HAIRY ROOT-GROWTH MODELS - EFFECT OF DIFFERENT BRANCHING PATTERNS

Root growth occurs by the formation of younger lateral branches on older parent branches. This growth process can be described by the delays that occur between subsequent branching events and summarized by a set of verbal rules describing the branching kinetics in detail. A method for converting such verbal rules to a mathematical model of the branch number in a root culture under constant environmental conditions is presented here. The model of branch number is then combined with an age distribution balance to give a model of the age distribution in a root culture. Exact solution of the model is possible for deterministic branching dynamics, but results in rather cumbersome expressions for large times. Approximate solutions, valid at large times, therefore are obtained from analysis of the model. From these solutions, one readily obtains the specific growth rate of the culture, solely in terms of the branching kinetics. The extension of the modeling concepts presented here to stochastic branching rules is briefly discussed.