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.
