Micromechanics of Anisotropic Cross-Linked Enzyme Crystals

Article pubs.acs.org/crystal

Cite This: Cryst. Growth Des. XXXX, XXX, XXX−XXX

Micromechanics of Anisotropic Cross-Linked Enzyme Crystals Marta Kubiak,*,† Jennifer Solarczek,‡ Ingo Kampen,† Anett Schallmey,‡ Arno Kwade,† and Carsten Schilde† †

Institute for Particle Technology, Technische Universität Braunschweig, Volkmaroder Str. 5, 38104 Braunschweig, Germany Institute for Biochemistry, Technische Universität Braunschweig, Spielmannstraße 7, 38106 Braunschweig, Germany

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‡

ABSTRACT: Catalytic activity of protein crystals correlates with their particle size due to diffusion limitations. However, because the particles need to be restrained during, e.g., a filtration process, keeping a minimum particle size is required. Thus, knowledge of mechanical properties of enzyme crystals is needed for downstream process design in the biopharmaceutical industry to avoid particle breakage. In this study, hardness and Young’s modulus of cross-linked lysozyme crystals and cross-linked halohydrin dehalogenase from Ilumatobacter coccineus (HheG) crystals are evaluated using atomic force microscopy. The results show that hardness of lysozyme and HheG crystals is in the range of 2−22 MPa. For Young’s modulus of lysozyme crystals, values between 40 and 1820 MPa are measured, while HheG crystals ranging between 40 and 1200 MPa, respectively. The results for lysozyme crystals are comparable to those published in the current literature on native protein crystals. Hence, the cross-linking seems not to significantly affect both values. The investigation of the mechanical properties of HheG is pioneered in this study. Moreover, the mechanical properties are described as a cumulative distribution and fitted using the Weibull theory. The results show that hexagonal protein crystals have a multimodal distribution of mechanical properties, and hence, hardness and Young’s modulus should not be reduced to their average values. In addition, this observation should be taken into consideration by further mechanical studies about protein crystals. 490 MPa.10 The values in dry conditions increased to 200 MPa and 4.2 GPa, respectively.10 The difference in the mechanical properties between wet and dry protein crystals can be explained by the content of intracrystalline (mobile) water. Therefore, weak molecular bonds within a crystal package easily lead to dislocations.8,10 Morozov et al. pioneered the measurements of the Young’s modulus of native and cross-linked triclinic lysozyme crystals with the aid of a mechanical resonance technique. They measured a Young’s modulus in the range of 290−1400 MPa and reported that cross-linking does not significantly affect the value range.11 Cornehl et al. studied the necessary breakage force for crushing single lysozyme crystals and estimated it to be 238.3 ± 124.5 μN.12 Lee et al. investigated the mechanical stability of cross-linked yeast alcohol dehydrogenase (YADH) crystals by shearing it with a rotating disc device. They observed no breakage of rod-shaped CLECs, but a breakage of hexagonalshaped CLECs at energy dissipation rates above 0.1 MW·kg−1.13 They also studied non-cross-linked YADH crystals and noticed a significant shift of the particle size distribution toward smaller particle sizes compared to crosslinked YADH.13

1. INTRODUCTION Biocatalysts, such as isolated enzymes, are increasingly used for the production of chemicals, especially in the pharmaceutical industry, where highly selective reactions at mild experimental conditions are needed.1−3 To be profitable at industrial scale, however, the enzyme catalyst needs to fulfill the following requirements: easy handling, high stability, and reusability.4 For this reason, soluble enzymes are often immobilized on a carrier or cross-linked as protein particles, either crystals (CLECs) or aggregates (CLEAs).5 Catalytic activity of CLECs or CLEAs correlates mainly with their particle size.1,5,6 Therefore, to prevent particle breakage during processing, knowledge of the mechanical properties of the particle, such as its hardness and Young’s modulus, is necessary for the design of an industrial process. Mechanical properties of protein crystals and aggregates depend on the structure of individual protein molecules, packing density, as well as the conformation within a threedimensional structure of protein particles.7 Until now, there are just few publications on the mechanical characterization of protein crystals. Koizumi et al. and Taschibana et al. measured the micro-Vickers hardness of wet lysozyme crystals at room temperature and reported values around 20 MPa8 or 2 MPa.9 Both measurements showed a strong dependence of crystal hardness on the water content. The hardness of dry lysozyme crystals has been determined to be 260 MPa8 and 200 MPa.9 Tait et al. estimated the nanohardness of wet lysozyme crystals to be about 15 MPa and the Young’s modulus to be around © XXXX American Chemical Society

Received: April 26, 2018 Revised: September 4, 2018 Published: September 5, 2018 A

DOI: 10.1021/acs.cgd.8b00637 Cryst. Growth Des. XXXX, XXX, XXX−XXX

Crystal Growth & Design

Article

determining hardness and elastic modulus from load−displacement data of previous publications. In 1992, Oliver and Pharr introduced an improved technique for estimating of the hardness and Young’s modulus for materials with nonlinear unloading curves.23 Figure 1 shows a complete loading and unloading cycle of a measurement obtained with the Berkovich indenter tip. The

AFM is commonly used for protein crystals imaging, characterizing their growth mechanisms14−16 and their surface energy.17 Recently, Guo et al. investigated the mechanical properties of insulin crystals using a nanoindentation technique. Using AFM, they found an elastic modulus in the range of 164 ± 10 MPa.7 Kiran et al. studied plastic deformation on ⟨011⟩ and ⟨100⟩ saccharin crystal faces. They determined the distinct faces to have a 5% variance in Young’s moduli, which is caused by anisotropic interaction within crystalline saccharin.18 To our knowledge, no indentation measurements on cross-linked enzyme crystals have been reported so far, especially on distinct crystallographic faces. Additionally, the statistical consideration of mechanical properties of CLECs has not been reported yet. In this work, we present AFM-based nanoindentation measurements of two distinct CLECs using lysozyme and the halohydrin dehalogenase HheG. Hen egg-white lysozyme was chosen as a standard protein due to its simple crystallization and the already existing literature on the mechanical properties of lysozyme crystals. In contrast, HheG crystals have not been studied for their mechanical properties yet. The bacterial halohydrin dehalogenase HheG from Ilumatobacter coccineus (HheG) was recently discovered by motif-based database mining.19 It is the first enzyme able to catalyze the selective epoxide ring-opening of cyclic epoxide substrates using different nucleophiles,20 which gives access to a number of cyclic building blocks for the synthesis of fine chemicals and pharmaceuticals. Hence, this enzyme is of special interest for future industrial applications. Moreover, HheG’s crystal structure was solved and it was shown to crystallize under various buffer conditions,20 facilitating the generation of CLECs for mechanical testing. In our study, the AFM was chosen for nanoindentation of both CLECs because of its small effective forces in the nanonewton range and, in consequence, small penetration depths in the range of several nanometers. With this, we wanted to prevent dislocations in the three-dimensional crystal lattice during nanoindentation.

Figure 1. Schematic illustration of nanoindentation load−displacement data showing important measured parameters.

three key parameters are the peak load (Pmax), the depth at peak load (hmax), and the slope of the unloading curve at maximal load (S).23 From this raw data, hardness (H) and the reduced Young’s modulus (Er) can be calculated according to formulas 1 and 2, where S is the contact stiffness and Ac is the contact area. Er =

π 2

S Ac

(2)

With knowledge of the indenter geometry, it is possible to calculate the area of contact from the contact depth hc (formulas 3 and 4). hc = hmax − hs

2. THEORY 2.1. Nanoindentation. The nanoindentation technique has been derived from classic hardness measurements, where a hard tip is pressed into the sample’s surface until the userdefined load is reached. The material hardness is calculated using the maximum load divided by the residual indentation area Ac, following formula 1.

(3)

(1)

Pmax (4) S ε is a geometric constant; it is noted 0.75 for conical, Berkovich, or spherical indenter tips.24 The presented nanoindentation method has been primarily developed for a sharp indenter like Berkovich or conical. Thus, the modification for spherical indenter has been implemented according to formula 5, derived from the classical Hertz’s theory.25

The classic hardness measurement technique presupposed that the residual contact area is large enough to be determined by imaging methods. However, estimation of the indentation area with high precision is challenging, if the indentation depth is in the range of several nanometers. Nanoindentation techniques enable evaluation of hardness and Young’s modulus of a material directly from the indentations load−displacement curves. This way, errors due to the optical measurement of very small impressions can be omitted.21 Tabor described for the first time a simplified method for retrieving mechanical properties from nanoindentation data, recorded with a hardened spherical indenter tip.22 Doerner and Nix summarized the most comprehensive methods for

4 E · · R ·δ1.5 (5) 3 1 − ϑ2 However, hardness measurements carried out with a spherical indenter are not necessarily comparable to those done with a Berkovich tip.25 For very thin layers,26 soft or biological materials,27 it is profitable to use an AFM for indentation. In contrast to a nanoindenter, the AFM is more flexible regarding indenter tip size and shape. The cantilever stiffness can be modified simply by the selection of a cantilever with the desired spring constant. The essential advantage of probing mechanical properties of protein crystals is certainly low forces in the range of pico- to nanonewton, which prevents damaging the

H=

Pmax Ac

hs = ε

F=

B



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aldehyde reacts with the free ε-amino groups of lysine residues in proteins. Cross-linking may occur intermolecularly (between different protein molecules) and intramolecularly (between groups in the same molecule).31,32 Wine et al. reported that cross-linking of lysozyme crystals is not random. The crosslinking process starts at a specific and preferable protein site by dimer formation, followed by trimer and tetramer formation. The authors reported that both glutaraldehyde and its polymeric form are involved in the cross-linking process.33

sample. However, there are some challenges in applying the AFM as a nanoindentation instrument. For loading force (F) estimation using Hooke’s Law (see formula 6), the corresponding cantilever deflection (dz) and its spring constant (ks) must be known accurately.28,29 F = −ksdz

(6)

Cantilever bending is detected using a laser beam that is reflected off the cantilever’s back side (see Figure 2). The deflection is measured on a photosensitive photodiode detector and converted into an electrical signal, which is proportional to the displacement of the cantilever.30

3. EXPERIMENTAL SECTION 3.1. Crystallization. Hen egg-white lysozyme (HEWL) (70.000 U/mg) was purchased from Sigma-Aldrich. A lysozyme stock solution (40 mg/mL) was prepared. A solution containing sodium chloride (9% (w/v)) and ethylene glycol (25% (v/v)) in sodium acetate buffer (100 mM, pH 4.8) was used as a precipitation agent. Crystallization was performed by the hanging drop method. A droplet (20 μL) composed of protein (12 μL) and precipitation agent (8 μL) was equilibrated against reservoir solution (1 mL) over 3 days at 5 °C. Tetragonal crystals with an average size of 250 μm were obtained (Figure 3, left).

Figure 3. Left: Tetragonal crystals of hen egg-white lysozyme (HEWL). Right: Hexagonal prism of halohydrin dehalogenase (HheG) crystals. Both crystals were achieved by crystallization conditions described above.

Figure 2. Schematic representation of the principle cantilever bending detection on the photodetector.

While cantilever deflection can be detected easily using a photodetector, the calculation of the spring constant inside a fluid cell can be more challenging, because it depends on the temperature inside the fluid cell. Moreover, exact knowledge of the geometry of the cantilever tip is necessary. If the cantilever tip size is in the nanometer range, Scanning Electron Microscopy (SEM) has to be used to determinate its radius and geometry. Otherwise, the possible error of contact area estimation might be significant. Indentation measurements performed by the AFM slightly differ from the instrumented nanoindentation measurements, which are typically applied for the quantification of nanoscale hardness. Whereas a nanoindenter records a force−displacement curve after approaching to the surface (see Figure 1), AFM records the path to the surface as well. In consequence, the resulting force−displacement curve has a positive range (approaching to the surface - baseline), a zero point (contact to the surface), and a negative range, if an indentation is performed (see further Figure 7). Because AFM responses are very sensitive on small obstacles, the surface approach allows an indication of any impurity in the sample and, if needed, repreparation. 2.2. Cross-Linked Enzyme Crystals. Compared to the conventional immobilization techniques, cross-linking of enzyme crystals provides many advantages. They include a stabilization of the crystal lattice by simultaneously retaining of the catalytic activity, as well as an improvement of the mechanical, thermal, and chemical stability. The cross-linking process includes two steps: (1) crystallization of target proteins and (2) cross-linking of the crystals. The most commonly used cross-linking agent is the glutaraldehyde. This bifunctional

Halohydrin dehalogenase G wildtype from Ilumatobacter coccineus (HheG) was heterologously produced in E. coli and purified as described previously.34 A protein stock solution (6 mg/mL) was prepared. For crystallization, a precipitation solution containing PEG 4000 (10% (w/v)) in HEPES buffer (100 mM, pH 7.5) was applied. A droplet (20 μL) composed of protein (15 μL) and precipitation agent (5 μL) was prepared and equilibrated against reservoir solution (500 μL) at 5 °C. After 3 days, hexagonal prisms with an average size of 100 μm were visible under an optical microscope (Figure 3, right). 3.2. Cross-Linking. Both enzyme crystals were cross-linked using the same method. First, the crystallization slurry was cooled down on ice for 2 h. After that, the mother liquor was removed from the droplet and crystals were washed with 10 μL of precipitation agent. 10 μL of cross-linking solution, containing glutaraldehyde (5% (v/v)) dissolved in the precipitation agent, was added to the crystals. The slurry was kept at 5 °C for several hours to complete the cross-linking process. Just before mechanical testing, cross-linked lysozyme and HheG crystals were washed and stored in pure water, having an ionic conductivity of 0.055 μS. 3.3. Indentation Measurements. AFM (JPK NanoWizard3) was used to determine hardness and Young’s modulus of both CLECs. All measurements were performed in equal environmental conditions and measurement parameters, shown in Table 1. A cantilever with a spherical tip as shown in Figure 4 (customized B300 on NCHAu, Nanotools) was used for all indentation measurements. It was not dismounted between individual measurement runs to avoid changes in the measurement setup. Indentation tests were carried out in force spectroscopy mode, and the load−displacement curves were analyzed using JPK Data Processing software. The contact point, indentation depth, and slope of the unloading curves were obtained and processed with the help of MATLAB2017a. C



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Table 1. Software and Cantilever Parameters Used for Determining Mechanical Properties of Protein Crystals by the AFM Nanoindentation Technique parameter

value

surface detection indentation force z-length indentation speed cantilever radius cantilever spring constant

100 nN 250 nN 1 μm 2 μm/s 300 nm 40 N/m

Figure 6. Schematic cantilever positions on the crystal surface of a hexagonal HheG crystal. Note that the indentation grid was individually set for each crystal.

retracting the cantilever from the crystal’s surface. No pop-ins or mechanical wear are visible on the recorded data. The contact area strongly depends on the indenter tip geometry. If its radius or shape is not exactly known, the calculation of the contact area is uncertain. Hence, SEM imaging of the cantilever tip is essential. SEM images of the used cantilever scanned before and after indentation measurements showed that the spherical cantilever tip, which is placed on the top of a pyramidal substrate, has been broken off during the measurements. The force−displacement curves resulting from measurements without spherical indenter geometry (e.g., due to contaminations or tip breakage) differ a little from those achieved with the spherical cantilever tip, because the remaining pyramidal substrate is still functioning as an indenter tip. However, the resulting displacement is usually smaller and the slope of the retracted curve is lower. Hence, the cumulative error by calculating of hardness and Young’s modulus is significant. Therefore, each curve has been proven individually by the Hertzian model (c.f. section 2). If an indentation is executed using a spherical indenter tip, the approaching curve is raising to the power of 1.5 (c.f. formula 5 and Figure 8) and the Hertzian model fits the approaching curve with negligible deviation. The deviation is calculated according to formula 7, which is the mean squared error between measured data and the Hertzian model.

Figure 4. SEM image of the cantilever with a spherical tip on the top of a pyramidal substrate. Because of the anisotropic behavior of protein crystals, more than 20 indentations were executed on 10 ⟨110⟩ faces of lysozyme and 14 ⟨1100⟩ HheG crystals. It should be noted that it was not possible to identify crystal faces from the crystallographic view. The notation ⟨110⟩ indicates one of four irregular hexagonal faces of tetragonal lysozyme crystals. The index ⟨1100⟩ means one of six rectangular faces of HheG crystals (see Figure 5).

Figure 5. Simplified crystallographic indication of the distinct crystal faces. Left: Indication of the ⟨110⟩ faces of tetragonal lysozyme crystals. Right: Indication of the ⟨1100⟩ faces of hexagonal HheG crystals.

∑ [Fi − Hertzian model(i)]2 /N

The indents were performed systematically on crystal faces ⟨110⟩ and ⟨1100⟩. An indentation grid was prepared individually for each crystal, dependent on the crystal’s size and location. Single force− displacement curves were recorded as described in the section 2: First, the crystal surface was detected and the baseline was recorded. In the second step, the indent was carried out until the user-defined force of 250 nN was reached. After that, the cantilever tip was retracted from the surface. No holding phase was applied during the indentation measurements. This way, all points of the indentation grid were examined. A schematic indentation pattern of an HheG crystal is shown in Figure 6.

(7)

The fit allows discarding curves obviously differing from this model if the residual RMS is greater than 1.5 nN. This is caused either by a nonspherical indenter tip or by an uneven/ rough crystal surface. For the calculation of hardness and elastic moduli from AFM raw data, the Oliver and Pharr method has been used. This model is used for describing the elastic-plastic behavior of various materials.21 However, Morozov et al. have already reported viscoelastic behavior of lysozyme crystals.11 Viscoelastic creep in the unloading phase may dramatically affect the slope of the retracting curve, leading to large uncertainties in the calculated elastic moduli.35 In this case, the Oliver and Pharr theory would not produce accurate results for the instantaneous hardness and elastic moduli. It can be seen in Figure 7 that the unloading curve is not affected by creep because of its relatively short measurement time and because the retracted curve does not exhibit a typical “nose” at peak

4. RESULTS AND DISCUSSION 4.1. Consideration of Results and Identification of Potential Errors. Figure 7 shows typical force−displacement curves achieved via force spectroscopy mode. The resulting curves are characterized by the absence of a jump into contact and the occurrence of very small adhesion forces while D



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Figure 7. Representative force−displacement data curves for instrumented nanoindentation on a lysozyme crystal (left) and an HheG crystal (right). The up arrow on the right graph shows the approaching curve, and the down arrow indicates the retracting curve.

Figure 9. Illustration of the pile-up (the left side) and sink-in (the right side) during an indentation measurement. The contact penetration depths resulting from pile-up or sink-in are also added to the sketch.

indenting at true nanometer scale, i.e., at penetrations depth smaller than 200 nm.39 Considering this scale, the probability of building pile-ups is negligible for this study. However, if pileup occurs, its effect is expected to be higher for HheG than for lysozyme crystals, taking deeper displacements into account (see further Figure 11, left, in section 4.2). The indenter tip size is another aspect that needs to be considered. Mollica, as well as Guo, reported about mechanical wear on the crystal surfaces during AFM measurements. Both authors used a very soft cantilever with an indenter tip radius smaller than 40 nm.7,17 The resulting force−displacement curves indicate the removal of protein molecules from the crystal surface during the indentation test.7,17 This observation has been confirmed by simple molecular dynamic simulation.7,17 Compared to this work, similar results have been achieved during the pretests. If the protein crystals were indented using a soft cantilever (kc = 0.2 N/m, indenter radius of 100 nm), removal of protein molecules from the top layer occurred (Figure 10). Moreover, if too high indentation forces were applied for a soft cantilever, strong cantilever bending away from the sample and in consequence C-shaped loading and unloading curves were observed. However, no related mechanical wear has been noticed by using a stiff cantilever with a radius of 150 nm, respectively, 300 nm (see Figure 7). Thus, a minimal radius of 150 nm combined with high spring constant is suggested to avoid damage of the top layer. Note that all measurements in this

Figure 8. Hertzian plot (green, dotted) fitting the HheG approaching curve (from Figure 7, right). In this case, the RMS value was in piconewton range, indicating very good agreement between measurement and the fit.

load, which would be characteristic for viscoelastic materials. For this reason, the raw data were processed using the Oliver and Pharr theory. Apart from creeping, pile-up effects must also be considered. For example, it may occur for viscoelastic samples effecting the contact area. As a result, the contact area is greater than predicted and both, hardness and elastic modulus, are overestimated by up to 60%.36 For conical indenter shapes, the parameter hf/hmax is used for estimating the pile-up threshold.36 For a spherical indenter, the situation is more complex: Because of the mean contact pressure, stress and strain increase with the depth of penetration.37 At low force (and shallow indentation depth), the deformation is elastic and the material around the indenter sinks. 37 By deeper penetration, the material may undergo an irreversible deformation. At this point, the material can be pushed toward the indenter (see pile-up and sink-in in Figure 9). The tendency for building pile-ups rises for increasing indenter penetration depths h/R.38 Tranchida et al. reported that pile-ups of viscoelastic materials can be minimized by E



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withstand the applied forces. The higher the indentation depth and, therefore, the deformation, the lower the material resistance (strength) against the applied forces. Figure 11 (right) indicates that at least 150 indents are needed for accurate describing of cumulative distribution. Larger number of indents does not reduce the confidence interval significantly. Here, the correlated standard deviation is a function of the variability on the sample. Both, HEWL and HheG crystals, exhibit wide deformation distributions in an approximate range between 5−60 nm and 7−100 nm, respectively. However, it can be easily observed that HheG crystals are notably less resistant against deformation than the HEWL crystals. The average indentation depth of HheG crystals is 30 nm, 3 times as high as the mean value of HEWL crystals. Compared to the mechanical properties derived from a data set like the slope of the unloading curve, indenter radius, etc., the deformation exhibits a direct material response on the mechanical stress and contains no errors due to calculation theory. Thus, the deformation should remain constant, even if the cantilever radius size will be changed slightly. Note that this phenomenon should appear, if the crystallization and cross-linking conditions, or measurement parameters remain unchanged. Especially, the cross-linking duration seems to play an important role for the material’s behavior under mechanical stress. Pretests by a cross-linking time of only 2 h showed an increased crystal deformation during the measurements. Measuring at wet conditions, penetration deepened continuously as if non-cross-linked proteins had been rinsed out of the crystals, and the crystal lattice stability decreases over time. For this reason, we cross-linked the crystals over several hours in this study. 4.3. Mechanical Properties of Cross-Linked Lysozyme and HheG Crystals. 4.3.1. Hardness Distribution on the Crystal Surfaces. The force−displacement response indicates a plastic-elastic deformation. The viscous deformation has no significant influence on the unloading curve (c.f. Figure 7). Hence, the raw data are evaluated according to the Oliver− Pharr theory, described in the section 2 and presented below. By indenting the crystal surface systematically (according to Figure 6), a dependence between mechanical properties and the tip position on the crystal surface was investigated. Figure 12 presents an example of this approach. In the threedimensional plots, the x-axes represent the “short edge” and the y-axes the “long edge” of two distinct HheG crystals. The zaxes represent the resulting hardness on the crystal surfaces.

Figure 10. Force−displacement curve of the AFM nanoindentation achieved by a soft cantilever with a radius of 100 nm. The red circle indicates mechanical wear on the crystal surface at the initial indentation phase.

publication were done using a stiff cantilever with a radius of 300 nm, as mentioned in the Experimental Section. Moreover, SEM images of the cantilever tip showed that, when the probability of occurrence of the small dents (irregularities) is the higher, the smaller the spherical tip radius. A nonperfectly spherical tip may lead to a nonuniform stress distribution and, therefore, local overload and mechanical wear. Moeller has examined the influence of an indenter’s radius on nanoindentation of viscoelastic materials. He reports a significant accuracy improvement for modulus measurements, if large end-radius tips with an appropriate cantilever stiffness are used for the experiment.40 4.2. Deformation of Cross-Linked Lysozyme and HheG Crystals. It is necessary to describe crystal deformations and all mechanical properties using a statistical or cumulative distribution, because of the high variability on the crystal surface, failures within the inner crystalline structure, and additional influencing factors (e.g., temperature drift). Compared to the mean value and standard deviation, this approach allows collection of detailed statistical data. Also, qualitative comparisons between results achieved by different crystallization or cross-linking conditions become possible. The boxplot in Figure 11 (left) shows the indentation depths of lysozyme and HheG crystals extracted from raw nanoindentation data (excluding discarded results, c.f. section 4.1). The displacement implies the ability of materials to

Figure 11. Left: Total deformation of protein enzymes at nanoindentation using a spherical indenter tip by the loading force of 250 nN. The boxplots comprise over 240 data for lysozyme crystals and over 230 for HheG crystals. The whiskers show the minimal and maximal indentation depth. Right: Influence of the indents number on the confidence interval around the mean value of the displacement for lysozyme crystals (confidence interval of 95%). F



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Figure 12. Hardness distribution of two single crystal surfaces of HheG crystals. The hardness on the left side ranges from 2 to 20 MPa and on the right side between 4 and 6 MPa, respectively. No dependency between mechanical properties and the cantilever position has been observed.

Figure 13. Cumulative hardness distribution for single cross-linked enzyme crystals. Left: ⟨110⟩ faces of lysozyme crystals show a uniform mechanical behavior, where the hardness ranging from 2 to 20 MPa. Right: The results of HheG crystals indicate different mechanical behavior on the ⟨1100⟩ crystal faces. Hardness of some of them ranging from 2 to 10 MPa. The residual faces have a broader hardness distribution between 2 and 22 MPa.

Figure 14. Summarized hardness distributions and Weibull plots of cross-linked enzyme crystal slurries. Left: Cumulative distribution of 10 crosslinked lysozyme crystals. Right: Cumulative distribution of 14 cross-linked HheG crystals. In order to show the differences between the ⟨1100⟩ faces, separated cumulative distributions for the face (a) and (b) are presented.

G



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investigate a suitable statistical distribution fit. Weibull analysis, which is often used for the mechanical characterization, emerges to be optimal for the fit.41 Therefore, three-parameter Weibull cumulative distributions are calculated according to the formula 8, where η is the scale, β is the shape/slope (Weibull modulus), and α is the location parameter. Weibull plots are shown in Figure 14 (light blue), and Weibull parameters are summarized in Table 3.

For the measured crystals, no systematic dependencies between mechanical properties and the cantilever position are detected. As can be seen from Figure 12, both crystals show different hardness distribution on the crystal surface. Whereas the hardness on the left side fluctuates between 2 and 20 MPa showing a broad distribution, the hardness of the crystal on the right side exhibits a narrow hardness distribution between 3.8 and 6 MPa with a negligible outlier by 7.8 MPa. In the second step, all results of the cross-linked enzyme crystals are ploted in Figure 13 as single cumulative distributions of the hardness to illustrate the variation of the mechanical properties on the regarded crystal surfaces ⟨110⟩ for lysozyme and ⟨1100⟩ for HheG. There is an obvious difference in the cumulative distribution of both protein enzymes. The hardness of the cross-linked lysozyme crystals exhibits an equal distribution, indicating that the examined ⟨110⟩ faces are similar and comparable with each other. In the case of HheG crystals, the slight disparity in the hardness distribution of the crystals surfaces is visible. As mentioned before, only the ⟨1100⟩ crystal faces are examined. In hexagonal prism crystals (see Figure 3), there are six similar rectangular faces, which are declared as ⟨1100⟩ faces. Their discrimination via optical methods is not possible, yet. Measurements from Figure 13 (right) indicate that, in contrast to lysozyme crystal faces, those crystal faces are not equivalent. Four of six faces evince a more homogeneous hardness distribution ranging from 2 to 10 MPa. The residual faces have a wide distribution ranging from 2 to 22 MPa. No similar phenomenon has been observed between four different ⟨110⟩ lysozyme faces. Here, the hardness varies between 2 and 20 MPa. Due to the distinct mechanical behavior of the HheG crystals, it is necessary to introduce an additional indication for the face ⟨1100⟩: (a) for the narrow and (b) for the broad cumulative distribution. For the characterization of crystal slurries, the results of single cross-linked enzyme crystals are summarized to the total cumulative distribution and presented in Figure 14 (dark blue curves). This allows extracting statistical data of the whole sample. For instance, the mean hardness of the lysozyme crystals is 11.4 MPa, of the HheG ⟨1100⟩ face (a) is 4.3 MPa, and of the face (b) is 8.9 MPa, respectively. Detailed statistic hardness data are summarized in Table 2. The illustrated hardness distributions show a wide variation in the results requiring a statistical analysis. Hence, all data are initially examined applying the Kolmogorov−Smirnov test to

F (x ) = 1 − e − (

min max mean median literaturea

2.7 20 11.4 11.9 15b

1.4 8.5 4.3 4.3

1.7 22.3 8.9 8.5

(8)

parameter

lysozyme

face (a)

face (b)

scale η shape β location α

12.2 4.1 0.4

4 2.6 0.8

9.1 1.7 0.6

Taking the magnitude of the results into consideration, differences in the hardness are very small and negligible for industrial processes. Both CLECs are soft and would probably not withstand high mechanical stress without damage. 4.3.2. Young’s Modulus Distribution on the Crystal Surfaces. Elastic moduli of both enzymes were determined analogously to the hardness results. Because of the distribution of Young’s modulus being very similar to the hardness, additional results are not shown; only the summarized cumulative distributions along Weibull fittings are presented in Figure 15. While getting comparable hardness results, there is a clear difference between the Young’s modulus of cross-linked lysozyme and halohydrin dehalogenase crystals. Lysozyme and HheG crystal faces declared as the face (b) have comparable Young’s moduli in the range of approximately 100 MPa to 1.7 GPa, and 1.2 GPa, respectively. The ⟨1100⟩ face (a) exhibits a narrow distribution in the range of 40− 580 MPa. The results are summarized in Tables 4 and 5. The calculated hardness values of examined CLECs are in the range of a few megapascal and, therefore, comparable to the literature results concerning protein crystals. The Young’s modulus is in the range of mega- to gigapascal and, thus, similar to those given in publications mentioned in the Introduction section. Surprisingly, the cross-linking process does not seem to affect the evaluated mechanical properties of protein crystals significantly. Morozov et al. have already examined cross-linked triclinic lysozyme crystals using a resonance method. They also observed only a slight influence of cross-linking on the elastic modulus of lysozyme crystals.11 The low hardness and elastic modulus of protein crystals correlate with the large amount of water within the crystal lattice. There are two distinct water types: immobile water strongly bound to the protein molecules42 and mobile water between the protein molecules.43 It can be expected that the mobile water leads to a viscous material behavior due to the movement in the crystal pores. Because of the low deformation during the indentation test, however, the viscous effect could not be seen in the recorded data. Hence, if the mechanical stress is acting on the surface, the protein molecules easily move against each other. The mechanical stress often leads to shifting of the slip planes, causing the characteristic pop-ins in

halohydrin dehalogenase face (b)

β

halohydrin dehalogenase

hardness/MPa

face (a)

)

Table 3. Detailed Weibull Parameter of the Fitting Plots for Hardness Cumulative Distributions

Table 2. Statistical Hardness Data of Cross-Linked Lysozyme and Halohydrin Dehalogenase Crystalsc

lysozyme

x−α η

a

Tait et al.10 bNote that the hardness and elastic modulus, mentioned in the literature, were estimated as an average value of approximately 16 indents. Compared to those measurements, almost 250 indents were done for each protein enzyme in this publication. cFor native tetragonal lysozyme crystals, the literature value has been added. H



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Figure 15. Summarized Young’s modulus distributions and Weibull plots of cross-linked enzyme crystal slurries. Left: Cumulative distribution of 10 cross-linked lysozyme crystals. Right: Cumulative distribution of 14 cross-linked HheG crystals. In order to show the differences between the ⟨1100⟩ faces, separated cumulative distributions for the faces (a) and (b) are presented.

hence, a lysozyme crystallized at similar conditions was used for comparison of the crystal structure.) The higher the Bfactor, the higher the flexibility (disorder) inside a crystal, which can be caused by a few or a weak intermolecular contacts. Summarized, the following reasons can explain the evaluated differences: slightly lower water content and lower flexibility within the crystal lattice of lysozyme crystals. On the other hand, the flexibility of the molecules in a protein crystal is also affected by the cross-linking treatment. Due to the cross-linking process, amino acid residues are covalently linked to each other. Glutaraldehyde connects lysine residues within a protein molecule, as well as between two adjacent molecules.32 Depending on the amount of lysine residues on the protein surface and the distance between two lysine residues on two adjacent molecules in the crystal lattice, different amounts of covalent bonds may be formed. Taking into account that 5 of the 282 amino acids of HheG and 6 of the 129 amino acids of lysozyme are lysine residues, it could be assumed that the lysozyme has a higher quantity of crosslinked bonds. An unequal cross-linking degree of both protein crystals can also be used to explain the distinct behavior of mechanical properties of different crystal faces. The halohydrin dehalogenase crystals show a clear difference between the six ⟨1100⟩ crystal faces. As the results indicate, four of those faces are softer and less stiff (face (a)) compared to the other two (face (b)). A possible reason for this observation could be a different molecular packing with regard to the distinct faces. Further, due to a low lysine content, an anisotropic cross-linking could occur. Moreover, the cross-linking process for the faces (a) may not be finished yet. It needs to be investigated in the future, whether a shift of the cumulative curves will be observed if the cross-linking duration time is shortened or prolonged. The measurement accuracy of an AFM itself for the determination of micromechanical properties, e.g., hardness and Young’s modulus, is significantly higher than the variance of the micromechanical properties measured in the series of crystals characterized in this study. Thus, apart from median values for hardness and Young’s modulus, the entire distribution of these values is a characteristic, which has to

Table 4. Statistical Young’s Modulus Data of Cross-Linked Lysozyme and Halohydrin Dehalogenase Crystalsb Young’s modulus/MPa halohydrin dehalogenase min max mean median literaturea

lysozyme

face (a)

face (b)

140 1819 1080 1073 490

39 577 288 283

106 1192 527 495

a

Tait et al.10 bFor native tetragonal lysozyme crystals, literature value has been added.

Table 5. Detailed Weibull Parameters of Young’s Modulus Cumulative Distribution Fitting halohydrin dehalogenase parameter

lysozyme

face (a)

face (b)

scale η shape β location α

1200 3.8 0

313 3.3 40

589 2.5 1

the force−displacement curves. But no slip dislocations have been observed, yet. It is possible that the cross-linking process reinforced the crystal lattice, which is why the low forces did not damage the domestic crystal structure. This is the main reason why the AFM has been used. Next, the difference between two distinct enzyme crystals will be considered. Cross-linked lysozyme crystals feature a slightly higher hardness; the elastic modulus is almost twice as high as those of HheG crystals. The difference might be explained by the molecular structure of both crystals. On the basis of the analysis done by Chruszcz, tetragonal lysozyme crystals have a lower solvent content value compared to the hexagonal HheG crystals (0.56 and 0.57, respectively).44 Moreover, the Wilson B-factorwhich indicates the degree of order in the crystalis higher for the HheG crystals (∼40 Å2),20 than for the lysozyme crystals (∼20 Å2).45 (No Xray diffraction data has been recorded for lysozyme crystals; I



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both protein crystals show a wide variation in the results and must be described as a cumulative distribution. The hardness of cross-linked lysozyme and HheG crystals is in the range of 2−22 MPa. For Young’s modulus of lysozyme crystals, values between 40 and 1820 MPa have been measured, while HheG crystals ranging between 40 and 1200 MPa. Whereas lysozyme crystals indicate a similar distribution of the mechanical properties on all ⟨110⟩ crystal faces, HheG crystals exhibit a clear distinction between their six ⟨1100⟩ crystal faces. The cumulative distributions have been plotted by the Weibull model, and the three statistical parameters (η, β, and α) have been calculated. Compared to HheG crystals, the anisotropy on the lysozyme crystals is relatively low and the flaws are clustered consistently on the surface.

be taken into account. The characterization of the distribution in mechanical properties via parameters derived from normal, log-normal, and Weibull statistics is a common method for biological materials, e.g., cells or particulate materials like crystals, agglomerates, and single grains.46−48 The median values as well as parameters, which describe the shape of the distribution in the micromechanical properties of protein crystals, are affected by the crystal material properties themselves (e.g., crystal faces, cross-linking) on the one hand, and the formulation and processing along the entire process chain of crystal synthesis on the other hand. Hence, characteristic values for the comparison of the distributed values are of basic importance. Typically, for aggregated and agglomerated systems, which are influenced by different distributed values, e.g., distribution in particle size, solid bond diameter and strength, coordination number, etc., the distribution of micromechanical properties can be described by log-normal distributions.41,49 In contrast, single grains or highly defined systems, such as the protein crystals investigated in this study, are often Weibull distributed.46 Weibull statistics is based on the principle of the weakest link in a defined chain. It gives the failure probability of a chain, which consists out of a number of links of a certain strength when load is applied.50 Thus, in the case of highly defined protein crystals, the parameters of the Weibull statistics should be used as characteristic values for the specification of the distribution of hardness and Young’s modulus. Beta (β) gives an information about the shape and art of the distribution (β = 1: exponential distribution; β ≈ 3.6: normal distribution), as well as a failure rate of a material; for instance, β > 1 indicates that failure rate increases with time, known as a wear-out failures. Figures 14 and 15 show that the hardness and the elastic modulus can be fitted by Weibull statistics. In the case of protein crystals, the Weibull modulus (β) is used to describe variability of the measured material.51 The higher the value, the slighter the variation in mechanical properties and the smaller the required number of indents to describe the evaluated sample. A low Weibull modulus value indicates a low reliability because of physical flaws, caused by inherent material behavior or the crystallization/cross-linking process. As presented in Tables 3 and 5, the established shape parameter shows the best value for the lysozyme crystals. Eta (η) is the scale parameter and has an influence on the stretching of the distribution. Because of the different behavior of both crystals and split of the HheG distribution, the scale parameter cannot be taken into consideration. Alpha (α) is the location parameter and characterizes a waiting time for the occurrence of high deformations on the crystal surface (time to failure). Because there is no shift in the cumulative distribution of the mechanical properties of lysozyme crystals, the distribution is reduced to a 2-parameter Weibull fit. It may be concluded that the anisotropy of lysozyme crystals is relatively low compared to HheG crystals, and the flaws are clustered consistently on the surface.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: +49 (0) 53139165533. Fax: +49 (0) 5313919631. ORCID

Marta Kubiak: 0000-0001-8463-9204 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank the German Research Foundation (DFG) for funding the DiSPBiotech priority programme (SPP 1934, SCHI 1265/3-1, and KW 9/27-1).

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Micromechanics of Anisotropic Cross-Linked Enzyme Crystals

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