Modeling HIV-1 viral capsid nucleation by dynamical systems

There are two stages generally recognized in the viral capsid assembly: nucleation and elongation. This paper focuses on the nucleation stage and develops mathematical models for HIV-1 viral capsid nucleation based on six-species dynamical systems. The Particle Swarm Optimization (PSO) algorithm is used for parameter fitting to estimate the association and dissociation rates from biological experiment data. Numerical simulations of capsid protein (CA) multimer concentrations demonstrate a good agreement with experimental data. Sensitivity and elasticity analysis of CA multimer concentrations with respect to the association and dissociation rates further reveals the importance of CA trimer-of- dimers in the nucleation stage of viral capsid self- assembly.