In silico simulation modeling reveals the importance of the Casparian strip for efficient silicon uptake in rice roots.

Silicon (Si) uptake by the roots is mediated by two different transporters, Lsi1 (passive) and Lsi2 (active), in rice (Oryza sativa). Both transporters are polarly localized in the plasma membranes of exodermal (outer) and endodermal (inner) cells with Casparian strips. However, it is unknown how rice is able to take up large amounts of Si compared with other plants, and why rice Si transporters have a characteristic cellular localization pattern. To answer these questions, we simulated Si uptake by rice roots by developing a mathematical model based on a simple diffusion equation that also accounts for active transport by Lsi2. In this model, we calibrated the model parameters using in vivo experimental data on the Si concentrations in the xylem sap and a Monte Carlo method. In our simulation experiments, we compared the Si uptake between roots with various transporter and Casparian strip locations and estimated the Si transport efficiency of roots with different localization patterns and quantities of the Lsi transporters. We found that the Si uptake by roots that lacked Casparian strips was lower than that of normal roots. This suggests that the double-layer structure of the Casparian strips is an important factor in the high Si uptake by rice. We also found that among various possible localization patterns, the most efficient one was that of the wild-type rice; this may explain the high Si uptake capacity of rice.

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.

Canalization-based vein formation in a growing leaf.

Vein formation is an important process in plant leaf development. The phytohormone auxin is known as the most important molecule for the control of venation patterning; and the canalization model, in which cells experiencing higher auxin flux differentiate into specific cells for auxin transportation, is widely accepted. To date, several mathematical models based on the canalization hypothesis have been proposed that have succeeded in reproducing vein patterns similar to those observed in actual leaves. However, most previous studies focused on patterning in fixed domains, and, in a few exceptional studies, limited tissue growth - such as cell proliferation at leaf margins and small deformations without large changes in cell number - were dealt with. Considering that, in actual leaf development, venation patterning occurs in an exponentially growing tissue, whether the canalization hypothesis still applies is an important issue to be addressed. In this study, we first show through a pilot simulation that the coupling of chemical dynamics for canalization and tissue growth as independent models cannot reproduce normal venation patterning. We then examine conditions sufficient for achieving normal patterning in a growing leaf by introducing various constraints on chemical dynamics, tissue growth, and cell mechanics; in doing so, we found that auxin flux- or differentiation-dependent modification of the cell cycle and elasticity of cell edges are essential. The predictions given by our simulation study will serve as guideposts in experiments aimed at finding the key factors for achieving normal venation patterning in developing plant leaves.