Mathematical Modeling And Dynamic Analysis Of HIV-1 Gag Transport,Polymerization And Assembly

The human immunodeficiency virus(HIV-1)is a retrovirus that causes the acquired immunodeficiency syndrome(AIDS),an infectious disease with high annual mortality.Gag,as the major structural protein of HIV-1,is necessary for the assembly of the HIV-1 sphere shell.An in-depth understanding of its trafficking,polymerization and assembly is important for gaining further insights into the mechanisms of HIV-1 replication and the design of antiviral drugs.In this dissertation,we establish three mathematical mod-els,including HIV-1 Gag transport and polymerization,HIV-1 like particles assembly in vitro,and HIV-1 immature capsids assembly in vivo.The details are as follows:(1)We develop a mathematical model to simulate two biophysical processes,specif-ically Gag monomer and dimer transport in the cytoplasm and the polymerization of monomers to form a hexamer underneath the plasma membrane.Using experimental data,an optimization approach is utilized to identify the model parameters,and the identifiability and sensitivity of these parameters are then analyzed,respectively.Based on our model,we analyze the weight of the pathways involved in the polymerization reactions and conclude that the predominant pathways for the formation of a hexamer might be the polymerization of two monomers to form a dimer,the polymerization of a dimer and a monomer to form a trimer,and the polymerization of two trimers to form a hexamer.We then deduce that the dimer and trimer intermediates might be crucial in hexamer formation.We also explore four theoretical combined methods for Gag suppression,and hypothesize that the N-terminal glycine residue of the MA domain of Gag might be a promising drug target.(2)In vitro,the recombinant HIV-1 Gag protein can generate a spherical particle with a diameter of 25-30 nm in a fully defined system.It has?79 building blocks,and its intermediates for assembly are abundant in geometry.Accordingly,there are a large number of nonlinear equations in the classical model.Therefore,it is difficult to compute values of geometry parameters for intermediates and make the mathematical analysis using the model.We develop a new model of HIV-1 like particles(HLPs)assembly in vitro by using six-fold symmetry of the HLP assembly to decrease the number of geometry parameters.This method will greatly reduce computational costs and facilitate the application of the model.Then,we prove the existence and uniqueness of the positive equilibrium solution for this model with 79 nonlinear equations.Based on this model,we obtain the interesting result that concentrations of all intermediates at equilibrium are independent of three important parameters,including two microscopic on-rate constants and the size of nucleating structure.Before equilibrium,these three parameters can influence the concentration variation rates of all intermediates.We also analyze the relationship between the initial concentration of building blocks and concentrations of all intermediates.Furthermore,the bounds of concentrations of free building blocks and HLPs are estimated,respectively.(3)In vivo,HIV-1 immature capsids(HICs)assembly is an essential step of HIV-1 lifecycle.A HIC is composed of?420 hexameric building blocks.Typically 5-6 min is required to complete the assembly of a single HIC.Lots of building blocks and its rapid assembly impede the full understanding of HICs assembly.Assuming that one free building block is aggregated to an intermediate every time,we develop a full model with 420 nonlinear equations and 840 geometry parameters.Because there are too many nonlinear equations in this full model and the stiffness of these equations is relatively strong,we fail to identify the values of parameters.Then,we take the following facts into consider,including six-fold symmetry of the HIC,the hexamer building blocks,and average?30 building blocks on the lips of intermediates.We assume that every time six free building blocks are aggregated to an intermediate simultaneously.Then,we obtain a reduced model with 70 equations and 140 geometry parameters.In the proofs of theorem,we transform a non-monotonic polynomial function to a strictly monotone increasing function by changing the highest-order term with the only positive coefficient to a constant.Then we use this strategy to prove the existence and uniqueness of the positive equilibrium point.Furthermore,we conclude that it might be not an effective way to decrease the concentration of HICs at equilibrium by decreasing the microscopic on-rate constants.Based on the experiment data,we estimate that it might take?6 hours to reach the equilibrium state for HICs assembly.We also estimate that the nucleating structure might be composed of seven building blocks,which is very small in relation to the HIC with 420 building blocks.This characteristic might explain that free building blocks hardly polymerize into the higher order polymer until the concentration of building blocks reaches the threshold value.This characteristic also ensures the sufficient free building blocks before the elongation process,and these sufficient free building blocks facilitate the high efficiency of the assembly in the elongation process.Compared with the previous virus assembly models in vitro,HICs assembly model in vivo is more conducive to the development of clinical drugs.