《MAT228C project report》.pdf

A Time-Dependent Model of Phloem Transport through Sieve Tubes with Elastic Walls Lifeng Han June 10, 2013 Abstract A time-dependent model based on the M¨unch Hypothesis of phloem transport was presented. Wall elasticity was included as an improvement of the previous modelling work. Two partial differential equations(PDEs) were derived from volume conservation and sugar conservation. A finite difference method was used to solve the two PDEs. An adaptive time step was chosen to ensure stability and efficiency. A refinement study was performed to validate the employed numerical schemes. 1 Introduction M¨unch Hypothesis, a.k.a, Pressure Flow Hypothesis or Mass Flow Hypothesis is the most recognized theory explaining mass flow in the phloem of plants. It was first proposed by Ernst M¨unch, a German plant physiologist in 1930. Generally speaking, the conductive elements of phloem consist of sieve tubes which connect source(e.g. leaves) and sink(e.g. roots). The sugar produced by photosynthesis is loaded actively through peripheral membrane into each sieve tube at one end(loading zone) and unloaded at the other end(unloading zone). Because of the high concentration of sugar near the source, water enters the sieve tube by osmosis. Vice versa, there is efflux of water near the sink. This mechanism result in a pressure gradient which drives the mass flow through phloem. M¨unch Hypothesis has been expressed in mathematical forms and formulated into mathematical models[1, 2, 3]. These models facilitate quantitative studies on phloem transport and the M¨unch Hypothesis. There have been experimental studies on phloem transport also using Carbon-11 labelling technology[4].