A mathematical model of phloem sucrose transport as a new tool for designing rice panicle structure for high grain yield.

Rice (Oryza sativa) is one of the most important food crops in the world. Numerous quantitative trait loci or genes controlling panicle architecture have been identified to increase grain yield. Yet grain yield, defined as the product of the number of well-ripened grains and their weight, is a complex trait that is determined by multiple factors such as source, sink and translocation capacity. Mechanistic modelling capturing capacities of source, sink and transport will help in the theoretical design of crop ideotypes that guarantee high grain yield. Here we present a mathematical model simulating sucrose transport and grain growth within a complex phloem network. The model predicts that the optimal panicle structure for high yield shows a simple grain arrangement with few higher order branches. In addition, numerical analyses revealed that inefficient delivery of carbon to panicles with higher order branches prevails regardless of source capacity, indicating the importance of designing grain arrangement and phloem structure. Our model highlights the previously unexplored effect of grain arrangement on the yield, and provides numerical solutions for optimal panicle structure under various source and sink capacities.