cross-links found in adult and children bone
result in different mechanical behavior of collagen
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Citation Depalle, Baptiste et al. "The different distribution of enzymatic collagen cross-links found in adult and children bone result in different mechanical behavior of collagen." Bone 110 (May 2018): 107-114 © 2018
As Published http://dx.doi.org/10.1016/j.bone.2018.01.024
Publisher Elsevier BV
Version Author's final manuscript
Citable link https://hdl.handle.net/1721.1/127641
Terms of Use Creative Commons Attribution-NonCommercial-NoDerivs License Detailed Terms http://creativecommons.org/licenses/by-nc-nd/4.0/
Immature divalent cross-link Mature trivalent cross-link Experimental dosage of enzymatic cross-links (HPLC)
Cross-linked collagen fibrils molecular modeling Tensile loading simulation Adult bones Children bones Cross-links associated with elastic deformation (E, We, y): cross-links maturity cross-links density Fibril stiffness (E) Mechanical VS structural statistical analysis Cross-links associated with plastic deformation (We, Wp, Wt, u): cross-links maturity cross-links density Fibril stiffness (E)
Highlights:
Collagen fibril elastic deformation is higher in children than in adults
Enzymatic cross-links maturity correlates with collagen fibril elastic deformation during the lifetime
Covalent connections from enzymatic cross-links correlate to stiffness parameters in children’s collagen fibril
Covalent connections from enzymatic cross-links correlate to toughness parameters in adult’s collagen fibril
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“The different distribution of enzymatic collagen crosslinks found in adult and children bone 1
result in different mechanical behavior of collagen”. 2
3
Baptiste Depalle a,b, Andre G. Duarte c, Imke A. K. Fiedler c, Laurent Pujo-Menjouet d, Markus 4
J. Buehler b, Jean-Philippe Berteau c 5
a Department of Materials, Imperial College London, UK 6
b Laboratory for Atomistic and Molecular Mechanics (LAMM), Department of Civil and 7
Environmental Engineering, MIT, USA 8
c Department of Physical Therapy, College of Staten Island, USA 9
d Institut Camille Jordan, Université de Lyon, France 10
11
Abstract 12
Enzymatic collagen cross-linking has been shown to play an important role in the 13
macroscopic elastic and plastic deformation of bone across ages. However, its direct contribution 14
to collagen fibril deformation is unknown. The aim of this study is to determine how covalent 15
intermolecular connections from enzymatic collagen cross-links contribute to collagen fibril 16
elastic and plastic deformation of adults and children’s bone matrix. We used ex vivo data 17
previously obtained from biochemical analysis of children and adults bone samples (n = 14; n = 18
8, respectively) to create 22 sample-specific computational models of cross-linked collagen 19
fibrils. By simulating a tensile test for each fibril, we computed the modulus of elasticity (E), 20
ultimate tensile and yield stress (σu and σy), and elastic, plastic and total work (We, Wp and Wtot)
21
for each collagen fibril. We present a novel difference between children and adult bone in the 22
deformation of the collagen phase and suggest a link between collagen fibril scale and 23
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macroscale for elastic behavior in children bone under the influence of immature enzymatic 1
crosslinks. We show a parametric linear correlation between We and immature enzymatic 2
collagen cross-links at the collagen fibril scale in the children population that is similar to the one 3
we found at the macroscale in our previous study. Finally, we suggest the key role of covalent 4
intermolecular connections to stiffness parameters (e.g. elastic modulus and We) in children’s 5
collagen fibril and to toughness parameters in adult’s collagen fibril, respectively. 6
7
Keywords: Cross-links; children bone; molecular modelling; biomechanical properties 8
9
1. Introduction 10
During childhood and adolescence, bone structure is altered by geometrical growth 11
associated with increases in mass, and alterations in tissue density (Bonjour et al., 1994; 12
Schoenau et al., 2001; Schoenau and Fricke, 2008). These processes build a bone with an 13
optimal size, shape, and architecture to withstand the normal physiological loads that might 14
come from children and teenagers’ – subadults’— “tendencies to explore, fall over, off and out 15
of things” (Currey, 2013). Indeed, it has been established that their bone mechanical properties 16
are different (Berteau et al., 2015, 2014; Bonjour et al., 1994; Burr, 1985; Currey, 2013, 1979; 17
Currey and Butler, 1975; Kontulainen et al., 2007) and that might come from both genetic and 18
environmental factors (Saito and Marumo, 2010). Furthermore, because the mechanical demand 19
on children’s bones is higher than in adults, it could be suggested that it is important for them to 20
have a higher macroscopic toughness and stress-dissipation capacity of bones, rather than 21
macroscopic stiffness (Currey, 2013; Irwin and Mertz, 1997). 22
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Both immature (i.e. children) and mature (i.e. adults) bone tissues are composed mainly 1
of an organic matrix of collagen (i.e. tropocollagen molecule — TC) with minerals (i.e. 2
carbonated apatite nanoplatelets — cAp) and water. In connective tissues, such as bone and skin, 3
TCs assemble into collagen fibrils and are stabilized by several posttranslational modifications 4
that allow the formation of intermolecular and interfibrillar collagen cross-links (Figure. 1a-b) 5
(Bala and Seeman, 2015; Eyre and Wu, 2005; Viguet-Carrin et al., 2006b). The two main kind of 6
collagen cross-links depicted are enzymatic and non-enzymatic. Enzymatic collagen cross-links 7
form intermolecular covalent liaisons between specific amino acids of tropocollagen helices to 8
stabilize collagen fibrils (Eyre and Wu, 2005; Fratzl et al., 2004; McNerny et al., 2014; Reznikov 9
et al., 2016; M Saito and Marumo, 2010). They come from a physiological enzymatic pathway 10
where the initial immature form links two collagen molecules together (i.e. hydroxylysino-11
norleucine (HLNL) and dihydroxylysino-norleucine (DHLNL)) (Figure. 1c). With time, 12
immature enzymatic collagen cross-links further react with another collagen molecule to mature 13
into a trivalent form (i.e. pyridinoline (PYD) and deoxypyridinoline (DPD)) (Figure. 1c). This 14
conversion can be quantified as enzymatic collagen cross-links maturity which is defined by the 15
ratio of trivalent (i.e. mature) and divalent (i.e. immature) cross-links (Berteau et al., 2015; 16
McNerny et al., 2014; Saito et al., 2006; Vetter et al., 2009). Enzymatic collagen cross-links can 17
only form in few very specific locations of the terminal domains of the collagen molecule 18
yielding a finite number of possible enzymatic collagen cross-links formation (Snedeker and 19
Gautieri, 2014) and their density correspond to the amount of intermolecular covalent liaisons 20
per mol. of collagen formed during this process. The chemical reactions leading to the formation 21
of mature enzymatic collagen cross-links is a non-reversible continuous process (Eyre and Wu, 22
2005; Eyre, 1987; Knott and Bailey, 1998; M Saito and Marumo, 2010; Viguet-Carrin et al., 23
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2006a), and effectively turns the individual tropocollagen molecules into a large interconnected 1
polymer structure. Non-enzymatic collagen cross-links come from Glycation process and are 2
depicted as Advanced Glycation End-products (AGEs). They are associated with aging or 3
pathological conditions (diabetes) and impair collagen matrix normal function (Bailey et al., 4
1998; Gautieri et al., 2014; Bailey, 2001). They can form in multiple locations along the length 5
of the collagen and their density can be significantly larger that physiological enzymatic collagen 6
cross-links (Gautieri et al., 2014; Reznikov et al., 2016). Their positioning occurs randomly 7
compared to enzymatic collagen cross-links (Viguet-Carrin et al., 2008, 2006b), they accumulate 8
with time where tissue turnover is slow (Avery and Bailey, 2006). Due to children’s high bone 9
turnover, AGEs are present in very few quantities in children’s bone (Berteau et al., 2015). 10
On one hand, TCs are mainly stabilized by intermolecular covalent liaisons from 11
enzymatic collagen cross-links (Bala and Seeman, 2015) to build a soft interconnected matrix (M 12
Saito and Marumo, 2010; S. Viguet-Carrin et al., 2010). On the other hand, the mineral phase is 13
made of several cAp that nucleate inside the collagen matrix and link with TC (Bala et al., 2013; 14
Follet et al., 2004; Fuchs et al., 2008) by several intermolecular forces (Dubey and Tomar, 15
2009), such as hydrogen or ionic bonds, to reinforce the soft matrix. Although enzymatic 16
collagen cross-links, TC-cAp interface and water molecules have been shown to be determinants 17
of the mechanical properties of bone; results are dependent on species, age, and testing method, 18
making it difficult to understand their specific contributions. Indeed, experimental results on 19
children’s bone mechanical properties are very diverse (Berteau et al., 2015, 2014; Currey, 2003; 20
Currey and Butler, 1975; Lefèvre et al., 2015; Öhman et al., 2011) and there is still a gap of 21
knowledge about the contribution of each bone element to children’s bone mechanical behavior. 22
In children population, pathologies affecting collagen such as lathyrism (an alteration of 23
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enzymatic collagen cross-links that does not affect the mineral (Paschalis et al., 2011)), Menkes 1
disease (a deficient activity of lysyl-oxidase that causes defective in enzymatic collagen cross-2
linking (Kanumakala et al., 2002)) and osteogenesis imperfecta (an alteration of collagen 3
structure and enzymatic collagen cross-links that seem to be regulated independently to mineral 4
crystallinity (Vetter et al., 2009)), impact bone biomechanics and leads to pathological fractures. 5
Therefore, understanding bone enzymatic collagen cross-links in children’s bone is pivotal to 6
improve both current therapies and diagnosis in children population affected by enzymatic 7
collagen cross-links related bone pathologies. 8
Although previous results indicate that enzymatic collagen cross-links density in children 9
bone is higher than in adult bone while enzymatic collagen cross-links maturity is lower (Berteau 10
et al., 2015; M Saito and Marumo, 2010), the respective contribution of enzymatic collagen 11
cross-links density and maturity to bone deformation remains unclear in the children population. 12
Our previous ex vivo mechanical tests of human bone samples have shown that enzymatic 13
collagen cross-links maturity negatively correlates plastic energy dissipated before bone fracture 14
at the macroscopic level. Our hypothesis is that in silico mechanical tests of collagen fibril –built 15
from the data of the human bone samples previously tested— will show that enzymatic collagen 16
cross-links maturity correlates with plastic energy dissipated before collagen fibril fracture. 17
Furthermore, we anticipate that the evolution of both enzymatic collagen cross-links density and 18
maturity is a significant contributor to collagen fibril mechanical behavior. To test our 19
hypothesis, we have built 22 computational models from a mesoscale coarse-grained model of 20
collagen fibrils (Depalle et al., 2015) created using sample-specific enzymatic collagen cross-21
links data ((HLNL+DHLNL) and (PYD+DPD)) taken from biochemical analysis of bone 22
samples of children and adults donors (Berteau et al., 2015). Collagen fibril mechanical 23
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properties (Modulus of Elasticity (E), ultimate and yield stress (σu, σy), strain for ultimate and
1
yield stress (εσu, εy) point elastic, plastic and total work (We, Wp and Wtot)) have been obtained
2
from computational tensile test to establish the link between collagen fibril elastic and plastic 3
deformation and collagen fibril composition. 4
5
2. Materials and methods 6
2.1 Biochemical characterization 7
A total of 22 parallelepiped cortical bone samples (children samples n=14 and adult samples 8
n=8) were obtained from fibula bones taken from 10 donors (7 children, ages = 11.6 ± 4.7 years 9
and 3 adults, ages = 74.3 ± 9.9 years). The samples were then prepared to perform biochemical 10
analysis to quantify the amounts of immature (HLNL +DHLNL) and mature (PYD+DPD) 11
collagen crosslinks. Details of experimental characterization can be found in our previous study 12
(Berteau et al., 2015). 13
2.2 Molecular model 14
A geometrically accurate mesoscale molecular model of a collagen fibril has been used in this 15
study, in which a bead-spring model of a single tropocollagen helix has been replicated to form 16
the collagen fibril (MATLAB r2014a, Mathworks Inc., Natick, MA, USA) (Depalle et al., 2015) 17
(Figure 1). Both immature and mature enzymatic collagen cross-links are introduced to the 18
model. Sample-specific models are created in which both enzymatic collagen cross-links density 19
and maturity are tailored to the biochemical analysis performed on bone samples. Following this 20
protocol, 22 fibrils have been created to represent the 22 bone samples previously described. 21
2.3 Simulation parameters and data analysis 22
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Numerical mechanical testing has been performed according to the protocol defined by Depalle 1
et al. (2015). The coarse-grained models of single collagen fibrils have been used to simulate a 2
tensile test until fracture at a constant loading velocity of 1 m/s. All the simulations have been 3
performed using the molecular dynamic code LAMMPS ((Large-scale Atomic/Molecular 4
Massively Parallel Simulator) (Plimpton, 1995) in a canonical ensemble with constant number of 5
particles (N), constant volume (V) and constant temperature (T) in the system (NVT ensemble) 6
with a temperature set to 300°K. The stress-strain curves computed from the simulations have 7
been analyzed according to standard for bone studies (Ritchie et al., 2008) to obtain modulus of 8
elasticity (E), ultimate and yield stress (σu, σy), strain at ultimate and yield stress (εσu and εσy)
9
elastic work (We), plastic work (Wp), and total work to failure (Wtot) which correspond to in silico
10
(i.e. numerical) energies dissipated before fracture. Failure was set as being the point of σu for
11
each individual fibril. To calculate We and Wp, the yield point (y) is obtained by using the 2% 12
offset method (Turner and Burr, 2001). We is obtained by measuring the area under the curve
13
from the beginning until εσy , and Wp from εσy until failure of the fibril. Wtot is the sum of We and
14
Wp. The mechanical analysis has been performed using a custom R script (R Development Core
15
Team, 2015). The raw data up to the failure point have been fitted to a fifth-order polynomial to 16
minimize the simulation noise when computing the yield points. In the analysis, the cross-linking 17
state has been analyzed by looking at the number of covalent liaisons per mole of collagen 18
formed during the enzymatic process. A divalent cross-link forms one intermolecular covalent 19
liaison between two collagen molecules and a trivalent cross-link links three molecules with two 20
intermolecular covalent liaisons. Enzymatic collagen cross-links maturity is quantified by the 21
collagen cross-link ratio which is the quotient of the quantity of trivalent (i.e. mature) collagen 22
cross-links divided by the quantity of divalent (i.e. immature) collagen cross-links for the same 23
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collagen fibril. We define a covalent liaison by a direct link between two molecules created by a 1
chain of covalently bonded atoms from an enzymatic cross-link. The quantification of the 2
amount of intermolecular covalent liaisons combine information about both the density and the 3
maturity of the cross-links. 4
2.4 Statistical analysis 5
Statistical analyses have been performed with SPSS (Version 11, IBM, Armonk, NY). Normal 6
distribution has been assessed with Shapiro-Wilk test; Pearson correlation has been performed in 7
the event of normal distribution, and Spearman correlation in the event of non-normal 8
distribution. Variance has been tested with Levene test. Differences between groups have been 9
evaluated with Student’s t-test for individual samples in case of normal distribution and with a 10
Welch correction in case of non-equal variance, Mann-Whitney test have been performed in case 11
of non-normal distribution. For all statistical tests, significance has been set at α = 5%. 12
13
3. Results 14
Two representative stress-strain curves of a child (15-year-old) and an adult (75-year-old) 15
are shown in Figure 2. The child fibril exhibits higher maximum stress and yield-point strain 16
than the adult fibril. The mechanical properties computed from the stress-strain curves are 17
summarized in Table 1 and all of them are displayed in Supplemental Table 1. For all numerical 18
models of collagen fibrils, collagen cross-links ratio and density (Supplemental Table 1) are 19
within 5% of the corresponding experimental values (Berteau et al., 2015). Level of significance 20
of parametric and non-parametric correlations are reported on Supplemental Table 2, and linear 21
coefficient and Spearman’s rho are reported accordingly. 22
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Comparing the average collagen fibril mechanical properties of children and adult 1
samples, We for collagen fibrils in the children group is significantly higher when compared to
2
the adult group (T-test, p=0.001). Similarly, E is significantly higher in the children’s group than 3
in the adult’s group (Mann Whitney test, p=0.02) (Figure 4). No difference was found for Wp, σu 4
and σy. Regarding the evolution of the mechanical properties through lifetime, we also found a 5
monotonically decreasing relationship between age and We (Spearman’s ρ =-0.51, p=0.015) 6
(Figure 3). More precisely a monotonically decreasing relationship has been found between age 7
and We for the fibrils from the adult’s group (Spearman’s ρ =0.71, p=0.045) but such 8
relationship has not been found in the children’s group. 9
As depicted in Table 1 for all collagen fibrils (n=22), our results show several significant 10
parametric relationships between both collagen cross-links ratio and intermolecular covalent 11
liaisons, and mechanical parameters related to elasticity. More precisely, for collagen fibril 12
related to the children population (n=14), our results show several significant parametric 13
relationships between divalent enzymatic collagen cross-links (DIV), covalent (COV) and 14
trivalent (TRI), and mechanical parameters related to elasticity such as y ,We. (Figure 4a) and E
15
(Figure 4c). However, for collagen fibril related to the adult population (n=8), our results show 16
several significant parametric relationships between divalent enzymatic collagen cross-links 17
(DIV), covalent (COV) and trivalent (TRI), and mechanical parameters such as σu, σy, εy, and
18
parameters related to toughness such as We , (Figure 4a)Wp and Wtot. (Figure 4b) with a high level
19
of R2 for all of these relationship (roughly 0.80). 20
We show a linear correlation between all fibril tested for We and intermolecular covalent
21
liaisons and collagen cross-links ratio (Supplemental Table 2) and also a distinct threshold 22
distinguishing between children and adults structure and mechanics: in children, most of the We
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values are above 60 MPa and, collagen cross-links ratio and intermolecular covalent liaisons are 1
above 2 and 1.75 respectively, while in adults, most of the We are below 60 MPa and, the
2
collagen cross-links ratio and intermolecular covalent liaisons below 2 and 1.75 respectively 3
(Figure. 2c,d). Thus, our results suggest that collagen fibril with a cross-link ratio above 2 have a 4
greater capacity for collagen fibril elastic deformation. 5
6
4. Discussion 7
In this work, we have used coarse-grained molecular modeling to investigate the link 8
between enzymatic collagen cross-links density and maturity, and fibrillar mechanical behavior 9
of bone collagen matrix. We first established a novel difference between children and adult bone 10
in the collagen fibril deformation. We show that in children, a high covalent liaisons number, 11
primarily formed by immature enzymatic cross-links, correlates mainly with elastic deformation 12
parameters (E, We, y) while in adults, despite the lower amount of covalent bond liaisons, 13
collagen fibrils which connected with stronger mature cross-links, correlates with energy 14
dissipation and toughness parameters (We, Wp, Wt, u). Our results show that the mechanical 15
response depends on the amount of both divalent and trivalent enzymatic collagen cross-links in 16
adults but only of divalent enzymatic collagen cross-links in children due to the low amount of 17
trivalent. As children bone contains large amounts of immature cross-links (high density) our 18
results show that a high number of interconnected molecules favor the elasticity of the collagen. 19
On the contrary, a lower connectivity but with stronger cross-links (more mature cross-links) as 20
observed in the adult population favors the plasticity of the collagen despite the global lower 21
cross-links density. 22
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However, the amount of intermolecular covalent liaisons is the best factor for predicting 1
collagen fibrils mechanics in both children and adults showing that the intermolecular 2
connectivity formed by cross-linking is the main feature providing high mechanical properties. 3
This suggests a continuous evolution of the mechanical properties of bone with age but more 4
data is necessary to confirm this trend. Our results also suggest a link between collagen fibril and 5
macroscopic elastic behavior in children bone under the influence of immature enzymatic 6
crosslinks by showing a parametric linear correlation between We and immature enzymatic 7
collagen cross-links at the collagen fibril scale in the children population similar to the one we 8
found at the macroscale in our previous study (Berteau et al., 2015). 9
While our results show that a cross-linked collagen fibril can reach about 30% 10
deformation (Figure 2) – which is consistent with previous experimental mechanical testing 11
(Svensson et al., 2013) – our results also show that We is dependent on the amount of
12
intermolecular covalent liaisons from enzymatic collagen cross-links and maturity, two factors 13
that are dependent on age. The high amount of immature enzymatic collagen cross-links in the 14
children group indicates that the matrix of the bone samples studied is composed predominantly 15
of newly synthesized collagen (Bailey, 2002). However, children’s collagen contains more 16
enzymatic collagen cross-links than adult collagen. More specifically, the number of 17
intermolecular covalent liaisons is larger in the children population, suggesting that the high 18
turnover in children’s bone sample is associated with a high enzymatic collagen cross-links 19
formation in order to maximize bone mechanical resistance. As a consequence, the results show 20
a clear threshold value of the collagen cross-links ratio and intermolecular covalent liaisons 21
between children and adults. Such structural difference could derive from a higher amount of 22
posttranslational modification that favors enzymatic collagen cross-links formation in children’s 23
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bone compared to adult’s bone. Then, at the collagen fibrils level, the difference of mechanical 1
behavior of the collagen fibrils between children and adults can be explained by both the density 2
and maturity of enzymatic collagen cross-links. The higher intermolecular connectivity in 3
children population allow the collagen fibrils to better sustain loads and then display a larger 4
elastic response than the adult population. Indeed, a collagen fibril can be considered like a 5
succession of springs connected both in series and in parallel. A minimum amount of cross-links 6
connected in series are necessary to insure the fibril integrity. Above this threshold, adding 7
interconnected molecules by cross-linking is equivalent to adding springs in parallel and 8
therefore increase the fibril’s stiffness. This explain why children collagen, which contains more 9
links, displays an increased stiffness compared to adult collagen. However, divalent cross-10
links are not as strong as trivalent cross-links and favor intermolecular sliding and 11
inhomogeneous deformation. This can explain the lack of link between cross-links density and 12
plastic deformation in children collagen. In the adult population, due to the lower amount of 13
intermolecular covalent liaisons, fewer molecules are interconnected explaining the lack of a 14
clear correlation with elastic properties. However since trivalent cross-links form strong liaison, 15
they minimize intermolecular sliding by connecting multiple molecules in one point. Therefore 16
collagen molecules are more likely to reach their plastic deformation regime simultaneously, 17
explaining the direct relationship between cross-linking and toughness (Wtot) in adults (Depalle et
18
al., 2015). This structural evolution of collagen could be a physiological response to the different 19
environmental challenges that children and adults’ skeletons are facing. In children, high 20
turnover leads to an incomplete enzymatic collagen cross-links conversion allowing for higher 21
toughness to account for larger risk of falls or injuries (green stick fractures) but at the expense 22
of a higher energetic cost. Similarly, in adults, as the risk of falls and fractures drops, the 23
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crosslink conversion rate could increase in order to make bone stronger and to allow for more 1
intense physical activities and to reduce the energetic cost associated with high turnover. 2
Although assessing differences in bone mechanical behavior between children and adults 3
has been a major research question for the last decade (Bachrach, 2007; Berteau et al., 2015, 4
2012; Farr et al., 2014; Jadhav and Swischuk, 2008; Lasaygues et al., 2012; Lefèvre et al., 2015; 5
Mehlman et al., 2012; Öhman et al., 2011; Walters, 2012), it is still difficult to define clear 6
trends regarding bone mechanical properties evolution across ages. During growth, mineral and 7
collagen phase mature simultaneously and this maturation process impacts bone mechanical 8
behavior (Gamsjaeger et al., 2014, 2010; M Saito and Marumo, 2010). For instance, using 9
samples extracted from the top part of the femur diaphysis (children aged from 4 to 15 and adults 10
from 22 to 61), Öhman and colleagues have shown a lower ex vivo cortical strength and stiffness 11
in children compared to adults and both depending on ash density (Öhman et al., 2011). 12
Although mineral is likely to take part in the elastic deformation regime, the contribution of 13
collagen to elasticity has been poorly described in the children population. Another study of 14
Currey (Currey, 1979), using samples extracted from the mid-shaft of the femur (age range: 2 to 15
48 years old), observed that the bone specimens taken from children were weaker and less stiff 16
(lower E) than those taken from adults, and also that they deflected more and absorbed more 17
energy, without statistical evaluation. However in Currey’s study, We was not significantly
18
different between children and elderly adults bone sample supporting our previous results about 19
bone elasticity (Berteau et al., 2014). With these new results, we present a difference in the 20
collagen fibril We and E between the collagen phase of children and adult bone samples. This is
21
in contradiction with the theoretical optimization hypothesis of stiffer bones in adults compared 22
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to children, which is currently used in computational models (Irwin and Mertz, 1997). The 1
development of newer approaches for modeling children bones is therefore necessary. 2
Like fibula, most of the bones have varying enzymatic collagen cross-links maturity 3
ratios across ages (Saito et al., 2006b; M Saito and Marumo, 2010). Furthermore, children 4
population presents a very low level of advanced glycation end products (Berteau et al., 2015). 5
Then, our results establish for the first time a significant contribution of collagen maturity and 6
density to collagen fibril elastic deformation of collagen across the lifetime (i.e. 5 - 96 year age 7
range). Furthermore, our results show that We is on average two times higher in children’s than 8
in adults’ collagen fibril models (Figure 4) and that 43% and 63% of the variance of We can be
9
explained by the variance of collagen cross-links ratio and intermolecular covalent liaisons, 10
respectively. When we separated adults and children, our results show that the variance of We
11
remains explained by intermolecular covalent liaisons at 91% for adults and at 29 % for children. 12
However, collagen cross-links ratio does not explain the variance of We neither for adults nor for
13
children. Moreover, while 66 % and 40% of the variance of E is explained by intermolecular 14
covalent liaisons and collagen cross-links ratio for all fibril tested, respectively; our results show 15
that the variance of E is solely explained in the children population sub group at 48% by 16
intermolecular covalent liaisons. By comparing these new results to our previous work (Berteau 17
et al., 2015), our study shows that the number of intermolecular covalent liaisons created during 18
the process of collagen fibril assembly is a key factor to understand the relationship between 19
enzymatic cross-linking and mechanical properties. Furthermore, while collagen cross-links ratio 20
is more and more investigated as a marker of bone mechanical behavior by using Raman or 21
Infrared Spectroscopy (Farlay et al., 2011; Paschalis et al., 2015, 2001), our results suggest that 22
4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 15
intermolecular covalent liaisons could be a better predictor regarding modulus of elasticity in 1
children population and toughness in adult population. 2
Here, no significant direct relationship between the present collagen fibril scale 3
mechanics and the macroscale mechanical properties measured in our previous study (Berteau et 4
al., 2015) have been depicted. However, we found a similar parametric linear correlation 5
between We and immature enzymatic collagen cross-links in the children population at both
6
length scales. Among the possible reasons for the absence of direct relationship between the 7
present collagen fibril scale mechanics and the macroscale mechanical properties measured in 8
our previous study is that the loading modes studied are different (i.e. in silico tensile loading 9
and ex vivo three-point bending). Also, while we focused on studying the collagen enzymatic 10
collagen cross-links maturity in this study, other components of cortical bone, such as mineral 11
content, hydration and hierarchical structure, are likely to play an important part in the 12
mechanical behavior of the tissue and should be considered in future development (Bala et al., 13
2011; Burr, 1985; Currey and Butler, 1975; Keller, 1994; McCalden et al., 1993; Zhu et al., 14
1994). Furthermore, because bone is known to be a hierarchical and heterogeneous material, a 15
direct relationship between collagen fibril scale and macroscale properties is unlikely to be 16
established (Reznikov et al., 2014). Additionally, other numerical simulation studies on 17
children’s bone mechanical properties mainly focus on mineral content (Irwin and Mertz, 1997) 18
and they also fail when results are compared to biomechanical tests (Kent et al., 2012, 2009; 19
Maltese et al., 2010). Therefore, further analyses of the interplay between bone constituents are 20
necessary. Finally, the bone samples we used cover a relatively short age range for both children 21
and adults, and next efforts should concentrate in obtaining samples covering the gap region (16 22
to 66 years old). 23
4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 16
The specificity of our collagen fibril molecular model is that the enzymatic collagen 1
links maturity and density can be modified to create fibrils with individual specific cross-2
linking compositions. In the molecular model, each collagen molecule presents two enzymatic 3
collagen links in its C-terminal and N-terminal domains, which follows the usual cross-4
linking pattern (Eyre et al., 2008; Hanson and Eyre, 1996; Mcnerny et al., 2015). The stochastic 5
nature of the fibrils creation algorithm implies that a 50% cross-linked fibril will have, on 6
average, one cross-link created per collagen molecule (Depalle et al., 2015). However, enzymatic 7
collagen cross-links distribution might not be equiproportional at each end of the collagen 8
molecule which could affect the fibrillar mechanical response (Hanson and Eyre, 1996). 9
Furthermore, each molecular model has been built from experimental densities that represent an 10
average value for the whole sample. Thus, since enzymatic collagen cross-links chemistry plays 11
an important role in bone mechanics (Mcnerny et al., 2015), introducing cross-link site-12
specificity and heterogeneities of density to the molecular model is necessary to investigate the 13
multiscale link between mechanical properties. 14
Additionally, our results are for collagen fibrils that sustain loads in tension. In the daily 15
life, loads in tension can be found in activities that involves hanging (pull-ups, climbing) or 16
throwing (disk, hammer), and also in activities that involves long bones because they act as 17
levers and are loaded in bending— combination of compression and tension— such as racket 18
sports. As many orthopedics injuries in children are related to sport practice, our findings add to 19
our global understanding of the mechanical properties of children bone and then might improve 20
our strategy to prevent bone fracture in children population. The present results are also 21
fundamental to understand the physiological and pathological phenomena occurring in aging. By 22
better understanding how bone is physiologically evolving with aging, development of better 23
4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 17
targeted therapies will be possible. While the link between enzymatic collagen cross-links and 1
macroscopic mechanical behavior of bone tissue has been broadly established (Bailey, 2001; 2
Banse et al., 2002; Currey, 2003; Depalle et al., 2015; Isaksson et al., 2010; McNerny et al., 3
2014; Saito et al., 2006; M Saito and Marumo, 2010; Stéphanie Viguet-Carrin et al., 2010), there 4
is still no means for pharmaceutical interventions to alter/repair enzymatic collagen cross-links 5
for children with bone pathologies. Indeed, preventive and therapeutic strategies for skeletal 6
diseases in children population rely on macroscopic mechanical properties standards that have 7
been established from an interpolation of experimental newborn bone values to experimental 8
adult bone values (Irwin and Mertz, 1997). The thesis of this interpolation is an incremental 9
increase of the stiffness marked by a step-wise mineralization of the collagen matrix. It is a direct 10
relationship between bone mineral density and modulus of elasticity. However, the validity of 11
this hypothesis shows limitations when pediatric numerical simulations are compared with 12
biomechanical tests (Kent et al., 2012, 2009; Maltese et al., 2010). In our previous publication 13
(Berteau et al., 2015), we established a parametric link between immature enzymatic collagen 14
cross-links and macroscopic ex vivo We in the same children group. Here, our in-silico data goes
15
beyond our experimental conclusion and show that 30% of the variance of collagen elastic 16
energy is explained by the amount of immature enzymatic collagen cross-links and 62% by the 17
amount of intermolecular covalent bonds formed by cross-linking, thus strongly suggesting that 18
collagen maturation process is a major determinant of children’s bone elasticity. 19
The higher amount of divalent crosslinks in children compared to adult might be 20
explained by a faster remodeling rate of children’s bone tissue than in adults. Indeed, when the 21
remodeling rate is high there is not enough time for enzymatic collagen crosslinks to reach full 22
maturity before the destruction of the bone occurs (i.e. higher amount of trivalent cross links than 23
4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 18
divalent). Then, children bone matrix is mainly composed of newly remodeled bone with a high 1
amount of divalent crosslink compared to trivalent crosslinks. While the high amount of divalent 2
crosslinks in children allow the bone to better sustain falls and not break, the remodeling rate of 3
the bone is also dependent on the mechanical action on the osteocytes that activate osteoclasts – 4
destruction of the bone matrix. Then, between the fact that children's bones have to sustain more 5
falls and that activates the remodeling process, and children’s bone have more divalent crosslinks 6
that allow them to sustain more falls by preventing the bone to break, it is not clear which of the 7
two events should be considered the cause and which should be considered the effect. Whatever 8
the explanation, we believe that enzymatic collagen cross-links could be enhanced using 9
mechanical loading by means for musculoskeletal rehabilitation. Indeed, hyper- and micro-10
gravity, weight-bearing, and low intensity pulsed ultrasound (LIPUS) have shown distinct 11
biological effects on bone collagen cross-links formation in vitro and in vivo (Mitsuru Saito and 12
Marumo, 2010). Furthermore, we believe that diagnostic tools that detect collagen cross-links ex 13
vivo – Raman spectroscopy (Paschalis et al., 2001) and biochemistry analysis (Gineyts et al.,
14
2010; M Saito and Marumo, 2010) might be key to improve bone pathologies diagnosis in 15 children. 16 17 Conclusion 18
We established a novel difference between children and adult bone in the elastic 19
deformation of the collagen phase. Across lifetime and in parallel to the evolution of mineral 20
density, our study indicates that the intermolecular connectivity in collagen induced by 21
enzymatic cross-linking is a potential marker of elastic deformation in bone. This intermolecular 22
connectivity is directly dependent on both enzymatic collagen cross-links maturity and density. 23
4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 19
Furthermore, and for the first time, we established a link between collagen fibril and 1
macroscopic mechanical behavior by showing a similar parametric linear correlation between We
2
and immature collagen cross-links in the children population at two different bone scales. Our 3
results extend the key role of collagen maturity in bone mechanical behavior to children’s bone 4
elasticity and then yield to new approaches for improving preventive and therapeutic strategies 5
regarding skeletal diseases in children population. 6
7
Compliance with Ethical Standards: 8
Funding: BD is supported by the Wellcome Trust grant WT097347MA. JPB, AD, IF are 9
supported by CSI startup funds, PSC-CUNY Cycle 46 and CSI Provost Grants. Simulation have 10
been performed under Penzias HPCC; CUNY HPCC is operated by the College of Staten Island 11
and funded, in part, by grants from the City of New York, State of New York, CUNY Research 12
Foundation, and National Science Foundation Grants CNS-0958379, CNS-0855217 and ACI 13
1126113. Additional support from NIH U01 (TUFTS-5U01EB014976 and WUSTL-14
5U01EB016422) is acknowledged by MJB and BD. Conflict of Interest: The authors declare 15
that they have no conflict of interest. 16
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43 44
4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 25 Captions 1
Figure. 1 (a) Hierarchical structure of a collagen fibril. (b) Representative section of the 2
molecular model of ca collagen fibril. The characteristic gap and overlap region are clearly 3
visible. (c) Representative forms of both divalent and trivalent cross-links (top) and 4
representation in the molecular model (bottom). Over time, immature divalent cross-links will 5
evolve into the mature trivalent form. 6
7
Figure. 2 Two representative stress-strain curves of a child (15-year-old) and an adult (75-year-8
old). The child fibril exhibits higher maximum stress and yield-point strain than the adult fibril 9
10
Figure. 3 Children’s and adults’ data combined (all collagen fibrils, n=22) present a dissimilar 11
monotonic relationship with age (Spearman’s ρ =-0.51, p=0.015) 12
13
Figure. 4 Positive parametric linear relationship between numerical We and covalent
14
intermolecular connections (COV) for children’s and adults’ data separated (a), Positive 15
parametric linear relationship between numerical Wtot and covalent intermolecular connections
16
(COV) only for adults’ data (b), positive parametric linear relationship between numerical E and 17
covalent intermolecular connections (COV) only for children’s data (c) and positive parametric 18
linear relationship between numerical We and cross links ratio (CXLR) for children’s and adults’
19
data combined (d) 20
4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 26
Figure. 5 Mean of collagen fibrils’ We in children’s group is significantly higher when 1
compared to adults’ group (T-test, p=0.001); similarly, Modulus of Elasticity is significantly 2
higher in children’s group than in adults (Mann Whitney test, p=0.02) 3
4
Table 1 Collagen fibril mechanical properties (Modulus of Elasticity (E), maximum and yield 5
stress (σmax σyield) and elastic and plastic (We and Wp)) obtained from computational tensile 6
test of 22 fibrils that have been created to represent 22 parallelepiped cortical bone samples 7
8
Supplemental Table 1 Summary of the cross-links data measured experimentally for each bone 9
sample and corresponding data used in the molecular modeling models. The mechanical 10
properties computed from the models are also reported for each fibrils. 11
12
Supplemental Table 2 correlation coefficients between cross-links structural parameters and the 13
mechanical properties computed from the collagen fibrils molecular models for all samples, the 14
children group and, the adult group. 15