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

人类活动正在改变流入地球生态系统的养分供应。最近的一项研究表明，营养供应极大地改变了大麦黄矮病毒和谷物黄矮病毒两种植物病毒的流行率和相互作用强度。由于病毒劫持宿主细胞机制进行复制，这需要氮和磷来合成核酸和蛋白质，如果氮和磷的含量更高，人们会期望看到更多的病毒复制。通过研究和理解关键营养素与疾病动态之间的复杂关系，我们可以帮助规划和建议未来的农业实践。该项目还将为本科生和研究生提供研究和教学环境的机会；研究生的跨学科培训和专业发展；并将我们的研究成果广泛传播给数学家、建模师、生态学家和生物医学研究人员。我们的努力将为不同民族/种族背景的本科生和研究生提供跨学科交流和探索的第一手教育经验。所有的细胞都是由化学元素构成的。生态化学计量学（ES）是研究生态相互作用中化学元素平衡的学科。人们发现，ES和进化论是观察和理解微生物种群和群落动态的关键透镜。ES涵盖了多个生物尺度，它允许基于细胞营养水平构建健壮的、机械的和预测的数学模型。在这一理论中，能量和多种化学元素（特别是碳、氮和磷）在生物和环境之间的利用占据了中心位置。然而，ES框架尚未有效地整合到宿主-病原体相互作用的建模中。该项目旨在确定一些关键的生物机制与在模拟宿主（植物）-病原体模型中观察到的丰富动态之间的关系，这些模型包括宿主和病原体种群的营养质量和数量。这些关系可能为更好地控制植物病害提供新的见解。具体来说，我们将构建基于经验发现的宿主-病原体相互作用的数学模型。研究小组将研究的模型在数学和计算上都是新颖的，因为它们将激发非线性微分方程和延迟微分方程的定性和计算研究领域的挑战性问题。

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.