Process-based modelling of isoprene emission by oak leaves

The emission rate of the volatile reactive compound isoprene, emitted predominantly by trees, must be known before the level of photo-oxidants produced during summer smog can be predicted reliably. The emission is dependent on plant species and local conditions, and these dependencies must be quantified to be included in any empirical algorithm for the calculation of isoprene production. Experimental measurements of isoprene emission rates are expensive, however, and existing data are scarce and fragmentary. To overcome these difficulties, it is promising to develop a numerical model capable of precisely calculating the isoprene emission by trees for diverse ecosystems, even under changing environmental conditions. A basic process-based biochemical isoprene emission model (BIM) has therefore been developed, which describes the enzymatic reactions in leaf chloroplasts leading to the formation of isoprene under varying environmental conditions (e. g. light intensity, temperature). Concentrations of the precursors of isoprene formation, 3-phosphoglyceric acid and glyceraldehyde 3-phosphate, are provided by a published light fleck photosynthesis model. Specific leaf and enzyme parameters were determined for the pedunculate oak (Quercus robur L.), so that the BIM is capable of calculating oak-specific isoprene emission rates as influenced by the leaf temperature and light intensity. High correlation was observed between isoprene emission rates calculated by the BIM and the diurnal isoprene emission rates of leaves measured under controlled environmental conditions. The BIM was even capable of describing changes in isoprene emission caused by midday depression of net photosynthesis

A user’s guide to PDE models for chemotaxis

Mathematical modelling of chemotaxis (the movement of biological cells or organisms in response to chemical gradients) has developed into a large and diverse discipline, whose aspects include its mechanistic basis, the modelling of specific systems and the mathematical behaviour of the underlying equations. The Keller-Segel model of chemotaxis (Keller and Segel in J Theor Biol 26:399–415, 1970; 30:225– 234, 1971) has provided a cornerstone for much of this work, its success being a consequence of its intuitive simplicity, analytical tractability and capacity to replicate key behaviour of chemotactic populations. One such property, the ability to display “auto-aggregation”, has led to its prominence as a mechanism for self-organisation of biological systems. This phenomenon has been shown to lead to finite-time blow-up under certain formulations of the model, and a large body of work has been devoted to determining when blow-up occurs or whether globally existing solutions exist. In this paper, we explore in detail a number of variations of the original Keller–Segel model. We review their formulation from a biological perspective, contrast their patterning properties, summarise key results on their analytical properties and classify their solution form. We conclude with a brief discussion and expand on some of the outstanding issues revealed as a result of this work