Mechanical properties and stability considerations for a skin-like protein

One approach for novel developments and technological innovation is to draw inspiration from nature. Bio-based and bio-inspired materials are becoming increasingly interesting for industrial applications, not only because of their unique features, but also due to economic reasons and the need of sustainable development.
Collagen is considered as one of the most useful and promising biomaterials [1]. It is the most abundant protein in humans and is the main component of connective tissue [2]. The skin, for instance, consists to more than 50% of collagen being responsible for skin strength and elasticity. Like other bio-based materials it has several superior features such as excellent biocompatibility, weak antigenicity, and biodegradability rendering it an excellent scaffold for biomedical applications, in particular, in cosmetic surgery in the context of regenerating lost or damaged tissue, but also as drug delivery system [2]. Due to its exceptional mechanical characteristics, collagen is, however, also interesting for nanotechnological applications, for example, as a mechanomutable material or as template for de novo material design. Despite numerous experimental and computational studies, e.g. Refs. [3,4,5] and references therein, it is still not fully understood which factors are determining for the extraordinary structural and mechanical properties of collagen. It is important to understand the complex balance between effects like sterical influences of substituents, stereoelectronic effects, or interstrand interactions at the atomistic level for designing innovative products and materials with distinct properties.
For rational product design and product enhancement, a detailed understanding at the atomistic and molecular level is indispensable. In particular, the knowledge of structural properties is of utmost importance, since the function and other molecular properties are driven by the molecular structure. Molecular modeling is a versatile tool for providing critical insights into molecular structure, processes, and properties. A whole hierarchy of in silico methodologies offers the possibility to address problems at different length and time scales. Scienomics Materials Processes and Simulations (MAPS) platform  offers a wide range of simulation engines in the areas of quantum, classical, mesoscale, QSAR and thermodynamic modeling which gives researchers access to powerful building, visualization and analysis tools in a single user interface together with access to multiple simulation engines.
In this study we will present a detailed atomistic analysis of the mechanical properties of two model collagen molecules, and will offer an explanation of the observed mechanical properties based on the hydrogen bonds formed in the two systems, which also have a significant impact on the stability of the model systems. Force field based atomistic simulations empoloying the AMBER force field have been performed, and the stress strain relationship has been analyzed using two independent methods.
For investigating the elastic properties of collagen and for determining the influence of the hydroxyl group on the elasticity, molecular dynamics simulations have been performed. A crystal structure obtained from the RCBS database[6] with the PDB-ID 1V6Q [7] served as structural basis for our simulations, whose repeating sequence is Pro-Hyp-Gly. In the following, we will denote this model structure as PHG. Since we want to explore the influence of the hydroxy groups on the elasticity, a second model structure was generated by replacing the hydroxyl groups with a hydrogen atom. The second model structure consists thus of Pro-Pro-Gly triples and will be denoted PPG in the following. Both models were saturated with hydrogen atoms and water molecules were added using MAPS building tools after assigning Amber force field parameters [8,9]. Figure 1 shows the starting configurations of PHG in the a, b and c cell directions in a unit cell saturated with water.

Figure 1: Unit cell of collagen with water molecules. Left: View in a direction (bc plane), middle: view in b direction (ca plane), right: view in c direction (ba plane).

Two separate sets of molecular dynamics simulations were carried out for investigating the elastic properties. (1) A continuously increasing tensile stress was applied separately in x, y, and z direction, respectively. (2) A strain was applied by continuously deforming the cell separately in each of the three  spatial direactions.
For the first set of simulations, three individual runs were performed applying a tensile stress up to 1000 Atm, 2000 Atm, and 5000 Atm in x, y, and z direction, respectively, over a simulation time of 1 ns. The stress was monitored as a function of the strain. The elastic moduli in each of the three spatial direction were calculated as the slope of the linear region of the stress-strain curves. Figure 2 shows a typical stress strain curve for PHG in the z- direction, Table 3 lists the results for the experiments in all spatial directions.

Figure 2: Stress-strain curve of PHG in z- direction with fitted linear relationship

Table 3: Elastic modulus in GPa calculated as the slop of the stress-strain curve obtained from MD simulations in which a continuously increasing tensile stress was applied. The stress rates in x, y, and z direction were 1 Atm/ps, 2 Atm/ps, and 5 Atm/ps, respectively.

In both models the highest elastic modulus is found in z direction and is about 11-13 GPa, while the elastic moduli in x and y direction are clearly smaller and in a range between 2-5 GPa. This is in general in accordance with previous experimental and theoretical work where Young's moduli in a range between 0.4-12 GPa were observed. In z direction, i.e. along the longitudinal helix axis, the non-hydroxylated PPG is predicted to be stiffer than its hydroxylated counterpart. At first glance, this result might be somehow counterintuitive, since it can be assumed that at least to some extent hydrogen bond-like interactions should play a role in the PHG model and should therefore increase the stiffness. The results can, however, be rationalized by considering the orientation of the triple-helix in the unit cell. The orientation of the helix backbone is along c (z) which firstly explains the comparatively large modulus in z direction, but secondly implies that the forces are presumably dominated by bonded interactions and non-bonded interactions like hydrogen-bonds can be drowned. This should be different when applying a stress in x and y direction and stretching the helix bundles laterally which are held together by non-bonded interaction. And indeed, PHG shows a higher stiffness in x and y direction.
The same trend is found for the second set of simulations where the unit cell was progressively strained up to 5% of the initial box length. The corresponding values are listed in Table 4.

Table 4: Elastic modulus in GPa calculated as the slop of the stress-strain curve obtained from MD simulations where the simulation box continuously strained. Modulus in GPa. 5 % strain

To further confirm these results, we have also evaluated the number of hydrogen bonds taking only the hydrogen bonds of the helices and not of the water molecules into account. The mean values of hydrogen bonds during the stress experiments are listed in Table 5.

Table 5: Mean value of number of hydrogen bonds during stress experiments as implemented in MAPS. Min/Max values are listed in parentheses and only hydrogen bonds of the helices have been taken into account

Though the differences in the number of hydrogen bonds are rather small, by trend more hydrogen bonds are observed in PHG which is in line with the previously discussion. One reason for the comparatively small difference could be associated with the fact that a stabilization of collagen model peptides was observed experimentally despite the lack hydrogen-bonding substituents which was attribute to the presence of stereoelectronic effects. Although electronic effects are not directly reflected in force field-based simulations, they have been taken into account for the parametrization of Hyp [9] and are implicitly included in the MD simulations.

Overall, the results of the MD simulations are consistent and may provide a useful strategy for predicting mechanical properties collagenous materials in dependence of incorporated functional groups for the rational design of bio-based materials. Force field-based molecular dynamics simulations have been performed to investigate the impact of hydrogen bonding on the elastic properties of a collagenous triple-helix. Elastic constants were determined for each spatial direction by two different simulation approaches. The results suggest that the moduli perpendicular to the helix axis represent a appropriate measure for the influence of non-bonded interactions like hydrogen bonds. The stiffness of hydroxylated helices is in these two directions larger than without hydroxyl groups indicating that hydrogen bond-like interactions seem to influence the mechanical properties. This is supported by the analysis of the number of hydrogen bonds over the simulation time, which is in the hydroxylated model slightly higher.

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