Stochastic Models of Viral Adsorption, Fusion and Replication

病毒感染并寄生于几乎所有的生物体。它们具有显著的传播倾向、适应不同宿主物种的能力以及相互之间的交叉互补，导致了各种各样的身体和行为特征。 由于病毒相关疾病的巨大影响，如在HIV或流感病毒的情况下，非常希望清楚地了解病毒感染进行和发展的途径，以便可以设计新的治疗方法。该项目的目标是开发数学模型，以了解病毒感染的一些基本步骤，与实验已知的事实或未解决的问题协同作用。通过使用数值和分析工具，本研究旨在：（a）通过考虑反应扩散方程来描述病毒与细胞表面扩散受体和辅助受体的结合，研究病毒吸附到健康细胞中。这些模型将允许研究人员探测不同的受体-辅助受体组合的影响，这是实验上未解决的，这将是一个有用的工具，为实验台和融合抑制剂药物的进步。(b)制定随机模型来研究病毒脱壳的未知机制，并考虑几个假设的途径。 所获得的结果和现有的数据之间的比较将有助于确定最可行的拆卸机制。(c)通过混合随机-确定性模型对耐药病毒株的出现进行建模，其中丰富的物种被视为确定性变量，突变株被视为随机变量。 将确定有利于大的耐药群体的条件。数学建模往往导致在开发新的范式和测试新的假设的重大进展。 在本研究项目中，将制定旨在了解病毒动力学的新模型。 这些模型将以生物制药为基础，并与实验室实验人员密切合作开发，以充分利用纳米级的最新进展，并为工作假设提供建议和非昂贵的测试。 几个数值和分析的子项目将形成强烈鼓励参与，教育和培训的研究生和本科生在他们的职业生涯的不同层次。

Viruses infect and parasitize almost all living organisms. Their remarkable proclivity for transmission, their ability to adapt to different host species and to cross-complement amongst themselves has lead to a wide variety of physical and behavioral features. Because of the tremendous effects of virus related diseases, as in the case of HIV or of the flu virus, it is extremely desirable to have a clear picture of the avenues along which viral infections proceed and thrive, so that novel therapies can be devised. The goal of this project is to develop mathematical models to understand some of the cardinal steps of viral infection, in synergy with experimentally known facts or unresolved issues. By using both numerical and analytical tools, this research aims to: (a) Study viral adsorption into healthy cells by considering reaction diffusion equations to describe binding of the virus to diffusing receptors and coreceptors at the cell surface. These models will allow the investigator to probe the effects of different receptor-coreceptor combinations, which is experimentally unresolved and which will be a useful tool for bench experimentalists and the advancement of fusion inhibitor drugs. (b) Formulate stochastic models to study the unknown mechanisms of viral uncoating and by considering several hypothetical pathways. A comparison between the results obtained and existing data will help determine the most viable disassembly mechanism. (c) Model the emergence of resistant viral strains by means of a hybrid stochastic-deterministic model where the abundant species are treated as deterministic variables and the mutant strains as stochastic ones. The conditions under which a large drug resistant population is favored will be determined. Mathematical modeling has often lead to significant progress in developing new paradigms and testing new hypothesis. In this research project, new models aimed at understanding viral dynamics will be formulated. These models will be biophysically based and developed in close collaboration with bench experimentalists to fully utilize recent advances at the nanoscale level and also to offer suggestions and non-expensive testing for working hypothesis. Several numerical and analytical subprojects will be shaped to strongly encourage the participation, education, and training of graduate and undergraduate students at different levels of their careers.