Figure 2
Assuming instantaneous redistribution of signalling shows that the fed-batch strategy is the most effective, but this assumption is not valid for typical culture systems. (a) Variation of transforming growth factor beta (TGF-β) concentration in a 24-well-plate well with time under the assumption that secreted TGF-β is instantaneously distributed throughout the cell-culture volume. Shown are the analytical solutions to the governing equations defined in Equations (1) and (2). (b) Spatial distribution of secreted TGF-β concentration after 1 day of static culture assuming finite diffusivity of D = 6.5 × 10−11 m2/second (dashed line, numerical solution of Equations (10) and (11) in Additional file 1) and infinite diffusivity (solid line, analytical solution of Equation (1) or (2) with Q = 0). Colour contours show a graphical representation of the concentration variation within the well at day 1 for each case. (a), (b) Cell population assumed constant at X = 105, and the secretion rate of TGF-β is r ϕ  = 1.94 × 10−6 pg/cell/day.