Mathematical modeling for intracellular transport and binding of HIV-1 Gag proteins

• We present a mathematical model for intracellular trafficking and trimerization of HIV-1 Gag proteins.
• We prove the existence and stability of the steady state solution of this initial-boundary value problem.
• Combined the finite difference method with Newton–Raphson iterative method to solve this initial-boundary value problem.
• Results show the relations between the timing of the initial appearance of HIV-1 virions on the cell membrane and parameters.

This paper presents a modeling study for the intracellular trafficking and trimerization of the HIV-1 Gag proteins. A set of differential equations including initial and boundary conditions is used to characterize the transport, diffusion, association and dissociation of Gag monomers and trimers for the time period from the initial production of Gag protein monomers to the initial appearance of immature HIV-1 virions near the cell membrane (the time duration Ta). The existence and stability of the steady-state solution of the initial boundary value problems provide a quantitative characterization of the tendency and equilibrium of Gag protein movement. The numerical simulation results further demonstrate Gag trimerization near the cell membrane. Our calculations of Ta are in good agreement with published experimental data. Sensitivity analysis of Ta to the model parameters indicates that the timing of the initial appearance of HIV-1 virions on the cell membrane is affected by the diffusion and transport processes. These results provide important information and insight into the Gag protein transport and binding and HIV-1 virion formation.