Capsid Assembly Kinetics: A Nucleation-and-Elongation Rate-Equation Model

This is the 2D counterpart to the 3D viral capsid self-assembly simulator, built on a completely different computational core. Rather than placing individual capsomers on a real geodesic icosahedral lattice and running a per-site Monte-Carlo attach/detach rule, this model tracks the concentration of every possible intermediate size — from the first nucleus up to a fully closed shell — as a coupled system of ordinary differential equations, integrated live with 4th-order Runge-Kutta. The result reproduces the classic experimentally-observed signature of capsid assembly: a lag phase while nucleation slowly seeds the first few partial shells, followed by a sharp burst once those seeds start elongating, and a plateau as the free-subunit pool is exhausted. Total subunit mass is conserved exactly by the equations themselves — the stacked chart's total height never moves. Push the nucleation-rate slider far enough and you can watch a second, less intuitive phenomenon emerge directly from the same equations: too much nucleation competing for a fixed monomer supply collapses the final yield instead of improving it, the "kinetic trap" seen in real in-vitro capsid assembly experiments.