Figure 1.

Physical principles of growth-induced mass flow. (a) Turgor pressure is induced by an osmotic gradient at the site of water uptake. Vesicles (circles) move towards the tip faster than it recedes, while the cytosol behind the growing tip moves forward at the rate of tip growth (Lew 2005). The conservation of volume dictates that as the tip expands, fluid flows towards the tips from the site of water uptake. This mass flow demonstrates the presence of a pressure gradient. (b) Suppose that a fungus grows out of an inoculum (square) and into a region (oval). Some of the material that becomes part of the fungi may come from within the oval region. The rest of the material must have travelled along the cords (edges) that cross the region's boundary. If the volume of fungi within the region increases by ΔV over a period of time t, and none of the material is drawn from within the region, it follows that the net current flowing into the region is ΔV/t. Furthermore, if the total cross-sectional area of the boundary crossing cords is a, the mean velocity of flow will be ΔV/at.