Stochastic Models of Viral Adsorption, Fusion and Replication

病毒感染并寄生在几乎所有的生物体内。它们显著的传播倾向、适应不同寄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物理和行为特征。由于病毒相关疾病的巨大影响，就像艾滋病毒或流感病毒的情况一样，非常希望清楚地了解病毒感染是如何发展和蓬勃发展的，以便能够设计出新的治疗方法。该项目的目标是开发数学模型，结合实验已知的事实或未解决的问题，了解病毒感染的一些基本步骤。通过使用数值和分析工具，本研究的目的是：(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，研究病毒在健康细胞中的吸附。这些模型将允许研究人员探索不同受体-辅受体组合的影响，这在实验上尚未解决，这将是实验者和融合抑制药物进展的有用工具。(B)建立随机模型，研究病毒脱壳的未知机制，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)利用随机-确定性混合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。将确定有利于大量抗药性人口的条件。数学建模通常在开发新范式和检验新假设方面取得重大进展。在这项研究项目中，将制定旨在了解病毒动力学的新模型。这些模型将以生物物理学为基础，并与实验室实验员密切合作开发，以充分利用纳米级的最新进展，并为工作假说提供建议和廉价的测试。将形成几个数值和分析子项目，以大力鼓励不同职业水平的研究生和本科生的参与、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.