Münch without tears: a steady-state Münch-like model of phloem so simplified that it requires only algebra to predict the speed of translocation.

Abstract

The pressure-driven mass-flow hypothesis of phloem translocation associated with Ernst Münch has become hegemonic and has been mathematically modelled in many, many different fashions - but not, apparently, in one chosen so that it gives simple algebraic predictions of (i) the speed of translocation; (ii) the saccharide concentration at the source; and (iii) the pressure offset due to translocation. To overcome this deficit, the problem was drastically simplified by assuming that: (i) radial variations could be neglected; (ii) osmotic water uptake was restricted to sink and source regions of negligible thickness; (iii) there was a constant rate of saccharide loading at the source; and (iv) the sink strength was sufficient to lower the photosynthate concentration at the extreme distal end of the sieve tube to levels at which it becomes unimportant. The resulting system of quadratic algebraic equations was then solved for the translocation speed, which was shown to vary as the square-root of the loading rate. Also found were the offset of the intra-tube hydrostatic pressure and the sap saccharide concentration at the source, which, likewise, vary as the square-root of the loading rate.