Modeling of photosynthesis light curves by linear splines

Abstract

The paper presents an example of the linear splines use to describe the photosynthesis light curves for microalgae culture. The main mathematical models of the relationship between photosynthesis rate and light are listed. Based on the previously formulated basic principles of modeling microalgae photobiosynthesis, a mathematical model is proposed that describes the dependence of the assimilation number of chlorophyll a on the value of the light flux by linear splines. The advantage of the proposed approach is a clear definition of the point of change of the limiting factor. It is shown that light-limited photosynthesis rate is determined not only by external irradiation, but also by the concentration of chlorophyll a. The light-saturated rate depends on the amount of a key enzyme complex, which limits the rate of energy exchange reactions in the cell. Verification of the proposed model on the example of the diatom microalgae Skeletonema costatum was carried out. It is shown that the higher the degree of cell adaptation to high irradiation, the better the photosynthesis curve is described by linear splines. If S. costatum cells are adapted to low irradiation, deviations of experimental data from the idealized broken line are observed, which are caused by changes in the pigment composition. When the experimental data are normalized, the cell adaptation factor is reduced, all points are described by a single broken line, which indicates the universality of the proposed approach.