Abstract
A superdiffusive random-walk action in the depletion zone around a growing protein crystal is considered. It stands for a dynamic boundary condition of the growth process and competes steadily with a quasistatic, curvature-involving (thermodynamic) free boundary condition, both of them contributing to interpret the (mainly late-stage) growth process in terms of a prototype ion-channeling effect. An overall diffusion function contains quantitative signatures of both boundary conditions mentioned and indicates whether the new phase grows as an orderly phase or a converse scenario occurs. This situation can be treated in a quite versatile way both numerically and analytically, within a generalized Smoluchowski framework. This study can help in (1) elucidating some dynamic puzzles of a complex crystal formation vs biomolecular aggregation, also those concerning ion-channel formation, and (2) seeing how ion-channel-type dynamics of non-Markovian nature may set properly the pace of model (dis)ordered protein aggregation.