Munoz-Alicea, Roberto, authorLiu, Jiangguo, advisorTavener, Simon, advisorChen, Chaoping, committee memberMueller, Jennifer, committee memberShipman, Patrick, committee member2007-01-032007-01-032013http://hdl.handle.net/10217/80960AIDS (acquired immune deficiency syndrome) is an infectious disease that takes away many people's lives each year. Group-specific antigen (Gag) polyprotein precursor is the major structural component of HIV, the causing agent of AIDS. Gag is essential and sufficient for the formation of new HIV virus-like particles. The late stages of the HIV-1 life cycle include the transport of Gag proteins towards the cell membrane, the oligomerization of Gag near the cell membrane during the budding process, and core assembly during virion maturation. The mechanisms for Gag protein trafficking and assembly are not yet fully understood. In order to gain further insight into the mechanisms of HIV-1 replication, we develop and analyze mathematical models and numerical algorithms for intracellular Gag protein trafficking, Gag trimerization near the cell membrane, and HIV-1 core assembly. Our preliminary results indicate that active transport plays an important role for Gag trafficking in the cytoplasm. This process can be mathematically modeled by convection-diffusion equations, which can be solved efficiently using characteristic finite element methods. We employ differential dynamical systems to model Gag trimerization and HIV-1 core assembly. For the Gag trimerization model, we estimate relationships between the association and dissociation parameters as well as the Gag arrival and multimerization parameters. We also find expressions for the equilibrium concentrations of the monomer and trimer species, and show that the equilibrium is asymptotically stable. For HIV-1 core assembly, we first consider a model developed by Zlonick and others, which regards assembly as a polymerization reaction. We utilize theoretical and numerical tools to confirm the stability of the equilibrium of CA intermediates. In addition, we propose a cascaded dynamical system model for HIV-1 core assembly. The model consists of two subsystems: one subsystem for nucleation and one for elongation. We perform simulations on the nucleation model, which suggests the existence of an equilibrium of the CA species.born digitaldoctoral dissertationsengCopyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright.viral assemblycapsidconvectiondiffusionequilibriumfinite elementsGagHIVmicrotubulestransporttrimerizationText