Role of clusters in nonclassical nucleation and growthof protein crystalsMike Sleutela,1 and Alexander E. S. Van Driesscheb,1

aStructural Biology Brussels, Flanders Interuniversity Institute for Biotechnology, and Vrije Universiteit Brussel, 1050 Elsene, Belgium; and bLaboratorio deEstudios Cristalograficos, Instituto Andaluz de Ciencias de la Tierra, Consejo Superior de Investigaciones Científicas and University of Granada, ParqueTecnológico Ciencias de la Salud, 18100 Armilla, Spain

Edited by Patricia M. Dove, Virginia Polytechnic Institute and State University, Blacksburg, VA, and approved December 18, 2013 (received for reviewMay 22, 2013)

The development of multistep nucleation theory has spurred onexperimentalists to find intermediate metastable states that arerelevant to the solidification pathway of the molecule underinterest. A great deal of studies focused on characterizing theso-called “precritical clusters” that may arise in the precipitationprocess. However, in macromolecular systems, the role that theseclusters might play in the nucleation process and in the secondstage of the precipitation process, i.e., growth, remains to a greatextent unknown. Therefore, using biological macromolecules asa model system, we have studied the mesoscopic intermediate,the solid end state, and the relationship that exists between them.We present experimental evidence that these clusters are liquid-like and stable with respect to the parent liquid and metastablecompared with the emerging crystalline phase. The presence ofthese clusters in the bulk liquid is associated with a nonclassicalmechanism of crystal growth and can trigger a self-purifying cas-cade of impurity-poisoned crystal surfaces. These observationsdemonstrate that there exists a nontrivial connection betweenthe growth of the macroscopic crystalline phase and the meso-scopic intermediate which should not be ignored. On the otherhand, our experimental data also show that clusters existing inprotein solutions can significantly increase the nucleation rateand therefore play a relevant role in the nucleation process.

prenucleation clusters | phase transition | self-purification

The process of crystallization is generally considered to occurin two consecutive but very different stages: nucleation and

growth. The first stage was already studied more than two cen-turies ago by Gibbs, who considered the nucleation of waterdroplets from a supersaturated vapor through the formation ofglobulae. He was the first to develop a thermodynamic formal-ism of nucleation by considering the generation of nuclei ofa liquid phase as a density fluctuation of the parent phase (1, 2).Since then, Gibbs’ nucleation theory has been extended to thenucleation of solid phases from solution and gaseous phasesfrom which the current paradigm (based on the capillary ap-proximation) for nucleation emerged, i.e., the classical nucle-ation theory [CNT (3–8)]. There is, however, an increasing bodyof evidence that shows that CNT can fail drastically when used incases where the implicit and explicit assumptions of CNT arepoorly justified (for a full dissection of the limitations, see refs.9–11). An obvious situation where CNT will have limited ap-plicability is in cases where the old and the new phases differ byat least two order parameters, e.g., density and structure (12).Recent theoretical, computational, and experimental efforts

have demonstrated that densification and local increase incrystallinity need not occur simultaneously (13–20). These resultshave inspired the development of a new approach that considersnucleation from solution as a multistep process attributing keyroles to metastable intermediate states, coined “multistep nu-cleation theory” (MNT). Although initially conceived for pro-teins by ten Wolde and Frenkel to describe nucleation close tothe critical point, the operational range of MNT was later ex-panded to also include regions in the phase diagram close to the

liquid–liquid binodal––the rationale being that macroscopicdroplets are formed that are enriched in protein, in which (dueto the reduced surface tension) crystal nucleation is greatly fa-cilitated. Even later, the discovery of long-lived mesoscopicclusters (105–106 monomers) in regions of the phase diagramdistant of both the critical point and the liquid–liquid binodalmakes it tantalizing to conclude that MNT may also dominatethese regions of phase space. These clusters, which exist in bothsuper- and undersaturated protein solutions, are hypothesized tobe precursors of nuclei of crystals, irrespective of the vicinity ofthe critical point in the phase diagram.However, contrary to what is sometimes suggested, no direct

experimental evidence has been presented that demonstratesthat these clusters are in fact prenucleation clusters taking part ina multistep nucleation scenario (9, 21). The occurrence of crys-tals within macroscopic dense protein droplets formed by liquid–liquid phase separation is an often-cited pro-MNT argument forprotein crystallization. However, for the specific proteins forwhich it has been observed, liq–liq phase separation is certainlynot a prerequisite for crystal nucleation––for these systems, thereare numerous observations of nucleation well above the liq–liqbinodal curve. Secondly, such qualitative observations give noinformation on the relative rates of the possible CNT and MNTcrystallization routes. Subsequently, no obvious relevance to anyMNT pathways can be attributed. Ultimately, these issues needto be addressed if the MNT concept is to be elevated from aninteresting, albeit academic exercise to a fully developed modelof wide applicability. As such, to date, MNT remains a plausibletheory, but a theory nonetheless.Notwithstanding the undeniable advances discussed above,

many questions specific to protein condensation remain open.Do nuclei form within the mesoscopic protein clusters or are

Significance

Intermediate metastable states are believed to be vital in theprocess of nucleation of crystalline material from solution. Ourexperimental evidence shows such intermediates can be liquid-like clusters that are stable with respect to the parent liquidand metastable compared with the emerging crystalline phase.Under given conditions, these clusters can contribute activelyto the nucleation process, and hence, at least in the case for theproteins tested, partake in a two-step nucleation process.Moreover, upon merging with the crystal lattice, these clusterslead to a nonclassical mechanism of crystal growth that triggersa self-purifying cascade of impurity poisoned crystal surfaces.

Author contributions: M.S. and A.E.S.V.D. designed research, performed research, ana-lyzed data, and wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.1To whom correspondence may be addressed. E-mail: Mike.Sleutel@vub.ac.be or sander@lec.csic.es.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1309320111/-/DCSupplemental.

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these clusters (merely) involved in a heterogeneous nucleationpathway? Or, even more boldly, are they at all involved in thenucleation process or is cluster formation simply a dead end inthe many conceivable pathways toward the crystalline state? Inthis contribution, we aim to start formulating answers to suchquestions using a number of different protein model systems. Webegin by characterizing the protein clusters in liquid as well asthe crystal–cluster interaction using both conventional and newermethods, i.e., static–dynamic light scattering, brownian micros-copy (BM), and laser confocal microscopy enhanced by differ-ential interference contrast. By combining both approaches wedemonstrate that the cluster presence in solution is directly cor-related to a well-known growth mechanism, i.e., instantaneousmultilayer formation. Secondly, we show that cluster removal fromthe bulk liquid can have a drastic effect on nucleation kinetics,demonstrating that these clusters might be a preferred in-termediate in protein crystallization––a strong argument in favorof MNT-like scenarios. Thirdly, and quite surprisingly, we revealthat cluster assimilation by the crystal can trigger a self-purifyingcascade of impurity-poisoned crystal surfaces. Stated differently,the coalescence of a cluster with an impurity-poisoned crystalsurface can lead to a rapid and complete cleansing of the entiresurface. From these observations we conclude that protein clusterscan have a strong positive impact on protein crystallization duringboth the nucleation as well as the growth stage.

Results and DiscussionNonclassical Crystal Growth Induced by Protein Clusters. The twoclassical mechanisms of layer generation during crystal growthfrom solution are spiral dislocations and 2D nucleation. In someworks, the spontaneous formation of closed looped macrosteps(also referred to as multilayer stacks or 3D islands) has beenreported as the dominating source of steps on dislocation-freesurfaces (22, 23). Here we aim to expand on the existing base ofobservations by actively searching for looped macrostep forma-tion on a number of different protein crystallization systems. Weuse the noninvasive laser confocal differential intereferencecontrast microscopy (LCM-DIM) technique, which, given itsmesoscopic field-of-view and relatively fast acquisition time, isideally suited for mapping the temporal dependence of thecrystal-wide topography of the selected surfaces. All of the sys-tems studied in this work (glucose isomerase, proteinase K, hu-man recombinant insulin, hen egg white lysozyme, xylanase,triosephosphate isomerase, and RNAseIIIA) displayed loopedmacrostep nucleation when pregrown seed crystals were exposedto supersaturated growth solutions (Fig. 1). Additional confocalimages of looped macrosteps and a time-lapse movie capturingthe actual genesis of these features can be found in SI Appendix,Fig. S1 and Movie S1. These looped macrosteps are differentfrom other macrostepped features observed on protein crystals

in that they are not the result of a complex growth mechanism[arising from, e.g., step bunching due to diffusion field overlap,solutal flow, Schwoebel effect, impurities, repeated 2D nucle-ation (24)] but rather nucleate seemingly unprompted enclosinga single elevated area on the surface. Subsequent lateral growththen yields an expanding mound that contains a considerableamount of steps (ranging from 2 to >100). This mechanism oflayer generation has also been observed for other proteins[STMV, thaumatin, canavalin, catalase, lumazine synthase (25–30)] as well as inorganic [e.g., gypsum, epitaxy of rodochrosite oncalcite (31, 32)] systems.Two different models have been postulated to account for the

quasi-instantaneous formation of multilayer stacks: the micro-crystal-sedimentation scenario (28, 33) and the cluster-assimila-tion scenario (34, 35). In brief, the former model assumescoincidental sedimentation of freshly bulk-nucleated micro-crystals in an at-random orientation onto the macrocrystal, fol-lowed by a rapid reorientation to align with the underlying latticeleading to a flawless merging of both phases (36). This modelfails to account for the following observation: looped macrostepscan form at very low supersaturation where the bulk 3D nucle-ation rate is effectively zero (this work and ref. 35). Although thelink between the presence of mesoscopic clusters in solution andthe de novo formation of looped macrosteps has certainly beensuggested (34, 35), no experimental proof is available thatdemonstrates causality between both observations.To establish a clear connection between protein clusters and

looped macrosteps, we monitored the (011) face of orthorhom-bic glucose isomerase crystals using LCM-DIM growing fromsolutions with and without mesoscopic protein clusters (see SIAppendix for details). When exposed to glucose isomerase sol-utions containing clusters, the (011) face displays instantaneouslooped macrostep formation irrespective of the supersatura-tion (no critical supersaturation was detected; example given inFig. 2A). However, growth solutions from which cluster con-centrations have been drastically lowered through rigorous fil-tration (three times with 0.2-μm cutoff; SI Appendix, Fig. S2) donot trigger the 3D growth mechanism (Fig. 2B). Secondly, thereis a strong correlation between the temporal dependence of thecluster number density and the nucleation rate of looped mac-rosteps (Fig. 2 C and D): Cluster number densities drop by oneorder of magnitude within approximately 1 h after sample prep-aration when monitored using BM (cluster instability is not in-duced by the BM observation; SI Appendix, Fig. S2). A similarresult is obtained for the nucleation rate Jclust of multilayer islands:we observe an initial burst of 104 m−2s−1 for the initial 5 h aftersample preparation, followed by zero events in the following 14 h.These observations demonstrate conclusively that 3D nucleationcan be prompted by the merging of the mesoscopic clusters withthe macroscopic crystals.

Fig. 1. Occurrence of looped macrosteps on the (011) face of orthorhombic glucose isomerase (A), tetragonal proteinase K (B), (100) face of rhombohedralinsulin (C), (110) face of tetragonal lysozyme (D), (011) face of orthorhombic xylanase (E), (011) face of trigonal triosephosphate isomerase (F), and (100) faceof trigonal RNAseIIIA (G).

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Long-Lived (Meta)stable Liquid-Like Protein Clusters. Given theirimpact on crystal growth and their suggested role in multistepnucleation, we proceeded by characterizing these clusters. Tomake an estimate of the cluster lifetime, we monitored super-saturated glucose isomerase solutions using BM (Movie S2).Tracked particles can disappear from the field-of-view by either(i) dissolution or (ii) diffusing outside of the focal plane––thistechnique cannot discern between both possibilities, and lifetimeestimates therefore represent lower limits. Based on tracking ofindividual particles, we conclude that the minimal cluster life-time is on the order of 10–20 s, which is comparable to the es-timated lifetime of lumazine synthase clusters (37) and threeorders of magnitude larger than the lower bound lysozymecluster lifetime of 15 ms based on dynamic light scattering (38).When freshly diluted stock solutions were monitored using

BM and dynamic light scattering (DLS), we found that clusternumber densities (and mean cluster size) drop monotonically asa function of time, approaching a nonzero value at larger time-scales (>24 h) (Fig. 2). Interestingly, the newly reached numberdensity is proportional to the bulk monomer concentration,demonstrating that the clusters are in equilibrium with the bulkliquid and that, given the slow relaxation of the system, kineticsof cluster dissolution is governed by a significant activationbarrier. This is a key difference with clusters discussed in otherworks which are reported to be metastable with respect to theliquid. If we reverse the experiment and start from cluster-free(i.e., filtered) solutions, we find that cluster reappearance isappreciably slower than cluster dissolution. The kinetics of clus-ter formation is however different from cluster dissolution: nu-cleation of these mesoscopic intermediates is only triggered whena critical monomer concentration is reached (e.g., a mg·mL−1

glucose isomerase solution did not yield any detectable clusterswithin a 72-h time frame, whereas in a dissolution experiment thediluted cluster-containing solution equilibrated after 12 h). Fo-cusing on the relationship between the clusters and the solid state,we conclude that the clusters are metastable with respect to thecrystalline phase. This is inferred from the homoepitaxial mergingof the clusters with the macroscopic crystal which would not occurwithout a decrease in free energy.Are these clusters of microcrystalline nature, or rather amor-

phous solid aggregates, or do they still have a liquid character?To answer this question we put forth two observations: (i) wehave witnessed the nucleation of multilayered islands on preex-isting macrosteps traversing the surface (Fig. 3A). The charac-

teristic interstep distance in these macrosteps [30–60 nm (39)] issignificantly smaller than the mean cluster diameter (250 ± 50nm). Incorporation of a solid amorphous cluster or a microcrys-tal on a sloped surface would not lead to a perfect merging ofboth phases (40), which contradicts numerous observations madein this work; (ii) on many occasions, we detected microcrystals thatsedimented on a single macrocrystal (Fig. 3C) and time-lapse

Fig. 2. (A) Exposing the crystal to a fresh and unfiltered solution immediately (i.e., within the dead time of collecting a confocal image) leads to loopedmacrostep formation (white arrows). (B) Filtration of a freshly prepared mother liquor before sample washing completely abolishes the nucleation rate ofmultileveled 2D islands (zero events on four different crystals during an 18-h observation time) on orthorhombic glucose isomerase crystals. (C) Temporaldependence of the number density of scattering objects in supersaturated glucose isomerase solutions. (Insets) Negative stills of BM time-lapse imaging fromwhich number densities were determined. (D) Temporal evolution of the particle size distribution reveals a decrease in particle concentration by one order ofmagnitude 6 h after sample preparation. (E) Temporal evolution of the normalized intensity correlation functions of a supersaturated glucose isomerasesolution: the disappearance of the shoulder at longer timescales corresponds to the decrease in the number density of mesoscopic clusters. (Inset) Temporaldependence of the inverse decay rate Γ−1 of the clusters suggests a decrease in characteristic size during cluster decay.

Fig. 3. Confocal observations that contradict with the microcrystal sedi-mentation–incorporation scenario. (A and B) Nucleation and growth ofa multistepped island on a macrostep leading to the formation of a loopedmacrostep on the (011) face of glucose isomerase; white arrow points to thenucleation event of a looped macrostep. (C and D) Simultaneous occurrenceof sedimented microcrystals and looped macrosteps on the (110) face oftetragonal lysozyme; the microcrystals remain fixed on the surface and donot merge with the underlying lattice of the macrocrystal, whereas thelooped macrosteps nucleate and expand with growth rates comparable toelementary steps. C is a wide-field white light microscopy image; white ar-row points to a sedimented microcrystal.

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imaging showed that these microcrystals are not a source of largemultilayer stacks, hence no successful fusion was made with bothlattices. Moreover, the nucleation sites of closed loop macrostepsdid not coincide with the location of (foreign) particles (Fig. 3 Cand D). Precise dissolution experiments on surfaces with freshlymerged and expanding clusters reveal the lack of etch pit for-mation at the exact sites of looped macrostep formation. Thisdemonstrates that no additional stress fields are generated uponcluster assimilation (Fig. 4).We conclude that these clusters aredense (compared with the bulk liquid, for they act as a substantialsource of steps) and liquid-like (in the sense that they still havesufficient spatial degrees of freedom to accommodate the orien-tational restrictions imposed by the underlying lattice).Probing for the driving force of cluster formation, we per-

formed static and dynamic light scattering on filtered glucoseisomerase stock solutions with protein concentrations rangingfrom 0.5 to 100 mg mL−1 (SI Appendix). The obtained normal-ized intensity correlation functions g2(τ) −1 are well fit witha single exponential decay with characteristic decay times rang-ing from 6 × 10−2 ms to 2 × 10−2 ms. Using static light scattering,the concentration dependence of KC/Rθ was determined (Fig.5A). Cast into a normalized Debye plot, we obtain an MWKC/Rθ

dependence which fits a second-order polynomial (printed insemilog to show the fit over the full concentration range; rawdata are shown in SI Appendix, Fig. S4). Second and third virialcoefficients are A2 = 2.4 × 10−7 mol·dm3·g−2 and A3 = 7 × 10−15

mol2·dm6·g−4. Normalizing A2 to its dimensionless form we ob-tain B2 = 31, i.e., positive and large, indicating strong repulsionbetween the glucose isomerase monomers. A similar conclusioncan be drawn from the DLS data (Fig. 5A, Inset): collectivediffusion coefficients Dc normalized by the single-particle diffu-sion coefficient D0 increase linearly as a function of protein con-centration. The slope kD = 2.9 × 10−2 cm3·g−1 is, similar to A2, anintegrative quantity that is determined by the pair interactionpotential. The positive sign of kD corresponds to accelerated dif-fusion at higher concentrations which can be erroneously inter-preted as a change in hydrodynamic radius, but actually stemsfrom solution nonideality. Here it corresponds to net solute–soluterepulsion, which is in accordance with the conclusion based on A2.Our force spectroscopy results obtained using atomic force mi-croscopy (AFM) are in apparent contradiction to the light scat-tering findings (SI Appendix). Under identical buffer conditions,we do record a clear attractive force between glucose isomerasemonomers (Fig. 5B). Interestingly, both the frequency of bindingas well as the strength of the interaction increases upon additionof the precipitant, i.e., ammonium sulfate. For 0, 400, and 800 mMammonium sulfate, the mean force of unbinding is 130, 160, and200 pN, respectively. This clearly demonstrates that the strength ofthe interaction scales with the ionic strength of the solution.

Can Clusters Enhance Protein Nucleation? The multistep nucleationmodel predicts an initial densification step followed by a local

Fig. 4. Dissolution of a freshly grown (011) glucose isomerase surface dominated by looped macrosteps: the points of nucleation of multilayered islands(indicated in A and after lateral expanding in B) do not correspond to sites of etch pit formation C when mildly lowering the supersaturation to −0.06 toinitiate slow dissolution.

Fig. 5. (A) Debye plot for filtered glucose isomerase solutions (100 mM Hepes pH 7.0). Full line represents a second-order polynomial fit from which thesecond osmotic virial coefficient A2 was determined. (Inset) Collective diffusion coefficient Dc normalized by the single-particle diffusion coefficient D0 asa function of protein mass concentration C. The positive slope (kD > 0) is interpreted as a net interparticle repulsion between the solute molecules. (B)Distribution of interglucose isomerase forces as determined by AFM force spectroscopy: stock solution conditions (100 mM Hepes pH 7.0, dark gray bars);crystallization condition (100 mM Hepes pH 7.0, 800 mM ammonium sulfate, light gray bars); positive values represent attraction. (Inset) Force spectrum forglucose isomerase and the supporting substrate.

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increase in crystallinity. Not surprisingly, experimental observa-tions of mesoscopic clusters have been linked to nonclassicalnucleation routes. There is, however, no experimental proof thatthese clusters actually represent an intermediate step in a multi-step nucleation pathway. Are they precursors to crystalline nu-clei? Or are they not involved in crystallization and merely partof a solidification pathway competing with the crystalline state?To shed light on these unresolved questions we performedcrystallization experiments with samples from which these clus-ters were removed through filtration (SI Appendix, Fig. S5). Forglucose isomerase, crystallization conditions were carefully op-timized to ensure appearance of crystals within 15 min of pro-tein–precipitant mixing. By choosing these conditions, we canguarantee that only minimal cluster decay–dissolution has takenplace from the onset of mixing. Doing so, we ensure nucleationto occur at the maximum cluster number density and minimizethe background contribution of heterogeneous nucleation. Pro-tein–precipitant mixing was performed at 313 K, above the liquid–solidus line (39) to avoid the formation of steep supersaturationgradients. After mixing, the samples were incubated at 298 K toinitiate nucleation. At a given time Δt after mixing, we countedthe number n of macroscopic crystals [n can be used as a proxyfor the nucleation rate J through n∼

RΔt0 JðσðtÞÞdt with V the

crystallization volume]. For glucose isomerase, no measurableimpact of filtration on nucleation kinetics could be detectedwhen using freshly prepared protein samples. Using older stocksolutions (90 d), however, a strong decrease in nucleation rate isobserved after filtration: nunfilt > 100 (for σ> 3.9) and nfilt ≤ 1after 1 h (Fig. 6). The dependence of protein stock solution ageon the crystallization outcome is perhaps not entirely unexpected.Works in the past have reported cluster maturation (i.e., increasein size) through an Ostwald-like ripening process (21, 41). We alsoobserve that the reduction in nucleation rate becomes more pro-nounced at higher σ-values––the nucleation rate drops to a basallevel after filtration which is independent of σ. σ was varied byincreasing the bulk protein concentration, and thus by exten-sion, the cluster number density in the mother liquor. The rel-evant parameter may therefore not be the supersaturation, butrather the cluster concentration. For lysozyme, a similar decreaseis observed upon filtration. For instance, at σ = 1.5, nunfilt ∼ 260and nfilt ∼ 20 after 48 h (SI Appendix, Figs. S5 and S6). Theseobservations lead us to conclude that the presence of mesoscopicclusters can significantly enhance the nucleation of protein crys-tals. This is in direct contradiction with one of the basic guide-lines used by molecular biologists pursuing structural elucidationof proteins of interest through crystallographic means, whichstates that one should ideally work with monodisperse proteinstock solutions.

An Accelerated Self-Purification Pathway Induced by Clusters. Crys-tals growing from contaminated solutions typically exhibit analtered surface topography and a reduction in step kinetics. In

virtually all cases, these effects are strongly supersaturation de-pendent. The predominant interpretation is that the crystalundergoes a self-purifying transition by moving from an impu-rity-saturated state at low supersaturation toward an effectivestate of impurity repulsion at high driving forces (42, 43). Thiscan be understood by realizing that the impurity surface con-centration at a given supersaturation depends on the ratio of thecharacteristic time of impurity adsorption and the exposure timeof the impurity binding sites on the surface (44). The latter isa strong inverse function of supersaturation (σ): an increase in σleads to an acceleration of steps, a faster formation of new layers,and an increase in the frequency of attachment of growth unitsonto the key binding sites (i.e., kinks). All these factors con-tribute to the diminishing exposure times and subsequent re-duction of impurity uptake at high σ even when bulk impurityconcentrations remain constant. Here we report on the accel-erated recovery of impurity-poisoned surfaces by the de novoformation of looped macrosteps. We monitored lysozyme crys-tals growing from highly impure solutions [94.5% (wt/wt), Sigma;ref. 45] and compared the kinetic response of areas free of loopedmacrosteps and steps generated on areas enclosed by macrosteps(SI Appendix, Fig. S7 and Movie S3). Significant changes in stepmorphology and growth kinetics are observed: new areas freshlyformed by the merger of a cluster and the crystal surface yieldfaster advancing steps with a morphology that more closelyresembles the pure case (Fig. 7). These data strongly suggest thatthese areas have a locally reduced surface impurity concentrationsurrounded by areas with high impurity coverage.Now why would cluster solidification induce a local enhanced

self-purification of the crystal surface? Perhaps the impuritycontent of protein clusters in solution is lower than the impurityconcentration in the mother liquor. The subsequent coalescenceand solidification with a crystal would lead to a crystalline moundon the surface relatively devoid of impurities (SI Appendix,Movie S3). However, exposure to the bulk liquid renders thesenew surfaces susceptible to poisoning through impurity adsorp-tion. As such, even areas that are initially devoid of surface-adsorbed impurities should become covered in due time andexhibit slower step kinetics. We put forth the following in-terpretation: the step velocity under impure conditions repre-sents a steady state arising from a complex interplay betweensupersaturation, terrace exposure time (τ), characteristic impu-rity adsorption time (τi), and the step kinetic coefficient. The denovo formation of an impurity-free terrace perturbs this steadystate by rapidly increasing the step density and reducing theimpurity concentration, which effectively reduces τ. When τ << τi,the timescale of surface regeneration becomes smaller than thetimescale of impurity adsorption (44). If this condition is met, alocal reduction in impurity coverage (as induced by cluster so-lidification) leads to an acceleration in the step velocity, thusreducing the terrace exposure time (compared with the surround-ing regions) diminishing the probability that an impurity molecule

Fig. 6. Microbatch crystallization of glucose isomerase as a function of protein concentration using unfiltered (Upper) and filtered (Lower) protein stocksolutions (images were recorded 1 h after precipitant–protein mixing); filtration leads to a prominent decrease in nucleation when using older stock solutions(93 d). Freshly prepared protein solutions (1 d) do not exhibit such a difference in nucleation kinetics (Right).

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will bind to the surface. Eventually, a new steady state will beestablished that is characterized by a higher lateral growth rate andquasipure morphology. These cluster-sedimentation events cantherefore be considered as local hotspots of self-purification thatgrow in size with a velocity set by the rate of advancement of themacrostep across the impure surface. Once the edges of the surfaceare reached, the surface is effectively cleansed from impurity poi-soning. Essentially, these events constitute a shortcut toward theself-purification scenario that would normally occur at far highersupersaturation values (46).

Concluding RemarksOur observations on this broad selection of protein crystals, com-bined with the existing literature data, show that looped macrostepformation is a widespread mechanism of layer generation whichcan be considered common to all instances of solution crystalli-zation. Given that mesoscopic clusters trigger this growth mecha-nism, one can reverse the argument: the ubiquity of loopedmacrostep formation reflects the ubiquity of cluster formation inprotein solutions. Moreover, the fact that cluster assimilationleads to step formation without any discernible defects dem-onstrates that they are predominantly composed of stable, regular,growth units.Secondly, these observed clusters are not the result of critical

density fluctuations. We base this conclusion on two arguments.For the conditions we tested there are no macroscopic con-densed liquid phases, indicating that we operated well above (interms of temperature) the metastable gas–liquid coexistenceregion. We also stress that the observed aggregates exist ona timescale that far exceeds the lifetime of dynamic clustersgenerated by thermal fluctuations. This indicates that they do notowe their existence to random collisions but rather are sustainedby attractive interparticle interactions. This beckons the ques-tion, what is the driving force for their formation? Althoughcluster formation is not a priori impossible for purely repulsiveinteraction potentials (47), such a scenario requires high volumefractions of the solute molecules. Given that the experiments inthis study were performed at relatively low protein concen-trations, it would seem unlikely that solute–solute repulsionwould lead to stabilized clusters.Theoretical treatments of cluster formation in colloidal sus-

pensions demonstrate that mesoscopic clusters can arise fromthe competition between short-range attractive (induced dipoles)and long-range repulsive (screened Coulomb) forces, with thelatter dominating at larger cluster sizes (48, 49). How do suchpredictions line up with our experimental results? From laser

light scattering we conclude that glucose isomerase monomersstrongly repel one another (for details see SI Appendix, Fig. S4).This is not surprising given the net negative charge of glucoseisomerase at pH 7 (pI ∼ 3). From force spectroscopy we knowthat there is a nonnegligible attractive component between themonomers as well. Such diverging observations can be reconciledby realizing that laser light scattering is an integrative techniquewhere large ensembles of monomers are sampled in a singleexperiment. As such, only orientationally averaged informationis obtained. If there are weak attractive interactions that corre-spond to specific orientations, their contribution to the osmoticcompressibility will be overclouded by strong repulsive inter-actions for all of the remaining orientations. In fact, for glucoseisomerase, the second virial coefficient is positive even for con-ditions conducive to crystallization (50). Such averaging does notoccur in force spectroscopy where only a limited number ofmonomers––ideally only two––are probed in a single run. Thistechnique is therefore more susceptible to identify rare, yet at-tractive events. In other words, the long-range electrostatic re-pulsion of the interaction will dominate the light scatteringresults. By increasing the ionic strength of the solution, both the

Fig. 7. Looped macrostep mediated self-purification of tetragonal lysozyme crystals. (A) Elementary step kinetics in the (110) direction under highly purified(full line) and impure conditions (colored symbols): classical recovery of impurity surface poisoning by a reduction of the characteristic terrace exposure timethrough nucleation and growth of elementary steps (purple spheres); steps of islands formed on the area enclosed by the looped macrostep shown inB growing from Sigma solution regain near-pure lateral growth rates (pink squares), whereas steps in the adjacent regions remain strongly inhibited (vstepreduced by one order of magnitude), even at identical supersaturation. Note that the critical supersaturation for self-purification is shifted to lower su-persaturation values for looped macrostep mediated growth compared with 2D nucleation dominated growth. (D–F) Progression of self-purification throughthe continuous expanding of the looped macrostep; 2D-island shape in the zone encircled by the macrostep more closely resembles the lens-shaped 2D islandsfound under pure conditions compared with the strongly pinned steps in the adjoining regions. C is a zoom-in of D.

Fig. 8. Comparison of classical (I–II) and nonclassical (III–V, III–IV–II) path-ways from the bulk liquid to the crystalline phase: contemporaneous den-sification and increase in crystallinity (I); temporal separation of cluster (III)and lattice (IV) formation; merging of clusters with the crystalline phase (V).

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number density and the characteristic size of the clusters increase(SI Appendix, Fig. S3). Screening of surface charges thereforeleads to an additional stabilization of the mesoscopic clusters.Surprisingly, we still observe clusters even at very low ionic

strength. A possible solution to this enigma was presented by Panand coworkers (51), who argue that cluster formation requiresthe presence of an additional protein species, i.e., impurities. Suchimpurities may be of microheterogeneous origin, i.e., (partially)unfolded species or stabilized oligomers consisting of, e.g., domainswapped units. Because the growth unit of glucose isomerase crys-tals is particularly resilient to thermal denaturation (50), (partial)unfolding is improbable. Glucose isomerase preparations are,however, not impurity-free. Chromatographic analysis indicatesthat the impurities are noncovalently bound glucose isomerasedimers that reversibly bind onto the crystal surface (SI Appendix,Fig. S8). The lack of stress fields at the point of cluster assimi-lation by the macrocrystal shows that the clusters are not enrichedwith these nonregular growth units. To what extent these dimerscontribute to cluster formation remains unclear at this point andwill be the subject of further study.Regardless of the origin of the observed mesoscopic clusters,

their impact on crystal nucleation is quite extensive, at least forthe two proteins tested here, glucose isomerase and lysozyme.For the former we detected a 100-fold reduction in nucleationrate upon removal of the clusters; for the latter a 10-fold de-crease was recorded. In the nucleation trials, there are ∼103clusters in the crystallization volume. The significant impact offiltration on the detected number of crystals shows that nucle-ation can be facilitated by clusters. Two possible conclusionsremain open: (i) the observed clusters represent an intermediatedensification step on route to crystallization, in accordance withMNT (Fig. 8) or (ii) the clusters act as local hotspots of het-erogeneous nucleation, e.g., by providing an interface that sta-bilizes (pre)critical clusters. In the latter option, clusters do notreorganize into nuclei, but rather, facilitate their formation. It isalso not clear whether these clusters are an absolute requirementfor nucleation. Crystals are still obtained after filtration: al-though no clusters could be detected with either BM or DLS,a fraction of clusters with sizes below the detection threshold

may still remain in solution, thus contributing to the experimentallydetermined nucleation rate after filtration. Secondly, it is strikingthat we find such a strong dependence of the nucleation kinetics––and the impact of filtration thereon––on protein stock solution age.This is reminiscent of two recent papers that have revealed thatprotein clusters undergo a gradual maturation, i.e., the meancluster size grows over time (21, 41). However, they report onprocesses operating on a timescale of hours and days, certainly notweeks and months, as is the case here. This discrepancy may sug-gest that cluster number density and characteristic size need not bethe sole characteristics that govern the effect on nucleation.Thirdly, we note that the assimilation of mesoscopic clusters

by the growing crystal is a decisively nonclassical mode of growth.In the classical limit, crystals are considered to grow by the ad-dition of monomeric units, oligomeric fragments, or even entireunit cells. The growth mechanism presented here operates ona scale that is entirely different. If one assumes that the mono-mer density in the clusters is comparable to the density in thecrystal, then each cluster is composed of 105–106 monomers. Thisis a staggering amount. The self-purification cascade that ensuesfrom cluster assimilation into the lattice is an escape route fromsurface poisoning that would otherwise lead to growth cessation.Intrinsic cleansing of impurity-poisoned surfaces is a well-knownphenomenon but typically requires the change of at least oneorder parameter of the system (solute or precipitant concentra-tion, temperature, etc.). Here, we described the virtually in-stantaneous and lasting ablation of the impurity adsorption layertriggered by the merging and transformation of two phases. Itdemonstrates that there exists a nontrivial connection betweenthe growth of the macroscopic crystalline phase and the meso-scopic intermediate which runs the risk of being overclouded bythe MNT discussion.

ACKNOWLEDGMENTS. M.S. gratefully acknowledges the kind assistance ofKoen Van Laer with the HPLC runs and Francesco Ielasi with the forcespectroscopy measurements. A.E.S.V.D. greatly appreciates the preparationof protein samples by Raquel Fernandez Penas. M.S. is grateful for thesupport by the Belgian PROgramme de Développement d’Expériences scien-tifiques under Contract ESA AO-2004-070. A.E.S.V.D. acknowledges the sup-port from the Ministerio de Ciencia é Innovación by BIO2010-16800.

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