3.1. Mechanical Properties of Wild-Type HheG Crystals in the Nanometer Range
Due to the increasing demands on the tailored properties of CLECs in terms of enzymatic activity, as well as mechanical stability, the elucidation of the relationships between the structure and the resulting properties is of particular interest. One of the most widely used linkers in the design of CLECs is glutaraldehyde [
32,
33,
34]. However, according to the manufacturer’s instructions, highly concentrated glutaraldehyde can be an irritant, toxic, or carcinogenic. In addition, reports indicate that excessive cross-linking with glutaraldehyde can lead to a reduction in catalytic activity [
35]. For these reasons, the motivation to search for alternative cross-linkers increases. Previous studies have reported on the micromechanical properties of wild-type HheG CLECs [
20], as well as the dominating influence of cross-linking bonds on the mechanical behavior of enzyme crystals [
22]. The present study focused on modeling the properties of cross-linked enzyme crystals such that the selection of linkers and their influence on the mechanical and, if necessary, catalytic properties can be explained and predicted.
Figure 4 compares the mechanical properties of wild-type crystals cross-linked with different linkers. Alternatively, for the glutaraldehyde, a mixture of three lysine linkers of defined length (6, 9, and 16 Å) was used for cross-linking. A single linker would not be sufficient to adequately cross-link the crystals; therefore, a mixture of linkers of different lengths had to be used.
Because glutaraldehyde tends to self-polymerize, the resulting cross-linking bond lengths are unpredictable [
36]. In addition, excessive cross-linking can lead to a decrease in enzymatic activity [
35]. For controllable and predictable cross-linking treatment, alternative linkers can be applied. However, our results showed that, using the alternative lysine cross-linker, the hardness of the anisotropic crystal faces decreased by about 70% compared to the cross-linking with the glutaraldehyde. Besides the high stability of CLECs cross-linked with GA, its low price is of great advantage. A kilogram of 50% glutaraldehyde solution costs only about EUR 70. In comparison, alternative linkers cost a thousand times more (DMP: 159 EUR/1 g; DST: 254 EUR/50 mg; Sulfo-EGS: 185 EUR/50 mg). Predicting the mechanical behavior based on a model can therefore bring advantages in terms of financial expenditure and experimental effort.
Table 3 summarizes the modeled direction-dependent crystal strength of all intermolecular bonds smaller than 10 Å (cross-linking with GA), or Lys–Lys* bonds with a well-defined distance for alternative cross-linker (6, 9, and 16 Å, compare with
Table 1).
In
Figure 5, a comparison of the experimental and modeled results is shown. The experimental and modeled data were interpreted by comparing the percentage differences between the anisotropic faces. For instance, the difference in the hardness of the basal face to the prismatic face of crystals cross-linked at the same conditions (glutaraldehyde or DMP, DST, Sulfo-EGS-linker mix, referred to as Lys–Lys* in
Table 3). These percentage differences are shown as a bar (experiment) in
Figure 5. Analogously, the percentage difference in the modeling results, e.g., between the anisotropic crystal faces, is shown as a dot–line plot (model). Since the mechanical properties are presented as a distribution, the lower and upper quartile (25% and 75%, respectively) were added for comparison and shown as error bars.
Originally, the model was developed by Kubiak et al. and used to explain the time-dependent anisotropy of wild-type HheG CLECs. The authors showed that crystal strength is direction-dependent due to the cross-linking bonds. The results showed that the crystal strength resulting from the Lys–Lys and Arg–Arg bonds was about 20% higher in the Z-direction (for the basal face), which is consistent with the experimental results. Looking at the cross-linking using the linker mix, it also turns out that the experiment agreed well with the model. The experimentally determined anisotropy between the basal and prismatic faces was about 24%. This corresponded to the difference in crystal strength due to the Lys–Lys bridges from the three defined linker lengths (see
Table 3, Lys–Lys*, ratio of bond strength of the Z-direction (174.68) and an average of X, Y + 60°, and Y − 60° (ca. 133.64)). Previously, it was found that the Lys–Lys and Arg–Arg bridges lead to the anisotropic behavior of the HheG crystals. Assuming that there are bonds of all the considered amino acid residue pairs in the crystal, the Arg–Lys bond here did not contribute to the anisotropic behavior of the wild-type HheG crystals, and the bonds in the defined directions were summed up and the total strength of the respective areas for differently cross-linked crystals was proportionally adjusted. The mechanical investigation showed that, due to the use of a linker mix instead of glutaraldehyde, the average hardness of the prismatic and basal crystal faces decreased by about 70%. The results corresponded to the modeling with some slight deviation.
The knowledge that a crystal structure can be used to predict the mechanical behavior of the surfaces saves an enormous amount of time through the targeted selection of the linker and the subsequent model prediction of the crystal strength based on the formed cross-link bridges. The model can be used, for example, to determine which binding-site distances occur most frequently and which crystal strength will correlate with this linker length, and the length of the linker can then be accordingly selected for experimental cross-linking. In addition, it can be determined whether other linkers, e.g., carboxyl or sulfhydryl instead of amine linkers, will provide better mechanical performance. By selectively combining different variants—linker length, type, with binding sites, e.g., far away from the catalytic site—the desired mechanical strength can be modeled in advance.
3.2. Mechanical Properties of Wild-Type HheG Crystals in the Micrometer Range
In the introduction, it was written that protein engineering is a common method for improving the performance of enzymes. Unfortunately, improvements in the properties of solubilized proteins are not always accompanied by improvements in the mechanical stability of the crystals.
Figure 6 shows a comparison of the fraction of elastic energy of the wild-type and the D114C crystals mechanically characterized in their native state. From the results, it can be seen that the fraction of elastic energy of the basal face of D114C crystals was significantly lower than that of the wild-type crystals. The difference was about 40% at a 200 nm penetration depth and even almost 60% at a 900 nm penetration depth. In comparison, the difference between prismatic crystal faces was much smaller and lay within the spread of the distribution of mechanical properties.
Most likely, the lowering of the elastic energy fraction of the basal crystal face was due to the point mutation of the crystal contact, which lay exactly along the
c-axis (Z-direction), as shown in
Figure 7. Since the crystals were held together in their three-dimensional form by crystal contacts, the mutation of such a site could contribute to the reduction of crystal strength. Kubiak et al. reported that the slip planes are aligned orthogonal to the indenter tip during nanoindentation of the basal crystal face, which is a reason for the easy and unhampered gliding of the planes [
22]. For the native D114C crystals, it seems to reduce the interactions between the slip planes such that a lower fraction of elastic energy can be observed.
In a previous study, Kubiak et al. presented and discussed, in detail, the influence of cross-linking on the mechanical behavior of enzyme crystals. The authors also investigated the dominating influence of cross-linking on the mechanical behavior of CLECs [
22]. In this section, the influence of the genetic modification of position D114 on the mechanical properties of CLECs is presented. By replacing it with cysteine, a cross-linking site was incorporated, which could be cross-linked by means of a suitable linker—in this case, a BMOE linker—in addition to the lysines. Hence, in the present study, crystals were partially cross-linked using glutaraldehyde and partially using a BMOE linker via the soaking method. In addition, some of the crystal samples were cross-linked first with GA and then with BMOE. All three samples were mechanically examined and compared with the cross-linked wild-type crystals.
In
Figure 8, the influence of the cross-linker on the elastic energy fraction of the prismatic and basal faces of D114C crystals is presented. From
Figure 8, it can be seen that the fraction of elastic energy for both anisotropic faces increased with the degree of cross-linking and was the lowest for cross-linking with the BMOE linker and highest for cross-linking with both linkers. Regarding the prismatic face at the penetration depth of 200 nm, the fractions of elastic energy were 39% (BMOE), 66% (GA), and 69% (GA + BMOE). In comparison, the fraction of elastic energy of the wild-type crystals cross-linked with GA was 64%, which was slightly lower than the median value of D114C crystals that were also cross-linked with GA. Analogous to the results presented earlier about the fractions of elastic energies of native crystals, the fraction of elastic energy decreased with increasing depth. At the penetration depth of 900 nm, the fraction of elastic energy of the crystals cross-linked with BMOE was the lowest at 20% and increased to 40% when the crystals were cross-linked with GA. Due to the double cross-linking (GA + BMOE), the fraction of elastic energy was 7% higher, and at 47%, it was ca. 20% higher than the wild-type crystals. Independent of the cross-linker used, both of the cross-linked crystal faces exhibited a higher fraction of elastic energy than the native crystal faces. It is remarkable for the basal crystal faces that, in contrast to the prismatic faces at the penetration depth of 200 nm, the D114Cs had a lower fraction of elastic energy after cross-linking with GA (64%) than the wild-type crystal (72%). However, the trend was reversed in the deep crystal regions, allowing for the quantification of the stronger influence of cross-linking for the D114C CLECs. For the double cross-linked CLECs, the fraction of elastic energy was the highest and was equal to 51% at a penetration depth of 900 nm. Based on those measurements, it can be concluded that a combination of both strategies—protein engineering and enzyme immobilization—can effectively contribute to the enhancement of mechanical properties of CLECs.
In
Section 3.1, the results of hardness measured using AFM at a penetration depth of less than about 30 nm for wild-type crystals were compared with the model. In this section, the model was used for correlation with other mechanical parameters, such as the fraction of elastic energy at a penetration depth of 900 nm. Thus, it was tested whether modeling from a small crystal section was sufficient for the global description of the mechanical behavior.
Table 4 shows the results of the direction-dependent crystal strength for the respective pairs of amino acid residues considered for further analysis.
Without cross-linking, plastic deformation is the dominant characteristic deformation behavior of the crystals, whereas with cross-linking, elastic deformation is a decisive factor [
22]. For this reason, it was assumed that the cross-linking via additives makes a significant contribution to the elastic stress state within the crystal and, thus, the structure-based modeling approach for the mechanical crystal behavior can be applied to describe the elastic crystal properties with regard to the different crystal directions. In
Figure 9, the results of the nanoindenter are presented, where the anisotropy of the wild-type (WT) crystals was again related to the model based on the differences in the fraction of elastic energy. The fraction of elastic energy of the basal face of the WT CLECs was, on average, about 14% higher than for the prismatic face. Comparing the percentage difference with the summed bond strengths from the bond pairs considered, i.e., Lys–Lys, Lys–Arg, and Arg–Arg, the modeling results also showed a difference of about 14.6% in the Z-direction compared to the X, Y + 60°, and Y − 60° directions (∑
Z-direction = 559.17 and mean of ∑
XY-direction = 477.59, cf.
Table 3). Thus, based on the modeling results, it can be concluded that all bond pairs contributed to the crystal mechanics in the deep crystal regions. This would also explain why the anisotropy between different crystal faces decreased with increasing penetration depth.
The crystal faces of D114C mutant cross-linked by GA show about a 6% difference in the elastic energy fraction. From
Table 4, it can be seen that the sum of Lys–Lys and Arg–Arg bonds (365.03 in the Z-direction and 343.88 in the X, Y + 60°, and Y − 60° directions) also showed about a 6% difference. A similar result concerned the cross-linking using GA and BMOE. Comparable to the cross-linking with GA, the difference between the model and the experimental results was negligible here. The deviation between the model and the result was the highest for cross-linking with BMOE and amounted to 30% when mean values were considered. The reason for this was that the cross-linking of cysteines alone was not sufficient to provide stable support to the crystal lattice such that increased dislocations were observed during the measurement, especially in deeper crystal regions, leading to the increased distribution width of the results. This distribution width could also be seen in the error bars. For example, a positive error bar meant that the percentage difference of the third quartile (75% of the distribution) of ca. 17% was about 90% higher than the percentage difference of the mean value (9%, see
Figure 9). Nevertheless, the model result was within the error or distribution width, which demonstrated the good representation by the experiment. A comparison of the respective crystal faces (basal or prismatic face) between the two crystal structures showed that there was about a 16% deviation of the model from both the third quartile for the prismatic face and from the mean value of the distribution for the basal face.
The most important causes, which can have a limiting influence on the modeling of the crystal behavior, can occur at three different stages of experimental execution: X-ray structure analysis, sample preparation, and mechanical measurements. For the model, the X-ray structure analysis was one of the most critical stages. Regarding crystal quality, parameters such as protein production batch or crystallization conditions and growth time may have a great influence. For the mutant D114C, the best-achieved resolution was unfortunately only 3.9 Å, which allowed for the determination of the positions of the atoms with a certain tolerance. During data processing, for example, the symmetry of the respective chains was calculated based on the crystallographic space group. Moreover, the coordinate origin was manually changed. In this process, the atoms were manually shifted to the same origin. However, the coordinates of the atoms were influenced by the B-factors and thus were not rigid but movable in the crystal and did not represent absolute positions but, rather, were relative to each other. The exact displacement measurement of the atoms was limited by the poor resolution, which is why deviations could occur. Due to the relativity of position within a crystal, this was not a critical problem when experiments and modeling were performed using the same crystal structure. However, the error may be significant if different crystal structures are compared to each other. Nevertheless, taking into account the fact that the accuracy of the crystal structures and the developed model were in the angstrom range, the agreement between the model and experiment was surprisingly high for different model proteins.
For the mechanical measurements, influencing factors such as the number of measurement points for a statistically validated estimation of the distribution of mechanical properties and the cantilever quality (geometry or durability of the measurement tip) are important. Using a careful working method, for example, by scanning the crystal surface to quantify the tilt or by regular SEM images of the cantilevers, these influences can be controlled and, if necessary, minimized.
Another serious factor that influences the modeling of the structure–property relationship is sample preparation. Depending on the formulation parameters, different crystal morphologies can be formed, resulting in differences in mechanical behavior. However, it happened that the mechanical behavior of crystals from different protein batches differed despite the crystal morphology remaining the same. This phenomenon was difficult to explain and was probably due to small differences in ions in the solution after, e.g., the purification or desalting step. Since these influencing factors are difficult to control or avoid despite using established and consistent preparation methods, sample preparation is considered a highly influential factor comparable to that of X-ray structure analysis. Nevertheless, the model reproduced the trends very well. Despite certain limitations, such as the poor resolution of the crystal structure, the model allowed for a reliable representation of the mechanical properties, both the hardness and the elastic part of the deformation energy, within the whole crystal.
The accuracy of this model could be refined by the addition of further information, e.g., regarding the bond strength as a function of bond length. Additionally, X-ray crystallographic studies of cross-linked crystals could also be performed, allowing for the resolution of systematic cross-linking bonds. Subsequently, the relevant distances/positions could be selected and modeled. It would also be possible to introduce a position-dependent strength of interactions instead of cross-linking bridges and, thus, additionally ensure the modeling of the mechanical behavior of non-cross-linked crystals. However, a prerequisite is that accurate quantifiable data on the force fields between individual molecules within the crystal are available, e.g., via molecular dynamics simulation. By combining the data from native and cross-linked crystals, the highest accuracy in terms of predicting the mechanical behavior should be achieved. However, a very high computational capacity is recommended to perform such calculations. The excerpt of crystal structures in this work was limited to 100 Å in space. Despite the relatively small crystal excerpt, the number of rows searched for targeted information in MATLAB was almost 30 million. In order to calculate the data more efficiently, the .pdb file had to be directly converted with suitable functions and limited to relevant information. In case a sensitivity analysis was to be performed using the model, all data must be available. With the help of a high-performance computer, all distances to each other could be calculated and clustered. On a qualitative basis, the amino acid positions could be located, which should be exchanged by the rational protein design to incorporate quite effective cross-linking sites. Assuming that the crystal structure will not be subject to major changes, it should therefore be possible to perform targeted mutations with this tool, which should contribute to enhancing cross-linking and mechanical properties.