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Incorporation of Macromolecules into α‑Lactose Monohydrate Crystals Alexander G. Shtukenberg,* Kelly Tripathi, Remi Ketchum, Jenny Jaehee Jeon, Ahmed Sanda, and Bart Kahr* Department of Chemistry and the Molecular Design Institute, New York University, 100 Washington Square East, New York, New York 10003-6688, United States S Supporting Information *

ABSTRACT: It had been discovered that crystals of α-lactose monohydrate can occlude and give kinetic stability to various proteins, an unexpected observation suggesting a process for storing protein vaccines and biopharmaceuticals at room temperature. The growth of α-lactose monohydrate with proteins is analyzed herein, emphasizing segregation coefficients, the relationships between protein incorporation and buffer composition, temperature, growth rate, and mass transport. Detailed examination of bovine serum albumin is supported by data for eight other proteins. A search for other crystals with lactose-like inclusivity of macromolecular guests is also reported.

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reviewed.4 Here, we consider the potential of ALM crystals to likewise encapsulate delicate biological agents. Crystals other than ALM can occlude macromolecules. Acidic peptides and proteins can readily incorporate into calcite7−11 and calcium oxalates,12−20 antifreeze proteins are occluded by ice crystals,21−27 and matrix-assisted laser desorption/ionization (MALDI) host crystals overgrow various proteins,28−32 not to mention the fact that proteins can serve as hosts for other proteins.33−37 Nevertheless, ALM is particularly aggressive in forming mixed crystals with proteins. Establishing whether or not ALM shares characteristics of these other proteinophilic crystals is a further aim of this research. We analyzed 10 proteins cocrystallizing with ALM. The effect of growth conditions was studied most systematically for fluorescein isothiocyanate (FITC)-labeled bovine serum albumin (BSA), which is commercially available and comparatively inexpensive. These data serve as the basis of building a model for adsorption consistent with measurable segregation coefficients. This is a first step to answering some of the aforementioned, more far-reaching questions.

INTRODUCTION In the late 1990s, it was discovered that α-lactose monohydrate (ALM) crystals can occlude micromolar quantities of various proteins during growth from aqueous solution.1,2 Moreover, proteins incorporate only into one growth sector (010) (Figure 1), and even within this sector overgrowth was sometimes much stronger in the subvolumes formed by the steps on growth hillocks of only one crystallographic orientation. Protein resistance to denaturation, by one measure, was increased inside crystals compared to proteins in solution. The findings suggested a strategy for storing and stabilizing immunogenic proteins or biopharmaceuticals inside ALM crystals, thereby eliminating the so-called “cold chain” required for the storage and transport of protein drugs.3 This research has also raised a number of fundamental crystal growth questions. What makes lactose an apparently unique host with regard to its incorporation and overgrowth of macromolecules? What is special about the (010) face? Why are so many proteins incorporated despite great differences in their structures? What are the characteristics of the few proteins that are not so incorporated? How much protein can be incorporated inside the crystal? What controls incorporation? How significant is the stabilization afforded by the crystalline matrix? Strategies for obviating the cold chain by encapsulation have engaged many research groups.4 The silk-based stabilization strategy pioneered by the Kaplan group is widely appreciated.5 Here, the crystallinity of the silk protein may play an important role. Calcium binding peptides have protected vaccines by selfmineralization.6 The benefits and deleterious consequences of freeze-drying, foam drying, and spray drying have been © XXXX American Chemical Society

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THEORY

To characterize incorporation of macromolecules (MM) a distribution coefficient, K, given as eq 1 was evaluated, Received: May 5, 2016 Revised: June 20, 2016

A

DOI: 10.1021/acs.cgd.6b00686 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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Figure 1. α-Lactose monohydrate crystals occluding different proteins. All images except that for hemoglobin show characteristic fluorescence of corresponding dyes. The hemoglobin image is an optical micrograph captured with λ = 410 nm illumination. The crystal morphology is shown in the central picture with the green pyramids highlighting two subsectors of (010) growth sector, which mainly incorporate macromolecules. Partially reproduced from ref 2 with permission. Copyright 2001 Elsevier Ltd.

K=

([MM]/[ALM])crystal ([MM]/[ALM])solution

=

xcALM x = c MM y

concentration in the solution. θmax is the maximum surface coverage, and factor n = [hMM/h] ≥ 1 corresponds to the number of host layers for which the molecule is still partially exposed to the solution (Figure 2). Brackets indicate rounding to a greater integer, hMM is the thickness of adsorbed MM, and h is the thickness of growing layer. Here, we assume as a starting point that the molecules cannot adsorb on top of one another; however aggregation may be significant. We also assume that the overall surface coverage by strongly adsorbed MMs is low so that the adsorbed molecules do not slow crystallization. This assumption is correct for ALM (morphology and average growth rates of ALM do not change in the presence of MM additive; the only exception is ribonuclease that slows down growth of the (010) face; Figure 1), but it is also true for incorporation of MM in many other hosts. If the surface coverage by the adsorbed MM becomes high enough to interfere with step propagation the present model should be corrected for nonlinear feedback effects38 that are beyond the scope of this paper. Since the growing surface is exposed only for the time τs = h/ R, where R is the normal growth rate, solution of eq 2 gives eq 3.

(1)

where [MM] and [ALM] are weight or molar concentrations, cALM and cMM are concentrations of in solution (g/L or mol/L), respectively, and x and y are weight ratios between MM and ALM in crystal and solution (mg MM/mg ALM), respectively. This definition of the distribution coefficient is more insightful from a thermodynamic perspective than an alternative formulation, K′ = [MM]crystal/[MM]solution, which is more useful for the analysis of fractionation and mass transport.33,37 The quantities can be easily interconverted if cALM is expressed in mol/L, K = K′ωcALM, where ω is a molar volume of ALM. The quantity of overgrown MM is a result of several adsorption−desorption processes on and near the surface. The surface coverage, θ, can be described by the Langmuir adsorption isotherm given by eq 2. Application of the Langmuir isotherm relies on several assumptions (flat surface, monolayer coverage, noninteracting adsorbate molecules), which may be not completely applicable. However, application of more sophisticated isotherms requires greater knowledge on the adsorption process, and the Langmuir isotherm is a good starting point. dθ = k+c MM(θmax − nθ ) − k −θ dt

θ0 = θeq(1 − exp(−τs/τa))

(3)

where θ0 is the actual surface coverage, θeq = θmaxk+cMM/ (nk+cMM + k−) is the equilibrium surface coverage and τa = 1/ (nk+cMM + k−) is the characteristic time of adsorption. As the adsorbed MMs collide with the advancing growth front, they

(2)

where t is time, k+ and k− are the rate constants for adsorption and desorption, respectively, and cMM is macromolecule (MM) B

DOI: 10.1021/acs.cgd.6b00686 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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x = xmax

⎛ h nk+c MM exp⎜⎜ − (nk+c MM + k −) ⎝ R

n

⎞

∑ ki−⎟⎟× i=1

⎡ ⎛ h ⎞⎤ ⎢1 − exp⎝⎜ − (nk+c MM + k −)⎠⎟⎥ ⎣ ⎦ R

⎠

(6)

The result becomes more transparent when eq 6 is rewritten as eq 7 by introducing a new variable n α = ∑i = 1 ki −/(nk+c MM + k −). ⎛ hα ⎞⎡ ⎛ h ⎞⎤ x = xeq exp⎜ − ⎟⎢1 − exp⎜ − ⎟⎥ ⎝ Rτa ⎠⎢⎣ ⎝ Rτa ⎠⎥⎦

(7)

Effect of growth rate on MM incorporation can be illustrated by plotting x/xeq curves for different α and h/(Rτa) (Figure 3)

Figure 3. Effect of growth rate R and adsorption/desorption parameters (embedded in α and τa) on incorporation of MMs in a growing crystal x/xeq as simulated using eq 7.

Figure 2. (A) Illustration of MM (red ellipses) incorporation into a crystal by step flow. (B) Views of growth steps exposed on the (010) face in ALM single crystals. Ovalbumin molecule, for example, is drawn to scale above.

and can be rationalized as in the following way: At very small growth rate R, the surface coverage of the exposed layer can be high, but all the adsorbed molecules have time to desorb. As a result, the first exponent tends to zero, and total concentration of MM in a crystal x is close to zero. If growth rate is too high MMs do not have time to adsorb and again x is close to zero. In between, there is a range of growth rates for which incorporation of MMs is significant and can reach xeq. If ατs ≪ τa ≪ τs = h/R incorporation of MM can be significant and will not strongly depend on growth rate. Here, eq 6 can be simplified as eq 8.

may be trapped by the crystal, but during MM exposure time τMM = nτs they are not completely occluded and can desorb. Following Chernov,39 desorption from the i = 1, ...n layer counting from the surface toward the crystal interior can be defined as dθi/dt = −ki−θi, where ki− are desorption rate constants of partially occluded molecules. The solution to the eq 2 can be combined with eq 4 to give the volume fraction of MMs in the crystal, Ω, (eq 5). θi = θi − 1 exp( −τski −)i = 1, ...n ⎛ h n ⎞ Ω = nθ = nθeq exp⎜⎜ − ∑ ki −⎟⎟× ⎝ R i=1 ⎠ ⎡ ⎛ h ⎞⎤ ⎢1 − exp⎜⎝ − (nk+c MM + k −)⎟⎠⎥ ⎣ ⎦ R

x = xeq = xmax

(4)

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nk+c MM nk+c MM + k −

(8)

EXPERIMENTAL SECTION

α-Lactose monohydrate (ALM, Sigma-Aldrich, 97%), bovine serum albumin (BSA, Sigma-Aldrich, >98%), chicken egg white albumin (Ova, Sigma-Aldrich, 98%), partially iron saturated human transferrin (Tf, Sigma-Aldrich), human hemoglobin (Hb, Sigma-Aldrich), myoglobin from horse skeletal muscle (Mb, Sigma-Aldrich), FITC (fluorescein isothiocyanate) labeled BSA (FITC-BSA, Life Technologies), Texas Red labeled bovine serum albumin (TR-BSA, Life Technologies), FITC labeled ovalbumin (FITC-Ova, Life Technologies), FITC labeled human serum transferrin (FITC-Tf, Life Technologies), Oregon green labeled human plasma fibrinogen (OG-Fg, Life Technologies), FITC labeled egg white avidin (FITCAvidin, Life Technologies), and recombinant green fluorescent protein (GFP, Creative Biomart) were used as obtained without any treatment.

(5)

The volume fraction Ω can be converted to the weight fraction of MMs, w, by multiplying to the ratio of MM and ALM densities w = ΩρMM/ρALM. For the small concentration of macromolecules, w < 0.1, weight fraction can be replaced with the weight ratio of MM to crystalline ALM, x [mg MM/mg ALM], to provide eq 6. C

DOI: 10.1021/acs.cgd.6b00686 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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Table 1. Properties of MMs Used, Their Maximum Detected Concentrations in ALM Crystals, x, Distribution Coefficients, K, and Spacing between MM on a Crystal Surface, l, for These Concentrations protein

Mw, kDa

pI

dav, nm

cMM, mg/mL

max x, mg/g

max x, μmol/mol

K

l, nm

bovine serum albumin, BSA FITC-BSA FITC-avidin ovalbumin, Ova FITC-Ova, FITC-Ova transferrin, Tf FITC-Tf, FITC-Tf Oregon green fibrinogen, OG-Fg green fluorescent protein, GFP hemoglobin A, Hb myoglobin, Mb FITC-hemagglutinin, FITC-HA data from ref 2 labeled Zn-cytochrome C FITC-lysozyme green fluorescent protein, GFP Texas red-lectin A. hypogaea acridine-Dickerson’s 12-mer oligonucleotide, DNA labeled dextran FITC-ribonuclease B (1 glyc) FITC-avidin (Man + GlcNAc) FITC-ribonuclease A (−) FITC-avidin (−)

66.5 67.5 68 45 46 80 81 340 27.3 64.5 17 65

4.7 4.7 10.5 4.6 4.6 5.5 5.5 5.2 6.2 6.9 7.4 8.4

5.4 5.4 5.4 4.7 4.7 5.7 5.7 9.2 4.0 5.3 3.4 5.3

88 4.7 1.82 44 3.0 14 0.38 0.65 0.04 34 18 0.03

1.9 2.4 0.34 6.6 1.1 1.4 0.45 3.7 0.10 7.9 0.61 0.39

10.3 12.8 1.8 52.8 8.3 6.3 2.0 4.0 1.3 43.8 13.0 2.2

0.006 0.22 0.11 0.056 0.11 0.050 0.30 1.7 1.21 0.14 0.021 1.6

55 48 137 24 66 69 126 64 194 24 64 126

12.5 14.3 27 25 4 10 15.9 16.5 13.7 16.5

10 11.4 6.2 6 5 7 9.45 10.5 9.6 10.5

3.1 3.2 4.0 3.9 2.1 2.8 3.3 3.4 3.2 3.4

0.5 0.5 0.04 0.5 0.5 0.5 0.5 0.5 0.5 0.5

0.06 0.07 0.10 2.8 0.11 0.39 0.49 0.78 0 0

1.7 1.8 1.3 40.0 9.9 14.0 11.1 16.7 0 0

0.05 0.06 1.2 2.3 0.1 0.3 0.4 2.7 0 0

190 184 189 32 95 67 70 56

A solution of recombinant influenza A virus H5N1 hemagglutinin (HA, Creative Biomart) was concentrated by ultracentrifugation using a filter with a molecular mass cut off of 25 kDa. HA was conjugated with FITC using a Sigma-Aldrich FluoroTag FITC Conjugation kit. ALM was placed into a scintillation vial, dissolved in a buffer, and slightly boiled to kill microorganisms. Phosphate buffer saline (PBS 1X, pH = 7.4) was used, but some experiments were performed in water (pH of ALM solution can vary between 3 and 7 due to impurities in commercial ALM40) or in phosphate buffers (PB) with pH = 6−8 or in 0.1 M TAPSO solution (pH = 3.6). The solution was cooled to ca. 30 °C, and then separately prepared protein stock solution was added. The total volume of solution varied in the range 0.6−7 mL. Then the small aliquot of solution (0.05−0.4 mL) was diluted with PBS 1X buffer to collect fluorescence emission or UV−vis absorption spectra. The main part of solution was incubated without stirring at growth temperatures of T = 4, 22, and 36 °C, and crystals spontaneously nucleated at the bottom of the vial. The solution supersaturation varied in the range σ = 0.5−3, but most experiments were performed at σ = 1.5−1.7 at T = 4 °C and σ = 1.1−1.7 at T = 22 °C. In this study the supersaturation is defined as σ = cALM/cALMeq − 1, where cALM is concentration of ALM in solution (g ALM/100 g buffer) and cALMeq is the standard ALM solubility,41−43 14.4, 23.0, and 32.4 g of ALM/100 g of water for T = 4, 22, and 36 °C, respectively. The crystallization time varied from a few hours to a few weeks but was usually between 1 and 10 days. Then the crystals were isolated from solution and washed thrice with deionized water. A small portion of crystals was placed on a glass slide and embedded into mineral oil beneath a coverslip prior to microscopic analysis. Crystals were dissolved in PBS 1X buffer to collect fluorescence emission or UV−vis absorption spectra. An aliquot (0.05−0.4 mL) of supernatant solution was diluted with PBS 1X buffer to determine protein concentration using fluorescence emission or UV−vis absorption spectra. The concentrations of proteins in crystals and solutions were determined by measuring fluorescence emission spectra for FITC, Oregon green, GFP, and autofluorescence of tryptophan with a Horiba Scientific spectrofluorometer Fluoromax-4 and measuring UV−vis absorption spectra for hemoglobin with a PerkinElmer Lambda 950 UV−vis spectrometer. Intensity and distribution of fluorescence inside crystals were imaged and analyzed using a Leica TCS SP8 X Laser

confocal microscope. Fluorescence images were also recorded with the Zeiss microscopes Axioskop 40 and Observer.Z1m. Protein aggregation was analyzed using dynamic light scattering (DLS) with a Malvern Zetasizer Nano-ZS analyzer. Average crystal growth rates were estimated by dividing the average crystal length in [010] direction, H [mm], by the total time of growth. The number of crystals in a crystallization batch was estimated as N = 24m/(ρALMH3), where m [mg] is the total mass of precipitated ALM, ρALM = 1.52 g/cm3 is the density of ALM crystal, and 24 is a form factor.

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RESULTS AND DISCUSSION

Proteins. A number of globular proteins were previously tested as guests in ALM host crystals.2 Here, this list is expanded (Table 1, Figure 1). Among all proteins tested only unglycosylated avidin and ribonuclease B showed no detectable incorporation.2 The presence of saccharide moieties is not, however, a precondition for incorporation since BSA, GFP, Hb, Mb, lysozyme, lectin, and cytochrome C are not glycoproteins but are easily incorporated into ALM crystals. The secondary structure of proteins can vary significantly from soft α-helical BSA to structures with compound α-helices and β-sheets in Ova, Tf, lysozyme, or HA to β-barrels in GFP and avidin. There is no noticeable difference in incorporation of FITC-BSA added to the mother liquor at room temperature or before the solution was boiled, after which it is partially denaturated.44 Small and large (12.5 kDa to 340 kDa), acidic and basic (pI = 4.6 to 11.4) proteins are equally well incorporated (Table 1). We presume that protein labeling with a fluorescent tag does not affect protein incorporation. This assumption was valid for Ova and Tf conjugated with FITC (Figure 7B,C below); however, a big difference in affinity for lactose was found for BSA and FITC-BSA (Figure 7A). Although labeled and unlabeled BSA approach the same maximum concentration in a crystal at high protein solution concentrations, for the concentration range y = 0.2−5 mg of protein/g of ALM D

DOI: 10.1021/acs.cgd.6b00686 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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incorporation of FITC-BSA is approximately 1 order of magnitude higher. This difference can be seen vividly for BSA and FITC-BSA mixtures. It is not clear what is responsible for such differences, especially since the labeling reagent, FITC, is overgrown within ALM crystals with K < 0.15, and fluorescein does not go into ALM crystals at all. Moreover, BSA labeled with Texas Red is characterized by a similar distribution coefficient as FITC-BSA purchased from the same company. Macromolecule Distribution in α-Lactose Monohydrate Crystals. ALM crystallizes in the monoclinic space group P21 with lattice constants a = 7.982(2), b = 21. 562(3), c = 4.824(1) Å, β = 109.57(3)°.45 In accordance with the previous results,1,2 all proteins evaluated were incorporated only in the (010) growth sector (Figure 1). Under the supersaturation range used in this study, the (010) faces grow by the dislocation spiral mechanism with formation of elongated growth hillocks emanating from steps running parallel to the [100] and [001] directions. The height of elementary steps is b/2 but due to the anisotropy of growth kinetics steps bunch to form risers of height b = 2.2 nm.46 Sometimes, subsectors within the (010) growth sector formed by the steps running parallel to [100] contain several times more protein than subsectors formed by the steps running parallel to [001] (Figure 4). In such crystals, the concentration

Figure 5. Fine zoning (striations) in distribution of OG-Fg in ALM crystal visualized with a confocal fluorescence microscope.

to the growing surface. On the other hand, the average protein transport rate in the mother liquor seems to be fast enough; crystallization of FITC-BSA on the bottom of the vial under natural convection resulted in K = 2.1, whereas crystallization of the second portion of the same solution under the same conditions with vigorous stirring resulted in K = 1.6. Fluorescence of crystals was mainly homogeneous assuming incorporation of protein in molecular form. These data are corroborated with the absence of aggregation in supernatant BSA containing solution (cBSA = 16 mg/mL) analyzed by DLS. Sometimes, however, aggregates of protein were detected for FITC-BSA, FITC-Tf, FITC-avidin, OG-Fg, and Hb. Protein Concentration in Solution. At low protein concentration in the mother liquor protein concentration in a crystal increases linearly so that the distribution coefficient K = x/y = const (Figure 7). In most cases, at a certain y this proportionality breaks down, and eventually protein concentration in a crystal reaches saturation, x = xmax (Figure 7). For OG-Fg and Hb only linear dependencies were observed, and for some proteins the data available were not sufficient to determine the functional dependence, or the overall behavior for all proteins follows the same pattern (Figure 8). All data can be fitted with eq 9, a modification of eq 8, to determine the apparent adsorption constant Kads = k+/k−. y x = xmax y + 1/(nK adscALM) (9)

Figure 4. Subsector zoning in distribution of FITC-Ova in ALM crystal visualized with a confocal fluorescence microscope. Numbered arrows indicate concentration of FITC-Ova, mg/g ALM, estimated from the distribution of fluorescence intensity and average concentration (x = 0.14 mg/g ALM) in the corresponding batch of crystals.

The MM separation l can be estimated from eq 10. ⎞ ⎛ πρ f MM l = dav ⎜⎜ − 1⎟⎟ ⎠ ⎝ 4ρALM x

(10)

Equation 10 was deduced for spherical protein particles of average diameter dav adsorbing on a surface over a square grid. The densities were taken as ρMM = 0.94 g/cm3 and ρALM = 1.52 g/cm3. The factor f = 0.5 accounts for MM incorporation only in the (010) growth sector that approximately constitutes 50% of the crystal volume. The inter-MM separation values l were found to vary from 24 to 230 nm (Table 1). This value can be compared to the diameter of the critical nucleus Lc = 2ωγ/Δμ, where ω = 2.4 × 10−4 m3/mol is molar volume of ALM and γ = 0.03 J/m2 is the surface energy.47−49 The driving force for crystallization, the difference in chemical potentials, Δμ = RgTln(σ + 1), where Rg is the universal gas constant and T is the absolute temperature. For the typical supersaturation range used in this study, σ = 1−2, calculation gives Lc = 5.3−8.4 nm.

of protein is minimal in the proximity of the dislocation line so that the difference between highest and lowest concentration in the cross section can be as high as 10 times (Figure 4). Subsector zoning was observed for FITC-BSA, FITC-Ova, FITC-avidin, and GFP. It was obtained for whole temperature and supersaturation range used in this study, but more often subsector zoning was observed for crystallization at 4 °C. Along with sector zoning and subsector zoning related to specific protein adsorption on the crystal surface, ALM crystals show concentric zoning or striations (Figure 5) most likely related to convectional instability in a mother liquor. Sometimes, crystals showed diffuse inhomogeneity in the protein distribution inside the (010) growth sector (Figure 6), evidence of an inconsistent supply of protein from the growth medium E

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Figure 6. Inhomogeneous distribution of FITC-HA inside the (010) growth sector of ALM crystal visualized with a fluorescence microscope (left) and confocal fluorescence microscope (all other images). Fluorescence is homogeneous in the crystal portions corresponding to early growth but later becomes inhomogeneous reflecting a hindered supply of protein to the crystal surface.

Figure 7. Relationship between solution composition y, mg of MM/mg of ALM and crystal composition x, mg of MM/mg of ALM for various proteins. (A) FITC-BSA (triangles and diamonds) and BSA (circles and squares); (B) FITC-Ova (triangles) and Ova (circles and squares); (C) FITC-Tf (triangles) and Tf (circles); (D) OG-Fg; (E) FITC-avidin; (F) Hb. Growth temperature: 4 °C (blue squares and down triangles); 22 °C (black circles and up triangles); 36 °C (diamonds). Black straight lines correspond to K = 1; green lines are fits to eq 9.

Since l ≫ Lc the growth step propagation should not be significantly affected by the adsorbed MM; the same morphologies and growth rates were observed in the presence and in the absence of additives. The distribution coefficients for the concentration range, where x is proportional to y, vary from 0.1 to 12.9 (Tables 2

and S1), in line with K = 0.02−4 measured for protein incorporation into a variety of hosts including calcium oxalate dihydrate, 19 calcite, 10 ice, 22,25−27 2,5-dihydroxybenzoic acid,29,31,32 2,4-dihydroxybenzoic acid,31 succinic acid,30 lysozyme,33,37 and ferritin.33 Many crystals have very small distribution coefficients, K → 0, and are resistant to protein F

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coefficient and growth rate (Figure S3). The second possibility is plausible if one assumes the formation of an adsorption layer with high surface coverage but consisting of molecules differently bound to the surface. Most molecules are not bound strongly enough to become overgrown, but they can prevent other molecules from adsorbing strongly. Growth Conditions. Additional details are provided in the text of the SI. FITC-BSA incorporation in ALM crystals significantly decreases as the salt concentration (ionic strength) in the mother liquor increases (Figure S1). Effect of pH was analyzed for two series of experiments with FITC-BSA and one series of experiments with FITC-avidin (Table S1). In general, the effect of pH is not strong, even though it is well-known that, generally speaking, pH can greatly affect surface charge and consequent protein adsorption to surfaces.54 In accordance with typical temperature behavior of adsorption, incorporation of FITC-BSA and, to some extent, Hb, FITC-Ova, and FIC-Tf, into ALM crystals increases at lower growth temperatures (Figures 7 and S2, Table 2). Incorporation of FITC-BSA does not depend on growth rate R (Figure S3). The absence of K(R) dependence justifies using eq 9 and significantly simplifies analysis of the data. It also assumes that τa < τs = h/R or characteristic adsorption time τa is much less than 0.5 s. This time is much less than the typical τa ≫ 1 min for specific strong MM adsorption to calcium oxalate monohydrate55−57 or ice.53,58−60 Even under constant crystallization conditions (protein concentration, temperature, buffer, supersaturation) distribution coefficients can vary significantly. Although factors responsible for such behavior are not well understood, one empirical correlation has been established. Distribution coefficients for FITC-BSA are much smaller in experiments with a high nucleation rate (many small crystals, high rate of supersaturation lowering) compared to experiments with a low nucleation rate (Figure S4). A similar correlation was established for FITC-Ova and FITC-Tf. As shown above the difference in the distribution coefficient cannot be directly explained by the existing differences in protein transport toward the growth face. Moreover, sometimes clearly different nucleation rates obtained for two portions of the same solution lead to essentially the same distribution coefficient. Hosts Other than ALM. Incorporation of FITC-BSA and FITC-avidin into a variety of crystalline hosts was tested with a fluorescence microscope for spontaneously nucleated crystals (Table S2). We screened nontoxic compounds that deposit large, well-formed crystals as potential hosts for the storage of vaccines and drugs. Sector zoned incorporation was detected only for L-cystine61 and L-ascorbic acid. (Phthalic acid was also good but quite toxic.62) Both hosts are not suitable for the analysis of protein incorporation because L-cystine crystallizes very slowly and L-ascorbic acid is quite acidic. Diffuse nonspecific incorporation into all crystal faces was detected for several other carboxylic acids, but again these crystals have formed at acidic conditions where proteins may have been degraded. Because of dramatic decreases in distribution coefficients with increased ionic strength (Figure S1), well dissociating salts cannot serve as good hosts either. However, it is not clear why most of amino acids, sugars, and other molecular crystals show negligible protein uptake. The only feature that makes ALM special with respect to other host crystals is a very high step riser (2.2 nm) that can create stronger interactions of MMs

Figure 8. Summary of protein incorporation into ALM crystals. The lines correspond to averaging of experimental data (green lines in Figure 7); symbols are shown if only a few experimental data points were available.

Table 2. Protein Concentration Range y, for which K = x/y = const, Corresponding Average Distribution Coefficients, along with Maximal Protein Concentration in a Crystal and Calculated Adsorption Constant protein

a

T, °C

FITC-BSA

4

FITC-BSA

22, 36

FITC-Ova

4

FITC-Ova

22

FITC-Tf

4

FITC-Tf

22

FITC-avidin

4, 22

OG-Fg

4

Hb

4

Hb

22

range of y, mg/mg ALM 2 × 10−6 to 2 × 10−4 1 × 10−5 to 2 × 10−4 2 × 10−6 to 1 × 10−4 3 × 10−6 to 1 × 10−4 1 × 10−6 to 5 × 10−5 1 × 10−6 to 5 × 10−5 7 × 10−6 to 2 × 10−4 2 × 10−6 to 3 × 10−3 6 × 10−3 to 3 × 10−2 3 × 10−3 to 9 × 10−2

K

xmax, mg/g

Kads, L/mol

6.5

2.3

228

3.5

2.3

707

2.5

3.0

70

1.4

3.0

208

1.75

0.5

250

1.25

0.5

583

0.11

n/da

n/d

2

n/d

n/d

0.14

n/d

n/d

0.10

n/d

n/d

n/d, no data.

incorporation (see list in SI and the section below Hosts Other than ALM). But, to date, distribution coefficients greater than 4 were observed only for ALM. ALM leads the pack in its ability to overgrow MMs on particular facets. For BSA, Ova, and Tf, the values of xmax and Kads were determined (Figure 7, Table 2). Adsorption constants, Kads = 70−700 L/mol, are very small compared to Kads > 106 L/mol determined for adsorption of acidic proteins onto hydroxyapatite50−52 or antifreeze proteins onto ice crystals.53 This indicates weak and reversible binding between ALM surfaces and MMs. The minimum spacing between BSA, Ova, and Tf molecules was calculated (eq 10) as 49, 24, and 69 nm, respectively (Table 1). The corresponding maximum surface coverage, xmaxρALM/ρMM = 0.004, 0.011, and 0.002, respectively, is ≪1 assuming either kinetically driven deviation from equilibrium surface coverage (eq 6) or a complex structure of the adsorption layer. The first possibility is unlikely because of the absence of a clear relationship between distribution G

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Crystal Growth & Design with the growth step. Note that another host crystal, L-cystine, showing preferential incorporation of labeled BSA is also characterized by high step risers (5.6 nm) on the growth (0001) faces.61

CONCLUSIONS Previously, substantial incorporation of MMs into ALM (010) growth sectors was observed for all eight MMs (including six proteins) tested.2 Here, we tested seven new proteins and found significant incorporation for all of them in the same (010) sector. The detailed study performed for FITC-BSA and, to lesser extent, for FITC-Ova, FITC-Tf, OG-Fg, FITC-avidin, and Hb has shown that the MM/ALM ratio in a crystal is proportional to the ratio in the mother liquor for low MM concentrations. As the MM concentration in solution increases, MM concentration in a crystal reaches saturation, 0.3−8 mg/g ALM or 10−4 to 10−6 mol/mol ALM, corresponding to surface coverage by the adsorbed MM equal to 0.002−0.011. The reason why the maximum achievable surface coverage is so low is not clear. The substantial independence of protein incorporation of growth rate provides an estimate of the characteristic adsorption time τa < 0.5 s, much smaller than typical τa for adsorption of MM on growing crystals. The data suggest that MM adsorption onto ALM (010) is neither strong nor sensitive to the type of protein or protein orientation on the crystal surface, but nevertheless the crystal can occlude protein molecules with high distribution coefficients (up to 12 for FITC-BSA). Likely this is achieved by a very high step edge riser (2.2 nm) that can create a large contact area and stronger interactions at the growth step. Protein incorporation slightly increases as growth temperature decreases, and it strongly drops as ionic strength of the mother liquor increases. MM incorporation has been considered here from a macroscopic or phenomenological perspective. The implication is that there is a microscopic perspective. We hope to provide such a viewpoint in future. In situ atomic force microscopy has been used to study the interactions and overgrowth of proteins with L-cystine61 and calcite with micelles.63 We aim to couple this work with an in situ AFM analysis of lactose growth in the presence of proteins. The astute reader will recognize that not all the questions framed at the outset have been answered. There is nevertheless now a framework for identifying crystals and crystallization conditions that might serve to store and stabilize MM guests.

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REFERENCES

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.cgd.6b00686. Effect of ionic strength on distribution coefficient, effect of growth temperature on distribution coefficient, effect of average growth rate on distribution coefficient, distribution coefficient vs number of crystals formed, effect of pH on MM incorporation, MM incorporation into different crystalline hosts (PDF)

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ACKNOWLEDGMENTS

This work was supported primarily by the MRSEC Program of the National Science Foundation under Award Number DMR1420073. The work was also supported by National Science Foundation grant DMR-1105000 and National Institutes of Health grant NIH-5R21GM107774-02. A.S. was also supported by New York University Global Public Health Research Challenge Fund (GPHRCF), Project R9953. R.K. was supported with a stipend from New York University Abu Dhabi and by NYU Dean’s Undergraduate Research Fund Grant. K.T. is grateful for the DURF grant from the New York University College of Arts and Science.

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AUTHOR INFORMATION

Corresponding Authors

*(A.G.S.) E-mail: [email protected]. *(B.K.) E-mail: [email protected]. Notes

The authors declare no competing financial interest. H

DOI: 10.1021/acs.cgd.6b00686 Cryst. Growth Des. XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.cgd.6b00686 Cryst. Growth Des. XXXX, XXX, XXX−XXX