Two-Step Crystal Nucleation Is Selected Because of a Lower Surface Free Energy Barrier

Abstract

Solution crystallization underpins a vast range of phenomena, from solidification of rocks in molten magma, through hardening of live tissues by the formation of biological minerals, to protein crystallization associated with a plethora of diseases. Recently, it was demonstrated that the nuclei of many important crystalline materials do not assemble directly in the solution but rather form in two steps. In the first step, disordered precursors arise, which in the second step host and enhance crystal nucleation. Here we address why two-step nucleation is preferred to direct nucleus assembly despite the low volume occupied by the precursor population. We demonstrate that nucleation of insulin crystals, which occurs with a highly regulated rate in mammalian pancreases as a part of insulin biosynthesis, is assisted by protein-rich clusters of radius 160−200 nm that occupy ca. 10 −6 to 10 −5 of the solution volume. We show that the surface free energy γ encountered by newly nucleated crystals is at least 10-fold lower than the independently determined surface free energy of the crystal−solution interface; the latter value dictates the barrier for direct crystal nucleation in the solution. This comparison indicates that two-step nucleation is faster than the direct pathway and is selected as a phase transformation route due to a lower surface free energy barrier and suggests that nucleation of crystals can be controlled by manipulating the properties of the disordered precursors. Article pubs.acs.org/crystal

Shear-Induced Crystallization and Rheological Analysis of a Therapeutic Protein

“…After this stage ( t > 40 min), the shear viscosity reaches a constant value, which is similar to what happens at low insulin concentrations (Figure ). Due to the high insulin concentration, many small crystals of variable size [Figure -(c)] or even clusters, possibly related to the additional nucleation events, are formed while still in the decreasing stage of the shear viscosity (Figure ).…”

“…After this stage (t > 40 min), the shear viscosity reaches a constant value, which is similar to what happens at low insulin concentrations (Figure 12). Due to the high insulin concentration, many small crystals of variable size [Figure 13-(c)] or even clusters, 44 possibly related to the additional nucleation events, 45 are formed while still in the decreasing stage of the shear viscosity (Figure 12). Low shear rates (20 and 100 s −1 ) are characterized by a random molecular distribution, which results in a consecutive increase of the shear viscosity over time at both high and low shear rates (Figure 14).…”

Understanding crystal nucleation mechanisms: where do we stand? General discussion

“…A possible explanation of why two-step nucleation hosted by a precursor with high solute concentration is preferred to direct nucleation in the dilute solution centers on the lower surface free energy between the nucleus and its environment during two-step nucleation. 36 For a more detailed discussion of nonclassical nucleation scenarios, see our recent review. 37…”

Controlling the π-Stack Growth Direction in Organic π-Conjugated Microcrystals

“…Recently, a two-step nucleation theory has been proposed as one way to explain crystallization that does not fit the criteria of classical nucleation theory. In the two-step nucleation theory, the formation of ordered crystalline nuclei is preceded by the formation of densified disordered clusters. , Evidence for this two-step nucleation theory has been seen in the growth of various organic crystals, including cyanine dyes, flufenamic acid, and perylene diimides . In each of these cases, the initial densification and further ordering were observed using either cryogenic or liquid phase electron microscopy.…”