A Mathematical Model for Characterizing the Biomass and the Physiological/Biochemical Indicators of Salvia miltiorrhiza Based on Growth-Defense Tradeoff

Carbon(C) and nitrogen(N) metabolisms are important for plant growth and defense, and enzymes play a major role in these two metabolisms. Current studies show that the enzymes of N Metabolism, C Metabolism, and defense are correlated with biomass. Then, we conducted this research under the assumption that enzymes could characterize the relationship based on growth-defense tradeoff, and some of the enzymes could be used to represent the plant growth. From the mechanism model, we picked out 18 physiological/biochemical indicators and obtained the data from 24 tissue culture seedlings of Salvia miltiorrhiza (S.miltiorrhiza) which were grafted with 11 endophytic fungi. Then, the relationship between the biomass and the physiological/biochemical indicators was investigated by using statistical analysis, such as correlation analysis, variable screening, and regression analysis. The results showed that many physiological/biochemical indicators, especially enzyme activities, were related to biomass accumulation. Through a rigorous logical reasoning process, we established a mathematical model of the biomass and 6 key physiological/biochemical indicators, including glutamine synthetase (GS), glutamate synthase (GLS), glutamate dehydrogenase (GDH), peroxidase (POD), catalase (CAT), and soluble protein from Cobb-Douglas production function. This model had high prediction accuracy, and it could simplify the measurement of biomass. During the artificial cultivation of S.miltiorrhiza, we can monitor the biomass accumulation by scaling the key physiological/biochemical indicators in the leaves. Interestingly, the coefficients of Lasso regression during our analysis were consistent with the mechanism of growth-defense tradeoff. Perhaps, the key physiological/biochemical indicators obtained in the statistical analysis are related to the indicators affecting biomass accumulation in practice.