Relationship between Cross-Linking Reaction Time and Anisotropic

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

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Relationship between Cross-Linking Reaction Time and Anisotropic Mechanical Behavior of Enzyme Crystals Marta Kubiak,* Karl-Falco Storm, Ingo Kampen, and Carsten Schilde

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Institute for Particle Technology, Technische Universität Braunschweig, Volkmaroder Str. 5, 38104 Braunschweig, Germany ABSTRACT: The application of protein particles as useful biocatalysts in the chemical or pharmaceutical industry is restricted due to their fragility and sensitivity to changes of environmental conditions. The cross-linking method for enzyme crystal immobilization provides an enhancement of crystal stability. However, cross-linking conditions and the linker type strongly affect the mechanical properties of the cross-linked protein particles. Our work examines the cross-linking reaction time’s influence on mechanical properties of cross-linked HheG crystals. An atomic force microscopy-based nanoindentation is used for mechanical measurements. Our results show that cross-linking of amino acid residues takes place inhomogeneously within the crystal lattice. Hardness and Young’s modulus of prismatic crystal faces remain constant above 24 h of cross-linking. At this time, however, basal crystal faces show around 30% higher mechanical stability compared to prismatic faces. The detection of anisotropies between prismatic crystal faces is interpreted as a function of the cross-liking reaction time. On the basis of the crystal’s structure and possible functional groups for cross-linking, the distance distribution within a supercell is evaluated. The developed mathematical model is then used for a differentiation between mechanical properties depending on reaction time and structural anisotropies. range of 2.2 × 103 to 6.8 × 105 W·kg−1. The authors found out that large hexagonal crystals break at energy dissipation rates above 1.0 × 105 W·kg−1; however, no breakage of rod-shaped crystals occurs over the entire range.11 Kubiak et al. measured the micromechanical properties of CLECs using atomic force microscopy (AFM) nanoindentation. The examination of hardness and Young’s modulus showed different distributions of mechanical properties on distinct crystal faces. The investigated hardness of cross-linked lysozyme and HheG crystals is in the range of 2−22 MPa. Young’s modulus ranges from 40 to 1820 MPa for lysozyme crystals and from 40 to 1200 MPa for HheG crystals.12 Cross-linking of biocatalysts has an influence on both, a crystal’s mechanical properties as well as its catalytic activity. An incrementation in cross-linking time leads to improved mechanical stability, but excessive cross-linking may cause protein precipitation and a loss in activity.13 A large number of studies describe the correlation between cross-linking degree and mechanical properties of polymeric and biopolymeric materials.14−16 However, they focus on the examination of linker concentration rather than on the cross-linking duration. As far as we know, there are no similar studies investigating the influence of cross-linking reaction time on mechanical properties of protein crystals evaluated systematically using AFM. This paper provides an important opportunity to advance the understanding of the relationship between crystal

1. INTRODUCTION Because of highly selective reactions, safety, and sustainability, the industrial use of biocatalysts has been expanded to many manufacturing sectors, like chemical or pharmaceutical production.1,2 Despite the great potential of protein enzymes, their practical industrial applications are restricted in terms of stability, catalytic efficiency, and specificity.2−4 For this purpose, enzyme immobilization has gathered interest in recent decades.4,5 Cross-linking of enzyme crystals (CLECs) is a cost-efficient immobilization method, which enhances the catalysts stability without dilution of their activity.4 Apart from very high catalytic activity per unit volume, cross-linking provides additional benefits for bioprocessing like easy separation of the protein particles from the product and their reusability.3,6 One of the mostly used linkers of CLEC designs is glutaraldehyde (GA)3,7,8 because of its low cost, easy handling, and safety.3,8 Because of its self-polymerization, the resulting cross-linked bonds within a crystal are unpredictable,9 making it a highly effective linker.8 Glutaraldehyde was already used in the study on mechanical properties of CLECs described in recent studies. For instance, Morozov et al. examined parent and cross-linked triclinic lysozyme crystals with the aid of a resonance technique and measured Young’s modulus of parent protein crystals in the range of 290−1400 MPa. They also reported no significant influence of the cross-linking of protein crystals on this value range.10 Lee et al. investigated the breakage probability of different shaped cross-linked YADHI crystals using a rotating disc shear device. In this study, the rate of CLEC breakage depending on energy dissipation rate was measured over the © XXXX American Chemical Society

Received: February 19, 2019 Revised: May 21, 2019 Published: June 26, 2019 A

DOI: 10.1021/acs.cgd.9b00232 Cryst. Growth Des. XXXX, XXX, XXX−XXX

Crystal Growth & Design

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Figure 1. Schematic self-polymerization of glutaraldehyde in aqueous solution.

glutaraldehyde and its polymeric forms, are involved in the cross-linking process.25 Mechanical Measurements. Compared to conventional instrumented nanoindentation measurements, the AFMindentation method is fundamentally different. The AFM uses a cantilever with a well-defined tip size, shape, and stiffness. During the AFM nanoindentation process, the cantilever deflection is tracked continually by a position sensitive photodetector (PSPD). The deflection results from a laser beam being reflected from the backside of the cantilever. The force between the cantilever tip and the sample is not directly measured, but calculated in regard to the cantilever stiffness (ks) and its deflection (dz), according to formula 1.

structure, cross-linking progress, and resulting anisotropic mechanical behavior in consideration of application in industrial processes. For the experiments, the crystals of bacterial halohydrin dehalogenase from Ilumatobacter coccineus (HheG) were used. HheG is the first enzyme being able to catalyze the selective epoxide ring-opening of cyclic epoxide substrates using different nucleophiles, giving access to a number of cyclic building blocks for the synthesis of fine chemicals and pharmaceuticals.17 Hence, this enzyme is of special interest for future industrial applications.

2. THEORY Cross-Linking of Enzyme Crystals. Because of insertion of covalent bonds in the crystal lattice, chemical cross-linking provides many advantages compared to conventional immobilization methods, e.g., insolubility in aqueous media, resistance to changes in pH value, temperature, and proteolytic enzymes, and enhancement of mechanical properties.7 The cross-linking process includes two steps: (1) crystallization of target proteins and (2) cross-linking of the crystals. As motioned in the Introduction, glutaraldehyde is one of the commonly used cross-linking agents. This bifunctional aldehyde reacts particularly with the free ε-amino groups of lysine residues in proteins. However, glutaraldehyde and its polymerization products may react with several functional groups like amine, thiols, phenols, or imidazoles.18 In aqueous media, the free aldehyde groups of GA are very reactive and exhibit different tendencies for self-polymerization, depending on environmental factors like pH and linker concentration.5,19 When GA concentrations are increased or alkaline conditions are used,19,20 the affinity for self-polymerization also increases. In acidic conditions, GA shows low polymerization rates.21 Figure 1 shows two possible polymerization forms of glutaraldehyde in aqueous solution. The polymerization process is characterized by the repeatable addition of monomers while water is being eliminated. Cross-linking may occur intramolecularly (between groups in the same molecule) or intermolecularly (between different protein molecules).22 The intermolecular contacts are necessary in order to maintain the crystal structure in environments differing from the crystallization liquor.23 For a successful cross-linking, an appropriate distance between two adjacent moiety groups on the protein surface is required.24 Wine et al. examined cross-linked lysozyme crystals using an Xray method. They reported that cross-linking of crystals is not a random process. The cross-linking process starts at preferred protein sites specified by dimer formation, followed by trimer and tetramer formation. The authors reported that both,

F = −ksdz

(1)

The conventional nanoindenter records a force−displacement curve only after approaching the sample’s surface, whereas the AFM records the approach phase as well. In consequence, its resulting force−displacement curve has a positive range (surface approach is denoted as baseline), a zero point (contact to the surface), and a negative range (force− displacement curve) while an indentation is performed (Figure 2). Because low forces in the range of pico- to nanonewton prevent damaging of the sample, AFM is preferred for the measurement of very thin layers,26 soft or biological materials.27 Moreover, due to AFM nanoindentation, the

Figure 2. Fit of the Oliver and Pharr analysis to the AFM force− displacement curve. B



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using the precipitation solution. Just before mechanical testing, the crystals were washed one last time and then stored in pure water. Microcompression. The Hysitron TriboIndenter was used for microcompression tests of native and cross-linked HheG crystals. Because the measurements were executed in a liquid environment, the crystal surface was detected with a set point of 1000 μN. Then, both faces were compressed between two parallel surfaces, displacementcontrolled with a flat punch indenter (Ø 100 μm). For native crystals, a maximum displacement of 1 μm, with a constant loading rate of 1700 nm/s, was applied. For cross-linked HheG crystals, the displacement varied between 30 and 80 μm, depending on the crystal’s size. The indentation speed’s influence on the crystal’s behavior was examined through variation of the indentation speed from several dozen to a few thousand nanometers per second. The breakage capability of native and cross-linked protein crystals investigation is based on more than 100 crystals. AFM Nanoindentation. The measurements using AFM (JPK NanoWizard 3) were performed as described previously.12 However, in the current study, a cantilever with a radius of 150 nm instead of 300 nm was applied for systematic indentation on both crystal faces (prismatic and basal; see Figure 4). In order to present the

influence of viscoelastic behavior of protein crystals on creep during a measurement can be considerably reduced.12,28 Hence, the calculation of hardness and Young’s modulus based on force−displacement curves can be executed according to the Oliver and Pharr theory.29 When this method is adapted to the force−displacement curves measured with the AFM, the necessary key parameters (the peak load Pmax, the depth at the peak load hmax, and the slope of unloading curve S) can be extracted as shown in Figure 2. Hardness H is determined according to formula 2, where Ac is the projected area. For a spherical indenter tip, the area is calculated following formula 3. H=

Pmax Ac

(2)

Ac = 2·π ·R ·hc − π ·hc2

(3)

With knowledge of the indenter tip geometry, the contact depth hc can be calculated using formula 4, where ε is a geometric constant. For a spherical indenter tip, ε is noted to 0.75.30 hc = hmax − ε

Pmax S

(4)

The reduced Young’s modulus can be finally calculated according to formula 5. Er =

π S · 2 Ac

(5)

3. EXPERIMENTAL SECTION

Figure 4. Schematic identification of distinct crystal faces of a hexagonal protein crystal.

Crystallization and Cross-Linking. Crystallization of halohydrin dehalogenase G wildtype was performed using the hanging drop method. A 20 μL droplet, composed of protein stock solution (23 mg/mL) and precipitation solution (PEG 4000 (10% (w/v)) in HEPES buffer (10mM, pH 7.3)), was equilibrated against the reservoir solution (500 μL) at 5 °C. After 24 h, hexagonal crystals with an average size of 70 μm were observed under an optical microscope (see Figure 3) and prepared for cross-linking using the soaking method.

micromechanical properties as a cumulative distribution, a sufficiently large number of indents were performed on each of the considered crystal faces and on various crystals. Systematic examination of the cross-linked HheG crystal’s surface allows detection of the small changes on the crystal surface, e.g., caused by creation of anisotropic covalent bonds. In order to visualize distinctions between single crystal faces, approximately 20 force−displacement curves were recorded on each of examined faces. For the 10 crystals used, different positions were chosen. The mechanical properties are plotted as a cumulative distribution for each of the crystal faces (cf. Figure 4). All results of the cross-linking-time variation are compared in order to characterize micromechanical characteristics of each crystal slurry.

4. RESULTS AND DISCUSSION Effect of Cross-Linking on the Crystal Breakage Behavior. Recently, determination of relationships between a material’s structure and its mechanical properties is being focused on. Diverse materials are included, starting at inorganic ceramic materials31−34 to soft organic biological samples.35 They provide dependencies and models to describe the structure−property relationship, especially for colloidal structures. In the case of porous protein crystals filled with water up to 70%, the protein molecules are held in the threedimensional lattice only due to interactions with each other, like van der Waals forces and hydrogen bonds. In the highly ordered crystal lattice, small external forces may easily change the relative protein’s positions and, hence, upset it, leading to destruction of the whole crystal structure. Owing to crosslinking and, hence, building of strong covalent bonds between

Figure 3. Hexagonal crystal prism of HheG proteins.

In the beginning, the crystals were washed on ice three times using precipitation solution to remove the mother liquor and free, uncrystallized proteins. Then, 10 μL of the cross-linking solution (5% (v/v) glutaraldehyde dissolved in the precipitation solution) was added to the crystals. The crystal slurries were left for 4, 12, 24, and 48 h at 5 °C. After this well-defined time, the cross-linking agent was removed from the crystal slurry and the crystals were washed again C



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withstand a thousand times higher forces without breakage or shattering. The effect of structure deformation on liquid diffusion, and, therefore, the catalytic activity of the CLECs, is not part of this work, but an interesting topic for further studies. Mechanical Performance of HheG Crystals by Short Cross-Linking Reaction Time. Concerning their mechanical properties, the effectiveness of cross-linking treatment on protein crystals is proved by mechanical AFM testing of CLECs at an aqueous environment. For short cross-linking reaction times (4 h and less), the mechanical stability of CLECs changes during the indentation measurements. Figure 6 shows the crystals’ penetration depths (displacements over time) of three separate samples, each three or four

protein molecules within the crystal lattice, an enhancement of crystal structure stability is realized.23 The reinforcing effect of cross-linking on the crystal structure was examined using a microcompression test. Those experiments were performed on over 10 native HheG crystals for each of the considered crystal faces as described in section 3. For all examined crystal faces, an evident crystal breakage was observed. On the basis of the corresponding force−displacement curves (not shown in the paper), it can be determined that the native HheG crystals decay during the surface detection on contact with the flat punch indenter. Hence, the breakage occurs at forces lower than 1 mN (set point for surface detection; see section 3). Then, the crystal fragments were compressed until the predefined maximum displacement of 1 μm was reached. Because the decay occurs already during the approaching phase, the exact estimation of breakage force was not possible. Figure 5 reveals an example for a native crystal before (A) and after (B) the compression of the prismatic crystal face.

Figure 6. Boxplot presentation of displacement results. Three samples have been cross-linking for 4 h; three random crystals from samples 1 and 2 and four crystals from sample 3 were chosen for indentation measurements. At increased measurement duration, the crystals exhibit continuously deeper displacements, although a constant force of 250 nN was applied.

crystals, prepared at cross-linking times of 4 h. It can be seen that the first crystals of each new sample exhibit a relatively low penetration depth, ranging at approximately 70 nm at a constant indentation force of 250 nN. At the second and third crystals, an increase in penetration depth up to 125 nm (median value) can be measured. Detailed measurement data are summarized in the boxplots. The whiskers indicate the highest and lowest displacement values. The mean value of each measure is symbolized by the square. The crystals were prepared as described in section 3. After the transfer from the cross-linking solution into water, liquid diffusion within the molecular package took place until an equilibrium was recreated. The formation of cross-linked bonds proceeds from the crystal’s outsides to the crystal’s insides, and therefore, at short treatment durations, the crosslinking is inhomogeneous and incomplete within the crystal’s lattice. Measurement of three crystals within each sample takes nearly an hour. During this time, unbounded protein molecules either may slightly change their position within the crystal lattice or are even rinsed out from the crystal. Note that the structural changes can only be detected during the measurements. The optical appearance of crystals does not show any dissolution features, e.g., soft crystal edges. Notwithstanding the above, crystals lose their highly ordered, three-dimensional structure, resulting in an increasing penetration depth during the indentation measurement. Although the equilibrium was established after an incubation time of ca. 1 h, no further

Figure 5. Native and cross-linked HheG crystals before (A, C) and after (B, D) microcompression test. An enhancement of crystal stability after cross-linking treatment is observed. The length of the compressed prismatic faces is approximately 60 μm.

In contrast to this, no breakage of cross-linked HheG crystals has been observed during the microcompression tests, although more than 100 different sized crystalsconsidering both faceswere examined. Moreover, no dependency on compression rate or cross-linked time was identified. One example of a compressed prismatic face of a cross-linked HheG crystal is shown in Figure 5C,D. Cross-linked crystals show a strong and complex viscoelastic-plastic behavior. It increases by a rising cross-linking degree, causing the formation of stress-resistant materials. During our experiments, the maximal applied forces range to 1 N. No significant recovery of the compressed crystals has been observed, indicating irreversible plastic deformation. The first question addressed in this study is the determination of cross-linking treatment’s influence on the global stability of protein crystals. As mentioned above, an enhancement of crystal lattice stability due to the formation of covalent bonds is described in numerous prior studies. However, the mechanical stability was improved by a great extent: Compared to the native protein crystals, CLECs D



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Figure 7. Hardness and Young’s modulus of cross-linked HheG crystals’ prismatic faces as a function of the cross-linking time. Each boxplot consists of more than 200 indentations.

Figure 8. Left: Cumulative hardness distributions of single cross-linked HheG crystals at a cross-linking time of 12 h indicate anisotropic mechanical behavior on prismatic faces. Right: The cumulative hardness distributions after 24 h cross-linking time do not show these clear differences between the single faces of HheG crystals.

modulus doubles from 200 to 510 MPa (median values). Durations longer than 24 h do not change the values significantly anymore; merely higher variation of mechanical properties on crystal surfaces is observed. For the hardness, the boxplot’s whiskers, meaning the minimum and the maximum values, range from 7.9−15.1 MPa to 6.7−16.7 MPa. The minimum and maximum values of Young’s modulus range from 353−698 MPa to 258−695.73 MPa. The outliers, if they occur, are shown as black diamonds. Another point concluded from Figure 7 is the asymmetric, wide distribution of mechanical properties on the crystal surface at 12 h of cross-linking. Detailed examination of the cumulative distribution of single crystal faces shows a slight disparity between distinct faces, illustrated in Figure 8. On the right side, a cumulative hardness distribution for the crosslinking time of 24 h is added. As mentioned before, only the prismatic faces were examined, in fact, only those which are parallelly aligned toward the indenter tip. The results show that the prismatic faces, although optically similar, differ from each other. After the cross-linking time of 12 h, circa two-thirds of the crystal faces evince a homogeneous hardness distribution ranging from 4.8 to 9 MPa. The residual one-third of crystal faces range from 9 to 14.5 MPa. The cumulative hardness distributions after 24 h cross-linking time do not show these clear

measurements were performed after this time. In fact, the relatively high penetration depth would result in an incorrect calculation of the contact area, which is needed for investigation of hardness and Young’s modulus. Thus, for the calculation of mechanical properties, all results achieved in the time until the equilibrium was reached are taken into account. This way, the mechanical properties of CLECs are summarized to their average values, describing the dynamical system. No similar phenomenon has been observed by residual experiments after longer cross-linking time. Effect of Cross-Linking Time on Micromechanical Properties of HheG Crystals. Figure 7 presents hardness and Young’s modulus of cross-linked HheG crystals as a function of the cross-linking time. The boxplots evaluate 10 crystals (20 indentations for each crystal). They reveal distinct distributions depending on the reaction time. 150 indents per crystal are the minimal sample size that must be considered as reliable for performing statistical measurements.12 In this study, more than 200 measurements were done for each distribution. Please also note the results concerning mechanical properties of the prismatic face of HheG crystals (see Figure 4). As shown in Figure 7, the first 24 h of cross-linking time plays a main role for mechanical stability. During this time, hardness almost triples from 4.2 to 11 MPa, and Young’s E



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the analytical approach for careful investigation and explanation of the relation between the crystal structure and the resulting mechanical properties is derived. Computational-Modeling Approach to Structure− Function Analysis. Glutaraldehyde and its polymerization products may react with several functional groups like amine, thiols, phenols, or imidazoles.18 However, the cross-linking effect is dominated by reactions of ε-amines and lysine residuals.18,36 The cross-linking mechanism of protein molecules with glutaraldehyde is very complex and not fully understood yet. Therefore, the explanation of cross-linking bridges is challenging, even if empirical data are available.25,37 The cross-linking formation requires the existence of two reactive functional groups at an adequate distance.24 The relevant distances for systematic cross-linked bonds using glutaraldehyde are in the range of 3−8 Å as reported in the current literature, depending on the crystal’s morphology as well as its functional groups taking part in the cross-linking reactions.25,37−39 Based on their information, a MATLAB toolbox for the calculation of anisotropic distances between three residual pairs: ε-amines of lysine residues (Lys-Lys), two neighbored arginine residues (Arg-Arg), and arginine and lysine residues (Arg-Lys) was developed. Next, possible crosslinking bonds were analyzed regarding their distance and direction. From this analysis, dominant crystal faces were deducted; a higher number of bonds result in a higher strength of the crystal face. Functional Computational Model. The developed toolbox allows for Protein Data Bank (PDB) readout, a crystal structure replication, and, finally, a distance calculation of selected atoms of relevant functional groups. PDB files basically describe the basic structure of three-dimensional molecules. In order to archive this, they contain position data of all relevant atoms describing the asymmetric unit. The asymmetric unit is the smallest portion of a crystal structure to which symmetry operations can be applied for generating the unit cell. All replication steps, beginning with a single protein molecule (the tetramer), are shown in Figure 10. After all necessary symmetry operations for creation the supercell are applied, distances and directions between possible bonds are determined on a qualitative basis using vector algebra. For assessment purposes, length- and directiondependent clusters, statistical analysis, and plots are created as well. Application of the Structure Analysis Toolbox. When the length of monomeric glutaraldehyde and its polymeric form is taken into consideration, a maximum distance of 10 Å is expected for potential cross-linking bonds. Longer distances were therefore neglected. For HheG wildtype crystal, all bonds within a unit cell and its surrounding of 100 Å (50 asymmetric units, a supercell; see Figure 10) were identified and stored in

differences between the single faces of HheG crystals. The increased hardness ranges from 8 to 15 MPa. The cross-linking process takes place faster than on the other faces for one-third of the faces. After 24 h of crosslinking, no such clear distinction between prismatic faces can be observed anymore. Hence, the cross-linking of all faces seems to be completed. After this period, the mechanical properties of the crystals are dominated by covalent crosslinked bonds and distributed homogeneously over all six prismatic faces of the HheG crystals. In a second step, the hardness of prismatic and basal crystal faces at the same cross-linking time was tested. In order to prevent an anisotropy between distinct prismatic faces (due to different cross-linking kinetics), a cross-linking time of 24 h was chosen. Because of the correlation being very similar to the hardness, additional results of Young’s modulus are not shown. In Figure 9, hardness for both crystal faces is presented. The median value is about 30% higher for the basal face than for

Figure 9. Hardness comparison on distinct crystal faces of homogeneous cross-linked crystals at 24 h cross-linking time.

the prismatic face. The distribution width is similar for both faces, showing the same molecular variability within the whole crystal. The analogous anisotropy of the HheG crystals, especially of the prismatic faces, is already described in a publication about micromechanical properties of CLECs. The authors state different molecular packing with regard to the distinct faces, low lysine contents within a crystal, or an uncompleted cross-linking process as possible reasons.12 The experimental results of this study confirm the latter. After 24 h cross-linking reaction, there had been no measurable anisotropy on the prismatic crystal faces. However, the different cross-linking durations needed for complete crosslinking must correlate with the crystal structure. Therefore, molecular packing and its influence on the accessibility of functional groups, their distances to each other, and their anisotropic distribution should be analyzed in detail. Hence,

Figure 10. Replication of the HheG protein structure in order to build a large crystal structure, the supercell, according to the symmetry mates P3121. F



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fication using a smaller asymmetric unit, and hence more easy to trace, is necessary. Intra- vs Intermolecular Bonds within a Supercell. First, all relevant bonds within the asymmetric unit consisting of one tetramer and three dimers are investigated and classified as being intra- or intermolecular. In Figure 12, just to illustrate the difference, an example for investigation of intermolecular Lys-Lys bridges is presented. The arrows represent two intra(brown) and one intermolecular (green) bridges. For instance, two intramolecular bonds with a maximal distance of 10 Å exist in a well-defined direction within the tetramer; the single intermolecular bond between the first and the second dimer is highlighted. Each bond is identified by its exact length and its start and end positions. Next, all intermolecular bonds are identified and used in the further calculations. In detail, the asymmetric unit contains only one intermolecular Lys−Lys bond and one Arg− Arg bond within the range of 10 Å. With the identified intermolecular bonds, the asymmetric unit is then duplicated in order to build the supercell. Thus, the now resulting new bonds have new positions and lengths and differ from those of the asymmetric unit. They are then also classified to be intermolecular. After replication of the asymmetric unit according to the symmetry mates P3121,17 the intramolecular bonds are filtered. This way, only intermolecular bonds within the supercell are analyzed. Data Computing for Investigation of Relative FaceDependent Crystal Strength. In the following, we show a three-dimensional representation excerpt of the unit cell for better understanding of the bond’s location. Figure 13 starts showing all intra- and intermolecular bonds in the Z direction (z plane; see further Figure 14). On the left side, a molecule orientation within a unit cell and the correlated space group, which represents a description of the symmetry of the crystal, is presented. Potential anisotropic intra- and intermolecular cross-linking bonds of Lys−Lys, Arg−Lys, and Arg−Arg pairs are marked in their specific colors on the right side. It can be concluded that, even in the interspace between the molecules, intermolecular bonds exist. Our first approach for the evaluation of direction-dependent crystal strength is based on the assumption that intermolecular

our database. Figure 11 gives an overview of the three bond types regarding their length−frequency.

Figure 11. Distribution of intra- and intermolecular bond lengths defined between Arg−Arg, Arg−Lys, and Lys−Lys residuals within a supercell.

From this data, we can see that Lys−Lys bonds result in the lowest count. The distance between these bonds range mostly between 5−6, 9−10 Å. Arg−Lys bonds are distributed statistically between 6 and 9 Å, and Arg-Arg residuals provide the dominated ratio of the total potential bonds with a highest fraction between 6−7, 8−10 Å. Moreover, Arg−Arg bonds are the only ones to be smaller than 5 Å. For the estimation of anisotropic crystal strengths, the intraand intermolecular bonds are considered separately, assuming that only intermolecular bonds contribute to the enhancement of a crystal’s structure stability in environments different from the crystallization liquor.23,40 The model protein (halohydrin dehalogenase) used for this experiment is a homotetramer, a protein complex containing four identical subunits being associated, but not bound covalently. However, this protein is stable in its tetrameric form, so that all bonds within this tetramer are assumed to be intramolecular. In order to distinguish between intra- and intermolecular bonds within a supercell, an accurate identi-

Figure 12. Intra- and intermolecular Lys−Lys bonds within an asymmetric unit with a maximal distance of 10 Å. On the right side, the intermolecular bond between the first and the second dimer is highlighted. G



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Figure 13. Crystal excerpt showing functional cross-linking bonds and their direction and length. Intramolecular bonds (gray) and intermolecular (color) are compared on the right-hand side; the orientation inside the space group is shown on the left-hand side.

crystal face’s strength. All bonds are then proportionally summed regarding each face (crystal lattice resistance against normal force). The correlation analysis between direction-dependent bond counts within a supercell is given in Figure 15. Only intermolecular bonds, which contribute to the enhancement of mechanical stability of the crystal lattice, have been taken into account. It is apparent from Figure 15 that direction-dependent crosslinking may occur, indicating an anisotropy between basal and prismatic faces. All given functional pairs have a higher number of possible bonds in the Z direction, starting at 3% by Arg−Lys bonds and rising up to 28% by the Lys−Lys bonds. Moreover, Arg−Arg bonds with an average length of 6−7 Å, especially Lys−Lys bonds, respectively, are very frequent and, therefore, may have the strongest influence on stability enhancement of the basal face. This mathematical model can be used to analyze the state when all possible bonds are set. Compared to our measurement, this is achieved after a cross-linking time of 24 h. After this time, the distributions of mechanical properties on all prismatic faces are similar (see Figure 8, right). This corresponds with our theoretical analysis. Moreover, the increase in mechanical strength of the basal face is about 30%, which is qualitatively in good agreement to the mathematical calculations. In order to explain the anisotropic behavior of prismatic faces after the cross-linking time of 12 h, possible reasons were analyzed. Regarding the breaking behavior during the sample preparation, a discrete crystal splitting was observed. This leads to the assumption that channels inside the crystals exist in a systematic pattern. Figure 16 illustrates HheG crystals just after changing of the mother liquor against a wash solution. If the cross-linking treatment is not executed as described in section 3, an osmosis-driven exchange of mainly water molecules occurs, leading to the crystal cracking near the large channels.

Figure 14. Presumed orientation of the unit cell and face’s normals (⊥) across XYZ coordinates within the hexagonal crystals used for calculation of the intermolecular bonds. Z ⊥ basal face; X, Y + 60°, Y − 60° ⊥ prismatic faces.

cross-linked bonds mainly influence the mechanical crystal properties. Furthermore, the strength of these bonds depends on their orientation in relation toward the applied force. Similar examinations of anisotropic particle strength dependent on porosity, particle structure, or size were already published in the current literature. Rumpf examined a continuum-based model for the tensile strength of aggregates. It bases on all partial stress contributions in a cross-sectional area of the structure in the direction of the applied force.41 Schilde et al. report that this model can also be transferred for measuring compression strength of aggregates via nanoindentation.31,33,34 On the basis of this, the portion of each bond in the load’s direction for each stressed crystal surface is calculated. Hence, the sinus of the angle between the crystal face’s normal (⊥) and the bond’s direction is used as a factor. As long as the function of the bonds’ strengths regarding type and length is unknown, we assume them to be both, equal and length-independent. Following this assumption, each bond is mapped onto all crystal surface normal according to Figure 14 (Z plane: basal face; X, Y + 60°, Y − 60°: prismatic faces). This way, we receive a representative value for the overall H



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Figure 15. Direction-dependent bond counts of the three different cross-linking pairs as a function of the bond length.

Figure 16. Crystal cracking caused by the osmotic shocks after exchanging of the mother liquor.

Both, the mechanism of osmotic shock and the influence of cross-linking on cracks formation, have been explained previously in detail.42,43 This observation contributed to the analysis of correlations between positions of intermolecular bonds and molecular packing arrangement of the crystal. In Figure 17, inter- and intramolecular bonds are presented in the XY orientation, giving their distribution near the crystal channels. Considering the molecular arrangement on the left side, it can be seen that most of the intermolecular Arg−Arg, Arg− Lys, and Lys−Lys bonds are located next to a large channel within the crystal. Those big channels and other related small channels are shown in Figure 18. For assessment purposes, a larger crystal’s excerpt is presented, where the molecules from Figure 17 are marked in red. The presence of potential cross-linking bridges along the large and small channels in the crystal can be identified. Those channels run parallel between the opposite prismatic faces, making cross-linker diffusion over this region more effective. It

is conceivable that two prismatic faces, which are placed above and underneath those channels, are cross-linked faster, because of better accessibility and, hence, improved diffusion. Therefore, the hardness and Young’s modulus of the prismatic faces at an incomplete cross-linking time of 12 h are ca. 60%, respectively, 46% higher than that of the other four faces (see Figure 8). Hence, in contrast to the structurally derived increase of mechanical properties of the basal face, the different cross-linker diffusion kinetics through the large channels in different prismatic directions may lead to a time-dependent anisotropic behavior of the mechanical properties of the crystal. The scope of this mathematical model is limited in terms of a lack of empirical data. We considered all possible bonds having a maximum distance of 10 Å. Because of this assumption, the calculated direction-dependent crystal strength is much higher, than the real one. Wine et al. pointed out that the cross-linking bonds are created at specific and preferred molecule sites.25 In this case, the count of cross-linked bonds, I



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Figure 17. All possible anisotropic intra- (gray arrows) and intermolecular cross-linking bonds (colored arrows) of Lys−Lys (blue), Arg−Lys (red), and Arg−Arg (green) pairs. The maximal distance of 10 Å is filtered. On the left side, an image of correlated molecules within a unit cell is presented.

Figure 18. Illustration of large and small channels within the crystal packing viewed from the XY orientation.

predictable bridges, which can be easily and fully resolved by the X-ray analysis.

which indeed occur within a crystal lattice, would get lost in the considered big data amount. Next, the bonds have been calculated as being equal and length-independent. In reality, the bond’s strength depends on many factors, like type of the bond and its length, which has to be taken into account for an accurate calculation. The involved protein residues depend strongly on the protein structure and cross-linking condition; therefore, for an accurate investigation of anisotropic crystal strength and comparison of the bond formation, an X-ray crystallography of cross-linked HheG crystals is required. However, our model gives an overview about the quantitative and direction-dependent distribution of potential inter- and intramolecular bonds and allows better visualization of bonds, leading to crystal structure- and diffusion-dependent explanations for different mechanical behavior. Moreover, it can be easily adapted to the empirical data from X-ray measurements, giving accurate quantitative and graphical results about the influence of created cross-linking bonds on mechanical properties of protein crystals. This model is especially recommended for other, more specific, cross-linkers, which react with desired amino acids, creating systematic and

5. CONCLUSION The present study was designed to determine the effect of cross-linking duration on mechanical properties of HheG crystals. Using the AFM-nanoindentation technique, we were able to investigate small changes in the mechanical properties, namely, hardness and Young’s modulus, on distinct crystal faces. One of the most significant findings to emerge from this study is that the cross-linking reaction takes place in the first 24 h. In this time, both, hardness as well as Young’s modulus, increase almost 3-fold, compared to the reaction time of 4 h and stay constant at ca. 11.5 MPa (prismatic face) and 500 MPa, respectively. The second major finding was the evaluation of 30% higher mechanical stability for the basal face. The evidence of this study suggests an anisotropic behavior within the three-dimensional crystal lattice, which was subsequently analyzed using a mathematical model. On the basis of the crystal structure of HheG wildtype, a MATLAB J



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tool was developed for calculation of anisotropic distances between functional groups with the potential for cross-linking, like Arg-Arg, Arg-Lys, and Lys-Lys within a supercell. The applied model enables the quantification of theoretical bonds of considered amino acid residues, having a maximum distance of 10 Å and the identification of inter- and intramolecular bridges. Moreover, direction-dependent analysis allowed a hypothesis for the measured anisotropy of HheG crystals. Graphical illustration of all possible bonds allows identification of most of them near large and small channels between stacked molecules within the crystal. Hence, the measured anisotropy might be caused by the different direction-dependent amount of bonds on the one hand, and distinct channel orientation within the crystals on the other hand. Additionally, the results of the microcompression tests show considerably higher mechanical stability against normal forces for cross-linked HheG wildtype crystals, compared to the native crystals. Despite its great linking potential, glutaraldehyde may also contribute to inactivation of biocatalysts, if excessive crosslinking occurs. Therefore, cross-linking time duration, crosslinking method, and linker selection require an individual consideration for each protein, if catalytically active and stable biocatalysts should be produced.

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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 We thank Prof. Dr. Anett Schallmey and Jennifer Solarczek (Institute for Biochemistry, TU Braunschweig) for production and purification of halohydrin dehalogenase wildtype proteins. Financial support by the German Research Foundation (DFG) within the DiSPBiotech Priority Programme (SPP 1934, SCHI 1265/3-1) is gratefully acknowledged.

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Relationship between Cross-Linking Reaction Time and Anisotropic

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