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 Re = 1–3 Å. The potential energies ɛ (per particle) of these multicharged Morse clusters at their equilibrium configuration (with bond length r0) were analyzed in terms of the liquid drop model. This resulted in the relation ε=(a¯C0/r0)n2/3+(a¯v0D/αr0)+[a¯s0D/(αr0)3/2]n−1/3, where the reduced parameters a¯C0 (for the Coulomb energy), a¯v0 (for the interior energy) and a¯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)[(2a¯s0/a¯C0)(D/α3/2r01/2)]−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.