Modelling cell separation during plant organ abscission

A simple mathematical model is presented to describe the cell separation process that plants undertake in order to deliberately shed organs. The focus here is on modelling the production of the enzyme polygalacturonase, which breaks down pectin that provides natural cell-to-cell adhesion in the localised abscission zone. A coupled system of three ordinary differential equations is given for a single cell, and then extended to hold for a layer of cells in the abscission zone. Simple observations are made based on the results of this preliminary model and, furthermore, a number of opportunities for applied mathematicians to make contributions in this subject area are discussed.

Calculation of the oxygen isotope discrimination factor for studying plant respiration

Measurement of discrimination against 18O during dark respiration in plants is currently accepted as the only reliable method of estimating the partitioning of electrons between the cytochrome and alternative pathways. In this paper, we review the theory of the technique and its application to a gas-phase system. We extend it to include sampling effects and show that the isotope discrimination factor, D, is calculated as –dln(1 + δ)/dlnO*, where δ is isotopic composition of the substrate oxygen and O*=[O2]/[N2] in a closed chamber containing tissue respiring in the dark. It is not necessary to integrate the expression but, if the integrated form is used, the resultant regression should not be constrained through the origin. This is important since any error in D will have significant effects on the estimation of the flux of electrons through the two pathways.