Abstract

Molecular dynamics modeling is used to simulate, model, and analyze mechanical deformation behavior and predictive properties of three different synthetic collagen proteins obtained from RSC-PDB, 1BKV, 3A08, and 2CUO, with varying concentrations of hydroxyproline (HYP). Hydroxyproline is credited with providing structural support for the collagen protein molecules. Hydroxyproline's influence on these three synthetic collagen proteins' mechanical deformation behavior and predictive properties is investigated in this paper. A detailed study and inference of the protein's mechanical characteristics associated with HYP content are investigated through fraying deformation behavior. A calculated Gibbs free energy value (ΔG) of each polypeptide α chain that corresponds with a complete unfolding of a single polypeptide α-chain from a triple-helical protein is obtained with umbrella sampling. The force needed for complete separation of the polypeptide α-chain from the triple-helical protein is analyzed for proteins to understand the influence of HYP concentration and is discussed in this paper. Along with a difference in ΔG, different unfolding pathways for the molecule and individual chains are observed. The correlation between the fraying deformation mechanical characteristics and the collagen proteins' hydroxyproline content is provided in this study via the three collagen proteins' resulting binding energies.

Introduction

Biomedical field applications profoundly rely on natural and synthetic biomaterials. Biomaterials combine the needed structural control of matter by integrating living and nonliving systems into technologies and their interfaces, making them an essential solution for today's challenging problems. Protein-based biomaterials, which have been extensively studied over the past decade, take it further by being biocompatible and biodegradable, and flexible in their usage and applications [1]. Thus, the comprehension of these proteins spanning from their lowest scale level becomes integral for developing and successfully integrating the resulting biomaterials. These properties are dependent on the biomaterial's elaborate hierarchical structures and their specific macromolecular components that lay the foundation for the complex mechanical behavior of all connective tissues [2]. One such protein-based biomaterial is collagen, which is the primary source for scaffold manufacturing.

Scaffolds are a fundamental aspect of tissue engineering and provide the appropriate environment for the regeneration of tissues and organs. They provide the template for tissue formation and are typically seeded with cells and growth factors and exposed to a bioreactor [3]. Thus, the design and manufacturing of the scaffold are imperative for the field. Collagen, a triple helical protein, encompasses all three essential requirements needed for biomaterials for scaffold manufacturing. Whether it is bovine, porcine, or human collagen, scaffold manufacturing copiously depends on natural sources for collagen extraction. A search for a sustainable replacement leads to new research on alternate biomaterials and synthetic polymers [35].

Collagen is the most abundant structural protein in mammals involved in many cellular functions and developmental processes such as tissue homeostasis, making it biocompatible and biodegradable [6]. It is an extracellular matrix protein that constitutes approximately 25% of mammals' total dry weight. Collagen is a triple-helical structure with three coiled subunits wound around each other with a length of 300 nm and a diameter of less than 2 nm. Each molecule subunit comprises three left-handed polypeptide α-chains that twist together to form the unique right-handed triple helix. In turn, each helix consists of approximately 1024 amino acids and a molecular weight of approximately 285 kDa [7,8].

The mechanical properties of collagen have garnered interest in the past few years due to its inherent properties of biocompatibility and biodegradability. Modern experimental methods have been employed to probe collagen's mechanical properties at different hierarchical levels, including single molecules [9]. Atomic force microscopy, X-ray diffraction, Brillouin light scattering, microelectromechanical systems stretching, and optical tweezing methods have been used to measure collagen fibrils and single collagen molecules' strength [10,11]. In addition, computational modeling and simulations have also been used to investigate the single collagen molecule and fibrils' properties, including tensile strength and modulus values using atomistic, coarse-grain, and reactive atomistic modeling [9,10]. Different studies have reported different modulus values for collagen fibrils and molecules using a wide range of techniques [110,1221] Studies on the relationship between the amino-acid sequence and thermal stability have shown how changing a single residue in the sequence can change the protein's melting point [22]. However, research on the dependency of amino acid sequence on collagen's mechanical properties is still limited. One key aspect of interest is the mechanical fraying deformation of individual α-chains. This work focuses on how the amino acid sequence at the molecular level influences the proteins' mechanical characteristics, which can drastically change collagen fibers' macrolevel properties. A fundamental understanding of this relationship between the amino-acid sequence and the collagen molecules' mechanical fraying deformation characteristics at the triple-helical protein level is addressed in this paper. As discussed in this paper, the complete separation of the individual α-chains provides detailed insights into their unfolding mechanics for the collagen molecule. These can lead to a better understanding of the intramolecular interactions within the protein molecule and the interpeptide interactions between individual α-chains.

Even though natural collagen possesses unique and exceptional properties, its extraction from biological sources can be time-consuming and costly. It is also difficult to render and can pose undesired biological and pathogenic changes. Synthetic collagen is an alternative that has similar properties that mimic those present in natural collagen and allows for customization [22,23]. Its nanoscale assembly from amino acids makes it cheaper to manufacture than traditional extraction methods from biological sources while allowing the freedom to customize the collagen molecules toward specific applications. For example, changing the amino acid sequence within the chains can alter the collagen molecules' characteristics, and properties can be matched to specific applications [22,24]. The relationship between the amino acid sequence and the mechanical characteristics of collagen is investigated in this paper due to varying hydroxyproline (HYP) content of the collagen mimetic proteins and subjecting them to fraying deformation. Literature notes hydroxyproline's role as an essential factor in providing structural support for the triple helical protein. Hydroxyproline in X-position stabilizes the triple helix, and in the Y-position, it increases the triple helix's thermal stability [25].

For this work, collagen mimetic proteins 3A08 and 2CUO retrieved from the Research Collaborative for Structural Bio-informatics Protein Data Bank (RSCB PDB) were used to investigate the stability and mechanical properties under fraying deformation. (Figure 1) 3A08 collagen molecule has three polypeptide α-chains, with 23 residue/amino-acid units each, making it a 72-unit molecule. 3A08 molecule has a double collagen structure and is used to model and simulate hybrid structures. 2CUO had a sequence of the length of 27 amino acids, with a total of 79 amino acids between the three polypeptide α-chains. We expected a difference in the two collagen mimetic proteins' characteristics and properties with different amino acid sequences between them. A previous study by the authors investigated collagen mimetic protein 1BKV, also derived from RSC-PDB. 1BKV collagen molecule has three polypeptide α-chains, with 30 residue/amino-acid units each. It is an 89-unit molecule. Compared to natural collagen, all three investigated protein molecules are much shorter in length while still having a diameter of approximately 2 nanometers and are composed mainly of Glycine and Proline residues [2628].

Fig. 1
Amino acid sequences for 1BKV, 2CUO, and 3A08 collagen (from left to right)
Fig. 1
Amino acid sequences for 1BKV, 2CUO, and 3A08 collagen (from left to right)
Close modal

Figure 1 shows the amino-acid composition of the two synthetic collagen proteins, 3A08, and 2CUO used for this study, and also 1BKV collagen protein from our previous study with similar structure and sequences [29]. This study investigates the mechanical properties of the collagen mimetic proteins and their correlation to hydroxyproline content. Accordingly, the main differences between the three collagen proteins 1BKV, 3A08, and 2CUO are their hydroxyproline composition. 1BKV has the most hydroxyproline residues with 21 residues; 3A08 has only two hydroxyproline residues within the polypeptide α-chains, and 2CUO has no hydroxyproline residues. Another difference between the three collagen molecules is the size difference between them, with 1BKV being the largest, 2CUO being in the middle, and 3A08 being the smallest. A detailed comparison is given below in Table 1.

Fig. 2
Snapshots from the 2CUO pull simulation for the (a) ψ polypeptide α-chain, (b) χ polypeptide α-chain, and (c) γ polypeptide α-chain with the breaking of the hydrogen bonds between triple helix
Fig. 2
Snapshots from the 2CUO pull simulation for the (a) ψ polypeptide α-chain, (b) χ polypeptide α-chain, and (c) γ polypeptide α-chain with the breaking of the hydrogen bonds between triple helix
Close modal
Table 1

Comparison of natural collagen with the synthetic collagen proteins used for this study

PropertiesNatural collagen1BKV collagen3A08 collagen2CUO collagen
Amino acid compositionGly–Pro–HypGly–Pro–HypGly–Pro–Pro + (2 Hyp)Gly–Pro–Pro
Sequence length341302327
Number of HYP residues1132160
Molecular length∼300 nm<10 nm<10 nm<10 nm
Diameter<2 nm<2 nm<2 nm<2 nm
PropertiesNatural collagen1BKV collagen3A08 collagen2CUO collagen
Amino acid compositionGly–Pro–HypGly–Pro–HypGly–Pro–Pro + (2 Hyp)Gly–Pro–Pro
Sequence length341302327
Number of HYP residues1132160
Molecular length∼300 nm<10 nm<10 nm<10 nm
Diameter<2 nm<2 nm<2 nm<2 nm

Methods

The synthetic collagen proteins' mechanical properties are investigated using steered molecular dynamics (SMD) simulations and Umbrella sampling by submitting individual polypeptide α-chains to traction along the principal axis. Open-source MD analysis software gromacs 4.5.4 was used in conjunction with visualization software visualmoleculardynamics (vmd) and pymol [3032]. SMD simulations are performed via gromacs to simulate the dynamics of the fraying behavior in a 0.1 M sodium chloride (NaCl) solution at a temperature of 300 K and pressure of 1 bar. For all the simulations, the collagen structures were placed in a rectangular box with simple point charge water, to which 100 mM NaCl was added (see Supplemental Materials available on the ASME Digital Collection) [33]. Energy minimization along with temperature and pressure equilibration is performed via constant number, volume, and temperature (NVT) and constant pressure and temperature (NPT) ensembles, respectively. The NVT equilibration was performed with constrained bonds and a velocity rescaling modified Berendsen thermostat. For the pressure equilibration, the NPT ensemble employed Parinello–Rahmen barostat, which allows for the corresponding changes in the simulation cell box's shape. Both NVT and NPT equilibrations were analyzed for a minimum time duration of 1 ns, ensuring the system was adequately equilibrated. A modified Amber99SB force field, of the form given by Eq. (1), was used due to the inclusion of the Hydroxyproline parameters [3437]:
U(x)=bondskb(xxi)2+angleskθ(θθi)2+torsions12Un(1+cos(nωγ)+i=1N1j=i+1N{ϵij[(σijxij)122(σijxij)6]+qiqj4πϵ0xij}
(1)

After NVT and NPT equilibrations, the system is used as the initial configuration for the SMD simulations. SMD is also referred to as pull simulations performed for a simulation period of 1 ns. The system at the end of this dynamic MD analysis was subsequently used for the umbrella sampling models. For SMD, each polypeptide α-chain was pulled from the triple-helical individually to compare the binding energy needed for complete fraying of the α-chains. The SMD simulations emulate the fraying of each α-chain from the triple-helical, causing the deformation and unfolding of the collagen protein molecule as the triple helical structure is broken and the protein denatures. The system's physical and mechanical analysis was performed by visualizing the simulation with vmd and calculating the hydrogen bonds, force-distance curves, and binding energies.

Umbrella Sampling.

One of the common ways of investigating proteins and other biomaterials' mechanical properties is via biased molecular dynamics, specifically through umbrella sampling simulations [38]. Due to the inherent difficulty of obtaining high-resolution structural data of the nanoscale collagen mimetic proteins and their self-assembly or disassembly, MD simulations, along with umbrella sampling, are useful in analyzing the macromolecular interactions. The name umbrella sampling is due to the separated regions' connection in the phase space via the bias potential. Here, a bias/pulling velocity is applied to part of the molecule along a reaction coordinate by either aiming at a single simulation or several simulations (windows), where the distribution overlaps. Potential mean force (PMF) values can be calculated within these individual sampling windows [38]. The reaction coordinate is restrained and pulled to a target value by a bias potential sampling the entire momentum space in a series of windows combined with either an umbrella integration or a weighted histogram analysis method. This procedure calculates the Gibbs free energy (ΔG) from several simulations conducted on n configurations generated from a single steered molecular dynamics simulation. The free energy's exact derivation is given by the following equation [39]:
Gi(ξ)=(1β)lnPib(ξ)ωi(ξ)+Fi
(2)
β=1/(kBT)
(3)
Fi=(1/β)ln(exp[βωi(ξ)])
(4)

In the above Eqs. (2)(4), G is the Gibbs free energy, kB being the Boltzmann's constant, ξ is the reaction coordinate P(ξ) is the time average, ωi is the bias potential, Fi is the constant associated with Eq. (2), and superscript b denotes the biased quantities. It should be noted that these equations are presented here for completeness on a theoretical basis for the binding energy.

Umbrella sampling, utilizing steered molecular dynamics pull simulations, provides the PMF needed for the binding energy calculations. Umbrella sampling and PMF analysis emulate an atomic force microscope cantilever's effects acting on a protein, applying a varied bias potential to pull the system from one state to another. The binding energy (ΔG) was derived directly from gromacs MD analysis using the PMF curves. This work obtained the binding energy by calculating the difference between the highest and lowest values for each polypeptide α-chains' PMF curve after it converges at large center of mass (COM) distances.

One of the PMF analysis' main aims of the binding energy (ΔG) for the collagen mimetic proteins is the correlation between the hydroxyproline content within the collagen molecules and their fraying mechanical characteristics. A direct comparison of the binding energies of each polypeptide α-chains between the three collagen molecules cannot be made as the nomenclature and grouping for the polypeptide α-chains of each collagen molecule were done by the authors while modeling these proteins. For example, comparing the binding energy of the ψ chain for all three molecules does not give a precise insight into these molecules' mechanical properties. It would end up as comparing apples to oranges. Therefore, this study took an average of the binding energy of all three polypeptide α-chains of each collagen molecule for a better comparison of the fraying mechanical characteristics between them.

Results

Multiple simulations with different configurations were completed and analyzed, with three simulations, for each polypeptide α-chain pulled for both 2CUO and 3A08 collagen molecules. All systems were simulated in the same ionic environments. A list of all the systems is given in Table 2. Complete results and analysis of the 1BKV collagen molecule have been published in another study by the authors [29]. The results of the other two systems studied are presented in detail in this paper and the correlation of hydroxyproline differences between these three systems.

Table 2

Details of the six different collagen molecular systems

System numberCollagen moleculeDescriptionSimulation detail
12CUO2CUO ψ (blue)Pulling on 2CUO ψα-chain
22CUO2CUO χ (red)Pulling on 2CUO χα-chain
32CUO2CUO γ (green)Pulling on 2CUOγα-chain
43A083A08 ψ (blue)Pulling on 3A08 ψα-chain
53A083A08 χ (red)Pulling on 3A08χα-chain
63A083A08 γ (green)Pulling on 3A08 γα-chain
System numberCollagen moleculeDescriptionSimulation detail
12CUO2CUO ψ (blue)Pulling on 2CUO ψα-chain
22CUO2CUO χ (red)Pulling on 2CUO χα-chain
32CUO2CUO γ (green)Pulling on 2CUOγα-chain
43A083A08 ψ (blue)Pulling on 3A08 ψα-chain
53A083A08 χ (red)Pulling on 3A08χα-chain
63A083A08 γ (green)Pulling on 3A08 γα-chain

Umbrella sampling simulations are used to determine the Gibbs free energy ΔG of the unbinding/separation along the reaction coordinate in the X-direction, along which is the chain direction. Using the various number of sampling windows for different simulations along the X-axis, PMF curves were obtained for each system. This analysis process yields ΔG of fraying for each polypeptide α-chain of the triple helical protein for all three collagen molecules. Snapshots for each system were taken and used to track the SMD simulations' progression.

2CUO Collagen.

All three polypeptide α-chains of the 2CUO protein were modeled to investigate the fraying behavior of 2CUO collagen by pulling on each polypeptide α-chain individually and elucidate the unfolding behavior of the protein. All three polypeptide α-chains were individually subjected to a constant force of 1000 kJ/mol/nm at a constant pull rate of 10 nm/ns in the x-direction. The other two polypeptide α-chains are held fixed, as shown in Fig. 2. As pulling started on the polypeptide α-chains, the hydrogen bonds between the chains are found to break. The initial constraint to such separation is found to ease with further pulling and capturing one chain's fraying characteristics from the bundle. The fraying behavior insights are relevant to the self-assembly of these collagen protein structures and their stability. They provide details into the folding and unwinding behavior of these proteins. The binding energy and the unfolding pathway provide insights into how these individual peptide chains bind together and fold into a triple helical structure.

Fig. 3
Pull force applied to all three 2CUO polypeptide α-chains for complete fraying
Fig. 3
Pull force applied to all three 2CUO polypeptide α-chains for complete fraying
Close modal

Figure 3 shows the force versus COM separation distance from the initial position. The force needed for separation of the α-chain was derived directly from gromacs. The force builds up until the separation point is reached; the intramolecular interactions such as the hydrogen bonds and hydrophobic interactions are disrupted, causing the α-chain to separate from the triple-helical molecule. Pull force analysis results indicated that a maximum spring constant force of 2099.09 kJ/mol/nm, along with a COM displacement of 2.62 nm, was needed for complete fraying/separation of the ψ chain from the triple-helical. Compared to the ψ chain, the χ chain took a slightly lesser force of 1891.87 kJ/mol/nm and COM displacement of 2.34 nm for complete separation. In comparison, γ polypeptide α-chain took further slightly lesser force than both the ψandχ chains, with 1870.34 kJ/mol/nm and COM displacement of 2.33 nm for complete separation to occur. These differences indicate a hierarchical difference in bonding strength between the three polypeptide α-chains within the triple helical molecule.

Fig. 4
PMF for 2CUO α-chains yielding a ΔG value of approximately (a) ψ polypeptide α-chain: 40.12 kcal/mol, (b) χ polypeptide α-chain: 56.88 kcal/mol, and (c) γ polypeptide α-chain: 32.45 kcal/mol
Fig. 4
PMF for 2CUO α-chains yielding a ΔG value of approximately (a) ψ polypeptide α-chain: 40.12 kcal/mol, (b) χ polypeptide α-chain: 56.88 kcal/mol, and (c) γ polypeptide α-chain: 32.45 kcal/mol
Close modal

The external force/bias application to cause the COM displacement of the pulled α-chains disturbs the system equilibrium, preventing the calculation of thermodynamic quantities directly from the SMD trajectory without significant errors. However, it does allow for the calculation of work, which is a path-dependent quantity. Thus, umbrella sampling is useful in extracting free energies from the nonequilibrium SMD trajectories for a direct quantitative comparison. After completing the pull simulation for the individual chains, several simulation windows with a COM separation of 0.2 nm were generated for performing MD simulations for 10 ns for umbrella sampling. These 0.2 nm windows provide the atomistic level details to understand the unfolding behavior of collagen proteins further.

Pull simulations allow for monitoring the interactions over time when each α-chain is separated from the molecule. The α-chains within the triple helical are held together by intramolecular interactions such as hydrogen bonds, salt bridges, and side-chain packing. The energy/work needed to break the intramolecular interactions caused by the separation of the α-chains is quantified via the free energy yielded from the PMF calculation. The PMF curve (Fig. 4) for 2CUO collagen yielded varying binding energies for all three polypeptide α-chains with a ΔG value of approximately 40.12 kcal/mol for the complete separation/unfolding of the ψ chain from the triple-helical molecule. In comparison, the ψ chain needed higher binding energy for the separation of the χ chain. The amount of energy needed for complete fraying had a ΔG value of approximately 56.88 kcal/mol for complete separation from the triple helix via the breaking of the hydrogen bonds. The binding energy for the γ chain, ΔG 32.45 kcal/mol, was lower than the energy for both the ψ and χ chains. These energy differences further indicate the presence of different interhelical mechanical properties for each of the polypeptide α-chains.

3A08 Collagen.

3A08 protein molecule, with two hydroxyproline residues in each α-chain, was modeled similar to the 2CUO molecule. We investigated its fraying behavior by pulling on each polypeptide α-chain individually to study the protein's unfolding behavior. All three polypeptide α-chains were individually subjected to a spring constant force of a 1000 kJ/mol/nm with a constant pull rate of 10 nm/ns in the x-direction while holding the other two polypeptide α-chains fixed, as seen in Fig. 5. As pulling started on the polypeptide α-chains, the hydrogen bonds between the chains are broken off.

Fig. 5
Snapshots from the 3A08 pull simulation for the (a) ψ polypeptide α-chain, (b) χ polypeptide α-chain, and (c) γ polypeptide α-chain with breaking of the hydrogen bonds between triple helix
Fig. 5
Snapshots from the 3A08 pull simulation for the (a) ψ polypeptide α-chain, (b) χ polypeptide α-chain, and (c) γ polypeptide α-chain with breaking of the hydrogen bonds between triple helix
Close modal

Analysis of the pull force results (Fig. 6) yielded a maximum spring constant force of 1952.40 kJ/mol/nm, along with a COM displacement of 2.54 nm needed for complete fraying/separation of the ψ chain from the triple-helical. Compared to the ψ chain, the χ chain took less amount of force (1756.64 kJ/mol/nm) and COM displacement of 2.17 nm for complete separation to occur. Finally, the γ chain took the least amount of force of all three polypeptide α-chains, with a force value of 1720.94 kJ/mol/nm and COM displacement of 2.28 nm for complete separation to occur. These variations further confirm a difference in interpeptide interactions between the three polypeptide α-chains within the triple helical molecule.

Fig. 6
Pull force applied to all three 3A08 polypeptide α-chains for complete fraying
Fig. 6
Pull force applied to all three 3A08 polypeptide α-chains for complete fraying
Close modal

Umbrella sampling was performed again after completing the pull simulation to obtain the potential mean force necessary for complete unfolding and separation from the 3A08 triple helix. Analysis of the PMF curve (Fig. 7) for 3A08 collagen once again yielded varying binding energies for the free energies of all three polypeptide α-chains, with a ΔG value of approximately 60.63 kcal/mol for the complete separation/unfolding of the ψ chain from the triple-helical molecule. Compared to the ψ chain, higher binding energy was needed to separate the χ chain, with a ΔG value of approximately 71.71 kcal/mol for complete separation from the triple helix via the breaking of the hydrogen bonds. The binding energy for the γ chain, ΔG 55.68 kcal/mol, was once again lower than the energy for both the ψ and χ chains. This energy variation further indicates the presence of varied interhelical mechanical properties for each of the polypeptide α-chains.

Fig. 7
PMF for 3A08 polypeptide α-chains yielding the unbinding process with a ΔG value of approximately (a) ψ polypeptide α-chain: 60.63 kcal/mol, (b) χ polypeptide α-chain: 71.71 kcal/mol, and (c) γ polypeptide α-chain: 55.68 kcal/mol
Fig. 7
PMF for 3A08 polypeptide α-chains yielding the unbinding process with a ΔG value of approximately (a) ψ polypeptide α-chain: 60.63 kcal/mol, (b) χ polypeptide α-chain: 71.71 kcal/mol, and (c) γ polypeptide α-chain: 55.68 kcal/mol
Close modal

Discussion

Numerous experiments and simulations have been conducted for investigating the modulus of collagen fibrils and collagen molecules, resulting in a range of values [1,9,10,1221,4044]. Modulus values ranging between 4.8 GPa and 18.82 GPa have been reported in the literature, with a recent study listing a modulus of 7.4 GPa [44]. Varying molecular tensile pulls (failure) and strand separation (fraying) methods have been reported, with each providing more prolific data and insights compared to those obtained in the wet-lab [9]. The variations in the mechanical failure behavior that were investigated were different in all prior studies. Some studied elongation and elasticity; few other studies focused on the unfolding properties, such as separating the strands [9,17,40,43]. Detailed analysis of these proteins' behavior under fraying is still lacking. This work studied the relation between the amino-acid sequence and the fraying deformation behavior of different collagen mimetic proteins with varying hydroxyproline content. Polypeptide α-chains of these collagen mimetic proteins were subjected to a spring constant to completely separate from the triple-helical molecule. As mentioned before, a prior study by the authors looked at the fraying behavior of the 1BKV collagen mimetic protein. This paper focused on two additional collagen mimetic proteins, 2CUO and 3A08, which have a lesser hydroxyproline concentration [29]. This work focused on the fraying/unfolding behavior of the individual polypeptide α-chains. The correlation between the hydroxyproline and the collagen proteins' mechanical properties is investigated by employing the three different collagen mimetic proteins with varying hydroxyproline content.

An explicit solvent was used for this study to properly account for the electrostatic interactions, which implicit solvent models fail to represent accurately [38]. Both similarities and differences were observed with all the polypeptide α-chains subjected to a spring constant force for the fraying simulation. Table 3 lists the summary of the pull force and ΔG values for all three systems with binding energy calculated for the complete separation of each of the polypeptide α-chains from 2CUO, 3A08, and 1BKV collagen from a previous study.

Table 3

Pull force and binding energy for each system [29]

System numberCollagen moleculeNumber of HYP residuesPolypeptide α-chainsPull force (kJ/mol/nm)ΔG (kcal/mol)Average ΔG (kcal/mol)
12CUO0ψ (blue)2099.0940.1243.15
22CUO0χ (red)1891.8756.88
32CUO0γ (green)1870.3432.45
43A082ψ (blue)1952.4060.6362.67
53A082χ (red)1756.6471.71
63A082γ (green)1720.9455.68
N/A1BKV7ψ (blue)1959.6140.6867.70
N/A1BKV7χ (red)1884.2885.76
N/A1BKV7γ (green)1957.6976.67
System numberCollagen moleculeNumber of HYP residuesPolypeptide α-chainsPull force (kJ/mol/nm)ΔG (kcal/mol)Average ΔG (kcal/mol)
12CUO0ψ (blue)2099.0940.1243.15
22CUO0χ (red)1891.8756.88
32CUO0γ (green)1870.3432.45
43A082ψ (blue)1952.4060.6362.67
53A082χ (red)1756.6471.71
63A082γ (green)1720.9455.68
N/A1BKV7ψ (blue)1959.6140.6867.70
N/A1BKV7χ (red)1884.2885.76
N/A1BKV7γ (green)1957.6976.67

The maximum spring constant force analysis needed for complete separation of all three polypeptide α-chains for both the proteins yielded some similarities. A difference in the separation force is observed between the three chains for all the collagen molecules. The pull force for the separation of the ψ chain was higher than both the χ and γ chains for both 2CUO and 3A08 collagen proteins. 1BKV collagen protein had the same behavior, with the ψ chain having the highest pull force of all three polypeptide α-chains [29]. As shown in the simulation screenshots (Figs. 2 and 5), there was a noticeable difference in each chain's unfolding behavior/pathway for both collagen molecules. The differences in the unfolding pathway and spring constant force needed for complete separation between the three α-chains for both the collagen proteins suggest a variation in the interpeptide interactions and the resulting mechanical deformation characteristics of the individual α-chains within the triple helix.

A previous study by Buehler et al. on the pulling of a single polypeptide α-chain from a tropocollagen molecule with a length of 300 nm and width of 1.5 nm, using namd software yielded a maximum force of 6.925×1015Nmol for the complete separation of the α-chain. The order of magnitude of maximum force of 2.099×1015Nmol for 2CUO, 1.952×1015Nmol for 3A08, and 1.959×1015Nmol for 1BKV, based on the 10 nm long triple helix molecules from this work are in good agreement [1,29]. The variation can also be attributed to the use of different CHARMM force-field parameters, refined since Buehler et al. and 30 times longer collagen molecule. The mechanical behavior of the nanoscale collagen mimetic proteins studied in this work is thus comparable to the natural collagen molecule. However, it should be noted that the force–displacement curves generated from gromacs pull simulations alone are insufficient to conclusively determine the α-chains stability in terms of the Gibbs free energy; the α-chain separation/fraying behavior is a path-dependent process. It cannot be compared to other simulations unless the separation/fraying path is similar. Therefore, the use of umbrella sampling provides an accurate insight into the mechanics of the collagen molecules.

In all cases, the binding energy (ΔG) values indicate these synthetic collagen proteins' excellent mechanical characteristics. PMF analysis yielded a difference in the binding energy (ΔG) between the three polypeptide α-chains for both the 2CUO and 3A08 collagen molecules, as well as 1BKV collagen. These binding energy variations can be attributed to arise mainly from the differences in the interpeptide interactions between the three chains within the triple helical structure. While they are expected to be uniformly bound, the differences in the three polypeptide α-chains' binding energies suggest a variance in the molecular interactions and mechanics of fraying deformation. Hydrogen bond analysis was performed to confirm whether hydrogen bonding played a role in the differences of binding energies between the three polypeptide α-chains (Fig. 8).

Fig. 8
Number of hydrogen bonds for the system after the complete separation of individual chains for (a) 2CUO and (b) 3A08 collagen molecules
Fig. 8
Number of hydrogen bonds for the system after the complete separation of individual chains for (a) 2CUO and (b) 3A08 collagen molecules
Close modal

As listed in Table 3, the binding energy decreases as the amount of hydroxyproline within the collagen molecules decreases. The 1BKV collagen, with the most hydroxyproline content, had the highest ΔG average among the three. The 3A08 collagen with a lesser hydroxyproline content had a smaller average binding energy than 1BKV. The same 3A08 collagen had a higher average binding energy value than the 2CUO, which has no hydroxyproline. Thus, the binding energy is found to increase with HYP residue content. There are seven HYP residues in each α-chain of 1BKV collagen, while 3A08 collagen with only two residues for each α-chain. However, this reduced HYP residue content resulted only in a slightly lower binding energy than 1BKV. It can be due to other amino-acid residues, Alanine, Arginine, Leucine, Isoleucine, and Threonine, in the α-chains of 1BKV. The 2CUO collagen, which has no HYP residues, had a much smaller binding energy. The reduced binding energy indicates that the unfolding/separation of individual α-chains from the triple helical protein is easier with lesser HYP concentration. A direct correlation between the collagen molecules' hydroxyproline content to the binding energy and characteristics under a fraying deformation can thus be inferred (Fig. 9).

Fig. 9
Binding energy (ΔG) increases with hydroxyproline in the collagen molecule
Fig. 9
Binding energy (ΔG) increases with hydroxyproline in the collagen molecule
Close modal

There was a similarity in the complete fraying of the χ and γ chains for 2CUO collagen, while a difference in the fraying mechanism of the ψ chain was observed. The χ and γ chains pulled away, with the entire polypeptide alpha pulling out from the triple-helical as a whole. In comparison, the ψ chain was noted to be fraying systematically from the top to the bottom of the polypeptide α-chain, like peeling a banana. In the case of 3A08 collagen, the ψ and γ chains peeled away similarly, with the χ chain, separating with the entire polypeptide alpha pulling off from the triple-helical as a whole. This entire separation caused a steeper decrease in the number of hydrogen bonds that remained for the χ and γ chains; a higher number of bonds were broken when the entire polypeptide α-chain started fraying from the triple helix (Fig. 8). For 3A08, the χ chain saw a steeper decrease in the number of hydrogen bonds than the ψ and γ chains. There were no significant differences in the hydrogen bonding between the three chains before and after the collagen molecules' separation, as seen from the standard deviation in Table 4.

Table 4

Average number of bonds for before and after separation of the α-chains for each system [29]

System numberCollagenHYP contentPolypeptide α-chainsAverage bonds (before separation)Average bonds (after separation)Standard deviation (before separation)Standard deviation (after separation)
12CUO0ψ (blue)17.47 6.336.73 1.93
22CUO0χ (red)17.522.726.58 1.56
32CUO0γ (green)18.97 5.976.36 1.92
43A082ψ (blue)13.685.765.66 1.63
53A082χ (red)15.304.597.08 1.75
63A082γ (green)12.094.98 5.971.84
N/A1BKV7ψ (blue)24.407.366.953.08
N/A1BKV7χ (red)21.2810.717.272.78
N/A1BKV7γ (green)20.5110.777.472.57
System numberCollagenHYP contentPolypeptide α-chainsAverage bonds (before separation)Average bonds (after separation)Standard deviation (before separation)Standard deviation (after separation)
12CUO0ψ (blue)17.47 6.336.73 1.93
22CUO0χ (red)17.522.726.58 1.56
32CUO0γ (green)18.97 5.976.36 1.92
43A082ψ (blue)13.685.765.66 1.63
53A082χ (red)15.304.597.08 1.75
63A082γ (green)12.094.98 5.971.84
N/A1BKV7ψ (blue)24.407.366.953.08
N/A1BKV7χ (red)21.2810.717.272.78
N/A1BKV7γ (green)20.5110.777.472.57

Electrostatic interactions can affect the collagen protein molecules, including attraction/repulsion between the individual α-chains, breaking of the hydrophobic interactions, or salt bridges within the triple helical. The presence of ions in the simulation setup allowed us to investigate the role of electrostatic interactions, if there is one, on mechanical behavior. No significant involvement of the Na+ or Cl ions was found to play a role in the fraying process. Further, no significant interactions between the ions and protein were noticed in all cases. The ions maintained their proximity to the collagen molecule throughout the complete fraying of the α-chains.

The fraying behavior can be further compared to the collagen molecules' tensile failure behavior in a future study; in this case, the entire molecule is stretched under a tensile strain and used to calculate a Young's modulus value. Young's modulus values in the literature for natural collagen fibrils and molecules report a range of modulus values from 2.4 to 4.8 GPa, with higher HYP content credited for increased structural support and modulus. The highest calculated binding energy for the synthetic 1BKV collagen protein (85.76 kCal/mol or 358.82 kJ/mol) can be attributed to the high concentration of the hydroxyproline residues, which can provide structural stability to the molecules [25].

Conclusion

This paper has demonstrated three different nanoscale collagen mimetic proteins' fraying behavior, employing MD simulations that incorporated explicit solvents, COM pulling, and umbrella sampling. All three individual polypeptide α-chains were individually separated from the collagen proteins' triple-helical structure to investigate the fraying mechanical characteristics via the binding energy needed for disassociation. The resulting binding energy suggests excellent mechanical strength of the three collagen mimetic proteins. This work showed good mechanical characteristics based on the separation/fraying of the synthetic collagen's α-chains. An analysis of the ΔG values for all three collagen proteins shows a correlation between the collagen molecules' hydroxyproline content and fraying mechanical characteristics. The lowest HYP content was in 2CUO collagen at 0%, with 3A08 collagen having the intermediate at 10.6% and 1BKV with the highest content at 28.9%. The increase in average ΔG of the collagen molecules with increasing HYP content was 45.23% for 3A08 compared to 2CUO and 56.37% for 1BKV than 2CUO. Between 3A08 and 1BKV, there was an 8% increase in the average ΔG. The higher binding energy can be attributed to the higher hydroxyproline residues providing structural stability [25].

A difference in the unfolding pathway and the separation force needed for complete fraying of each peptide chain from the triple helical protein is also highlighted in this study. Variation in the spring constant force and the unbinding energy between the chains can be attributed to the staggered structure of the polypeptide α-chains within the triple helical molecule and the varying electrostatic interactions due to individual amino-acid interactions between the chains.

In future studies, SMD simulations can investigate the tensile deformation behavior of collagen proteins compared to fraying behavior. These tensile deformations would provide a comprehensive picture and understanding of their mechanical properties.

Funding Data

  • Army Research Office (W911NF-11-1-0168; Funder ID: 10.13039/100000183).

References

1.
Buehler
,
M. J.
,
2006
, “
Atomistic and Continuum Modeling of Mechanical Properties of Collagen: Elasticity, Fracture, and Self-Assembly
,”
J. Mater. Res.
,
21
(
8
), pp.
1947
1961
.10.1557/jmr.2006.0236
2.
Gautieri
,
A.
,
Vesentini
,
S.
,
Redaelli
,
A.
, and
Ballarini
,
R.
,
2013
, “
Modeling and Measuring Visco-Elastic Properties: From Collagen Molecules to Collagen Fibrils
,”
Int. J. Non-Linear Mech.
,
56
, pp.
25
33
.10.1016/j.ijnonlinmec.2013.03.012
3.
O'Brien
,
F. J.
,
2011
, “
Biomaterials & Scaffolds for Tissue Engineering
,”
Mater. Today
,
14
(
3
), pp.
88
95
.10.1016/S1369-7021(11)70058-X
4.
Miranda-Nieves
,
D.
, and
Chaikof
,
E. L.
,
2017
, “
Collagen and Elastin Biomaterials for the Fabrication of Engineered Living Tissues
,”
ACS Biomater. Sci. Eng.
,
3
(
5
), pp.
694
711
.10.1021/acsbiomaterials.6b00250
5.
Ulery
,
B. D.
,
Nair
,
L. S.
, and
Laurencin
,
C. T.
,
2011
, “
Biomedical Applications of Biodegradable Polymers
,”
J. Polym. Sci. B
,
49
(
12
), pp.
832
864
.10.1002/polb.22259
6.
Parenteau-Bareil
,
R.
,
Gauvin
,
R.
, and
Berthod
,
F.
,
2010
, “
Collagen-Based Biomaterials for Tissue Engineering Applications
,”
Materials
,
3
(
3
), pp.
1863
1887
.10.3390/ma3031863
7.
Kaur
,
P. J.
,
2017
, “
Design of Collagen-Mimetic Peptides
,”
Ph.D. thesis
,
The City University of New York
,
New York
.https://academicworks.cuny.edu/cgi/viewcontent.cgi?article=2942&context=gc_etds
8.
Li
,
Y
,
2009
, “
The Mechanism of Collagen Self-Assembly: Hydrophobic and Electrostatic Interactions
,”
Ph.D. dissertation
, Materials Science and Engineering,
The University of Florida
, Gainesville, FL.
9.
In’T Veld
,
P. J.
, and
Stevens
,
M. J.
,
2008
, “
Simulation of the Mechanical Strength of a Single Collagen Molecule
,”
Biophys. J.
,
95
(
1
), pp.
33
39
.10.1529/biophysj.107.120659
10.
Gautieri
,
A.
,
Vesentini
,
S.
,
Redaelli
,
A.
, and
Buehler
,
M. J.
,
2011
, “
Hierarchical Structure and Nanomechanics of Collagen Microfibrils From the Atomistic Scale Up
,”
Nano Lett
,
11
(
2
), pp.
757
766
.10.1021/nl103943u
11.
Kwansa
,
A. L.
,
De Vita
,
R.
, and
Freeman
,
J. W.
,
2016
, “
Tensile Mechanical Properties of Collagen Type I and Its Enzymatic Crosslinks
,”
Biophys. Chem.
,
214–215
, pp.
1
10
.10.1016/j.bpc.2016.04.001
12.
Cusack
,
S.
, and
Miller
,
A.
,
1979
, “
Determination of the Elastic Constants of Collagen by Brillouin Light Scattering
,”
J. Mol. Biol.
,
135
(
1
), pp.
39
51
.10.1016/0022-2836(79)90339-5
13.
Eppell
,
S. J.
,
Smith
,
B. N.
,
Kahn
,
H.
, and
Ballarini
,
R.
,
2006
, “
Nano Measurements With Micro-Devices: Mechanical Properties of Hydrated Collagen Fibrils
,”
J. R. Soc. Interface
,
3
(
6
), pp.
117
121
.10.1098/rsif.2005.0100
14.
van der Rijt
,
J. A.
,
van der Werf
,
K. O.
,
Bennink
,
M. L.
,
Dijkstra
,
P. J.
, and
Feijen
,
J.
,
2006
, “
Micromechanical Testing of Individual Collagen Fibrils
,”
Macromol. Biosci.
,
6
(
9
), pp.
697
702
.10.1002/mabi.200600063
15.
Shen
,
Z. L.
,
Dodge
,
M. R.
,
Kahn
,
H.
,
Ballarini
,
R.
, and
Eppell
,
S. J.
,
2008
, “
Stress-Strain Experiments on Individual Collagen Fibrils
,”
Biophys. J.
,
95
(
8
), pp.
3956
3963
.10.1529/biophysj.107.124602
16.
Sasaki
,
N.
, and
Odajima
,
S.
,
1996
, “
Elongation Mechanism of Collagen Fibrils and Force-Strain Relations of Tendon at Each Level of Structural Hierarchy
,”
J. Biomech.
,
29
(
9
), pp.
1131
1136
.10.1016/0021-9290(96)00024-3
17.
Gautieri
,
A.
,
Buehler
,
M. J.
, and
Redaelli
,
A.
,
2009
, “
Deformation Rate Controls Elasticity and Unfolding Pathway of Single Tropocollagen Molecules
,”
J. Mech. Behav. Biomed. Mater.
,
2
(
2
), pp.
130
137
.10.1016/j.jmbbm.2008.03.001
18.
Sasaki
,
N.
, and
Odajima
,
S.
,
1996
, “
Stress-Strain Curve and Young's Modulus of a Collagen Molecule as Determined by the X-Ray Diffraction Technique
,”
J. Biomech.
,
29
(
5
), pp.
655
658
.10.1016/0021-9290(95)00110-7
19.
Harley
,
R.
,
James
,
D.
,
Miller
,
A.
, and
White
,
J. W.
,
1977
, “
Phonons and the Elastic Moduli of Collagen and Muscle
,”
Nature
,
267
(
5608
), pp.
285
287
.10.1038/267285a0
20.
Vesentini
,
S.
,
Fitie
,
C. F.
,
Montevecchi
,
F. M.
, and
Redaelli
,
A.
,
2005
, “
Molecular Assessment of the Elastic Properties of Collagen-Like Homotrimer Sequences
,”
Biomech. Model. Mechanobiol.
,
3
(
4
), pp.
224
234
.10.1007/s10237-004-0064-5
21.
Gautieri
,
A.
,
Russo
,
A.
,
Vesentini
,
S.
,
Redaelli
,
A.
, and
Buehler
,
M. J.
,
2010
, “
Coarse-Grained Model of Collagen Molecules Using an Extended MARTINI Force Field
,”
J. Chem. Theory Comput.
,
6
(
4
), pp.
1210
1218
.10.1021/ct100015v
22.
Persikov
,
A. V.
,
Ramshaw
,
J. A.
, and
Brodsky
,
B.
,
2005
, “
Prediction of Collagen Stability From Amino Acid Sequence
,”
J. Biol. Chem.
,
280
(
19
), pp.
19343
19349
.10.1074/jbc.M501657200
23.
Kotch
,
F. W.
, and
Raines
,
R. T.
,
2006
, “
Self-Assembly of Synthetic Collagen Triple Helices
,”
Proc. Natl. Acad. Sci.
,
103
(
9
), p.
9
.10.1073/pnas.0508783103
24.
Persikov
,
A. V.
,
Ramshaw
,
J. A.
,
Kirkpatrick
,
A.
, and
Brodsky
,
B.
,
2002
, “
Peptide Investigations of Pairwise Interactions in the Collagen Triple-Helix
,”
J. Mol. Biol.
,
316
(
2
), pp.
385
394
.10.1006/jmbi.2001.5342
25.
Shoulders
,
M. D.
, and
Raines
,
R. T.
,
2009
, “
Collagen Structure and Stability
,”
Annu. Rev. Biochem.
,
78
(
1
), pp.
929
958
.10.1146/annurev.biochem.77.032207.120833
26.
Hongo
,
C.
,
Noguchi
,
K.
,
Okuyama
,
K.
,
Tanaka
,
Y.
, and
Nishino
,
N.
,
2005
, “
Repetitive Interactions Observed in the Crystal Structure of a Collagen-Model Peptide, [(Pro-Pro-Gly)9]3
,”
J. Biochem.
,
138
(
2
), pp.
135
144
.10.1093/jb/mvi108
27.
Kramer
,
R. Z.
,
Bella
,
J.
,
Mayville
,
P.
,
Brodsky
,
B.
, and
Berman
,
H. M.
,
1999
, “
Sequence Dependent Conformational Variations of Collagen Triple-Helical Structure
,”
Nat. Struct. Biol.
,
6
(
5
), p.
4
.10.1038/8259
28.
Okuyama
,
K.
,
Morimoto
,
T.
,
Narita
,
H.
,
Kawaguchi
,
T.
,
Mizuno
,
K.
,
Bächinger
,
H. P.
,
Wu
,
G.
, and
Noguchi
,
K.
,
2010
, “
Two Crystal Modifications of (Pro-Pro-Gly)4-Hyp-Hyp-Gly-(Pro-Pro-Gly)4 Reveal the Puckering Preference of Hyp(X) in the Hyp(X):Hyp(Y) and Hyp(X):Pro(Y) stacking Pairs in Collagen Helices
,”
Acta Crystallogr. D
,
66
(
1
), pp.
88
96
.10.1107/S0907444909046642
29.
Rawal
,
A.
,
Rhinehardt
,
K. L.
, and
Mohan
,
R. V.
,
2019
, “
Mechanical Behavior of Collagen Mimetic Peptides Under Fraying Deformation Via Molecular Dynamics
,”
ASME
Paper No. IMECE2019-11492.10.1115/IMECE2019-11492
30.
Berendsen
,
H. J. C.
,
Spoel
,
D. V D.
, and
Drunen
,
R. V.
,
1995
, “
GROMACS: A Message-Passing Parallel Molecular Dynamics Implementation
,”
Comput. Phys. Commun.
,
91
(
1–3
), pp.
43
56
.10.1016/0010-4655(95)00042-E
31.
Schrodinger
,
L. L. C.
,
2015
, “
The PyMOL Molecular Graphics System, Version 1.8
,” PyMoL.
32.
Humphrey
,
W.
,
Dalke
,
A.
, and
Schulten
,
K.
,
1996
, “
VMD: Visual Molecular Dynamics
,”
J. Mol. Graph.
,
14
(
1
), pp.
33
38
.10.1016/0263-7855(96)00018-5
33.
Berendsen
,
H. J. C.
,
Postma
,
J. P. M.
,
van Gunsteren
,
W. F.
, and
Hermans
,
J.
,
1981
, “
Interaction Models for Water in Relation to Protein Hydration
,”
Intermol. Forces
,
14
, pp.
331
342
.10.1007/978-94-015-7658-1_21
34.
Wang
,
J.
,
Cieplak
,
P.
, and
Kollman
,
P. A.
,
2000
, “
How Well Does a Restrained Electrostatic Potential (RESP) Model Perform in Calculating Conformational Energies of Organic and Biological Molecules?
,”
J. Comput. Chem.
,
21
(
12
), pp.
1049
1074
.10.1002/1096-987X(200009)21:12<1049::AID-JCC3>3.0.CO;2-F
35.
DePaul
,
A. J.
,
Thompson
,
E. J.
,
Patel
,
S. S.
,
Haldeman
,
K.
, and
Sorin
,
E. J.
,
2010
, “
Equilibrium Conformational Dynamics in an RNA Tetraloop From Massively Parallel Molecular Dynamics
,”
Nucl. Acids Res
,
38
(
14
), pp.
4856
4867
.10.1093/nar/gkq134
36.
Sorin
,
E. J.
, and
Pande
,
V. S.
,
2005
, “
Exploring the Helix-Coil Transition Via All-Atom Equilibrium Ensemble Simulations
,”
Biophys. J.
,
88
(
4
), pp.
2472
2493
.10.1529/biophysj.104.051938
37.
Park
,
S.
,
Radmer
,
R. J.
,
Klein
,
T. E.
, and
Pande
,
V. S.
,
2005
, “
A New Set of Molecular Mechanics Parameters for Hydroxyproline and Its Use in Molecular Dynamics Simulations of Collagen-Like Peptides
,”
J. Comput. Chem.
,
26
(
15
), pp.
1612
1676
.10.1002/jcc.20301
38.
Lemkul
,
J. A.
, and
Bevan
,
D. R.
,
2010
, “
Assessing the Stability of Alzheimer's Amyloid Protofibrils Using Molecular Dynamics
,”
J. Phys. Chem. B
,
114
(
4
), pp.
1652
1660
.10.1021/jp9110794
39.
Kästner
,
J.
,
2011
, “
Umbrella Sampling
,”
Wiley Interdiscip. Rev.: Comput. Mol. Sci.
,
1
(
6
), pp.
932
942
.10.1002/wcms.66
40.
Lorenzo
,
A. C.
, and
Caffarena
,
E. R.
,
2005
, “
Elastic Properties, Young's Modulus Determination and Structural Stability of the Tropocollagen Molecule: A Computational Study by Steered Molecular Dynamics
,”
J. Biomech.
,
38
(
7
), pp.
1527
1533
.10.1016/j.jbiomech.2004.07.011
41.
Stultz
,
C. M.
,
2006
, “
The Folding Mechanism of Collagen-Like Model Peptides Explored Through Detailed Molecular Simulations
,”
Protein Sci.
,
15
(
9
), pp.
2166
2177
.10.1110/ps.062124606
42.
Wenger
,
M. P.
,
Bozec
,
L.
,
Horton
,
M. A.
, and
Mesquida
,
P.
,
2007
, “
Mechanical Properties of Collagen Fibrils
,”
Biophys. J.
,
93
(
4
), pp.
1255
1263
.10.1529/biophysj.106.103192
43.
Gautieri
,
A.
,
Vesentini
,
S.
,
Montevecchi
,
F. M.
, and
Redaelli
,
A.
,
2008
, “
Mechanical Properties of Physiological and Pathological Models of Collagen Peptides Investigated Via Steered Molecular Dynamics Simulations
,”
J. Biomech.
,
41
(
14
), pp.
3073
3077
.10.1016/j.jbiomech.2008.06.028
44.
Ge
,
H. B.
,
Zhang
,
C.
,
Song
,
Q. Y.
, and
Liu
,
Q.
,
2017
, “
Young's Modulus Determination of the Collagen Molecule Via GROMACS
,” The 8th International Conference on Computational Methods (
ICCM 2017
), Guilin, Guangxi, China, July 25–29.https://www.sci-en-tech.com/ICCM2017/PDFs/2705-7528-1-PB.pdf

Supplementary data