The kinetics of homogeneous and two‐step nucleation during protein crystal growth from solution

Abstract

Many experimental reports for the kinetics of crystal nucleation and growth, from an isothermal solution, point to a sigmoidal‐like behavior for the process. Here we consider three different nucleation models from the literature and show that all lead to sigmoidal or sigmoidal‐like behavior for the kinetics of nucleation. A two‐step nucleation process is known to occur within certain supersaturated protein solutions, and it is demonstrated in this report how the sigmoidal law yields kinetic information for the two‐step and homogeneous nucleation modes. We propose here that two‐step solute‐rich associates form in the solution around seed nuclei that are already present at or near the point in time when the solution is prepared. Using this hypothesis, we are able to model the time‐dependent volume of the two‐step phase per unit volume of solution and show that this compares well with reported experimental data. A kinetic model is given for the proposed process, which leads to a sigmoidal rate law. Additionally, a relation between the initial and final nuclei densities and the induction time is derived. As a result of this study, the conclusion is that two‐step activity increases with increasing initial supersaturation or increasing salt concentration.

Size Evolution and Composition of the Intermediate Phase During Nonclassical Protein Crystal Growth from Solution

“…where K is a constant which includes a shape factor. An essential part of the proposed propagation mechanism is for the associate seed nuclei density n to be given as [8] n…”

Size Evolution and Composition of the Intermediate Phase During Nonclassical Protein Crystal Growth from Solution

“…The associate propagation mechanism suggested in Ref. [8] is used again here. There is an initial seed density of n 1 upon which associates form.…”

“…where K is a constant which includes a shape factor. An essential part of the proposed propagation mechanism is for the associate seed nuclei density n to be given as [8]…”

“…The parameter k was estimated recently in Ref. [8] for the growth run studied here. n o and n 1 are estimated using the dimensional scale on the video included with the supplemental information for Ref.…”

“…It was further hypothesized in Ref. [8] that these early stage associates do not go on to form crystals themselves but are consumed by crystals growing in the solution formed upon homogeneous nuclei. There is significant experimental evidence for solute rich associates of an intermediate phase, during lysozyme crystal growth, being consumed by nearby growing crystals [3,10,11] Reported X-ray diffraction data [2], for a case of isothermal β-lactoglobulin (BLG) crystal growth, indicating the presence of the intermediate phase, leads us to propose here that the intermediate phase is actually composed of two distinct parts, a low density and high density phase.…”