Mathematical Model Equations of Biochemical Reaction in Tomato Plants Defense Mechanism

Abstract

The advancement in technology and smart Agriculture, is a multifaceted tussle involving the use of technology and scientific investment in strategies of improving production for commercial benefit and also to combat food security. Mathematicians are not left behind, but equally involved in theoretical analysis using modeling. Practical laboratory experiments and actual experimental procedures, measurements and continued modification of genetic materials, are expensive, time consuming and delicate endeavors that can be complimented if not supplemented by mathematical modeling and simulation, which is gaining prominence due to shorter simulation time, accuracy and ability to incorporate multiple parameters and variables. In this research study, biochemical reaction in plants as a defensive mechanism, is studied. The objective was to formulate a mathematical model describing defense mechanism biochemical reactions This was achieved by modeling enzyme-substrate transduction pathways, and forming differential equations using Michaelis-Menten Kinetic Reaction scheme. This research found a system of eight linear ordinary differential equations which describes fully the reaction fronts involved in plant defense mechanism induced by Potassium Phosphite elicitor. Model equations were formulated using differential equations, and simulation using SIMBIOLOGY showed that the use of Potassium Phosphite elicitor induced a chain of complex reactions of enzymes and substrates to produce defense mechanism compounds; viz pathogenic related proteins, phytoalexins, and defense genes which inhibited pathogenic attack, restrained fungal spread and reduced susceptibility of plant to viral and bacterial diseases. Simulated results showed that tolerance to Bacterial, Fungal and Viral infection was seen to be significantly high in treated plants as compared to untreated plants. Treated tomato plants were less susceptible to insect herbivory and infection, with susceptibility rate of, as compared to untreated plants susceptible at. It was also found that the yield of treated plants increased by, as compared to untreated healthy crops. Reduced susceptibility, less fungal infection, and reduced herbivory collectively indicate improved tolerance of treated plants, and consequent increase in yield. This is a contribution of mathematical modeling to mitigating food security challenge.