- Email: [email protected]
Toward rational algorithmic design of collagen-based biomaterials through multiscale computational modeling
Available online at www.sciencedirect.com
ScienceDirect Toward rational algorithmic design of collagen-based biomaterials through multiscale computational modeling Nan Zhang1,2, Yuan Cheng3, Xiaoling Hu1 and Jingjie Yeo3 Inspired by the complex diversity of collagenous materials in mammalian tissue, collagen-based biomaterials are increasingly utilized for developing drug delivery vehicles and regenerative tissue engineering. Collagen’s broad utility poses important engineering challenges for the rational and predictive design of the resultant biomaterial’s physical and chemical properties. We review the most recent developments in multiscale computational modeling of collagen-based biomaterials to determine their structural, mechanical, and physicochemical properties. Through the materials-by-design paradigm, these developments may eventually lead to rational algorithmic recipes for bottom–up multiscale design of these biomaterials, thereby minimizing the experimental costs of iterative material synthesis and testing. We also highlight the future perspectives and opportunities for expanding multiscale modeling capabilities to incorporate physicochemical and biological functions of collagen-based biomaterials. Addresses 1 School of Natural and Applied Science, Northwestern Polytechnical University, Xi’an, 710072, PR China 2 Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, 117575, Singapore 3 Institute of High Performance Computing, A*STAR, 1 Fusionopolis Way, Singapore 138632, Singapore Corresponding authors: Hu, Xiaoling ([email protected]), Yeo, Jingjie ([email protected])
Current Opinion in Chemical Engineering 2019, 24:79–87 This review comes from a themed issue on Materials engineering: bio-derived or bio-inspired material Edited by Jeannine M Coburn and David Kaplan
https://doi.org/10.1016/j.coche.2019.02.011
chemical compositions that heavily influence the functions of various tissues and organs [2]. Although the collagen family is incredibly diverse with 28 distinct members, every member minimally comprises one triple helical domain. The multiscale hierarchical structures, assemblies, and functions of all members of the collagen family were reviewed extensively recently [1,2] but generally, the collagen family has a common structural motif of a right-handed triple-helical secondary structure comprising three polypeptide chains in left-handed polyproline II helical configurations. Each chain contains at least one Gly-X-Y sequence with X and Y frequently being proline and 4-hydroxyproline respectively, and this unique motif serves to stabilize collagen’s triple helical structures. Inspired by nature, scientists and engineers increasingly use collagen-based biomaterials in biomedical applications, particularly for drug delivery vehicles and regenerative tissue engineering. These applications seek to harness the exceptional properties of collagen: excellent mechanical strength and flexibility [3], biocompatibility, biodegradability [4], and ease of synthesis into a broad variety of multiscale hierarchical morphologies [5]. Being a major component of the extracellular matrix (ECM), collagen is also important for cellular signaling and regulation. Perhaps ironically, this broad applicability of collagen as a biomaterial poses a challenging engineering problem. Can the sequence-structure-function of collagen-based biomaterials be rationally designed computationally so as to precisely achieve any desired combinations of physical and chemical properties (Figure 1a), thereby minimizing the experimental costs of iterative material synthesis and testing? Can the materials-by-design paradigm be harnessed for this purpose?
2211-3398/ã 2018 Elsevier Ltd. All rights reserved.
Computational modeling of collagen at multiple structural hierarchies Introduction Collagen is a remarkably versatile and abundant biomaterial. In mammals, collagen outnumbers all other protein families, accounting for approximately 30% of the total protein by mass [1]. Being the primary protein component of connective and soft tissues, collagen is a multifunctional protein with unique hierarchical structures and www.sciencedirect.com
The structural, physical, and chemical properties of collagen can be tailored to confer a broad range of mechanical and physicochemical stability, elasticity, and strength to the biomaterial [6]. These modifications can encompass a wide spectrum of structural hierarchies, from the sequence of the amino acids that constitute the collagen to the macroscale formation of random or ordered networks (Figure 1a). Multiscale computational modeling and simulations are indispensable for characterizing and Current Opinion in Chemical Engineering 2019, 24:79–87
80 Materials engineering: bio-derived or bio-inspired material
Figure 1
Collagen Sequence
(a)
(b)
Full atomistic model of the 3rd D-period
Triple Helix Collagen molecule
Multiscale Structures & Properties
d2ol
Fibril
d2gp
d3oI
d3gp
d4ol
C-terminal
d4gp
D-period
Material
Collagen microfibril
(c)
Overlap region (0.46D)
Gap region (0.54D)
D3gp-seg1
D3ol-seg2
30
0%
0%
25
εI=20%
εI=20%
30% 30% εc=35% εf=48%
Force (nN)
10%
10%
20 15 10
εc=42%
5
εf=59%
0 0.0
(e)
(d)
0.1
60%
49%
0.2
0.3 Strain
0.4
0.5
0.6
a
a b
c
b c
Current Opinion in Chemical Engineering
(a) Algorithmic design of the multiscale hierarchical structures and properties of collagen from atoms to materials. (b) Fully atomistic models of Type I collagen microfibril to explore the mechanical behavior and unfolding mechanism of the overlapping and gap regions (reproduced with permission from Springer Nature [17]). (c) Type I collagen microfibril had significant mechanical heterogeneity in various overlap and gap regions of collagen microfibrils (left, right) as determined from SMD simulations (center) (reproduced with permission from Springer Nature [18]). (d) Representative molecular configurations of tropocollagen (left) and SMD simulations (right) showed that the Young’s moduli of the second overlapping and gap regions had differing strain rate dependence (reproduced with permission from Elsevier [20]). (e) SMD simulations of the mechanical response of collagen microfibril deformed under different strains (top), demonstrating the shear-dominant mode of failure mechanism under tensile loads (bottom) (reproduced with permission from Nature Publishing Group [22] under CC-BY 4.0).
designing various properties of collagen within these diverse structural hierarchies, using either bottom–up or top–down approaches. These features were elucidated with an expansive gamut of numerical techniques, including fully atomistic or mesoscale coarse-grained molecular dynamics (MD) simulations [7,8] and finite element (FE) methods [9,10]. Finer details on the application of these computational methods for realizing the materialsCurrent Opinion in Chemical Engineering 2019, 24:79–87
by-design paradigm was extensively reviewed previously [11]. Several earlier reviews also detailed the nanomechanical [12,13] and molecular physicochemical properties [14] of collagen. Here, we provide a bottom–up perspective of the most recent developments in atomistic to continuum scale computational analysis of the viscoelastic deformation and physicochemical properties of collagen and collagen-based biomaterials. www.sciencedirect.com
Toward rational algorithmic design of collagen-based biomaterials Zhang et al. 81
Mechanical properties of collagen Collagen peptides, fibrils, and fibers
At the molecular level, collagen comprises individual peptide strands that self-assemble into triple-helical tropocollagen molecules. The biomechanical features in tropocollagen, especially elasticity, are determined by the uniformity of the Gly-X-Y repeating motifs. Ghanaeian et al. performed steered MD (SMD) simulations to investigate the effects of the most abundant residues at the X and Y sites, proline and hydroxyproline, as well as on collagen stiffness and elasticity [15]. The stiffnesses and Young’s moduli of collagen ranged from 823.00 to 3344.00 pN/nm and 4.22 to 22.05 GPa, respectively. Increased proline content was related to higher mechanical stiffness, while elevated hydroxyproline content had the opposite effect of improving the elasticity [15]. With the distinct exception of Type IV collagen, other categories of collagen molecules generally assemble into similar structures of long and thin fibrils. In particular, Type I collagen fibrils have a unique repeating tertiary structure where each repeat is known as the D-period, resulting in visible striations from electron micrographs [16]. Early computational models frequently assumed that collagen fibrils were homogenous rod-like structures, but recent research challenged this assumption [17]. Through SMD simulations, Zhou et al. found significant mechanical heterogeneity in various overlap and gap regions of collagen microfibrils [17,18] (Figure 1b,c). These microfibrils were modelled after the structure of full length Type I collagen molecule that was experimentally verified in situ [19]. To probe the molecular origins of this heterogeneity, further SMD simulations were performed to explore the mechanical behavior and unfolding mechanism of the second overlapping region and gap region of Type I collagen microfibrils at different strain rates [20] (Figure 1d). The Young’s modulus of a single collagen molecule diminished as the strain rate decreased, but converged to approximately 3.2 GPa and 3.4 GPa for the overlapping and gap regions respectively when the strain rates were lower than 1.3 108% s 1 [20]. Every overlap and gap regions in Type I collagen fibrils was also studied in detail with SMD simulations using a strain rate of 6.5 107% s 1 and heterogeneous mechanical properties were found for each region [17]. The fibrillar structure of collagen is stabilized further through intermolecular and interfibrillar crosslinks from various posttranslational modifications. Depalle et al. established a three-dimensional Coarse-Grained (CG) model to explore the effects of enzymatic crosslinking on collagen fibril mechanics at the mesoscale scale [21]. On the one hand, the stiffness in the regime of large deformation was heavily influenced by both the crosslink type and density as the number of interconnected molecules increased. On the other hand, the failure strain and strength of the fibril was dictated by the strength of the crosslinks [21]. www.sciencedirect.com
Therefore, the toughness and strength of fibrillar collagen-based biomaterials can possibly be tuned by varying the crosslinking strength and density. The mechanical properties of the collagen fibers that constitute any collagen-based biomaterials can influence their failure behavior, but mechanical damage in these constituent collagen fibrils and fibers at the molecular level can also cause further changes in material behavior. Although no significant macroscopic damage might be detectable, molecular-scale damage mechanisms could be resolved using carboxyfluorescein (CF) labeled collagen hybrid peptide (CHP) that bound to unfolded collagen triple helices [22]. Utilizing SMD simulations, Zitnay et al. illustrated that a shear-dominated failure mechanism led to the unfolding of the triple helices during mechanical injury to connective tissue, thereby allowing the CHP to bind and detect this molecular damage (Figure 1e). Finally, the viscoelastic creep behavior of collagen was also investigated using the SMD method. The results indicated that the steady-state Young’s modulus of the collagen microfibril assembly ranged from 2.24 to 3.27 GPa, which was consistent with reported experimental measurements [23]. Fibrillar collagen networks
Although the mechanical properties of collagen ranging from the molecular scale to the scale of single fibers were examined extensively, the structural and mechanical response of fibrillar collagen networks to local strains or deformations is still poorly understood. To address this gap, Lee et al. developed a three-dimensional, beadspring model to mimic elastic collagen fiber networks (Figure 2a). The fiber network’s mechanical behavior under various biophysical conditions was investigated, including collagen density, crosslinker strength and density, and fiber orientation. Interestingly, the mechanical properties of these fiber networks were largely influenced by the network geometry compared to the other parameters. The evolution of the fiber network structure and mechanics with local deformation was also captured accurately, such as strain stiffening [24]. Additionally, relatively simple 2D and 3D lattice-based network and 2D Mikado network models were developed that could account for the stiffness of Type I collagen networks in the nonlinear elastic regime [25] (Figure 2b). Uniquely, the nonlinear Young’s modulus in collagen networks appeared to be independent from concentration. This property was attributed to three factors of stress scaling linearly with stiffness, the response of the network being dominated by bending in the linear elastic regime, and the constituent fibers responding in an athermal, simple elastic manner. To further understand the microscale mechanics of collagen fiber networks, Jones et al. constructed a 2D lattice-based computational model to elucidate the general properties of extracellular matrices Current Opinion in Chemical Engineering 2019, 24:79–87
82 Materials engineering: bio-derived or bio-inspired material
Figure 2
(a) Shear modulus [Pal]
(b) 4mg/ml 300
3mg/ml
200
2mg/ml 1mg/ml
100 0
800
ssl
Strain=0
(a)
Δy 0
10
den
sity
200
15
[ N]
Cr
th
]
Pa
[K
g en
tr
rs
ke
os
n sli
2D Mikado
2D Lattice
(d)
Y
X 0.2
0.3
0 2
4 6 8 time (s)
(d)
Δd
0.1
er
400
Force in + x direction
(b)
(c)
ink
Strain=0.1
displacement (μm)
(c)
600
5
Cro
0.2
Δd
0 π
Δy
-0.1
-0.4 0 -0.2
0 Δx (µm)
0.2
-0.2
0.4 Δx (µm)
-0.3 Current Opinion in Chemical Engineering
(a) Shear deformation of a bead-and-spring collagen fiber network model derived from SEM images of collagen fibers from a normal mouse mammary gland (left) and the variation of the shear moduli with crosslinking density and strength (right) (reproduced with permission from PLOS [24] under CC-BY 4.0). (b) Stiffening response (top left: differential shear modulus K versus shear stress s for reconstituted collagen I networks) of 2D Mikado (bottom left) and lattice network models (bottom right) derived from 3D confocal image of a reconstituted Type I collagen network (top right) (reproduced with permission from the National Academy of Science [25] under CC-BY 4.0). (c) Micromechanical response in collagen gel using optical traps (reproduced with permission from the National Academy of Science [26]). (d) FE modeling (left) of a heart valve deforming (right) while accounting for tissue remodeling (reproduced with permission from Elsevier [27]).
[26]. This model successfully captured the remodeling of the micromechanical properties surrounding a contracting cell (Figure 2c). Beyond microscale network models, network properties at the tissue level were probed with FE methods. For instance, the remodeling of collagen networks in heart valve tissues were much more stable and favorable at aortic pressure conditions in comparison with tissue remodeling at pulmonary pressure conditions [27] (Figure 2d). Pierce et al. proposed a constitutive model solved with 3D FE simulations and accurately reproduced the mechanical properties of the multi-directional collagen-reinforced composite system based on articular cartilage [28]. Physicochemical properties of collagen
The physicochemical properties of collagen are also vital considerations for the design of collagen-based biomaterials. Important properties include collagen’s biocompatibility, biodegradability, and thermal stability. For instance, maintaining the mechanical and thermal stability of triple-helical collagen structures requires an intricate balance of numerous physicochemical factors, such Current Opinion in Chemical Engineering 2019, 24:79–87
as stereoelectronic and steric effects between the collagen chains and amino acids. Using ab initio quantum chemical calculations, Schweizer et al. proposed an atomistic model of collagen-like material for systematic analysis of favorable hydroxyproline conformations and their impact on triple-helical stability [29] (Figure 3a). Stereoelectronic gauche-effect and intramolecular hydrogen bonds had a profound effect on the stability of the triple helix. Furthermore, 4S-hydroxyproline in collagen might have a destabilizing effect as intramolecular hydrogen bonds interfered with interactions between the collagen strands [29]. To assess thermal stabilities at larger spatiotemporal scales, a phenomenological CG MD model was devised (Figure 3b) to simulate the melting trends of single-chain collagen-like peptides (CLP) and CLP co-polymerized with other proteins such as elastin-like peptides (ELP) [30]. By incorporating additional bonded interactions, the CG MD model reproduced experimental trends of increasing melting temperatures in tandem with increasing repeats of collagenous Pro-Hyp-Gly motifs. Moreover, co-polymerizing CLP with protein sequences that www.sciencedirect.com
Toward rational algorithmic design of collagen-based biomaterials Zhang et al. 83
Figure 3
(a)
(b)
exo pucker
4S trans amide
4R
endo pucker
trans amide
a
(c)
260
Polyanionic system Polycationic system
Polyanionic system Polycationic system
760 740
c
240
Number of CI ions
b
Number of Na ions
a
b
280
(d)
220 200
720 700 680
180 660 160 0
Gd@C82(OH)22
640
2,000 4,000 6,000 8,00010,000 Simulation time (ps) d
c
0
230
Polyanionic system
0.840
2,000 4,000 6,000 8,000 10,000 Simulation time (ps) Polyanionic system Polycationic system
Polycationic system
Number of Ca ions
g water per g collagen
220 0.835 0.830 0.825 0.820
0.810 0
200 190
0.815
C60(OH)24
210
2,000 4,000 6,000 8,000 10,000 Simulation time (ps)
180 0
2,000 4,000 6,000 8,000 10,000 Simulation time (ps)
Current Opinion in Chemical Engineering
(a) Ab initio structural optimization of hydroxyproline stereoisomers showing different conformational preferences (top). Further MD simulations of a triclinic system of collagen-like peptides (bottom) showed an anisotropic elastic moduli (reproduced with permission from Elsevier [29]]). (b) CG MD models of (POG)12 and (PKG)4(POG)4(DOG)4 collagen-like peptide systems and simulations of their melting characteristics (reproduced with permission from American Chemical Society [30]). (c) Fully atomistic MD modeling of metallofullerenes and fullerenes as additives for stabilizing collagen fibrillation (reproduced with permission from The Royal Society of Chemistry [33]). (d) MD simulations of ions, water molecules and mineralization precursors traversing the collagen structures in the presence of polyanionic and polycationic electrolytes (reproduced with permission from Nature Publishing Group [35]).
had charged residues lowered the melting temperature due to electrostatic repulsion [30]. Electrostatic interactions were also found to be vital for improving the crosslinking quality of chrome-tanned collagen through the addition of anions [31]. Crosslinking collagen with chrome (III) is a technique traditionally used in the leather-making industry, but understanding the crosslinking mechanisms at the molecular level will also be very useful for devising crosslinking strategies in collagen-based biomaterials. Results from MD simulations with a modified Chemistry at HARvard www.sciencedirect.com
Macromolecular Mechanics (CHARMM) force field [32] showed that adding perchlorate ions might enhance the structural stability of tanned collagen as a large number of hydrogen bonds could be formed between the perchlorate ions, the side chains of collagen, and polychromium [31]. Other than ions, nanoparticles can also be added to interact directly with collagen and significantly alter the structural and physicochemical properties of collagen. Yin et al. performed fully atomistic MD simulations to illustrate the substantial effects of Gd@C82(OH)22 Current Opinion in Chemical Engineering 2019, 24:79–87
84 Materials engineering: bio-derived or bio-inspired material
metallofullerene and C60(OH)24 fullerene additives on the structural stability of collagen triple helices as well as the formation and stability of collagen oligomers [33] (Figure 3c). Both fullerene derivatives anchored and limited the relative rotation between the three collagen strands, thereby stabilizing the collagen complex. Furthermore, hydrogen-bonding between the fullerene derivatives and multiple collagen peptides might enhance the nucleation and formation of oligomers or microfibrils [33]. Finally, understanding the mechanisms that regulate collagen fiber biomineralization and aggregation has critical significance for designing biomaterials used in regenerative tissue engineering. For example, variations in the biomineralization process was elucidated through fully atomistic MD simulations, where collagen peptides were mixed with different types of ions, namely Ca2+, HPO42 , and OH [34]. Calcium and phosphate ions formed stable clusters as determined from the radial distribution functions and coordination number profiles. Also, fully atomistic MD simulations confirmed experimental observations that collagen intrafibrillar mineralization could be mediated by polycations and polyanions in a delicate balance between long-range electrostatic interactions and osmotic equilibrium [35] (Figure 3d). This method of mineralization can potentially supplement current techniques of generating mineralized collagen. With fully atomistic MD simulations and the TIGER2 replica exchange algorithm [36], Kulke et al. studied the initiation of fibrillogenesis via aggregation of collagen triple helices and their interactions with heparin and telopepetides [37]. They hypothesize that hydrophobic aggregation of collagen triple helices initiated fibrillogenesis, leading to a parallel alignment of the strands. Heparin acted as a spacer between the triple helices which reduced the inter-strand interactions, thus increasing the radius of the fibril. Asymmetric binding due to the telopeptides might also cause irregular networks to form [37]. Collagen-based biomaterials
A primary utility of collagen as a biomaterial is its good biocompatibility, thereby being very promising substrates for mimicking the properties of natural soft tissues and promoting cellular proliferation in highly hydrated environments. Multiscale computational simulations are also instrumental in probing the physical and chemical properties of gels, scaffolds, and composites derived from collagen, with significant utility in bottom–up designs of novel biomaterials for regenerative engineering. Computational models are vital tools for examining the regulation of cellular behavior by the biomechanical properties of the surrounding matrix, and predicting the deformation and remodeling process of the collagen hydrogel matrix caused by mechanical interactions between cells and the matrix. To this end, models of Current Opinion in Chemical Engineering 2019, 24:79–87
even greater multiscale complexity were developed recently [38–41]. Parameters for an FE model of collagen gel was obtained from macroscale dynamic rheological testing and microscale measurements using optical magnetic twisting cytometry (OMTC) [38] (Figure 4a), thereby capturing the multiscale mechanics of collagen-based gels. Also, a nonlinear poro-elastic finite element (FE) model was developed to faithfully reproduce the poro-viscoelasticity of collagen hydrogels in combination with rheological and permeability data from experiments [39]. Furthermore, Manzano et al. formulated a comprehensive FE framework that incorporated traction forces generated by embedded cells, cellular concentration and distribution, and the effects of cellular migration and proliferation [41]. Hydrogel morphology was found to be exquisitely dependent on the model’s mechanical parameters in a manner that is similar to biological phenomena (Figure 4b). An existing worm-like chain (WLC) model was adapted for deeper analysis of collagen gel’s mechanical behavior, including changes in stiffness and elastic behavior of collagen hydrogel at varying concentrations and enzymatic cross-linking [42]. The rigidity of non-crosslinked collagen gel varied linearly with collagen concentration while crosslinking with transglutaminase caused a more rapid transition to strain-stiffening [42]. Lin et al. also aimed at capturing the mechanical response of collagen scaffolds that were crosslinked at different amounts of non-enzymatic glycation and collagen concentrations [43]. A coupled fiber-matrix numerical model was generated by a Voronoi network embedded in a matrix and validated with previously published experimental data. When ribose concentration was below 100 mM, there was a linear correlation between the scaffold modulus and both the matrix stiffness and the collagen concentration. Increased ribose concentration altered the microstructure of the fiber network, leading to highly nonlinear correlations [43] (Figure 4c). The fracture mechanics of double-notched collagen gel under tension was modelled with a multiscale FE model, where every Gauss point of each element was a microscopic-scale network generated at different degrees of fiber alignments [44]. This multiscale model predicted patterns of crack propagation that was in remarkable agreement with experimental tensile tests. Both the time-dependent and time-independent mechanical responses of collagen gel were also modelled with a hyperelastic and generalized Maxwell viscoelastic model directly parameterized from experimental analysis of the gel’s relaxation time distribution spectrum [45]. The viscoelastic behavior of collagen gel was hypothesized to be heavily influenced by relaxation at the fiber, interfibril, and fibril levels. By understanding the mechanical and fracture behavior of collagen gels, novel bio-inspired collagen-based composite materials can be designed to www.sciencedirect.com
Toward rational algorithmic design of collagen-based biomaterials Zhang et al. 85
Figure 4
(a)
Displacement
Day 0
(b)
Twisting field
Day 3
Day 6
Day 7
Day 9
Magnetizing field
Collagen Matrix
Day 13
Day 14
Day 15
Day 17
Day 20
Day 21
(b)
(c)
Collagen Network
Matrix
Collagen Scaffold (a)
(a)
(b)
(d)
b 30
1.2 Load [N]
True stress,σ [MPa]
a 1.5
0.9 0.6
20
10 0.3 0
0
0.03 0.06 0.09 0.12 0.15 True strain,ε
0
0
2
8 4 6 Deflection [mm]
Current Opinion in Chemical Engineering
(a) Schematic representation of the optical magnetic twisting cytometry experiment to obtain the input parameters for FE modeling (top) and the corresponding contour plots of the strain field distribution in the collagen matrix (bottom) (reproduced with permission from American Chemical Society [38]). (b) Dimensional changes in collagen hydrogel after culturing cells over 21 days and the corresponding FE model of the hydrogel (reproduced with permission from Springer Nature [41]). (c) A coupled fiber-matrix numerical model was generated by a Voronoi network embedded in a matrix (top row), capturing various scaffold behavior under load (bottom row) (reproduced with permission from by MDPI [43] under CC-BY 4.0). (d) Multiscale FE model where every Gauss point of each element was a microscopic-scale network generated at different degrees of fiber alignments (top row), thereby predicting the fracture behavior in the simulated gels (bottom row) (reproduced with permission from ASME International [44]). (e) Experimental setup of the mechanical ball-indentation of collagen thin film and the corresponding FE model (left). Different fiber arrangements were included in the model, leading to variations in the loading curves (right) (reproduced with permission from Elsevier [46]).
have mechanical behavior that mimics natural tissue. Inspired by collagen’s spatial arrangement in the cornea, Sharabi et al. fabricated composites of polyacrylamide– alginate reinforced with collagen fibers. Hyperelastic FE models were constructed to reproduce the mechanical behavior of these bio-composites, paving the way toward www.sciencedirect.com
designing future soft tissue substitutes with alternative complex structures [46] (Figure 4d).
Perspectives and opportunities The recent developments in multiscale computational tools reviewed herein demonstrated the impressive utility Current Opinion in Chemical Engineering 2019, 24:79–87
86 Materials engineering: bio-derived or bio-inspired material
for harnessing these tools for characterizing the viscoelasticity, mechanical deformation, and physicochemical properties of collagen-based biomaterials. These tools are now at the vanguard of rationally designing the sequence-structure-function of collagen-based biomaterials to precisely achieve any desired combinations of physical and chemical properties, paving the way toward realizing the materials-by-design paradigm. However, critical challenges must be overcome before truly algorithmic, bottom–up design can be attained. The first of these challenges pertains to high-throughput data generation and analysis to produce a library that comprehensively maps any input of collagen amino acid sequences to their multiscale structural, mechanical, physicochemical, and biological functions. This will require computational scientists to expansively diversify from the current dominance of studies on the mechanics of collagen and collagenous derivatives. Secondly, advances in computational techniques are required to bridge the gap in time-scales and length-scales to be fully congruent with experimental data and to understand how changes in collagen at the molecular level propagates to alter macroscale properties along a continuum, rather than merely being discrete information at any single scale. Finally, although mechanical deformations in the collagen gel networks as a result of cellular interactions were analyzed in detail herein, characterizing the inverse process proves to be more elusive computationally. New numerical techniques must be developed to probe how the underlying physical and chemical properties of the collagen structure will interact with eukaryotic cells to determine cellular signaling, growth, and proliferation. Moving forward, solving these disparate challenges will undoubtedly require ample and deep cross-disciplinary connections between the realms of biophysical chemistry and mechanics, as well as experimental and computational research.
Author contributions The manuscript was written by all the authors and they have given approval to the final version of the manuscript.
Conflict of interest statement Nothing declared.
Acknowledgement Y.C. and J.Y. acknowledge support from Singapore’s Agency for Science, Technology and Research (A1786a0031).
References and recommended reading Papers of particular interest, published within the period of review, have been highlighted as: of special interest of outstanding interest 1.
Ricard-Blum S: The collagen family. Cold Spring Harb Perspect Biol 2011, 3.
2.
Mouw JK, Ou G, Weaver VM: Extracellular matrix assembly: a multiscale deconstruction. Nat Rev Mol Cell Biol 2014, 15:771.
Current Opinion in Chemical Engineering 2019, 24:79–87
3.
Jung GS, Buehler MJ: Multiscale modeling of muscular-skeletal systems. Annu Rev Biomed Eng 2017, 19:435-457.
4.
Khan R, Khan MH: Use of collagen as a biomaterial: an update. J Indian Soc Periodontol 2013, 17:539-542.
5.
Patino MG, Neiders ME, Andreana S, Noble B, Cohen RE: Collagen as an implantable material in medicine and dentistry. J Oral Implantol 2002, 28:220-225.
6.
Sherman VR, Yang W, Meyers MA: The materials science of collagen. J Mech Behav Biomed Mater 2015, 52:22-50.
7.
Buehler MJ: Atomistic and continuum modeling of mechanical properties of collagen: elasticity, fracture, and self-assembly. J Mater Res 2006, 21:1947-1961.
8.
Buehler MJ: Nanomechanics of collagen fibrils under varying cross-link densities: atomistic and continuum studies. J Mech Behav Biomed Mater 2008, 1:59-67.
9.
Barkaoui A, Bettamer A, Hambli R: Failure of mineralized collagen microfibrils using finite element simulation coupled to mechanical quasi-brittle damage. Procedia Eng 2011, 10:3185-3190.
10. Hambli R, Barkaoui A: Physically based 3D finite element model of a single mineralized collagen microfibril. J Theor Biol 2012, 301:28-41. 11. Yeo J, Jung GSGS, Martı´n-Martı´nez FJFJ, Ling S, Gu GXGX, Qin Z, Buehler MJMJ: Materials-by-design: computation, synthesis, and characterization from atoms to structures. Phys Scr 2018, 93:053003. 12. Vesentini S, Redaelli A, Gautieri A: Nanomechanics of collagen microfibrils. Muscles Ligaments Tendons J 2013, 3:23-34. 13. Chang S-W, Buehler MJ: Molecular biomechanics of collagen molecules. Mater Today 2014, 17:70-76. 14. Domene C, Jorgensen C, Abbasi SW: A perspective on structural and computational work on collagen. Phys Chem Chem Phys 2016, 18:24802-24811. 15. Ghanaeian A, Soheilifard R: Mechanical elasticity of proline-rich and hydroxyproline-rich collagen-like triple-helices studied using steered molecular dynamics. J Mech Behav Biomed Mater 2018, 86:105-112. 16. Lodish H: Molecular Cell Biology. Macmillan; 2008. 17. Tang M, Li T, Gandhi NS, Burrage K, Gu YT: Heterogeneous nanomechanical properties of type I collagen in longitudinal direction. Biomech Model Mechanobiol 2017, 16:1023-1033. Detailed molecular dynamics simulations that probed the origin of heterogeneous nanomechanics in various regions of type I collagen microfibrils. 18. Zhou Z, Minary-Jolandan M, Qian D: A simulation study on the significant nanomechanical heterogeneous properties of collagen. Biomech Model Mechanobiol 2015, 14:445-457. 19. Orgel JPRO, Irving TC, Miller A, Wess TJ: Microfibrillar structure of type I collagen in situ. Proc Natl Acad Sci U S A 2006, 103 9001 LP-9005. 20. Tang M, Li T, Pickering E, Gandhi NS, Burrage K, Gu YT: Steered molecular dynamics characterization of the elastic modulus and deformation mechanisms of single natural tropocollagen molecules. J Mech Behav Biomed Mater 2018, 86:359-367. 21. Depalle B, Qin Z, Shefelbine SJ, Buehler MJ: Influence of crosslink structure, density and mechanical properties in the mesoscale deformation mechanisms of collagen fibrils. J Mech Behav Biomed Mater 2015, 52:1-13. 22. Zitnay JL, Li Y, Qin Z, San BH, Depalle B, Reese SP, Buehler MJ, Yu SM, Weiss JA: Molecular level detection and localization of mechanical damage in collagen enabled by collagen hybridizing peptides. Nat Commun 2017, 8. 23. Ghodsi H, Darvish K: Characterization of the viscoelastic behavior of a simplified collagen micro-fibril based on molecular dynamics simulations. J Mech Behav Biomed Mater 2016, 63:26-34. www.sciencedirect.com
Toward rational algorithmic design of collagen-based biomaterials Zhang et al. 87
24. Lee B, Zhou X, Riching K, Eliceiri KW, Keely PJ, Guelcher SA, Weaver AM, Jiang Y: A three-dimensional computational model of collagen network mechanics. PLoS One 2014, 9:1-12. 25. Licup AJ, Mu¨nster S, Sharma A, Sheinman M, Jawerth LM, Fabry B, Weitz DA, MacKintosh FC: Stress controls the mechanics of collagen networks. Proc Natl Acad Sci U S A 2015, 112:9573-9578. Comprehensive modeling and characterization of the nonlinear mechanics of fiber networks. 26. Jones CAR, Cibula M, Feng J, Krnacik EA, McIntyre DH, Levine H, Sun B: Micromechanics of cellularized biopolymer networks. Proc Natl Acad Sci U S A 2015, 112:E5117-E5122. Very elegant work that combined experimental characterization and 2D computational models to predict the micromechanics of cells interacting with collagen networks.
35. Niu LN, Jee SE, Jiao K, Tonggu L, Li M, Wang L, Yang YD, Bian JH, Breschi L, Jang SS et al.: Collagen intrafibrillar mineralization as a result of the balance between osmotic equilibrium and electroneutrality. Nat Mater 2017, 16:370-378. 36. Li X, Latour RA, Stuart SJ: TIGER2: an improved algorithm for temperature intervals with global exchange of replicas. J Chem Phys 2009, 130:174106. 37. Kulke M, Geist N, Friedrichs W, Langel W: Molecular dynamics simulations on networks of heparin and collagen. Proteins Struct Funct Bioinformatics 2017, 85:1119-1130. Used cutting-edge enhanced molecular dynamics sampling techniques to determine structural changes in collagen. 38. Li H, Xu B, Zhou EH, Sunyer R, Zhang Y: Multiscale measurements of the mechanical properties of collagen matrix. ACS Biomater Sci Eng 2017, 3:2815-2824.
27. Loerakker S, Ristori T, Baaijens FPT: A computational analysis of cell-mediated compaction and collagen remodeling in tissueengineered heart valves. J Mech Behav Biomed Mater 2016, 58:173-187.
39. Castro APG, Laity P, Shariatzadeh M, Wittkowske C, Holland C, Lacroix D: Combined numerical and experimental biomechanical characterization of soft collagen hydrogel substrate. J Mater Sci Mater Med 2016, 27:1-9.
28. Pierce DM, Ricken T, Holzapfel GA: A hyperelastic biphasic fibre-reinforced model of articular cartilage considering distributed collagen fibre orientations: continuum basis, computational aspects and applications. Comput Methods Biomech Biomed Eng 2013, 16:1344-1361.
40. Castro APG, Yao J, Battisti T, Lacroix D: Poroelastic modeling of highly hydrated collagen hydrogels: experimental results vs. numerical simulation with custom and commercial finite element solvers. Front Bioeng Biotechnol 2018, 6:1-8.
29. Schweizer S, Bick A, Subramanian L, Krokidis X: Influences on the stability of collagen triple-helix. Fluid Phase Equilib 2014, 362:113-117.
41. Manzano S, Moreno-Loshuertos R, Doblare´ M, Ochoa I, Hamdy Doweidar M: Structural biology response of a collagen hydrogel synthetic extracellular matrix with embedded human fibroblast: computational and experimental analysis. Med Biol Eng Comput 2015, 53:721-735.
30. Condon JE, Jayaraman A: Development of a coarse-grained model of collagen-like peptide (CLP) for studies of CLP triple Helix Melting. J Phys Chem B 2018, 122:1929-1939. 31. Ding YQ, Chen CL, Gu QR, Fu LH: Molecular simulation study of the effects of inorganic anions on the properties of chromecrosslinked collagen. Model Simul Mater Sci Eng 2014, 22. 32. Brooks BR, Brooks CL, Mackerell AD, Nilsson L, Petrella RJ, Roux B, Won Y, Archontis G, Bartels C, Boresch S et al.: CHARMM: the biomolecular simulation program. J Comput Chem 2009, 30:1545-1614. 33. Yin X, Zhao L, Kang SG, Pan J, Song Y, Zhang M, Xing G, Wang F, Li J, Zhou R et al.: Impacts of fullerene derivatives on regulating the structure and assembly of collagen molecules. Nanoscale 2013, 5:7341-7348. 34. Ma J: A molecular dynamics study on the nucleation of calcium phosphate regulated by collagen. J Mater Sci 2014, 49:3099-3106.
www.sciencedirect.com
42. Valero C, Amaveda H, Mora M, Garcı´a-Aznar JM: Combined experimental and computational characterization of crosslinked collagen-based hydrogels. PLoS One 2018, 13:1-16. 43. Lin S, Hapach LA, Reinhart-King C, Gu L: Towards tuning the mechanical properties of three-dimensional collagen scaffolds using a coupled fiber-matrix model. Materials (Basel) 2015, 8:5376-5384. 44. Vanderheiden SM, Hadi MF, Barocas VH: Crack propagation versus fiber alignment in collagen gels: experiments and multiscale simulation. J Biomech Eng 2015, 137:121002. 45. Xu B, Li H, Zhang Y: An experimental and modeling study of the viscoelastic behavior of collagen gel. J Biomech Eng 2013, 135:054501. 46. Sharabi M, Varssano D, Eliasy R, Benayahu Y, Benayahu D, HajAli R: Mechanical flexure behavior of bio-inspired collagenreinforced thin composites. Compos Struct 2016, 153:392-400.
Current Opinion in Chemical Engineering 2019, 24:79–87
ScienceDirect Toward rational algorithmic design of collagen-based biomaterials through multiscale computational modeling Nan Zhang1,2, Yuan Cheng3, Xiaoling Hu1 and Jingjie Yeo3 Inspired by the complex diversity of collagenous materials in mammalian tissue, collagen-based biomaterials are increasingly utilized for developing drug delivery vehicles and regenerative tissue engineering. Collagen’s broad utility poses important engineering challenges for the rational and predictive design of the resultant biomaterial’s physical and chemical properties. We review the most recent developments in multiscale computational modeling of collagen-based biomaterials to determine their structural, mechanical, and physicochemical properties. Through the materials-by-design paradigm, these developments may eventually lead to rational algorithmic recipes for bottom–up multiscale design of these biomaterials, thereby minimizing the experimental costs of iterative material synthesis and testing. We also highlight the future perspectives and opportunities for expanding multiscale modeling capabilities to incorporate physicochemical and biological functions of collagen-based biomaterials. Addresses 1 School of Natural and Applied Science, Northwestern Polytechnical University, Xi’an, 710072, PR China 2 Department of Mechanical Engineering, National University of Singapore, 9 Engineering Drive 1, 117575, Singapore 3 Institute of High Performance Computing, A*STAR, 1 Fusionopolis Way, Singapore 138632, Singapore Corresponding authors: Hu, Xiaoling ([email protected]), Yeo, Jingjie ([email protected])
Current Opinion in Chemical Engineering 2019, 24:79–87 This review comes from a themed issue on Materials engineering: bio-derived or bio-inspired material Edited by Jeannine M Coburn and David Kaplan
https://doi.org/10.1016/j.coche.2019.02.011
chemical compositions that heavily influence the functions of various tissues and organs [2]. Although the collagen family is incredibly diverse with 28 distinct members, every member minimally comprises one triple helical domain. The multiscale hierarchical structures, assemblies, and functions of all members of the collagen family were reviewed extensively recently [1,2] but generally, the collagen family has a common structural motif of a right-handed triple-helical secondary structure comprising three polypeptide chains in left-handed polyproline II helical configurations. Each chain contains at least one Gly-X-Y sequence with X and Y frequently being proline and 4-hydroxyproline respectively, and this unique motif serves to stabilize collagen’s triple helical structures. Inspired by nature, scientists and engineers increasingly use collagen-based biomaterials in biomedical applications, particularly for drug delivery vehicles and regenerative tissue engineering. These applications seek to harness the exceptional properties of collagen: excellent mechanical strength and flexibility [3], biocompatibility, biodegradability [4], and ease of synthesis into a broad variety of multiscale hierarchical morphologies [5]. Being a major component of the extracellular matrix (ECM), collagen is also important for cellular signaling and regulation. Perhaps ironically, this broad applicability of collagen as a biomaterial poses a challenging engineering problem. Can the sequence-structure-function of collagen-based biomaterials be rationally designed computationally so as to precisely achieve any desired combinations of physical and chemical properties (Figure 1a), thereby minimizing the experimental costs of iterative material synthesis and testing? Can the materials-by-design paradigm be harnessed for this purpose?
2211-3398/ã 2018 Elsevier Ltd. All rights reserved.
Computational modeling of collagen at multiple structural hierarchies Introduction Collagen is a remarkably versatile and abundant biomaterial. In mammals, collagen outnumbers all other protein families, accounting for approximately 30% of the total protein by mass [1]. Being the primary protein component of connective and soft tissues, collagen is a multifunctional protein with unique hierarchical structures and www.sciencedirect.com
The structural, physical, and chemical properties of collagen can be tailored to confer a broad range of mechanical and physicochemical stability, elasticity, and strength to the biomaterial [6]. These modifications can encompass a wide spectrum of structural hierarchies, from the sequence of the amino acids that constitute the collagen to the macroscale formation of random or ordered networks (Figure 1a). Multiscale computational modeling and simulations are indispensable for characterizing and Current Opinion in Chemical Engineering 2019, 24:79–87
80 Materials engineering: bio-derived or bio-inspired material
Figure 1
Collagen Sequence
(a)
(b)
Full atomistic model of the 3rd D-period
Triple Helix Collagen molecule
Multiscale Structures & Properties
d2ol
Fibril
d2gp
d3oI
d3gp
d4ol
C-terminal
d4gp
D-period
Material
Collagen microfibril
(c)
Overlap region (0.46D)
Gap region (0.54D)
D3gp-seg1
D3ol-seg2
30
0%
0%
25
εI=20%
εI=20%
30% 30% εc=35% εf=48%
Force (nN)
10%
10%
20 15 10
εc=42%
5
εf=59%
0 0.0
(e)
(d)
0.1
60%
49%
0.2
0.3 Strain
0.4
0.5
0.6
a
a b
c
b c
Current Opinion in Chemical Engineering
(a) Algorithmic design of the multiscale hierarchical structures and properties of collagen from atoms to materials. (b) Fully atomistic models of Type I collagen microfibril to explore the mechanical behavior and unfolding mechanism of the overlapping and gap regions (reproduced with permission from Springer Nature [17]). (c) Type I collagen microfibril had significant mechanical heterogeneity in various overlap and gap regions of collagen microfibrils (left, right) as determined from SMD simulations (center) (reproduced with permission from Springer Nature [18]). (d) Representative molecular configurations of tropocollagen (left) and SMD simulations (right) showed that the Young’s moduli of the second overlapping and gap regions had differing strain rate dependence (reproduced with permission from Elsevier [20]). (e) SMD simulations of the mechanical response of collagen microfibril deformed under different strains (top), demonstrating the shear-dominant mode of failure mechanism under tensile loads (bottom) (reproduced with permission from Nature Publishing Group [22] under CC-BY 4.0).
designing various properties of collagen within these diverse structural hierarchies, using either bottom–up or top–down approaches. These features were elucidated with an expansive gamut of numerical techniques, including fully atomistic or mesoscale coarse-grained molecular dynamics (MD) simulations [7,8] and finite element (FE) methods [9,10]. Finer details on the application of these computational methods for realizing the materialsCurrent Opinion in Chemical Engineering 2019, 24:79–87
by-design paradigm was extensively reviewed previously [11]. Several earlier reviews also detailed the nanomechanical [12,13] and molecular physicochemical properties [14] of collagen. Here, we provide a bottom–up perspective of the most recent developments in atomistic to continuum scale computational analysis of the viscoelastic deformation and physicochemical properties of collagen and collagen-based biomaterials. www.sciencedirect.com
Toward rational algorithmic design of collagen-based biomaterials Zhang et al. 81
Mechanical properties of collagen Collagen peptides, fibrils, and fibers
At the molecular level, collagen comprises individual peptide strands that self-assemble into triple-helical tropocollagen molecules. The biomechanical features in tropocollagen, especially elasticity, are determined by the uniformity of the Gly-X-Y repeating motifs. Ghanaeian et al. performed steered MD (SMD) simulations to investigate the effects of the most abundant residues at the X and Y sites, proline and hydroxyproline, as well as on collagen stiffness and elasticity [15]. The stiffnesses and Young’s moduli of collagen ranged from 823.00 to 3344.00 pN/nm and 4.22 to 22.05 GPa, respectively. Increased proline content was related to higher mechanical stiffness, while elevated hydroxyproline content had the opposite effect of improving the elasticity [15]. With the distinct exception of Type IV collagen, other categories of collagen molecules generally assemble into similar structures of long and thin fibrils. In particular, Type I collagen fibrils have a unique repeating tertiary structure where each repeat is known as the D-period, resulting in visible striations from electron micrographs [16]. Early computational models frequently assumed that collagen fibrils were homogenous rod-like structures, but recent research challenged this assumption [17]. Through SMD simulations, Zhou et al. found significant mechanical heterogeneity in various overlap and gap regions of collagen microfibrils [17,18] (Figure 1b,c). These microfibrils were modelled after the structure of full length Type I collagen molecule that was experimentally verified in situ [19]. To probe the molecular origins of this heterogeneity, further SMD simulations were performed to explore the mechanical behavior and unfolding mechanism of the second overlapping region and gap region of Type I collagen microfibrils at different strain rates [20] (Figure 1d). The Young’s modulus of a single collagen molecule diminished as the strain rate decreased, but converged to approximately 3.2 GPa and 3.4 GPa for the overlapping and gap regions respectively when the strain rates were lower than 1.3 108% s 1 [20]. Every overlap and gap regions in Type I collagen fibrils was also studied in detail with SMD simulations using a strain rate of 6.5 107% s 1 and heterogeneous mechanical properties were found for each region [17]. The fibrillar structure of collagen is stabilized further through intermolecular and interfibrillar crosslinks from various posttranslational modifications. Depalle et al. established a three-dimensional Coarse-Grained (CG) model to explore the effects of enzymatic crosslinking on collagen fibril mechanics at the mesoscale scale [21]. On the one hand, the stiffness in the regime of large deformation was heavily influenced by both the crosslink type and density as the number of interconnected molecules increased. On the other hand, the failure strain and strength of the fibril was dictated by the strength of the crosslinks [21]. www.sciencedirect.com
Therefore, the toughness and strength of fibrillar collagen-based biomaterials can possibly be tuned by varying the crosslinking strength and density. The mechanical properties of the collagen fibers that constitute any collagen-based biomaterials can influence their failure behavior, but mechanical damage in these constituent collagen fibrils and fibers at the molecular level can also cause further changes in material behavior. Although no significant macroscopic damage might be detectable, molecular-scale damage mechanisms could be resolved using carboxyfluorescein (CF) labeled collagen hybrid peptide (CHP) that bound to unfolded collagen triple helices [22]. Utilizing SMD simulations, Zitnay et al. illustrated that a shear-dominated failure mechanism led to the unfolding of the triple helices during mechanical injury to connective tissue, thereby allowing the CHP to bind and detect this molecular damage (Figure 1e). Finally, the viscoelastic creep behavior of collagen was also investigated using the SMD method. The results indicated that the steady-state Young’s modulus of the collagen microfibril assembly ranged from 2.24 to 3.27 GPa, which was consistent with reported experimental measurements [23]. Fibrillar collagen networks
Although the mechanical properties of collagen ranging from the molecular scale to the scale of single fibers were examined extensively, the structural and mechanical response of fibrillar collagen networks to local strains or deformations is still poorly understood. To address this gap, Lee et al. developed a three-dimensional, beadspring model to mimic elastic collagen fiber networks (Figure 2a). The fiber network’s mechanical behavior under various biophysical conditions was investigated, including collagen density, crosslinker strength and density, and fiber orientation. Interestingly, the mechanical properties of these fiber networks were largely influenced by the network geometry compared to the other parameters. The evolution of the fiber network structure and mechanics with local deformation was also captured accurately, such as strain stiffening [24]. Additionally, relatively simple 2D and 3D lattice-based network and 2D Mikado network models were developed that could account for the stiffness of Type I collagen networks in the nonlinear elastic regime [25] (Figure 2b). Uniquely, the nonlinear Young’s modulus in collagen networks appeared to be independent from concentration. This property was attributed to three factors of stress scaling linearly with stiffness, the response of the network being dominated by bending in the linear elastic regime, and the constituent fibers responding in an athermal, simple elastic manner. To further understand the microscale mechanics of collagen fiber networks, Jones et al. constructed a 2D lattice-based computational model to elucidate the general properties of extracellular matrices Current Opinion in Chemical Engineering 2019, 24:79–87
82 Materials engineering: bio-derived or bio-inspired material
Figure 2
(a) Shear modulus [Pal]
(b) 4mg/ml 300
3mg/ml
200
2mg/ml 1mg/ml
100 0
800
ssl
Strain=0
(a)
Δy 0
10
den
sity
200
15
[ N]
Cr
th
]
Pa
[K
g en
tr
rs
ke
os
n sli
2D Mikado
2D Lattice
(d)
Y
X 0.2
0.3
0 2
4 6 8 time (s)
(d)
Δd
0.1
er
400
Force in + x direction
(b)
(c)
ink
Strain=0.1
displacement (μm)
(c)
600
5
Cro
0.2
Δd
0 π
Δy
-0.1
-0.4 0 -0.2
0 Δx (µm)
0.2
-0.2
0.4 Δx (µm)
-0.3 Current Opinion in Chemical Engineering
(a) Shear deformation of a bead-and-spring collagen fiber network model derived from SEM images of collagen fibers from a normal mouse mammary gland (left) and the variation of the shear moduli with crosslinking density and strength (right) (reproduced with permission from PLOS [24] under CC-BY 4.0). (b) Stiffening response (top left: differential shear modulus K versus shear stress s for reconstituted collagen I networks) of 2D Mikado (bottom left) and lattice network models (bottom right) derived from 3D confocal image of a reconstituted Type I collagen network (top right) (reproduced with permission from the National Academy of Science [25] under CC-BY 4.0). (c) Micromechanical response in collagen gel using optical traps (reproduced with permission from the National Academy of Science [26]). (d) FE modeling (left) of a heart valve deforming (right) while accounting for tissue remodeling (reproduced with permission from Elsevier [27]).
[26]. This model successfully captured the remodeling of the micromechanical properties surrounding a contracting cell (Figure 2c). Beyond microscale network models, network properties at the tissue level were probed with FE methods. For instance, the remodeling of collagen networks in heart valve tissues were much more stable and favorable at aortic pressure conditions in comparison with tissue remodeling at pulmonary pressure conditions [27] (Figure 2d). Pierce et al. proposed a constitutive model solved with 3D FE simulations and accurately reproduced the mechanical properties of the multi-directional collagen-reinforced composite system based on articular cartilage [28]. Physicochemical properties of collagen
The physicochemical properties of collagen are also vital considerations for the design of collagen-based biomaterials. Important properties include collagen’s biocompatibility, biodegradability, and thermal stability. For instance, maintaining the mechanical and thermal stability of triple-helical collagen structures requires an intricate balance of numerous physicochemical factors, such Current Opinion in Chemical Engineering 2019, 24:79–87
as stereoelectronic and steric effects between the collagen chains and amino acids. Using ab initio quantum chemical calculations, Schweizer et al. proposed an atomistic model of collagen-like material for systematic analysis of favorable hydroxyproline conformations and their impact on triple-helical stability [29] (Figure 3a). Stereoelectronic gauche-effect and intramolecular hydrogen bonds had a profound effect on the stability of the triple helix. Furthermore, 4S-hydroxyproline in collagen might have a destabilizing effect as intramolecular hydrogen bonds interfered with interactions between the collagen strands [29]. To assess thermal stabilities at larger spatiotemporal scales, a phenomenological CG MD model was devised (Figure 3b) to simulate the melting trends of single-chain collagen-like peptides (CLP) and CLP co-polymerized with other proteins such as elastin-like peptides (ELP) [30]. By incorporating additional bonded interactions, the CG MD model reproduced experimental trends of increasing melting temperatures in tandem with increasing repeats of collagenous Pro-Hyp-Gly motifs. Moreover, co-polymerizing CLP with protein sequences that www.sciencedirect.com
Toward rational algorithmic design of collagen-based biomaterials Zhang et al. 83
Figure 3
(a)
(b)
exo pucker
4S trans amide
4R
endo pucker
trans amide
a
(c)
260
Polyanionic system Polycationic system
Polyanionic system Polycationic system
760 740
c
240
Number of CI ions
b
Number of Na ions
a
b
280
(d)
220 200
720 700 680
180 660 160 0
Gd@C82(OH)22
640
2,000 4,000 6,000 8,00010,000 Simulation time (ps) d
c
0
230
Polyanionic system
0.840
2,000 4,000 6,000 8,000 10,000 Simulation time (ps) Polyanionic system Polycationic system
Polycationic system
Number of Ca ions
g water per g collagen
220 0.835 0.830 0.825 0.820
0.810 0
200 190
0.815
C60(OH)24
210
2,000 4,000 6,000 8,000 10,000 Simulation time (ps)
180 0
2,000 4,000 6,000 8,000 10,000 Simulation time (ps)
Current Opinion in Chemical Engineering
(a) Ab initio structural optimization of hydroxyproline stereoisomers showing different conformational preferences (top). Further MD simulations of a triclinic system of collagen-like peptides (bottom) showed an anisotropic elastic moduli (reproduced with permission from Elsevier [29]]). (b) CG MD models of (POG)12 and (PKG)4(POG)4(DOG)4 collagen-like peptide systems and simulations of their melting characteristics (reproduced with permission from American Chemical Society [30]). (c) Fully atomistic MD modeling of metallofullerenes and fullerenes as additives for stabilizing collagen fibrillation (reproduced with permission from The Royal Society of Chemistry [33]). (d) MD simulations of ions, water molecules and mineralization precursors traversing the collagen structures in the presence of polyanionic and polycationic electrolytes (reproduced with permission from Nature Publishing Group [35]).
had charged residues lowered the melting temperature due to electrostatic repulsion [30]. Electrostatic interactions were also found to be vital for improving the crosslinking quality of chrome-tanned collagen through the addition of anions [31]. Crosslinking collagen with chrome (III) is a technique traditionally used in the leather-making industry, but understanding the crosslinking mechanisms at the molecular level will also be very useful for devising crosslinking strategies in collagen-based biomaterials. Results from MD simulations with a modified Chemistry at HARvard www.sciencedirect.com
Macromolecular Mechanics (CHARMM) force field [32] showed that adding perchlorate ions might enhance the structural stability of tanned collagen as a large number of hydrogen bonds could be formed between the perchlorate ions, the side chains of collagen, and polychromium [31]. Other than ions, nanoparticles can also be added to interact directly with collagen and significantly alter the structural and physicochemical properties of collagen. Yin et al. performed fully atomistic MD simulations to illustrate the substantial effects of Gd@C82(OH)22 Current Opinion in Chemical Engineering 2019, 24:79–87
84 Materials engineering: bio-derived or bio-inspired material
metallofullerene and C60(OH)24 fullerene additives on the structural stability of collagen triple helices as well as the formation and stability of collagen oligomers [33] (Figure 3c). Both fullerene derivatives anchored and limited the relative rotation between the three collagen strands, thereby stabilizing the collagen complex. Furthermore, hydrogen-bonding between the fullerene derivatives and multiple collagen peptides might enhance the nucleation and formation of oligomers or microfibrils [33]. Finally, understanding the mechanisms that regulate collagen fiber biomineralization and aggregation has critical significance for designing biomaterials used in regenerative tissue engineering. For example, variations in the biomineralization process was elucidated through fully atomistic MD simulations, where collagen peptides were mixed with different types of ions, namely Ca2+, HPO42 , and OH [34]. Calcium and phosphate ions formed stable clusters as determined from the radial distribution functions and coordination number profiles. Also, fully atomistic MD simulations confirmed experimental observations that collagen intrafibrillar mineralization could be mediated by polycations and polyanions in a delicate balance between long-range electrostatic interactions and osmotic equilibrium [35] (Figure 3d). This method of mineralization can potentially supplement current techniques of generating mineralized collagen. With fully atomistic MD simulations and the TIGER2 replica exchange algorithm [36], Kulke et al. studied the initiation of fibrillogenesis via aggregation of collagen triple helices and their interactions with heparin and telopepetides [37]. They hypothesize that hydrophobic aggregation of collagen triple helices initiated fibrillogenesis, leading to a parallel alignment of the strands. Heparin acted as a spacer between the triple helices which reduced the inter-strand interactions, thus increasing the radius of the fibril. Asymmetric binding due to the telopeptides might also cause irregular networks to form [37]. Collagen-based biomaterials
A primary utility of collagen as a biomaterial is its good biocompatibility, thereby being very promising substrates for mimicking the properties of natural soft tissues and promoting cellular proliferation in highly hydrated environments. Multiscale computational simulations are also instrumental in probing the physical and chemical properties of gels, scaffolds, and composites derived from collagen, with significant utility in bottom–up designs of novel biomaterials for regenerative engineering. Computational models are vital tools for examining the regulation of cellular behavior by the biomechanical properties of the surrounding matrix, and predicting the deformation and remodeling process of the collagen hydrogel matrix caused by mechanical interactions between cells and the matrix. To this end, models of Current Opinion in Chemical Engineering 2019, 24:79–87
even greater multiscale complexity were developed recently [38–41]. Parameters for an FE model of collagen gel was obtained from macroscale dynamic rheological testing and microscale measurements using optical magnetic twisting cytometry (OMTC) [38] (Figure 4a), thereby capturing the multiscale mechanics of collagen-based gels. Also, a nonlinear poro-elastic finite element (FE) model was developed to faithfully reproduce the poro-viscoelasticity of collagen hydrogels in combination with rheological and permeability data from experiments [39]. Furthermore, Manzano et al. formulated a comprehensive FE framework that incorporated traction forces generated by embedded cells, cellular concentration and distribution, and the effects of cellular migration and proliferation [41]. Hydrogel morphology was found to be exquisitely dependent on the model’s mechanical parameters in a manner that is similar to biological phenomena (Figure 4b). An existing worm-like chain (WLC) model was adapted for deeper analysis of collagen gel’s mechanical behavior, including changes in stiffness and elastic behavior of collagen hydrogel at varying concentrations and enzymatic cross-linking [42]. The rigidity of non-crosslinked collagen gel varied linearly with collagen concentration while crosslinking with transglutaminase caused a more rapid transition to strain-stiffening [42]. Lin et al. also aimed at capturing the mechanical response of collagen scaffolds that were crosslinked at different amounts of non-enzymatic glycation and collagen concentrations [43]. A coupled fiber-matrix numerical model was generated by a Voronoi network embedded in a matrix and validated with previously published experimental data. When ribose concentration was below 100 mM, there was a linear correlation between the scaffold modulus and both the matrix stiffness and the collagen concentration. Increased ribose concentration altered the microstructure of the fiber network, leading to highly nonlinear correlations [43] (Figure 4c). The fracture mechanics of double-notched collagen gel under tension was modelled with a multiscale FE model, where every Gauss point of each element was a microscopic-scale network generated at different degrees of fiber alignments [44]. This multiscale model predicted patterns of crack propagation that was in remarkable agreement with experimental tensile tests. Both the time-dependent and time-independent mechanical responses of collagen gel were also modelled with a hyperelastic and generalized Maxwell viscoelastic model directly parameterized from experimental analysis of the gel’s relaxation time distribution spectrum [45]. The viscoelastic behavior of collagen gel was hypothesized to be heavily influenced by relaxation at the fiber, interfibril, and fibril levels. By understanding the mechanical and fracture behavior of collagen gels, novel bio-inspired collagen-based composite materials can be designed to www.sciencedirect.com
Toward rational algorithmic design of collagen-based biomaterials Zhang et al. 85
Figure 4
(a)
Displacement
Day 0
(b)
Twisting field
Day 3
Day 6
Day 7
Day 9
Magnetizing field
Collagen Matrix
Day 13
Day 14
Day 15
Day 17
Day 20
Day 21
(b)
(c)
Collagen Network
Matrix
Collagen Scaffold (a)
(a)
(b)
(d)
b 30
1.2 Load [N]
True stress,σ [MPa]
a 1.5
0.9 0.6
20
10 0.3 0
0
0.03 0.06 0.09 0.12 0.15 True strain,ε
0
0
2
8 4 6 Deflection [mm]
Current Opinion in Chemical Engineering
(a) Schematic representation of the optical magnetic twisting cytometry experiment to obtain the input parameters for FE modeling (top) and the corresponding contour plots of the strain field distribution in the collagen matrix (bottom) (reproduced with permission from American Chemical Society [38]). (b) Dimensional changes in collagen hydrogel after culturing cells over 21 days and the corresponding FE model of the hydrogel (reproduced with permission from Springer Nature [41]). (c) A coupled fiber-matrix numerical model was generated by a Voronoi network embedded in a matrix (top row), capturing various scaffold behavior under load (bottom row) (reproduced with permission from by MDPI [43] under CC-BY 4.0). (d) Multiscale FE model where every Gauss point of each element was a microscopic-scale network generated at different degrees of fiber alignments (top row), thereby predicting the fracture behavior in the simulated gels (bottom row) (reproduced with permission from ASME International [44]). (e) Experimental setup of the mechanical ball-indentation of collagen thin film and the corresponding FE model (left). Different fiber arrangements were included in the model, leading to variations in the loading curves (right) (reproduced with permission from Elsevier [46]).
have mechanical behavior that mimics natural tissue. Inspired by collagen’s spatial arrangement in the cornea, Sharabi et al. fabricated composites of polyacrylamide– alginate reinforced with collagen fibers. Hyperelastic FE models were constructed to reproduce the mechanical behavior of these bio-composites, paving the way toward www.sciencedirect.com
designing future soft tissue substitutes with alternative complex structures [46] (Figure 4d).
Perspectives and opportunities The recent developments in multiscale computational tools reviewed herein demonstrated the impressive utility Current Opinion in Chemical Engineering 2019, 24:79–87
86 Materials engineering: bio-derived or bio-inspired material
for harnessing these tools for characterizing the viscoelasticity, mechanical deformation, and physicochemical properties of collagen-based biomaterials. These tools are now at the vanguard of rationally designing the sequence-structure-function of collagen-based biomaterials to precisely achieve any desired combinations of physical and chemical properties, paving the way toward realizing the materials-by-design paradigm. However, critical challenges must be overcome before truly algorithmic, bottom–up design can be attained. The first of these challenges pertains to high-throughput data generation and analysis to produce a library that comprehensively maps any input of collagen amino acid sequences to their multiscale structural, mechanical, physicochemical, and biological functions. This will require computational scientists to expansively diversify from the current dominance of studies on the mechanics of collagen and collagenous derivatives. Secondly, advances in computational techniques are required to bridge the gap in time-scales and length-scales to be fully congruent with experimental data and to understand how changes in collagen at the molecular level propagates to alter macroscale properties along a continuum, rather than merely being discrete information at any single scale. Finally, although mechanical deformations in the collagen gel networks as a result of cellular interactions were analyzed in detail herein, characterizing the inverse process proves to be more elusive computationally. New numerical techniques must be developed to probe how the underlying physical and chemical properties of the collagen structure will interact with eukaryotic cells to determine cellular signaling, growth, and proliferation. Moving forward, solving these disparate challenges will undoubtedly require ample and deep cross-disciplinary connections between the realms of biophysical chemistry and mechanics, as well as experimental and computational research.
Author contributions The manuscript was written by all the authors and they have given approval to the final version of the manuscript.
Conflict of interest statement Nothing declared.
Acknowledgement Y.C. and J.Y. acknowledge support from Singapore’s Agency for Science, Technology and Research (A1786a0031).
References and recommended reading Papers of particular interest, published within the period of review, have been highlighted as: of special interest of outstanding interest 1.
Ricard-Blum S: The collagen family. Cold Spring Harb Perspect Biol 2011, 3.
2.
Mouw JK, Ou G, Weaver VM: Extracellular matrix assembly: a multiscale deconstruction. Nat Rev Mol Cell Biol 2014, 15:771.
Current Opinion in Chemical Engineering 2019, 24:79–87
3.
Jung GS, Buehler MJ: Multiscale modeling of muscular-skeletal systems. Annu Rev Biomed Eng 2017, 19:435-457.
4.
Khan R, Khan MH: Use of collagen as a biomaterial: an update. J Indian Soc Periodontol 2013, 17:539-542.
5.
Patino MG, Neiders ME, Andreana S, Noble B, Cohen RE: Collagen as an implantable material in medicine and dentistry. J Oral Implantol 2002, 28:220-225.
6.
Sherman VR, Yang W, Meyers MA: The materials science of collagen. J Mech Behav Biomed Mater 2015, 52:22-50.
7.
Buehler MJ: Atomistic and continuum modeling of mechanical properties of collagen: elasticity, fracture, and self-assembly. J Mater Res 2006, 21:1947-1961.
8.
Buehler MJ: Nanomechanics of collagen fibrils under varying cross-link densities: atomistic and continuum studies. J Mech Behav Biomed Mater 2008, 1:59-67.
9.
Barkaoui A, Bettamer A, Hambli R: Failure of mineralized collagen microfibrils using finite element simulation coupled to mechanical quasi-brittle damage. Procedia Eng 2011, 10:3185-3190.
10. Hambli R, Barkaoui A: Physically based 3D finite element model of a single mineralized collagen microfibril. J Theor Biol 2012, 301:28-41. 11. Yeo J, Jung GSGS, Martı´n-Martı´nez FJFJ, Ling S, Gu GXGX, Qin Z, Buehler MJMJ: Materials-by-design: computation, synthesis, and characterization from atoms to structures. Phys Scr 2018, 93:053003. 12. Vesentini S, Redaelli A, Gautieri A: Nanomechanics of collagen microfibrils. Muscles Ligaments Tendons J 2013, 3:23-34. 13. Chang S-W, Buehler MJ: Molecular biomechanics of collagen molecules. Mater Today 2014, 17:70-76. 14. Domene C, Jorgensen C, Abbasi SW: A perspective on structural and computational work on collagen. Phys Chem Chem Phys 2016, 18:24802-24811. 15. Ghanaeian A, Soheilifard R: Mechanical elasticity of proline-rich and hydroxyproline-rich collagen-like triple-helices studied using steered molecular dynamics. J Mech Behav Biomed Mater 2018, 86:105-112. 16. Lodish H: Molecular Cell Biology. Macmillan; 2008. 17. Tang M, Li T, Gandhi NS, Burrage K, Gu YT: Heterogeneous nanomechanical properties of type I collagen in longitudinal direction. Biomech Model Mechanobiol 2017, 16:1023-1033. Detailed molecular dynamics simulations that probed the origin of heterogeneous nanomechanics in various regions of type I collagen microfibrils. 18. Zhou Z, Minary-Jolandan M, Qian D: A simulation study on the significant nanomechanical heterogeneous properties of collagen. Biomech Model Mechanobiol 2015, 14:445-457. 19. Orgel JPRO, Irving TC, Miller A, Wess TJ: Microfibrillar structure of type I collagen in situ. Proc Natl Acad Sci U S A 2006, 103 9001 LP-9005. 20. Tang M, Li T, Pickering E, Gandhi NS, Burrage K, Gu YT: Steered molecular dynamics characterization of the elastic modulus and deformation mechanisms of single natural tropocollagen molecules. J Mech Behav Biomed Mater 2018, 86:359-367. 21. Depalle B, Qin Z, Shefelbine SJ, Buehler MJ: Influence of crosslink structure, density and mechanical properties in the mesoscale deformation mechanisms of collagen fibrils. J Mech Behav Biomed Mater 2015, 52:1-13. 22. Zitnay JL, Li Y, Qin Z, San BH, Depalle B, Reese SP, Buehler MJ, Yu SM, Weiss JA: Molecular level detection and localization of mechanical damage in collagen enabled by collagen hybridizing peptides. Nat Commun 2017, 8. 23. Ghodsi H, Darvish K: Characterization of the viscoelastic behavior of a simplified collagen micro-fibril based on molecular dynamics simulations. J Mech Behav Biomed Mater 2016, 63:26-34. www.sciencedirect.com
Toward rational algorithmic design of collagen-based biomaterials Zhang et al. 87
24. Lee B, Zhou X, Riching K, Eliceiri KW, Keely PJ, Guelcher SA, Weaver AM, Jiang Y: A three-dimensional computational model of collagen network mechanics. PLoS One 2014, 9:1-12. 25. Licup AJ, Mu¨nster S, Sharma A, Sheinman M, Jawerth LM, Fabry B, Weitz DA, MacKintosh FC: Stress controls the mechanics of collagen networks. Proc Natl Acad Sci U S A 2015, 112:9573-9578. Comprehensive modeling and characterization of the nonlinear mechanics of fiber networks. 26. Jones CAR, Cibula M, Feng J, Krnacik EA, McIntyre DH, Levine H, Sun B: Micromechanics of cellularized biopolymer networks. Proc Natl Acad Sci U S A 2015, 112:E5117-E5122. Very elegant work that combined experimental characterization and 2D computational models to predict the micromechanics of cells interacting with collagen networks.
35. Niu LN, Jee SE, Jiao K, Tonggu L, Li M, Wang L, Yang YD, Bian JH, Breschi L, Jang SS et al.: Collagen intrafibrillar mineralization as a result of the balance between osmotic equilibrium and electroneutrality. Nat Mater 2017, 16:370-378. 36. Li X, Latour RA, Stuart SJ: TIGER2: an improved algorithm for temperature intervals with global exchange of replicas. J Chem Phys 2009, 130:174106. 37. Kulke M, Geist N, Friedrichs W, Langel W: Molecular dynamics simulations on networks of heparin and collagen. Proteins Struct Funct Bioinformatics 2017, 85:1119-1130. Used cutting-edge enhanced molecular dynamics sampling techniques to determine structural changes in collagen. 38. Li H, Xu B, Zhou EH, Sunyer R, Zhang Y: Multiscale measurements of the mechanical properties of collagen matrix. ACS Biomater Sci Eng 2017, 3:2815-2824.
27. Loerakker S, Ristori T, Baaijens FPT: A computational analysis of cell-mediated compaction and collagen remodeling in tissueengineered heart valves. J Mech Behav Biomed Mater 2016, 58:173-187.
39. Castro APG, Laity P, Shariatzadeh M, Wittkowske C, Holland C, Lacroix D: Combined numerical and experimental biomechanical characterization of soft collagen hydrogel substrate. J Mater Sci Mater Med 2016, 27:1-9.
28. Pierce DM, Ricken T, Holzapfel GA: A hyperelastic biphasic fibre-reinforced model of articular cartilage considering distributed collagen fibre orientations: continuum basis, computational aspects and applications. Comput Methods Biomech Biomed Eng 2013, 16:1344-1361.
40. Castro APG, Yao J, Battisti T, Lacroix D: Poroelastic modeling of highly hydrated collagen hydrogels: experimental results vs. numerical simulation with custom and commercial finite element solvers. Front Bioeng Biotechnol 2018, 6:1-8.
29. Schweizer S, Bick A, Subramanian L, Krokidis X: Influences on the stability of collagen triple-helix. Fluid Phase Equilib 2014, 362:113-117.
41. Manzano S, Moreno-Loshuertos R, Doblare´ M, Ochoa I, Hamdy Doweidar M: Structural biology response of a collagen hydrogel synthetic extracellular matrix with embedded human fibroblast: computational and experimental analysis. Med Biol Eng Comput 2015, 53:721-735.
30. Condon JE, Jayaraman A: Development of a coarse-grained model of collagen-like peptide (CLP) for studies of CLP triple Helix Melting. J Phys Chem B 2018, 122:1929-1939. 31. Ding YQ, Chen CL, Gu QR, Fu LH: Molecular simulation study of the effects of inorganic anions on the properties of chromecrosslinked collagen. Model Simul Mater Sci Eng 2014, 22. 32. Brooks BR, Brooks CL, Mackerell AD, Nilsson L, Petrella RJ, Roux B, Won Y, Archontis G, Bartels C, Boresch S et al.: CHARMM: the biomolecular simulation program. J Comput Chem 2009, 30:1545-1614. 33. Yin X, Zhao L, Kang SG, Pan J, Song Y, Zhang M, Xing G, Wang F, Li J, Zhou R et al.: Impacts of fullerene derivatives on regulating the structure and assembly of collagen molecules. Nanoscale 2013, 5:7341-7348. 34. Ma J: A molecular dynamics study on the nucleation of calcium phosphate regulated by collagen. J Mater Sci 2014, 49:3099-3106.
www.sciencedirect.com
42. Valero C, Amaveda H, Mora M, Garcı´a-Aznar JM: Combined experimental and computational characterization of crosslinked collagen-based hydrogels. PLoS One 2018, 13:1-16. 43. Lin S, Hapach LA, Reinhart-King C, Gu L: Towards tuning the mechanical properties of three-dimensional collagen scaffolds using a coupled fiber-matrix model. Materials (Basel) 2015, 8:5376-5384. 44. Vanderheiden SM, Hadi MF, Barocas VH: Crack propagation versus fiber alignment in collagen gels: experiments and multiscale simulation. J Biomech Eng 2015, 137:121002. 45. Xu B, Li H, Zhang Y: An experimental and modeling study of the viscoelastic behavior of collagen gel. J Biomech Eng 2013, 135:054501. 46. Sharabi M, Varssano D, Eliasy R, Benayahu Y, Benayahu D, HajAli R: Mechanical flexure behavior of bio-inspired collagenreinforced thin composites. Compos Struct 2016, 153:392-400.
Current Opinion in Chemical Engineering 2019, 24:79–87