Stochastic Models of Viral Adsorption, Fusion and Replication

病毒感染并寄生于几乎所有的生物体。它们显著的传播倾向，它们适应不同宿主物种的能力，以及它们之间的交叉互补，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，如艾滋病毒或流感病毒，对病毒感染进行和繁殖的途径有一个清晰的了解是非常可取的，这样就可以设计出新的治疗方法。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受体的结合，研究病毒在健康细胞中的吸附。这些模型将使研究者能够探索不同受体-辅助受体组合的影响，这是实验上尚未解决的问题，这将是实验室实验人员和融合抑制剂药物进步的有用工具。(b)制定随机模型，研究未知的病毒脱壳机制，并考虑几种假设途径。将获得的结果与现有数据进行比较将有助于确定最可行的拆卸机制。(c)采用混合随机-确定性模型对耐药病毒株的出现进行建模，其中将丰富的物种视为确定性变量，将突变株视为随机变量。将确定有利于大量耐药种群的条件。数学建模常常在发展新范式和检验新假设方面取得重大进展。在这个研究项目中，旨在理解病毒动力学的新模型将被制定。这些模型将以生物物理学为基础，并与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。几个数值和分析子项目将形成，以强烈鼓励研究生和本科生在其职业生涯的不同层次的参与，教育和培训。

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.