Pickard William F
Department of Electrical and Systems Engineering, Washington University, St Louis, Missouri 63130, USA. Email.
Funct Plant Biol. 2012 Jun;39(6):531-537. doi: 10.1071/FP12004.
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.
与恩斯特·明希相关的韧皮部运输压力驱动质量流假说已占据主导地位，并已用许多不同方式进行数学建模——但显然没有一种方式能给出关于以下方面的简单代数预测：（i）运输速度；（ii）源端的糖类浓度；（iii）因运输导致的压力偏移。为克服这一不足，通过假设对问题进行了大幅简化：（i）可忽略径向变化；（ii）渗透吸水仅限于厚度可忽略不计的源端和库端区域；（iii）源端糖类装载速率恒定；（iv）库强足以将筛管最远端的光合产物浓度降低到可忽略不计的水平。然后求解由此产生的二次代数方程组以得到运输速度，结果表明运输速度随装载速率的平方根而变化。还得出了管内静水压力的偏移以及源端汁液糖类浓度，同样，它们也随装载速率的平方根而变化。
