Figure 3
Assuming instantaneous redistribution of inhibitory signals overpredicts the effectiveness of fed-batch cultures. Effect of flow rate Q on the concentration of transforming growth factor beta (TGF-β) at the bottom of a 24-well-plate well of initial media height h 0 = 5 mm (corresponding to 1 ml culture). Shaded grey area shows the effect of continuous dilution into the top of the culture (Equation (4)), and coloured lines show the effect of uniform dilution throughout the culture (numerical solution of Equations (10) and (11) in Additional file 1). Solid black line represents the model of Csaszar and colleagues [8], given by the analytical solution of Equation (1), whereby spatial concentration gradients are ignored (D → ∞). The diffusivity is D = 6.5 × 10−11 m2/second, the cell population is assumed constant at X = 105, and the secretion rate is r ϕ  = 1.94 × 10−6 pg/cell/day.