# Collagenous Extracellular Matrix Biomaterials for Tissue Engineering: Lessons from the Common Sea Urchin Tissue

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## Abstract

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## 1. Introduction

## 2. Collagenous Scaffold Design

#### 2.1. Connective Tissues with Properties of Mutability (MCTs)

#### 2.2. Structural and Mechanical Compatibility

## 3. Collagen Fibril Biomechanics

#### 3.1. Stress-Strain Relationship of MCT

#### 3.2. Shear Action Underpins the Mechanism of Collagen Fibril Reinforcement of MCT

#### 3.3. Interfibrillar Shear Response by Elastic Stress Transfer Directs the Stiffening of the MCT

_{TC}represents the shear resistance between the two molecules and L

_{CL}the contact length between two adjacent molecules. Let F be the axial force generated within the molecule, which parameterizes the resistance to the shear action. To order of magnitude, we can identify the F with the product of τ

_{TC}and L

_{CL}, i.e.,

_{TC}L

_{CL},

_{TC}L

_{TC},

_{TC}is the length of a collagen molecule and η = L

_{CL}/L

_{TC}. The stress, σ

_{TC}, associated with F is,

_{TC}= F/α

_{TC},

_{TC}is the molecular cross-sectional area. The homogeneous shear mode assumes that the shear deformation is uniformly distributed throughout the interface of any two collagen molecules; this is expected to occur during initial loading. By virtue of the axial staggering of the collagen molecules, F increases linearly with L

_{CL}. Upon evaluating a multiscale model numerically—where the lower length scale level addresses the contribution of the interactions of atoms in the respective molecules to molecular deformation, and the next higher length scale level addresses the contribution of the sliding action of the molecules to the fibril deformation—Buehler has shown that the stress developed in the fibril follows a linear response to increasing strain up to a strain of 0.05 [110,111]. Interestingly, there is no appreciable toe region at initial loading [110,111].

_{CF}be the half-length of a collagen fibril and Z (=z/L

_{CF}) be the normalized axial coordinate (z) which parameterizes the axial distance of the fibril starting from the fibril centre (z = 0) and ending at the fibril end, i.e., z = L

_{CF}. It follows that the rate of change of the axial stress (σ

_{z}) at any point along the fibril is proportional to the difference between the axial displacement of the fibril (u

_{CF}) at that point within the fibril and the corresponding axial displacement of the interfibrillar matrix at the same point if the fibril were not presence, (u

_{m}) [80],

_{z}(Z)/dZ = H[u

_{CF}− u

_{m}],

_{CF}be the cross-sectional area of the (i.e., uniform cylindrical) fibril, r

_{0}the fibril radius, and r

_{m}the average radius of the interfibrillar matrix surrounding the fibril. Solving Equation (4) for uniform cylindrical fibrils, one finds that σ

_{z}and interfacial shear (τ) stress generated at the collagen fibrillar surface are given by [27,80]

_{z}(Z) = E

_{CF}ε[1 + cosh(β

_{Cox}{Z})/cosh(β

_{Cox})],

_{CF}ε√(G

_{m}/[2E

_{CF}ln(r

_{m}/r

_{0})])sinh(β

_{Cox}[Z])/cosh(β

_{Cox}),

_{Cox}= √(G

_{m}2πL

_{CF}

^{2}/[A

_{CF}E

_{CF}ln(r

_{m}/r

_{0})]),

_{CF}, the shear modulus of the interfibrillar matrix, G

_{m}, and the average strain in the fibril, ε. Figure 7B illustrates a typical axial stress distribution in the fibril under tension during elastic stress transfer. This profile applies to a fibril which possesses a uniform cylindrical shape, which is a common assumption for many tissues where the ends could not be observed. Thus, the shear-lag model predicts that the stress in the collagen fibril peaks at the fibril centre and decreases non-linearly to zero at the fibril end. In particular, the decrease is (1) gradual for a large portion of the fibril, around the fibril centre, (2) rapid towards the fibril end. For fibrils which possess tapering ends, the stress distribution profile has been predicted to differ appreciably from those of uniform cylinder [80,81]. This will be discussed further in Section 4.2.

_{m}) would be needed to enforce this.

#### 3.4. Interfibrillar Shear During Plastic Stress Transfer Directs the Compliance of MCT

_{z}along the fibril is proportional to product of the fibril radius (r), L

_{CF}and the fibril-matrix interfacial shear stress (τ) [97],

_{z}(Z)r

^{2}]/dZ = −2τr

_{0}L

_{CF}.

_{CF}/r

_{0}.

_{0}). Equation (8) is reduced to

_{z}(Z)/dZ = −2τq.

_{z}= 0 (i.e., a stress-free fibre end), the axial stress is given by

_{z}(Z) = 2τq[1-Z].

#### 3.5. Nucleation of Slip Pulse Predicts Collagen Fracture and Tissue Autotomy

_{TC}, and is of order of the applied tensile stress, σ

_{Grif}, to cause the MCT to rupture. Let A

_{TC}be the cross-sectional area of the collagen molecule. Thus, σ

_{Grif}is expressed as

_{Grif}= √(2E

_{TC}γ

_{TC}),

_{TC}is the Young modulus of an individual collagen molecule and γ

_{TC}parameterizes the energy required to nucleate a slip pulse [110]. When σ

_{TC}< σ

_{Grif}, the deformation of the collagen molecules is regulated by homogeneous shear (the homogeneous shear theory) between the molecules (Section 3.3). When σ

_{TC}> σ

_{Grif}, nucleation of slip pulses can occur (i.e., the slip pulse theory). Thereafter, a critical molecular length, i.e.,

_{S}= [√(2E

_{TC}γ

_{TC})]A

_{TC}/{ητ

_{TC}},

_{TC}≤ χ

_{S}; slip pulses predominates if L

_{TC}> χ

_{S}. If the tensile force, F, in each collagen molecule (Equation (1)) reaches the breaking force of the molecule, F

_{max}, before homogeneous shear could occur or even before slip pulses are nucleated, further occurrence of failure is governed by a second critical molecular length scale,

_{R}= F

_{max}/[ητ

_{TC}],

_{TC}> χ

_{R}; homogeneous (intermolecular) shear predominates if L

_{TC}≤ χ

_{R}. By combining these length scale arguments, it is further proposed that the interplay of the critical length-scales, expressed in the form of a ratio χ

_{S}/χ

_{R}, regulate the deformation mechanisms. It follows that slip pulse nucleation predominates at large molecular lengths only when χ

_{S}/χ

_{R}< 1; rupture of the collagen molecule predominates when χ

_{S}/χ

_{R}> 1.

^{9}Pa and stiffness of the collagen fibril ranges 6 GPa [110,117,118] to 40 GPa [118].

## 4. Structure-Function Relationship

#### 4.1. Vertebrates and Invertebrates with Spindle-Like Collagen Fibrils

_{l}be the collagen mass per unit length and ρ

_{Coll}be the density of collagen; m

_{l}is defined as the ratio of MN to 5D, where M is the mass of a collagen molecule (=290 kDa), N the number of molecules intersecting a fibril cross-section (through an overlap region) and D the so-called D period of a collagen molecule (Figure 4A and Figure 6C). A simple analytical argument, based on Holmes and co-workers [123], results in

_{l}/πρ

_{Coll}= 1-Z,

_{l}and Z corresponding to uniform cylindrical, conical (Figure 10A) and ellipsoidal (Figure 10C) shapes are given by the respective equations,

_{l}/πρ

_{Coll}= 1,

_{l}/πρ

_{Coll}= 1-Z

^{2},

_{l}/πρ

_{Coll}= −[1-Z]

^{2}.

_{l}-Z relationship follows a linear relationship (Figure 10D) in a fibril that has a paraboloidal shape (Figure 10B). On the other hand, the m

_{l}-Z plots (Figure 10D) for a fibril with conical ends (Figure 10A) and ellipsoidal shape (Figure 10C) show non-linear decreasing m

_{l}with increase in Z. In particular, the conical shape yields a concave profile while the ellipsoidal shape yields a convex profile (Figure 10D). Finally, we find that the uniform cylindrical shape yields an even distribution of m

_{l}independent of distance along the fibril.

_{l}-Z relationships were fitted to distribution of mass as a function of axial position along the fibril derived from scanning transmission electron micrographs of reconstituted collagen (as well as embryonic tissues). It is observed that the m

_{l}-Z relationship that best fit the experimental data corresponds to the paraboloidal shape. Thus the mass per unit length, m

_{l}, along all fibrillar ends increases almost linearly with increase in axial distance, z, from the fibril end [123,125]. One important implication of these findings is related to the accretion rate, which refers to the rate of collagen being added per unit area of the fibril surface. On the basis of these findings, it is concluded that accretion rate cannot be the same at any given site of the collagen fibril [123,125]. In particular, accretion rate is likely to decrease as the fibril diameter increases [123,125].

_{l}-Z relationships derived from the analytical model predict that fibrils with tapered ends would follow a non-uniform m

_{l}distribution.

#### 4.2. Taper in Fibrils Facilitates Even Distribution of Stress throughout the Fibril

#### 4.3. Fibrils Ought to Possess a Certain Slenderness for Appropriate Force Transmission

_{z}/σ

_{c}, along a fibril (paraboloidal shape), obtained for various values of q to illustrate the dependence of stress on q during elastic stress transfer [81]. For a given value of E

_{CF}/E

_{m}, it is shown that the magnitude of the stress increases when q increases. However, varying q has little effect on the profile of the stress distribution. It is also shown that the magnitude of the stress in the distribution is more sensitive to q at large E

_{CF}/E

_{m}than at small E

_{CF}/E

_{m}—the relationship between σ

_{z}/σ

_{c}at the fibre centre and q is shown in Figure 12B for two cases, corresponding to large E

_{CF}/E

_{m}and small E

_{CF}/E

_{m}. Thus, there are two important points of contention. First, the trend for each curve in Figure 12B reveals that the stress eventually converges at high q values. Second, the findings shown in Figure 12B predicts that q and E

_{CF}/E

_{m}could interact and mask the main effects. Further studies by experiment would be needed in order to clarify these points.

**8**) can be solved for the stress in the fibril by substituting the expression of r

_{0}, given by r

_{0}= [L

_{CF}/q]√(1-Z) for a paraboloid, and applying the boundary condition of σ

_{z}= 0 at Z = 1 [107]. This results in the following expression,

_{z}= [4/3]τq√(1-Z).

**19**) shows that the magnitude of σ

_{z}/τ in a paraboloidal fibril is linearly proportional to q but is independent of E

_{CF}/E

_{m}. Large values of q result in high magnitudes of σ

_{z}/τ during plastic stress transfer. Figure 12C shows the distributions of stress, σ

_{z}/τ, along a fibril (of paraboloidal shape), obtained for various values of q to illustrate the dependence of stress on q during plastic stress transfer [81]. Clearly, the profile of the stress distribution is not affected by varying q. The relationship between σ

_{z}/τ (for a given Z) and q is a linear one as shown in Figure 12D for Z = 0.

_{crit}) for fibril fracture, borrowed from engineering fibre reinforced composites [113,119], is important for understanding how a fibril fracture [27,100]. Thus, 2L

_{crit}is defined as the minimum length that a fibril must have for the stress at its centre to be equal to the fibril fracture strength [27,100]. For effective reinforcement, L

_{CF}should be large but less than L

_{crit}. Analytical models have predicted that tapered fibrils have longer L

_{crit}than uniform cylindrical fibrils, given all things being equal, i.e., r

_{0}and τ [27]. In particular, the L

_{crit}of a fibril with straight-tapered ends, paraboloidal ends and ellipsoidal ends are, respectively, 2, 3/2 and 4/π times longer than that of a uniform cylindrical fibril [27]. By an analogy to engineering composites [27,119], it may be argued that the longer the collagen fibrils, the tougher, stronger and stiffer will be the MCT, given all things being the same (i.e., r

_{0}and τ). Analytical models have also predicted that a fibril with tapered ends requires less volume of collagen material to synthesize as compared to uniform cylindrical fibrils, for a given L

_{CF}and r

_{0}[27]—this is another good reason for the collagen fibrils in the connective tissue of the sea urchin to possess tapered ends, as well as having high slenderness (i.e., high q).

#### 4.4. Small and Large Fibrils Have Distinct Roles in Regulating Mutability

_{E}), and the essential energy (u

_{F}) according to the principles of essential work of fracture of a fibre composite [58]. The u

_{E}is said to contribute primarily to tendon resilience (regulated by fibrils undergoing elastic deformation); the u

_{F}is said to contribute primarily to the resistance of the tendon to rupture (regulated by fibril rupture, leading to defibrillation and rupture of the interfibrillar matrix, Figure 8) [58]. By evaluating the frequency histograms of diameter for all age groups using the minimal number of normally distributed subpopulations, the mean fibril diameter of the respective subpopulation may be linearly added—weighted by coefficients that depend on the fibril diameter, fibril strength and interfacial shear stress—to give the u

_{E}and u

_{F}[58]. Using the mouse tail tendon as a tissue model, the minimal number of normally distributed subpopulations is found to be equal to two across all the age groups [58]. For the purpose of this discussion, we then let the smaller and larger mean diameters be D

_{D1}and D

_{D2}, respectively. Accordingly, the overall effect of fibril diameter on u

_{E}and u

_{F}may then be assessed by a multiple regression analysis [58]. It follows that increases in the resilience energy are associated with decreases in D

_{D1}and increases in D

_{D2}[58]. On the other hand, the energy to resist fracture is associated with increases in D

_{D1}, but independent of D

_{D2}. Thus, the fracture toughness argument emphasizes that at the physiological level, age variation in the fracture toughness is the result of changes in the energy for resilience and resistance to fracture; these two energy parameters are in turn influenced by the structural changes at the fibrillar level. It follows that small and large fibrils have distinct roles in the stiff state and only the small fibrils have a role in the complaint states, and hence lending to the mutability properties.

_{E}parameter is essentially associated with loading from the initial point until the end of the elastic region of the stress-strain curve, it is likely that the small and large fibrils have distinct roles in regulating mutability. While it is not clear why these fibrils are bestowed with distinct roles, the results suggest that the interplay of small and large fibrils help the tissue responds to external loads by absorbing the appropriate level of strain energy to achieve resilience (elastic stress transfer) and to resist fracture (plastic stress transfer).

#### 4.5. Fibril Slenderness and Relative Stiffness Interplay to Lower Stress Discontinuity in Fibril Interaction

_{z}/σ

_{c}, in the fibril at varying fibril-fibril axial overlap distance (λ) and the centre-to-centre lateral separation distance (ρ) as a function of axial distance along the fibril, for the case of the uniform cylindrical shape (Figure 14). When the neighbouring fibrils do not overlap, i.e., the α and β fibrils in the unit cell do not overlap along the axes (λ/L

_{CF}= 0), the stress uptake within the α fibril is modulated by the α fibrils from the adjacent unit cells (Figure 14A). Thus, σ

_{z}/σ

_{c}is maximum at the fibril centre (Z = 0) which then decreases steadily to zero at fibril end (Z = 1). The stresses are very evenly distributed throughout the bulk of the fibril (except at the fibril end) at high q. In contrast, the stresses show appreciable decrease in magnitude with increasing Z at low q values (results not shown). It must be pointed out that the stresses at high E

_{CF}/E

_{m}feature even distributions throughout the bulk of the fibril (except at the fibril end) for both cases of high and low q (results not shown). This is important because it suggests that the interplay of E

_{CF}/E

_{m}and q predominates in the fibril-fibril interaction. The result is higher axial stress even when the fibrils in the immediate vicinity are not overlapping with the primary fibril.

_{CF}> 0) (Figure 14B,C). Here, the stress uptake within the α fibril is modulated by the β fibril, as well as by the α fibrils from adjacent unit cells. This leads to higher σ

_{z}/σ

_{c}throughout the fibril compared to the case when overlap is absence (λ/L

_{CF}= 0). The stress discontinuity is described as an abrupt (stepwise) change in the σ

_{z}/σ

_{c}distribution, which is most pronounced at high q (Figure 14B,C), but somewhat less so at low q (results not shown). Additionally, the stress discontinuity (i.e., a sudden drop in stress) results in higher σ

_{z}/σ

_{c}at the non-overlapped region and lower σ

_{z}/σ

_{c}at the overlapped region (Figure 14B,C). It must be emphasized that the exact position of the stress discontinuity varies with the extent of overlap. Indeed, increasing λ/L

_{CF}displaces the discontinuity to the fibril centre. Interestingly, when axial overlap occurs, the magnitude of the stress at a given location in the fibril (within the overlap region) appears to be independent of the extent of the axial overlap, regardless of the point within or outside the overlap region. Thus, it is important to note that no further advantage (i.e., higher stress uptake) may be gained from increasing the overlapping region.

_{0}leads to small step-wise change in the stress uptake. This implies that the influence of the β fibril decreases with increasing ρ/r

_{0}(Figure 14). More importantly, the stress discontinuity disappears at high E

_{CF}/E

_{m}, regardless of q. Additionally, increasing the fibril-fibril separation distance has the effect of increasing the stress magnitude in the fibril. Thus the larger the fibril-fibril lateral separation distance the higher is the stress in the fibres. Secondary to this effect is the asymptotic increase of the stress magnitude to a steady value at large fibril-fibril separation (results not shown). Of course, these conclusions apply regardless of the extent of fibril-fibril overlap; in other words, these conclusions apply when λ/L

_{CF}= 0 or λ/L

_{CF}> 0. Clearly the case of λ/L

_{CF}= 0 implies that no axial overlap occurs, but this asymptotic increase in the stress magnitude with increasing fibril-fibril separation should not be interpreted to imply that the nearest (β) fibrils has no effect on the σ

_{z}/σ

_{c}. In this case, the effect on the stress with varying fibril-fibril separation distance is predominated by two factors: one, the stress field arising from the interactions with the nearest (β) fibrils where the tips of these fibrils are in line with the tip of the α fibril, and two, the effects of the bulk ECM surrounding the α fibril.

_{CF}the largest ρ/r

_{0}beyond which the effect of fibril-fibril interaction (i.e., directed by the nearest (β) fibres) diminishes may be determined from a plot of σ

_{z}/σ

_{c}(at a fixed Z) versus ρ/r

_{o}. To assess for convergence, note that at a given value of q at low E

_{CF}/E

_{m}, a plot of σ

_{z}/σ

_{c}(namely Z = 0, as the reference point) versus ρ/r

_{0}shows that σ

_{z}/σ

_{c}increases rapidly with increase in ρ/r

_{0}(graph not shown). More importantly, beyond a critical ρ/r

_{0}, σ

_{z}/σ

_{c}converges to a steady value.

_{CF}/E

_{m}. Consequently, one could expect that the larger the E

_{CF}/E

_{m}the higher is the force generated to stretch/contract the fibres. Estimates for E

_{CF}/E

_{m}ranges 10

^{3}–10

^{6}(Table 3) [80,81]. To what extent should crimp be exploited for ECM-DT, or even synthetic collagen fibrils in a synthetic matrix is not clear but the arguments of previous studies suggest that crimp presents some advantages for the tissue to stretch/contract, aided further by virtue of the high E

_{CF}/E

_{m}.

#### 4.6. Water and Charged Species within the Interfibrillar Matrix Contributes to the High Poisson Ratio of MCT

_{c}= v

_{CF}V

_{CF}+ v

_{m}V

_{m},

_{CF}and V

_{m}are volume fractions of the collagen fibrils and matrix, respectively, satisfying the condition of V

_{CF}+ V

_{m}= 1. By considering the upper and lower limits of V

_{CF}to be 0.8 and 0.2, respectively [40], the upper limit of v

_{CF}~2 [156], and the upper limit of v

_{c}~4 [157], the v

_{m}is found to range from 3 to 18. The estimated upper limit for the interfibrillar matrix is consistent with a material that exhibits very large change in volume during deformation.

_{CF}/E

_{m}, which represents the ratio of the stiffnesses of the fibril (E

_{CF}) to the interfibrillar matrix (E

_{m}), on collagen fibril stress uptake, it has been predicted that the higher the E

_{CF}/E

_{m}, the larger is the magnitude of the axial stress generated in the fibril (Figure 12A,B) [81]—the axial stress uptake is more sensitive to E

_{CF}/E

_{m}than q [81]. As high E

_{CF}/E

_{m}corresponds to an interfibrillar matrix in a compliant state while low E

_{CF}/E

_{m}corresponds to an interfibrillar matrix in a stiffened state (which could be the result of the exudation of water and other ECM components), this suggests that the stress uptake in a fibril is higher when the MCT is in a compliant state than stiffened state.

## 5. Framework for Collagenous ECM Mechanics, Prospects and Challenges for Scaffold Design

- (1)
- decrimping, elastic deformation by fibre–fibre sliding, fibre yielding, plastic deformation, and fibre defibrillation or rupture at the collagen fibre level;
- (2)
- the extinction of fibril waviness, uncoiling of the fibril-associated proteoglycan glycosaminoglycan side-chains, elastic stress transfer, intermediate modes (such as interfibrillar matrix cracks, partial delamination of interface between the interfibrillar matrix and fibril, and plastic deformation of the interfibrillar matrix), plastic stress transfer (with complete delamination of interface between the interfibrillar matrix and fibril), rupture of interfibrillar matrix, and fibril rupture and fibril pullout at the collagen fibril level;
- (3)
- the straightening of microfibrils, microfibrillar sliding and realignment of microfibril from its supertwist, exudation of water and solutes from the intermicrofibrillar matrix, microfibrillar stretching, disruption of microfibril-microfibril interactions and microfibril rupture at the microfibril level;
- (4)
- the straightening of kinks on the molecule, molecular stretching (involving axial deformation of the backbone, uncoiling the helices and helix–helix sliding) and intermolecular shear (nucleation of slip-pulse), and disruption to the intramolecular cross-links and intermolecular cross-links at the collagen molecular level.

## 6. Conclusions

- MCT deformation characteristics resemble those of mammalian tissues.
- Shear models, addressing elastic and plastic stress transfer, explain the mechanism of collagen fibril reinforcement of MCT during the stiff and compliant states, respectively.
- Nucleation of slip pulses, as a possible mode of collagen fracture, leading to failure of the MCT, could direct autotomy.
- The spindle-like shape in collagen fibrils modulates the stress uptake by ensuring a more uniform distribution of stress throughout the fibril.
- Fibrils with small diameters are responsible for regulating the property of mutability, by addressing the tissue resilience and fracture energy.
- Interplay between the fibril aspect ratio and relative stiffness of collagen to matrix is the key to reducing stress discontinuity in a fibril during fibril-fibril sliding.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

ACh | acetylcholine |

ASW | Artificial sea water |

CA | Catch apparatus |

ECM | Extracellular matrix |

ECM-DT | Extracellular matrix derived from decellularized tissue |

EGTA | Ethylene-bis-(oxyethylenenitrilo)-tetraacetic acid |

FACIT | Fibril associated collagens with interrupted triple helices |

MCT | Mutable collagenous tissue |

POI | Plane of interest |

RVE | Representative volume element |

TX | Triton X100 |

## Non-Greek Symbols

A_{CF} | Cross-sectional area of the (i.e., uniform cylindrical) fibril |

C | C-terminus (containing the carboxyl group) of the collagen molecule |

COMP | Cartilage oligomeric matrix protein |

D | The D period of the collagen fibril |

D_{D1} | Population of fibrils with smaller diameter (relative to D_{D2}) |

D_{D2} | Population of fibrils with larger diameter (relative to D_{D1}) |

E_{CF} | Tensile stiffness of the collagen |

F | Axial force generated within the collagen molecule |

F_{max} | Breaking force of the collagen molecule |

G_{m} | Shear modulus of the interfibrillar matrix |

H | Constant in the differential equation of the shear-lag model |

L_{crit} | Critical length for fibril fracture |

L_{CF} | Half-length of the fibril |

L_{CL} | Contact length between two adjacent collagen molecule |

L_{TC} | Length of the collagen molecule |

m_{l} | Collagen mass per unit length |

M | Mass of a collagen molecule |

N | Number of molecules intersecting a fibril cross-section (through an overlap region) |

N | Amino-terminus (containing an amine group) of the collagen molecule |

q | Fibril aspect ratio |

(r,θ,z) | Radial, azimuthal and axial coordinates, respectively, of the cylindrical polar coordinate system |

r_{m} | Radius of the matrix surrounding the fibril |

r_{0} | Radius of the (uniform cylindrical) fibril |

u_{CF} | Axial displacement of the fibril at that point within the fibril |

u_{m} | Axial displacement of the interfibrillar matrix at the same point if the fibril were not presence |

u_{E} | Strain energy density, relates to the tissue resilience |

u_{F} | Strain energy density, relates to the tissue rupture |

v_{c} | Poisson’s ratio of the tissue |

v_{CF} | Poisson’s ratio of the collagen fibril |

v_{m} | Poisson’s ratio of the interfibrillar matrix |

V_{CF} | Volume fraction of collagen fibrils |

V_{m} | Volume fraction of interfibrillar matrix |

Z | Normalized axial coordinate |

## Greek Symbols

α_{TC} | Molecular cross-sectional area |

β_{Cox} | Constant in the shear-lag model; appears in the argument of the trigonometrical functions |

ε | Average strain in the fibril |

γ_{TC} | Energy required to nucleate a slip pulse |

λ | Axial overlap distance between two adjacent fibrils |

ρ | Centre-to-centre lateral separation distance between two adjacent fibrils |

ρ_{Coll} | Collagen density |

σ_{c} | Stress acting on the tissue in the direction of the fibril |

σ_{Grif} | Applied tensile stress leading to the rupture of the MCT |

σ_{TC} | Stress associated with F |

σ_{z} | Collagen fibril axial stress |

τ_{β} | Shear stress at the fibril-matrix interface, generated during the mode β transition stage |

τ_{GAG} | Shear stress for rupturing the bonds between proteoglycan glycosaminoglycans |

τ_{RP} | Shear stress at the fibril-matrix interface, generated during the fibril rupture or pull-out |

τ | Shear stress at the fibril-matrix interface |

τ_{TC} | Shear resistance between the two collagen molecules |

η | Ratio of L_{CL} to L_{TC} |

χ_{S} | First critical molecular length |

χ_{R} | Second critical molecular length |

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**Figure 1.**Sketches of the spine-test system of the sea urchin. (

**A**) Cartoons of the sea urchin, represented by a sphere covered in spines, magnified view of the cross-section of the joint of the spine-test system and the hierarchical architecture of the catch apparatus (CA) tissue. The CA may be regarded as a ligamentous tissue as its ends are embedded in hard tissues of the spine and test; (

**B**) Two positions, i.e., X and Y, of the spine. Symbols: S, spine; NR, nerve ring; Bs, basiepidermal nerve plexus; E, epidermis; L, central ligament; M, spine muscle; T, test. Adapted from Smith et al. [14], Hidaka et al. [15,16] and Motokawa and Fuchigami [17].

**Figure 2.**The design process for a tissue engineering approach.

**Left panel**shows a flow-chart of the design process. The focus in this process is on the biomaterial for the scaffold development (highlighted in dark fonts). The flow of the design process is typical of engineering design, with the following key stages, statement of needs, problem definition, synthesis, analysis and optimization, evaluation and, finally, market [87]. Of note, some of the stages are expected to be iterative.

**Right panel**shows the tissue engineering triad, comprising biomaterials, cells and signaling molecules. The engineering triad is linked to the problem definition stage and continues through to the analysis and optimization stage. The desired specifications for the biomaterial scaffold are outlined in the box based on some of the key arguments developed by Trotter and co-workers [23].

**Figure 3.**Profiles of the stress versus strain curves of mutable collagenous tissues (MCTs). (

**A**) A sketch of the graph of stress versus strain of the CA, sea urchin (Anthocidaris crassispina) [15]; (

**B**) A sketch of the graph of stress versus strain of the catch apparatus, sea urchin (Anthocidaris crassispina) [16]; (

**C**) A sketch of the graph of stress versus strain of the tube feet tissue, sea urchin (Paracentrotus lividus) [70]; Sketches of (

**D**) the graph of displacement versus time, indicating the primary (#1), secondary (#2) and tertiary (#3) phases; thereafter rupture results; (

**E**) the graph of incremental stress versus strain and (

**F**) the graph of stress versus strain (derived from

**E**) of the compass depressor ligament, sea urchin (Paracentrotus lividus) [66]; (

**G**) Sketch of graph of stress versus strain of the dermis of the sea cucumber (Cucumbria frondosa) [23] for the purpose of comparison with the results from the sea urchin (

**A**–

**F**). Symbols in the graphs: ACh represents acetylcholine; ASW, artificial sea water; EGTA, ethylene-bis-(oxyethylenenitrilo)-tetraacetic acid (calcium chelator); TX, Triton X100.

**Figure 4.**General model of collagen fibril in extracellular matrix (ECM). (

**A**) An array of parallel collagen fibrils embedded in the ECM. The vertical dard bands and light shades represent the D-periodic patterns. (

**B**) Interaction of collagen fibrils in the matrix. Here the interaction is assumed to be aided somewhat by proteoglycans and glycosaminoglycans, although the exact identity of the proteoglycans has yet to be determined. Not shown in this schematic are the glycoproteins. (

**C**) A single collagen fibril modelled as a uniform cylinder. The fibril centre, O, defines the origin of the cylindrical polar coordinate system (r,θ,z), where the z axis coincides with the axis of the fibril. Of note, the single fibril-matrix model in part C provides the basic “template” for many of the discussions in this review where stress uptake in the fibril is the key concerned (see Figures 7A and 10A for similar schematics).

**Figure 5.**Fibre-matrix interfacial shear stress, τ, distributions [99,101]. (

**A**) Shear-lag model; (

**B**) Shear-sliding model. Here Z represents the normalized coordinate, i.e., Z = z/L

_{CF}, where z is the z coordinate of the cylindrical polar coordinate system and L

_{CF}represents the half-length of the fibril. Z is used to describe the distance along the fibre axis from the fibre centre, Z = 0, to the respective fibre ends, Z = 1 or −1.

**Figure 6.**Schematic of collagen molecules in tension in collagen fibrils. (

**A**) the Buehler bimolecular model [110], i.e., two collagen molecules sliding under a tensile force, F. Symbol L

_{TC}represents the length of the molecule; (

**B**) the axial-staggering of collagen molecules in a fibril. The staggered arrangement gives rise to light-dark bands (i.e., the D-periodic patterns) along the collagen fibril. Symbols D represents the D period of the collagen fibril; N and C denote the amino-terminus (containing an amine group) and C-terminus (containing carboxyl group) of the collagen molecule, respectively; (

**C**) Two adjacent collagen fibrils.

**Figure 7.**Collagen fibril axial stress, σ

_{z}, distributions. (

**A**) Model of connective tissue featuring a collagen fibril embedded in ECM. The proposed interfacial shear stress distributions in the (

**B**) Shear-lag and (

**C**) Shear-sliding models for collagen fibril biomechanics [99,101]. In part B and C, symbols F represents the force acting on the ECM (red arrow represents the direction of F); σ

_{c}represents the stress acting on the tissue in the direction of the fibril, r

_{m}represents the radius of the matrix surrounding the fibril; r

_{0}represents the radius of the fibril; L

_{CF}represents the half-length of the fibril; r and z are coordinates of the cylindrical polar coordinate system; Z represents the normalized coordinate of z (i.e., Z = z/L

_{CF)}which is intended to describe the fractional distance along the fibril axis from the fibre centre, Z = 0 (i.e., O), to the respective fibre ends, Z = 1 or −1; E and E’ represent the ends of a fibril (Figure 6).

**Figure 8.**Schematic of tissue rupture. The diagram shows a snapshot of the microenvironment of ECM undergoing failure. These failures are identified as a small crack in ECM, rupture of ECM and bridging of the ruptured site by intact collagen fibrils; at the ruptured site of ECM, fibrils may also be pulled out or fractured. Adapted from Goh et al. [58].

**Figure 9.**Schematics of the cross section of fibre reinforced composites. (

**A**) Continuous uniform cylindrical fibre reinforced composite (

**left panel**) from a 3D perspective. Corresponding 2D perspective showing the plane of interest (POI) containing the cross-sections of the uniform cylindrical fibre (

**right panel**); (

**B**) Discontinuous paraboloidal fibre reinforced composite (

**left panel**, 3D perspective). Corresponding plane of interest (POI) showing the cross-sections of the paraboloidal fibre (

**right panel**, 2D perspective). The fibres numbered, 1–8, in the 3D and 2D schematics are intended to illustrate their associations between the two views. In part (

**A**,

**B**), the force acting on the respective composites is in the direction of the fibre axis.

**Figure 10.**Tapered fibril reinforcing connective tissue. (

**A**) A fibril with conical ends, concentrically arranged within the ECM. In this general model (see illustrations at the bottom and middle panels), the fibril possesses mirror symmetry about the fibril centre, O, and axis symmetry, which defines the z-axis of the cylindrical polar coordinate system, so that one-quadrant of the complete model (see illustration at the top panel) need only to be illustrated. The fibril has a radius, r

_{0}, and a half-length, L

_{CF}; r

_{m}represents the radius of the model. The stress acting on the model is represented by σ

_{c}, acting in the direction of the axis. The other fibril shapes, namely a fibril with paraboloidal ends, and an ellipsoidal fibril are depicted in (

**B**,

**C**), respectively. These models also adopt similar assumptions of mirror and axis symmetry developed for the conical shape so that only one-quadrant of the complete model is illustrated in the respective subfigure (

**B**,

**C**). (

**D**) Graph of normalized fibril axial mass, m

_{l}/ρπ, versus Z from the centre to the end of collagen fibril for the respective shapes. The graphs are obtained by evaluating the respective Equations (15)–(18). Here, m

_{l}and ρ

_{Coll}represent the collagen mass per unit length and density, respectively.

**Figure 11.**The stress distributions along the fibril axis for collagen fibrils, modelled by four different fibril shapes, namely conical ends, paraboloidal ends, ellipsoid and uniform cylinder, undergoing elastic stress transfer (

**A**,

**B**) and plastic stress transfer (

**C**). Sketches of the (

**A**) graph of normalized axial stress, σ

_{z}/σ

_{c}, [104] and (

**B**) graph of interfacial shear stress, τ/σ

_{c}, [96] versus fractional distance along the fibril axis, Z. The results were evaluated at fibril aspect ratio, q = 3500, and relative stiffness of the fibril to the matrix, E

_{CF}/E

_{m}= 10

^{6}. (

**C**) Graph of normalized axial stress, σ

_{z}/τq, versus fractional distance along the fibril axis, Z obtained by evaluating the stress equations of the respective fibre shapes [107]. All graphs are shown for the stress plotted from the fibril centre (Z = 0) to one end (Z = 1). Here, symbols σ

_{c}represents the applied stress acting on the tissue in the direction of the fibril, τ represents the interfacial shear stress, r

_{m}represents the radius of the matrix surrounding the fibril; Z = z/L

_{CF}where z is the z coordinate of the cylindrical polar coordinate system and L

_{CF}represents the half-length of the fibril.

**Figure 12.**Effects of fibril aspect ratio, q, and ratio of moduli of the fibril to the interfibrillar matrix, E

_{CF}/E

_{m}, on the axial stress, σ

_{z}, in a fibril. Sketches of the (

**A**) graph of normalized axial stress, σ

_{z}/σ

_{c}, versus fraction distance, Z, along the fibril and the associated (

**B**) graph of σ

_{z}/σ

_{c}at the fibril centre (Z = 0) versus q (or E

_{CF}/E

_{m}) during elastic stress transfer [81]. Graphs of the (

**C**) normalized axial stress, σ

_{z}/τ, versus Z along the fibril and the associated (

**D**) graph of maximum σ

_{z}/τ (at Z = 0) versus q during plastic stress transfer; the results are obtained by evaluating the stress equation derived for the fibre with paraboloidal ends [107]. Thus, all results shown here apply to the fibril with a paraboloidal shape. The q values range 200 to 3500 (the arrow in part (

**A**,

**C**) indicates increasing q value). Of note, the authors of the paper describing these computer models have made clear the difficulties in meshing the model beyond an aspect ratio of 3500 and have defined a strategy that limits the analysis to within the constraints of the models; further details can be found in the reference [81]. Symbol σ

_{c}represents the applied stress acting on the tissue in the direction of the fibril and τ represents the fibril-matrix interfacial shear stress.

**Figure 13.**Model of ECM containing short (uniform cylindrical) collagen fibrils arranged in the square-diagonally packed configuration. (

**A**) A cross-sectional (plane of interest, POI) view; (

**B**) The longitudinal view of the unit cell. In part (

**A**), α refers to the primary fibril of interest; surrounding the α fibril are the β (secondary) fibrils of interest. Here, RVE represents representative volume element; λ and ρ represent the fibril-fibril axial overlap distance and the centre-to-centre lateral separation distance, respectively.

**Figure 14.**Fibril-fibril interaction. Sketches of the graph of axial tensile stress, σ

_{z}/σ

_{c}, in a fibril versus distance, Z, along the fibril axis (where Z = 0 and 1 correspond to the fibril centre and end, respectively) at (

**A**) λ/L

_{CF}= 0; (

**B**) λ/L

_{CF}=1/4 and (

**C**) λ/L

_{CF}= 3/4 for the uniform cylindrical shape at varying fibril-fibril separation distance, ρ/r

_{o}, adapted from the report of Mohonee and Goh [130]. Insets (right of each graph) show representative volume elements (RVEs, Figure 13) of fibrils embedded in the matrix at different overlap distance. In the report of Mohonee and Goh, all results have been obtained by setting the ratio of the stiffnesses of the fibril to the matrix, E

_{CF}/E

_{m}, equal to 10

^{2}(“low”) and the fibril aspect ratio q = 650 (“high”). Symbol σ

_{c}represents the applied stress acting on the tissue in the direction of the fibril, L

_{CF}represents the half-length of the fibril and r

_{0}represents the fibril radius (for the tapered fibril, this refers to the radisu at the fibril centre).

**Figure 15.**Framework of the ECM mechanics for the MCT [27]. The framework provides a systematic approach to map the mechanisms involve in regulating the mechanical response of ECM at the respective loading regimes, labelled 1–5. These mechanisms are identified across the length scale from molecular to bulk tissue level. At the tissue level, the graph illustrates a schematic representation of typical MCT stress-strain behaviour.

Tissue | Maximum Stress (MPa) | Stiffness (MPa) | Maximum Strain | Literature |
---|---|---|---|---|

Catch apparatus, sea urchin | 40 ^{†} | 400 ^{†} | 0.3 ^{†} | [15,16] |

Tube feet, sea urchin | 200 ^{#} | 2000 ^{#} | 2.0 ^{#} | [70] |

Compass depressor, sea urchin | 19.5 ± 5.5 | 40.0 ± 22.3 | 3.0 ± 2.4 | [66] |

^{†}indicates that the values are estimates derived from the graphs of stress versus strain.

^{#}indicates that the values are estimates derived from the bar-charts of the respective mechanical properties.

**Table 2.**Examples of the length, diameter and aspect ratio of collagen fibrils in marine invertebrates as well as land vertebrates.

Tissue | Length (L_{CF}), (μm) | Diameter (2r_{0}), (nm) | Aspect ratio (q) | Literature |
---|---|---|---|---|

Marine invertebrates | ||||

Dermis, starfish (Asterias amurensi) | 196 ^{¥} | 136 ^{¥} | 1441 ^{‡} | [132] |

Dermis, sea cucumber (Cucumaria frondosa) | 13.8–443.6 ^{@} | 75 ^{#} | 184–5914 ^{‡} | [133] |

Catch apparatus, sea urchin (Eucidaris tribuloides) | - | - | 2275–3300 ^{†} | [22] |

Catch apparatus, sea urchin (Eucidaris tribuloides) | 234 * | 75 ^{#} | 3120 ^{‡} | [126] |

Vertebrates | ||||

Skin, calf (acid-extracted collagen) | 9 * | 21 ^{¥} | 423 ^{‡} | [134,135] |

Tendon, embryonic chick | 18 * | 50 ^{#} | 360 ^{‡} | [122] |

Medial collateral knee ligament, rat | 21 * | 75 ^{#} | 282 ^{‡} | [120] |

^{¥}These are simple averages.

^{‡}These are derived from the ratio of the average length to the average diameter.

^{@}These are broadly observed by the authors of the paper.

^{#}These are estimated from the electron micrographs presented in the paper.

^{†}These are derived from the gradient of a straight line fitted to data points of length versus diameter. * These are estimated values derived from computing the mid-value between the lower and upper limit.

**Table 3.**Estimates of fibrillar and matrix-related Poisson’s ratio and modulus of elasticity parameters for understanding the behaviour of the interfibrillar matrix.

Parameters | Magnitudes | Literature |
---|---|---|

Poisson’s ratio of collagen fibril, v_{CF} | 2 | [156] |

Volume fraction of collagen, V_{CF} | 0.2–0.8 | [40] |

Poisson’s ratio of MCT, v_{c} | 0.7–4.2 | [157] |

Poisson’s ratio of interfibrillar matrix, v_{m} | 3–18 | This review, using Equation (20) |

E_{CF}/E_{m} | 10^{3}–10^{6} | [80,112] |

Interfibrillar Shear Stress | Magnitude (MPa) | Literature |
---|---|---|

Shear stress, τ_{β}, generated at the fibril/matrix interface during the mode β transition stage | 1–10 | [58] |

Shear stress, τ_{RP}, generated at the fibril/matrix interface during the fibril rupture or pull-out | 100 | [58] |

Shear stress, τ_{GAG}, for rupturing the bonds between proteoglycan glycosaminoglycans using optical tweezers | 7.5 | [58,166] |

Interfibrillar shear stress, τ, by notched tissue testing | 32 | [109] |

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## Share and Cite

**MDPI and ACS Style**

Goh, K.L.; Holmes, D.F.
Collagenous Extracellular Matrix Biomaterials for Tissue Engineering: Lessons from the Common Sea Urchin Tissue. *Int. J. Mol. Sci.* **2017**, *18*, 901.
https://doi.org/10.3390/ijms18050901

**AMA Style**

Goh KL, Holmes DF.
Collagenous Extracellular Matrix Biomaterials for Tissue Engineering: Lessons from the Common Sea Urchin Tissue. *International Journal of Molecular Sciences*. 2017; 18(5):901.
https://doi.org/10.3390/ijms18050901

**Chicago/Turabian Style**

Goh, Kheng Lim, and David F. Holmes.
2017. "Collagenous Extracellular Matrix Biomaterials for Tissue Engineering: Lessons from the Common Sea Urchin Tissue" *International Journal of Molecular Sciences* 18, no. 5: 901.
https://doi.org/10.3390/ijms18050901