Coulomb instability of multicharged proteins

We studied the energetics and fragmentation patterns of multicharged (A⁺)_n Morse clusters (n = 55-321), with a total cluster charge Z = n. The Morse pair-potential parameters were characterized by the dissociation energy D = 1-10 eV, range parameter α = 1-3 Å^-1, and interatomic equilibrium separation R_e = 1-3 Å. The potential energies ε (per particle) of these multicharged Morse clusters at their equilibrium configuration (with bond length r ₀) were analyzed in terms of the liquid drop model. This resulted in the relation ε =(ā_C⁰/r₀)n ^2/3+(ā_v⁰D/αr₀) +[ā_s⁰D/(αr₀)^3/2]n ^-1/3, where the reduced parameters ā_C⁰ (for the Coulomb energy), ā_v⁰ (for the interior energy) and ā_s⁰ (for the surface energy) are independent of the Morse pair-potential parameters. The Rayleigh fissibility parameter X = E(Coulomb)/2E(surface), which determines the fragmentation pattern (i.e., X < 1 for cluster fission and X > 1 for Coulomb explosion), was expressed in the form X=(Z²/n)[(2ā_s ⁰/ā_C⁰)(D/α^3/2r ₀^1/2)]^-1. The application of this result to the Coulomb instability of multicharged globular proteins reveals that X < 1 for the currently available data. The dominating fragmentation channel is expected to involve spatially anisotropic protein fission into a small number of large fragments, rather than spatially isotropic protein Coulomb explosion into a large number of small fragments.