Kinetic-thermodynamic effects accompanying model protein-like aggregation: The wave-like limit and beyond it

A fairly idealized, mainly spheroid-type (dis)ordered aggregation of proteins is considered. The consideration is basically given in terms of the nonequilibrium thermodynamics at a mesoscopic level, quite commonly abbreviated by MNET (mesoscopic nonequilibrium thermodynamics). The mesoscopic level of description offered is supplemented by some involvement of certain important microscale dynamic sub-effects, mostly the ones characteristic of growth-layer dynamics (towards non-Kossel crystal formation) and/or fibril formation within the growing object (towards spherulitic growth). It is argued that the kinetic part of the overall kinetic-thermodynamic description proposed is due to the memory effects originating from a deeper penetration of the time scale also involved in MNET. The thermodynamic part, in turn, is closely related with the Boltzmann-type free energy available for the protein-like aggregation, constituting the Kramers' barrier, that appears to be primarily dependent upon the curvature impact on the growing object, although one is able to diversify the description, depending whether the (un)constrained aggregation is assumed to occur on one nucleation seed or appears to take place on many of them. In both cases, the Smoluchowski-type equation, revealing the aggregation dynamics in a phase space, governs the overall spheroid-type formation, exemplified throughout the paper's body mainly by some lysozyme (poly)crystalline aggregates. The natural wave-like limit characteristic of ballistic growth is pointed out. A behavior of the system outside the limit is also discussed, and the morphological phase diagram of the nucleation-growth phase transformation is addressed in a sketchy way.