secreted soluble factor signaling in embryonic stem cell culture in microbioreactors: a mathematical model based study.

In our previous studies, we observed that cell-secreted BMP4 had a prominent influence on mouse embryonic stem cell (mESC) behaviors in a membrane-based two-chambered microbioreactor (MB), but not in a macro-scale culture (6-well plate/6WP). In this study, we investigated how the physical aspects of these cultures regulated BMP4 signaling by developing mathematical models of the cultures. The models estimated signaling activity in the cultures by considering size of the undifferentiated mESC colonies and their growth, diffusion of BMP4, and BMP4 trafficking process in the colonies. The models successfully depicted measured profile of BMP4 concentration in the culture medium which was two times higher in the MB than that in the 6WP during 5-day culture. The models estimated that, owing to the small volume and the membrane, cells were exposed to a higher BMP4 concentration in the top chamber of the MB than that in the 6WP culture. The higher concentration of BMP4 induced a higher concentration of BMP4-bound receptor in the colony in the MB than in the 6WP, thereby leading to the higher activation of BMP4 signaling in the MB. The models also predicted that the size of the MB, but not that of the 6WP, was suitable for maximizing BMP4 accumulation and upregulating its signaling. This study will be helpful in analyzing culture systems, designing microfluidic devices for controlling ESC or other cell behavior.