Modeling capsid kinetics assembly from the steady state distribution of multi-sizes aggregates

• Kinetics assembly from the steady state distribution of aggregates.
• Mean time to form a cluster.
• Modeling aggregation from diffusion.
• Computing the distribution of the largest aggregate.

The kinetics of aggregation for particles of various sizes depends on their diffusive arrival and fusion at a specific nucleation site. We present here a mean-field approximation and a stochastic jump model for aggregates at equilibrium. This approach is an alternative to the classical Smoluchowski equations that do not have a close form and are not solvable in general. We analyze these mean-field equations and obtain the kinetics of a cluster formation. Our approach provides a simplified theoretical framework to study the kinetics of viral capsid formation, such as HIV from the self-assembly of the structural proteins Gag.