Dynamics and Applications of Cell Quota Based Plant-Pathogen Interaction Models

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Human activities are altering the influx of nutrient supplies to Earth's ecosystems. A recent study reveals that nutrient supply dramatically changed the prevalence and interaction strength between two plant viruses, barley yellow dwarf virus and cereal yellow dwarf virus. Since viruses hijack host cell machinery to replicate which requires nitrogen and phosphorus to synthesis nucleic acids and proteins, given more amounts of nitrogen and phosphorus, one would expect to see higher numbers of virus replication. By studying and understanding the complex relationship between key nutrients and disease dynamics, we may help in planning and advising the future of agricultural practice. This project will also provide opportunities for undergraduates and graduate students in research and instructional environments; interdisciplinary training and professional development for graduate students; and broad dissemination of our results to a diverse range of mathematicians, modelers, ecologists and biomedical researchers. Our efforts will provide undergraduate and graduate students of diverse ethnic/racial backgrounds with first-hand educational experience in cross-disciplinary communication and exploration. All cells are made of chemical elements. Ecological stoichiometry (ES), is the study of the balance of chemical elements in ecological interactions. ES and the theory of evolution have been found to be crucial lenses through which one can view and understand the dynamics of populations and communities of microorganisms. ES covers multiple biological scales, and it allows the construction of robust, mechanistic, and predictive mathematical models based on cell nutrient levels. Within this theory, the utilization of energy and multiple chemical elements (especially carbon, nitrogen, and phosphorus) between organisms and their environment occupies a central position. However, the ES framework has yet to be effectively integrated into the modeling of host-pathogen interactions. This project seeks to identify the relationships of some key biological mechanisms to the rich dynamics often observed in simulating host (plant)-pathogen models incorporating nutrient quality and quantity in host and pathogen populations. These relationships may provide novel insights for better plant disease control. Specifically, we will construct mathematical models of host-pathogen interactions that are based on empirical discoveries. The models that the research team will investigate are novel both mathematically and computationally, as they will motivate challenging problems in areas of qualitative and computational studies of nonlinear differential equations and delay differential equations.