Observing classical nucleation theory at work by monitoring phase transitions with molecular precision

Abstract

It is widely accepted that many phase transitions do not follow nucleation pathways as envisaged by the classical nucleation theory. Many substances can traverse intermediate states before arriving at the stable phase. The apparent ubiquity of multi-step nucleation has made the inverse question relevant: does multistep nucleation always dominate single-step pathways? Here we provide an explicit example of the classical nucleation mechanism for a system known to exhibit the characteristics of multi-step nucleation. Molecular resolution atomic force microscopy imaging of the two-dimensional nucleation of the protein glucose isomerase demonstrates that the interior of subcritical clusters is in the same state as the crystalline bulk phase. Our data show that despite having all the characteristics typically associated with rich phase behaviour, glucose isomerase 2D crystals are formed classically. These observations illustrate the resurfacing importance of the classical nucleation theory by re-validating some of the key assumptions that have been recently questioned.

Figure 1. Glucose isomerase 2D crystals on muscovite as a function of [MgCl₂].

(a) 0 mM, no adsorption, (b) 20 mM, at random adsorption of glucose isomerase, (c) 50 mM, phase separation into a mobile diffusive layer and two-dimensional protein crystals, (d) 500 mM even at 30 mg ml⁻¹, the crystals do not grow in the vertical direction, (e) 2D crystallization using freshly cleaved phlogopite as a substrate.

Figure 2. Range of crystallographic defects.

(a) Twin boundaries within a single cluster (dashed lines) and a vacancy (arrow), (b) zoom-in of twin boundaries within a single cluster, (c) grain boundaries at the interfaces of independently nucleated clusters (white arrows) and (d) plastic crystal phase. The bulk composition was 10 mM Hepes pH 7.0, 50 mM MgCl₂ (a–c) and 500 mM MgCl₂ (d) with 0.05 mg ml⁻¹ (a,b) and 0.1 mg ml⁻¹ (c,d) glucose isomerase.

Figure 3. Reversible 2D crystallization as a function of [NaCl].

(a) At 10 mM NaCl, 2D crystals are readily formed, which after washing with 25 mM NaCl (b) fully redissolve to nucleate anew (c) when the [NaCl] is lowered again to 10 mM. Note that the number density of clusters is lower (compared with a) due to the shorter delay time between sample injection and the onset of imaging. The bulk composition was 0.05 mg ml⁻¹, 10 mM Hepes pH 7.0, 50 mM MgCl₂ and 10 mM and 25 mM NaCl.

Figure 4. Snapshots of individual clusters ranging in size from 1 to >50 molecules.

Remarkably, even the smallest clusters exhibit a highly ordered state commensurable with the lattice of larger sized clusters. However, the local symmetry is not perfect. Note for example the monomer on the left side of the pentameric cluster (black circle): it is out of registry with the lattice defined by the four other molecules (white circles). This displacement is not at random as it coincides with the lattice displacement corresponding to the twin boundaries (to illustrate this, the pattern is overlaid onto the largest sized cluster in the lower right panel). From Fig. 5, we estimate the critical size to be ~20 molecules. Circles in the panels of the upper row (1≤N≤10) represent tentative molecular assignments and only serve as a guide for the eye (consult Supplementary Fig. 7 to see more snapshots). Scale bar, 20 nm.

Figure 5. Real-time imaging of the nucleation and growth of 2D glucose isomerase crystals with molecular resolution.

The mica surface was initially exposed to a high [NaCl] solution (condition of middle panel of Fig. 3) to wet the surface without inducing nucleation. The AFM liquid cell was subsequently flushed with 0.01 mg ml⁻¹, 10 mM Hepes pH 7.0, 10 mM NaCl and 50 mM MgCl₂ to trigger crystal formation (t=0, scan direction for all images upwards). Crystalline clusters rapidly emerge with sizes ranging from 4 to ~40 molecules. Cross-correlating successive images reveal that smaller clusters (III and IV) have a predisposition to shrink or dissolve completely, whereas larger clusters (I and II) tend to amass monomers, notwithstanding temporal fluctuations. This is in accordance with one of the core concepts of classical nucleation, that is, the existence of a critical size that subdivides clusters in groups of either sub- or supercritical. More importantly, it suggests the presence of a local maximum in the cluster size dependence (the relevant order parameter) of the free energy. The presence of such an activation barrier demonstrates that the formation of the 2D crystalline phase occurs through nucleation and not by means of spinodal decomposition. Shortcuts across the nucleation barrier do occur by means of coalescence of independently formed subcritical clusters (black arrows), a pathway outside the scope of CNT.