Hierarchical structure and nanomechanics of collagen microfibrils from the atomistic scale up.

Abstract

Collagen constitutes one-third of the human proteome, providing mechanical stability, elasticity, and strength to organisms and is the prime construction material in biology. Collagen is also the dominating material in the extracellular matrix and its stiffness controls cell differentiation, growth, and pathology. However, the origin of the unique mechanical properties of collagenous tissues, and in particular its stiffness, extensibility, and nonlinear mechanical response at large deformation, remains unknown. By using X-ray diffraction data of a collagen fibril (Orgel, J. P. R. O. et al. Proc. Natl. Acad. Sci. 2006, 103, 9001) here we present an experimentally validated model of the nanomechanics of a collagen microfibril that incorporates the full biochemical details of the amino acid sequence of constituting molecules and the nanoscale molecular arrangement. We demonstrate by direct mechanical testing that hydrated (wet) collagen microfibrils feature a Young's modulus of ≈300 MPa at small, and ≈1.2 GPa at larger deformation in excess of 10% strain, which is in excellent agreement with experimental data. We find that dehydrated (dry) collagen microfibrils show a significantly increased Young's modulus of ≈1.8-2.25 GPa, which is in agreement with experimental measurements and owing to tighter molecular packing. Our results show that the unique mechanical properties of collagen microfibrils arise due to their hierarchical structure at the nanoscale, where key deformation mechanisms are straightening of twisted triple-helical molecules at small strains, followed by axial stretching and eventual molecular uncoiling. The establishment of a model of hierarchical deformation mechanisms explains the striking difference of the elastic modulus of collagen fibrils compared with single molecules, which is found in the range of 4.8 ± 2 GPa, or ≈10-20 times greater. We find that collagen molecules alone are not capable of providing the broad range of mechanical functionality required for physiological function of collagenous tissues. Rather, the existence of an array of deformation mechanisms, derived from the hierarchical makeup of the material, is critical to the material's ability to confer key mechanical properties, specifically large extensibility, strain hardening, and toughness, despite the limitation that collagenous materials are constructed from only few distinct amino acids. The atomistic model of collagen microfibril mechanics now enables the bottom-up elucidation of structure-property relationships in a broader class of collagen materials (e.g., tendon, bone, cornea), including studies of genetic disease where the incorporation of biochemical details is essential. The availability of a molecular-based model of collagen tissues may eventually result in novel nanomedicine approaches to develop treatments for a broad class of collagen diseases and the design of de novo biomaterials for regenerative medicine.

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rXXXX American Chemical Society
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pubs.acs.org/NanoLett
Hierarchical Structure and Nanomechanics of Collagen Microfibrils
from the Atomistic Scale Up
Alfonso Gautieri,†,‡Simone Vesentini,‡Alberto Redaelli,‡and Markus J. Buehler*,†,§,)
†Laboratory for Atomistic and Molecular Mechanics, Department of Civil and Environmental Engineering, Massachusetts Institute
of Technology, 77 Massachusetts Avenue Room 1-235A&B, Cambridge, Massachusetts 02139, United States
‡Department of Bioengineering, Politecnico di Milano, P.zza Leonardo da Vinci 32, 20133, Milano, Italy
§Center for Materials Science and Engineering,Center for Computational Engineering, Massachusetts Institute of Technology, 77
Massachusetts Avenue, Cambridge, Massachusetts 02139, United States
)
ABSTRACT: Collagen constitutes one-third of the human
proteome, providing mechanical stability, elasticity, and
strength to organisms and is the prime construction material
in biology. Collagen is also the dominating material in the
extracellular matrix and its stiffness controls cell differentia-
tion,growth,andpathology.However,theoriginoftheunique
mechanical properties of collagenous tissues, and in particular
itsstiffness,extensibility,andnonlinearmechanicalresponseatlargedeformation,remainsunknown.ByusingX-raydiffractiondata
ofacollagenfibril(Orgel,J.P.R.O.etal.Proc.Natl.Acad.Sci.2006,103,9001)herewepresentanexperimentallyvalidatedmodelof
the nanomechanics of a collagen microfibril that incorporates the full biochemical details of the amino acid sequence of
constituting molecules and the nanoscale molecular arrangement. We demonstrate by direct mechanical testing that hydrated
(wet) collagen microfibrils feature a Young's modulus of ≈300 MPa at small, and ≈1.2 GPa at larger deformation in excess of
10% strain, which is in excellent agreement with experimental data. We find that dehydrated (dry) collagen microfibrils show
a significantly increased Young's modulus of ≈1.8-2.25 GPa, which is in agreement with experimental measurements and
owing to tighter molecular packing. Our results show that the unique mechanical properties of collagen microfibrils arise due to
their hierarchical structure at the nanoscale, where key deformation mechanisms are straightening of twisted triple-helical
molecules at small strains, followed by axial stretching and eventual molecular uncoiling. The establishment of a model
of hierarchical deformation mechanisms explains the striking difference of the elastic modulus of collagen fibrils compared
with single molecules, which is found in the range of 4.8 ( 2 GPa, or ≈10-20 times greater. We find that collagen molecules
alone are not capable of providing the broad range of mechanical functionality required for physiological function of collagenous
tissues. Rather, the existence of an array of deformation mechanisms, derived from the hierarchical makeup of the material, is
critical to the material's ability to confer key mechanical properties, specifically large extensibility, strain hardening, and
toughness, despite the limitation that collagenous materials are constructed from only few distinct amino acids. The atomistic
modelofcollagenmicrofibrilmechanicsnowenablesthebottom-upelucidationofstructure-propertyrelationshipsinabroader
class of collagen materials (e.g., tendon, bone, cornea), including studies of genetic disease where the incorporation of
biochemical details is essential. The availability of a molecular-based model of collagen tissues may eventually result in novel
nanomedicine approaches to develop treatments for a broad class of collagen diseases and the design of de novo biomaterials
for regenerative medicine.
KEYWORDS: Collagen, mechanical properties, deformation, molecular simulation, nanomechanics, materiomics
C
mechanical stability, elasticity, and strength to connective tissues
such as tendons, ligaments, and bone, as well as the extracellular
matrix (ECM).1-3Yet, we understand relatively little about how
collagen molecules combine to form larger-scale structural ele-
ments such as fibrils and fibers and how they provide crucial
mechanical properties to organisms. It is known that virtually all
collagen-based tissues are organized into hierarchical structures,
where the lowest hierarchical level consists of triple helical
collagen molecules (Figure 1).2-9Collagen fibrils consist of
high-aspect-ratio polypeptides, tropocollagen molecules, with a
ollagen molecules represent the most abundant construc-
tion material in the human body, where they provide
length of ≈300 nm and a diameter of about 1.5 nm, which are
arranged in a staggered configuration. This structure creates an
observable periodicity known as the D-band, where D = 67 nm.
The collagen molecule's length is not a multiple of D, where in
terms of D the collagen molecule measures 4.46 D. According to
the Hodge-Petruska model,10a structural model of collagen
fibrils, molecules in a fibril are deposited side by side and parallel
but staggered with respect to each other, where the molecular
Received:
Revised:
November 10, 2010
December 7, 2010

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axes are parallel to the fibril direction. A gap between two
consecutive collagen molecules is known as the “gap region”
and measures 0.54 D, or ≈36 nm.10Collagen fibrils have a
diameterof100-500nmandalengthuptothemillimeterrange
and are formed through the bundling of several microfibrils that
each contain clusters of five collagen molecules.11At the next
level of the hierarchy, multiple fibrils make up the collagen fiber,
formed with the aid of cross-linking macromolecules such as
proteoglycans. In bone, the organic collagen protein matrix is
stiffened via the inclusion of mineral hydroxyapatite crystals that
emerge from the gap regions.3,7,12,13
To determine how collagen-based structures confer mechan-
ical properties to tissues like skin, tendon, and bone and to
identify how cells interact with the ECM, the understanding of
the mechanics at different hierarchical levels and their interplay
from a biochemical and molecular level upward is essential. Earlier
work has demonstrated that mechanical strainis distributed over
distinct hierarchical levels (molecules, fibrils, fibers)14-16and
that collagen tissue stretching involves concurrent deformation
mechanisms, where the measured stiffnesses of the tissue at
differentscalesvariesvastly.Significanteffortshavebeenmadein
recent years focused on characterizing the mechanical properties
ofcollagenbyusingexperimental,computational,andtheoretical
approaches.Areviewofrecentworksaimedattheunderstanding
of the structure and mechanical properties of collagen-based
tissues is nicely summarized in recent contributions.3,17Earlier
workwasmostlyfocusedonthemacroscopic,overallmechanical
properties of collagen fibers and related tissues with several
efforts that elucidated the mechanics of hierarchical struc-
tures.3,12,14,18-21Other studies focused solely on the properties
of individual tropocollagen molecules without linking to the
larger scale materials response.22-25Most recently, experimental
reports focused on the mechanical properties of individual
collagen fibrils, which provided important insight into the Young's
modulus and their nonlinear deformation behavior.26-28However,
most of these studies did not yet incorporate molecular details
into their investigations. To the best of the authors' knowledge,
exceptionsarethepioneeringworksbySasakiandOdajima29andby
Fratzl et al.30By applying X-ray diffraction methods these
groups investigated the elongation mechanism of tendon
collagen on the basis of the hierarchical structure of the tissue
and including the arrangement of collagen molecules in the
tissue. These authors proposed models to describe how
collagen molecules in fibrils are elongated and rearranged
due to external force.30,31
Molecular modeling provides apowerful approach to comple-
ment experimental approaches and to describe the molecular
mechanics ofcollagenfromthebottomupandatmultiplescales.
Most studies, however, were based on ultrashort collagen-like
peptides obtained from X-ray crystallography.32-35The early
molecular simulation studies used these short collagen
molecules36-41that were typically limited to less than 10 nm
length or more than a factor of 30 smaller than actual molecules
found in collagen tissues. The resulting elastic modulus of these
short collagen peptides was found to be in the range of 4.8 ( 2
GPaandmuchgreaterthanthetypicalYoung'smodulimeasured
for macro-scale collagen tissues, yet in agreement with single mole-
cule studies22,23,42-44(Table 1). The direct study of larger
assemblies ofcollagenmolecules intomicrofibrilsandfiberswith
fullatomisticsimulationmethodshasremainedelusiveduetothe
lack of an appropriate atomistic description and the size of the
system. Some reports of molecular modeling of collagen micro-
fibrils are based on a two-dimensional coarse-grained model,
where collagen molecules are described in a mesoscale bead-
spring model.45,46While the bead-spring model showed key
features of the stress-strain behavior found in experiments, a
disagreement of the magnitude of the predicted modulus was
identified that could not be reconciled. Furthermore, earlier
bead-spring models retained little information of the primary
sequence, did not include a description of the three-dimensional
arrangement of collagen molecules and lacked the ability to deal
with explicit water solvent (i.e., a model that includes the
simulation of all water molecules based on their atomic
structure). These issues are, however, likely important for
collagen mechanics and must be incorporated in a rigorous
bottom-up tissue mechanics description that links genetics to
structure to mechanics. The need of defining the material
properties of collagenous tissues from the biochemistry level
upward is clearly demonstrated when considering the effect of
mutations in collagen, which can result in incorrectly assembled
collagen protein that cause a variety of severe and sometimes
deadly pathologies, such as Ehlers-Danlos syndrome, scurvy or
osteogenesis imperfecta (brittle bone disease).47
2.ResultsandDiscussion. Hereweuseanatomisticcollagen
microfibril model that includes full-length molecules with the
actual amino acid sequence defined by the human collagen gene
and that thus completely captures the biochemical features of
collagen molecules to describe the mechanical behavior at the
microfibril level (see Materials and Methods for details). To the
best of our knowledge, no such modeling of the mechanical
properties at this scale has been previously attempted. The basis
of our microfibril model is the recently reported structure of native
in situ collagen in rat tail tendon.6,8By employing crystallo-
graphic techniques in X-ray fiber diffraction experiments, Orgel
etal.8obtainedthepackingarrangementofcollagenmoleculesin
Figure 1. Hierarchical structure of collagen protein materials.1-9Each
collagen molecule is made of three peptide chains that form the ≈300
nm long triple helical collagen molecule. Collections of collagen
molecules aggregate both in lateral and longitudinal directions to form
fibrils. Fibrils in cornea are normally thin (≈30 nm) and uniform in
diameter, while tissues such as tendon contain a wide-ranging distribu-
tion of diameters (100-500 nm). Fibrils include tiny hydroxyapatite
crystals in bone tissue, which provide stiffness and compressive load
resistance. In tendons and ligaments, multiple fibrils make up collagen
fiber, formed with the aid of proteoglycans.

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a collagen microfibril, resulting in the three-dimensional geome-
try of collagen molecules including the N- and C-telopeptides.
On the basis of the data from X-ray diffraction experiments,
however, only the positions of the CRbackbone atoms in the
collagen microfibril are available, and as a result the model
reported in ref 8 did not yet include all atomistic details of the
supermolecular assembly in collagen fibrils. To develop a full
atomistic representation, we use a computational approach to
add all missing atoms including the side chains into the structure
and identify the most stable configuration by using the all-atom
CHARMM force field and a statistical structure identification
approach (see Materials and Methods). Since the backbone
structure is known, this homology modeling followed by ex-
tensivemolecularequilibrationprovidesareliableestimateofthe
structure of the side chains.
The resulting atomistic model features full ≈300 nm long
collagenmoleculesincludingthetelopeptidedomainsattachedat
the ends of each molecule, and incorporates the complete three-
dimensional arrangement of collagen molecules arranged in a
periodic unit cell (Figure 2a). The unit cell dimension in the
Z-axis corresponds to the length of the characteristic D-period
observedforcollagenfibrils.Thus,afulllengthcollagenmolecule
spans five periodic cells in the Z-axis direction. Figure 2b shows
the N-terminalportion of theoriginalcollagen molecule (in red)
with four periodic images represented in gray, illustrating how
the unit cell represents a model for the larger-scale molecular
assembly into collagen microfibrils. Since the model uses peri-
odic boundary conditions, it resembles infinitely large collagen
microfibrils in each dimension. The staggering of the molecules
along the molecular axis leads to the well-known D-banding
periodicity (Figure 2c), while the molecules are arranged in a
quasi-hexagonal pattern in the orthogonal direction where five
molecules formthe characteristic
(Figure 2d).8Within each periodic cell, collagen molecules
interdigitate with neighboring molecules to form a supertwisted
right-handed microfibril. The characteristic banded structure of
the equilibrated atomistic model of the collagen microfibril
emerges naturally due tothe three-dimensional structure of both
single molecules and their assembly in the longitudinal and axial
directions, and is found to be stable in our molecular model.
Figure 2e illustrates a D-period with five molecular strands that
form a collagen microfibril, showing the gap and overlap regions
that arise because one of the strands forming the microfibril is
shorter than the D-period itself. The obtained D-banding repro-
duces experimental microscopy images of collagen fibrils well,
owing to the fact that our molecular model is based on X-ray
diffraction data and stable after molecular equilibration48
(Figure 3a,b).
We first report an account of the difference of the structural
features of a fully equilibrated full-atomistic collagen microfibril
in both hydrated (wet) and dehydrated (dry) conditions. In our
study,thedehydratedcollagenmicrofibrilmodelisusedtoassess
the effect of hydration on the mechanical properties of collagen
fibrils, which has been shown experimentally to be an important
factor in defining structure and properties of collagenous
tissues. The equilibration of the hydrated collagen microfibril
microfibrilstructure
Table 1. Comparison of Young's Modulus of Collagen Molecule (Solvated) and Collagen Microfibril (Including Hydrated [Wet]
and Dehydrated [Dry] States) As Predicted from Experimental and Theoretical Analyses67,68

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(Figure 3c) leads to a density of ≈1.19 g/cm3, a value that is
halfway between the density of water and the density of
dehydrated collagen, which has been estimated at 1.34 g/
cm3.49A Ramachandran analysis of the solvated system
(Figure 3e, center) shows that the collagen microfibril lies in a
region of the diagram (ψ ≈ 150?, φ ≈ -75?) that is character-
istic of thepolyprolineII chainand thus ofcollagen-like peptides
(Figure 3e, left), in good agreement with experimental structural
studies.50Thedensityofthedehydrated(dry)collagenmicrofibril
(Figure 3d) reaches a larger density, with a value of ≈1.29 g/cm3.
A Ramachandran analysis of the dehydrated collagen micro-
fibril (Figure 3e, right) shows that it also lies in a region of the
diagram that is characteristic of collagen-like peptides (ψ ≈150?,
φ ≈-75?);however, abroaderrange ofdihedralangles isfound
Figure2. Atomisticmodelofthecollagenmicrofibril.Thefull-atomisticmodelofthecollagenmicrofibrilisgeneratedstartingfromtheinsitustructure
of the backbone geometry of full length collagen type I molecule as identified by X-ray diffraction and using the associated information on the naturally
occurring crystallographic unit cell (a ≈ 40.0 Å, b ≈ 27.0 Å, c ≈ 678 Å, R ≈ 89.2?, β ≈ 94.6?, γ ≈ 105.6?)8(PDB ID 3HR2). Panel a shows that
homology modeling is used to obtain the full-atom structure of the human collagen type I molecule. The collagen supramolecular model of the
microfibril is generated by the periodic repetition of the unit cell. Panel b shows a portion of the original collagen molecule in red, while four periodic
images of the molecule are represented in gray. The molecular packing topology obtained by the periodic repetition of the unit cell leads to the well-
knownD-bandingperiodicityseeninAFMimagesofcollagenmicrofibrilsasshowninpanelc(inredtheoriginalmolecule,inbluetheperiodicimages).
Panel d shows the quasi-hexagonal packing of collagen molecules, which interdigitates with neighboring molecules to form a supertwisted right-handed
microfibril as depicted in panel e. This image is obtained wrapping all collagen atoms (which spans several periodic units, see panel a) into a unit cell in
order to visualize the microfibril periodic unit.
Figure 3. Structural analysis and validation of atomistic collagen microfibril models. Comparison of the D-periodic banding observed for the full-
atomistic microfibril model (panel a) and experimentally with SEM techniques (panel b, reprinted with permission from ref 48 (Copyright 2001
National Academy of Sciences, U.S.A.). Panel c shows a detailed view of the equilibrated structure in proximity of the gap-overlap region, showing
collagen molecules (in red, plus two highlighted moleculesin blueand green) and water molecules(cyan). Panel d shows a snapshot of the gap-overlap
transitionregionfortheequilibrateddehydratedcollagenmicrofibril,whichrepresentsamuchdenserpackingofmolecules.Ramachandrandiagramfor
a short collagen like peptide (left, panel e) and for the hydrated full atomistic microfibril (center, panel e) and for the dehydrated collagen microfibril
(right, panel e), showing that the configuration is close to that of the polyproline II chain (ψ ≈ 150?, φ ≈ -75?, yellow dot) and thus close to the
expected configuration of a collagen molecule. The dehydrated microfibril shows a more disperse distribution of dihedral angles.

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indicating some level of molecular unfolding. This suggests that
the loss of water results in a loss of structure at the molecular
scale, indicating that water is indeed needed to keep the
characteristic configuration of collagen molecules in microfibrils.
This agrees with earlier work on collagen-like peptides at the
singlemolecule scale where a greater level of disorder and loss of
H-bonding was found in vacuum studies.36Overall, our model
shows good quantitative agreement with available experimental
structural data of collagen microfibrils, which confirms that the
molecular representation based on X-ray data is a good starting
point for the analysis of its mechanical properties.
With this structurally validated collagen microfibril model at
hand, we now test the mechanical properties of a hydrated and
dehydrated collagen microfibril by applying constant stress
boundary conditions along the fibril axis and monitoring the
resulting strain at equilibrium. We assess stresses in the range
from0to200MPa,leadingtothestress-strainbehaviorsshown
in Figure 4a. We find that hydrated collagen microfibrils feature
two distinct deformation regimes. In the small-strain regime
(<10%), the predicted Young's modulus is ≈300 MPa, while in
the large-strain regime (>10%) the microfibril shows a severely
increased tangent stiffness with a Young's modulus of ≈1.2 GPa.
Notably, the results of nanomechanical testing of hydrated
collagen microfibril are in good agreement with available experi-
mental results obtained for the small strain regime based on
various techniques such as X-ray diffraction,29atomic force
microscopy (AFM),9,27and the use of microelectro-mechanical
systems (MEMS).26,28,51Figure 4b-d and Table 1 present a
systematic comparison with a broad range of experimental data
basedondifferenttechniques.Itisnotedthatforthelarger-strain
regime there exists less experimental information and available
results tend to be more scattered. For example, recent work28
showed a relatively large variability of collagen fibril behaviors at
large deformation, which suggested either strain-hardening or
strain-softening depending on the fibril investigated.
A direct comparison of the mechanical properties of single
collagen molecules versus that of collagen microfibrils suggests
that the mechanical properties are strongly scale dependent.
Specifically, we find a severe change of the modulus when
comparing a single collagen molecule to a collagen fibril, as
shown in Figure 4b and Table 1. A direct numerical comparison
suggests a factor of 10-20 difference in the Young's modulus
from several gigapascals for a single molecule to a few hundred
megapascals for collagen microfibrils, presenting a striking
change of mechanical properties at different hierarchical levels.
Thisfindingagreeswellwithexperimentaldataasisconfirmedin
Table 1.
We now examine the mechanical properties of dehydrated
collagen fibrils to test the effect of water solvent on the collagen
mechanical properties at the fibril level, which allows us to
explore an effect that had earlier been investigated in experi-
mental AFM studies.27Our simulation results suggest that
dehydrated collagen microfibrils show an almost perfect linear
elastic behavior, albeit with a much greater Young's modulus of
Figure 4. Collagen microfibril stress-strain behavior, comparison with single molecule mechanics, and quantitative comparison with experimental
results. The mechanical properties of both hydrated and dehydrated collagen microfibrils are determined imposing an increasing mechanical stress
(negativepressure)alongthefibrilaxiswhilemaintainingthepressureontheotheraxesconstantat1bar.Mechanicaltestingyieldsafibrillarsmall-strain
Young'smodulusof≈300MPaandalarge-strainmodulusof≈1.2GPaforthehydratedmodel,whileanalmostlinearbehaviorandanelasticmodulusof
≈1.8 GPa (approaching 2 GPa for larger strains) is found for the dehydrated model (panel a). This finding suggests that the dehydrated collagen
microfibril tends to have a greater stiffness, a finding that is in agreement with experimental results (see Table 1). (Panel b) Direct comparison of the
Young'smodulusobtainedforsolvatedsinglemoleculesandmicrofibrils,featuringvariousexperimentalresultsandthepredictionsfromourmicrofibril
mechanics model. The calculated Young's modulus for the solvated collagen microfibril (green) results in very good agreement with experimental
findingsbasedonavariety oftechniquesincludingSAXS,AFM,andMEMStesting,whichyieldasmallstrainfibrilYoung'smodulusinthe rangeoffew
hundred megapascals. (Panel c) Direct comparison of stress-strain curves obtained in this work and those obtained with experimental techniques.
(Panel d) Young's modulus over strain (obtained from the gradient of stress-strain curves), comparing experiment and simulation for hydrated
microfibrils.

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≈1.8 GPa (approaching ≈2.25 GPa for larger strains), or a
striking factor of 6.75 larger than the modulus of hydrated
collagen microfibril. Notably, a similar ratio of the moduli in
dehydrated versus hydrated states has been observed in
experiment27whereamodulusratioof9betweenthedehydrated
versus hydrated states of the has been identified (see Table 1).
These findings point to the great importance of water at the
nanoscale for the mechanical properties of collagen microfibrils.
Our atomistic model enables us to observe atomistic and
molecular deformation mechanisms not directly accessible to
experimental techniques, and thereby to explain the molecular
origin of mechanical properties at different hierarchical levels,
magnitudes of strain, and under different solvent conditions. We
first investigate the molecular mechanisms during fibril stretch-
ing, and our studies are specifically aimed at elucidating the
mechanisms behind the two regimes observed in the stress-
strain curve (Figure 4a) and the changed mechanical properties
in hydrated and dehydrated states. For the hydrated case, the
small deformation the collagen molecules' end-to-end distance
increases linearly until the microfibril strain reaches 10%
(corresponding to ≈50 MPa stress), the strain at which the
microfibril stiffness increases drastically. Beyond this point the
molecular end-to-end still continues to increase but the slope of
curve is significantly lower (Figure 5a). This can be explained by
the fact that below 10% strain the collagen molecule is straigh-
tenedwithin the microfibril and therebyloses its kinked arrange-
ment, while beyond 10% strain the molecule itself is being
stretched, resulting in a larger mechanical resistance to deforma-
tion. The monitoring of the dihedral energy of the systems
confirms this hypothesis and shows that for strains larger than
10% the dihedral energy increases, which directly shows that the
molecule is being deformed (Figure 5b).
The increase in the gap to overlap ratio in the small-strain
regime (Figure 5c) suggests that the initial straightening is
concentrated in the gap regions where the molecular packing
density is lower and molecules are less organized with more
Figure 5. Molecular deformation mechanisms during stretching for hydrated and dehydrated collagen microfibril. The two regimes observed in the
hydrated microfibril stress-strain curve (showing a larger modulus for strains in excess of10%, corresponding to anapplied stress of ≈50 MPa) can be
explained by analyzing the behavior of single molecules during microfibril stretching. At small deformation, the collagen molecule end-to-end distance
increaseslinearlyuntilthefibrilstressreaches≈50MPa.Aroundthispoint,thecollagenreachesitscontourlength.Beyondthispoint,themolecularend-
to-end distance still increases but the slope of curve is distinctly smaller (blue, panel a). This is due to the fact that below ≈10% strain the collagen
molecule is straightened within the microfibril, while beyond this point the molecule is actually stretched, resulting in a larger resistance of the whole
microfibril.Theanalysisofthedihedralenergyofthesystemsshowninpanelbconfirmsthisobservation,showingthatforstresslargerthan50MPathe
dihedralenergyincreaseandthusthatthemoleculeisdeformed(blue,panelb).Themolecularstraighteningisconcentratedinthegapregionsasshown
bytheincreasesinthegap/overlapratiointhelow-strainregime(blue,panelc).Thissuggestsamicrofibrildeformationmechanisminwhichmechanical
load initially straightens collagen molecules, particularly kinks formed in the gap regions, leading to an increase in the gap-to-overlap ratio. For larger
loads, collagen triple helices undergo stretching resulting in larger microfibril stiffness (panel d). (Schematics of fibrils adapted from Fratzl et al.30and
reprinted with permission from Elsevier). In the dehydrated microfibril, the molecular end-to-end distance (red, panel a) increases linearly in the stress
range analyzed, while the dihedral energy decreases (red, panel b). This suggests that in the dehydrated microfibril the deformation mechanism initially
involvesprimarilythestraighteningofthecollagenmoleculesandnotstretchingofthemoleculesitself(thisisconfirmedbytheobservationthattheend-
to-end distance at 200 MPa stress is 260 nm, much shorter than the collagen molecules' contour length). The analysis of the gap/overlap ratio (red,
panelc)showsthatthedeformationisinitiallydistributedinboththegapandoverlapregions(sincetheratioremainsconstant),anddeformationaffects
the gap region only for larger stresses as shown by the increase in the gap-to-overlap ratio.

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molecular-scale kinks. Our model thereby directly confirms a
suggestion made by Fratzl et al.3,17(Figure 5d). However, we
notethatthestraighteningofcollagenmoleculesisnotlimitedto
the gap regions as collagen molecules in the microfibril feature a
kinked geometry throughout the entire structure, which is
successively lost during deformation. Once the entire capacity
to molecular straightening is exhausted and all collagen mole-
cules assume a straight configuration oriented in the direction of
the pulling axis, collagen molecules themselves undergo stretch-
ing, leading to a greatly increased tangent microfibril stiffness at
strains in excess of 10%. The combination of these two mechan-
isms, molecular straightening and molecular stretching, effec-
tively lead to an increase of the D-period, in direct agreement
with experimental results.52Other mechanisms, such as molec-
ular sliding may take place at larger strains in excess of 30% as
described in earlier studies of the deformation mechanisms.29,30
Conversely, for the dehydrated collagenmicrofibril the deforma-
tion mechanisms in the investigated stress range involves pri-
marily the straightening of densely packed collagen molecules
withlittlestretchingofthecollagenmoleculeitself.Thisisshown
by the increasing molecular end-to-end distance (Figure 5a),
which increases linearly, and by the dihedral energy (Figure 5b),
which does not increases with the strain. The analysis of the gap-
to-overlap ratio (Figure 5c) further shows that deformation is
initially equally distributed in both the gap and overlap regions
(where the ratio remains constant) and that for larger stresses
deformation increasingly affects the gap region (shown by the
increase in the gap-to-overlap ratio).
3. Conclusion. We have achieved the development of the
first experimentally validated all-atom collagen microfibril
modelwithfull-lengthmoleculesandtheexplicitsimulationofall
water molecules with all chemical details. Our model captures all
major structural features of collagen microfibrils such as the
quasi-hexagonal molecular packing, the D-banding periodicity
(Figure 2), the distribution of dihedral angles (Figure 3) and
mostimportantly,theverybroadrangeofmechanicalbehaviorat
different hierarchical levels and different levels of mechanical
deformation (Figure 4 and Table 1). The most important out-
come of our study is that deformation of collagen microfibrils is
mediatedthrough mechanismsthatoperateatdifferenthierarch-
ical levels, involving straightening of disordered and helically
twisted molecules at small strains, first in the gap regions and
then in the entire fibril,followedby axial stretching of molecules,
and eventual molecular uncoiling (Figures 4 and 5). Our work
hasshownthatsinglecollagenmoleculesalonearenotcapableof
providing this broad range of mechanical functionality. Rather,
the existence of an array of deformation mechanisms, derived
from the hierarchical makeup of the material, is critical to the
material's ability to confer key mechanical properties, specifically
large extensibility, strain hardening and toughness, despite the
inherent limitation that confines the construction of collagenous
materials to the use of relatively few amino acids. The paradigm
discovered through this analysis exemplifies how functional
diversity is achieved through the reliance of structural variation
of few and simple building blocks at distinct length-scales
(Figure 1), rather than through a great diversity of building
blocks. Key architectural features of this material include the
formation of a triple helix, a twisted structure of collagen
molecules, and a staggered assembly of collagen molecules in
fibrils. To highlight the variation of Young's modulus and
bending rigidity for a variety of biological and synthetic fibers
we present a comparative analysis as shown in Figure 6. This
analysis demonstrates that collagen fibrils provide a significant
bending rigidity at relatively high Young's modulus.
Theobserveddeformationmechanismsatdistincthierarchical
levels explain the striking difference of the Young's modulus of
collagen microfibril compared with that of single molecules,
which is typically found in the range of 4.8 ( 2 GPa or
≈10-20 times greater than that of a collagen microfibril. This
resolvesalong-standingissueincollagenmechanicsthathasthus
far prevented the consolidation of experimental findings with
earlier computational results41,45,46and demonstrates the im-
portanceofgeometryandscaleofobservationindefiningmecha-
nical properties of protein materials in general.17,53-55Our
findings specifically show that the properties of collagen tissues
are strongly dependent on the hierarchical level, deformation
state(i.e.,strain)andhydrationlevel(watercontent)considered.
This suggests that many conventional continuum models of
collagen tissues may not be adequate to describe the complex
scale-dependent and nonlinear mechanical properties. This has
implications for the design of scaffolding materials based on
simple polymers, which must include a consideration of the
particular nonlinear and scale dependent mechanical properties
ofmatrixmaterialsratherthanfocusingonthesmall-deformation
bulkmodulusalone.Futureworkcouldbeintegratedwithrecent
studies on the effect of hierarchical bonelike materials and
provide a computational validation for predictions made about
the role of different hierarchies.55,56
Another key impact of the experimentally validated molecular
model of collagen microfibril mechanics reported here is that it
provides a basis to investigate collagenous tissues at the fibril
scale and larger. Indeed, with our model it is now possible to
assess from a bottom-up perspective how changes at the bio-
chemical and atomistic level (such as amino acid mutations,
Figure 6. Mechanical properties of materials at the nanoscale, compar-
ing both biological and synthetic materials. Biological fibrils and fibers
present a vast range of mechanical properties in terms of Young's
modulus and bending rigidity.69-73However, most of the protein
materials feature Young's moduli in the range of 100 MPa to 10 GPa,
well below the stiffness of many synthetic nanostructured material such
as carbon nanotubes. On the other hand,bending rigidityshows a much
greatervariability.Collagenmicrofibrilsandfibrilspresentasignificantly
enhanced bending rigidity with only a relatively small decrease in the
Young's modulus compared to a single molecule, showing a greatly
effective fibril packing. The analysis shows that collagen fibrils provide a
significant bending rigidity at relatively high Young's modulus.

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LETTER
cross-linkpatternsordensity,andothermoleculardefects)affect
the structural and mechanical properties at the mesoscale,
microscale, and macroscale. This, together with the study of
the interaction of collagen fibrils with other biomolecules (e.g.,
proteoglycans), will provide critical detailsfor the understanding
of structure-property relationships in the broader class of
collagen tissues. Challenges remain with respect to the greater
levelofdisorderthatisexpected tobefoundincollagenfibrils,as
outlinedinref57andhowthesestructuralimperfections,defects,
and flaws will influence the mechanical properties. Mechanical
models of hierarchical materials and structures suggested that
mechanisms exist that mitigate the effects of these defects
through flaw-tolerance mechanisms.58-60The good agreement
between our simulations of perfect microfibrils with experimen-
tal results of ones that contain defects may suggest that perhaps
an inherent mechanism of flaw-tolerance exists in these struc-
tures.
Our model represents a collagen “microfibril”, whereas larger-
scale collagen fibrils may feature additional interfaces and
disorder between them that could affect the mechanical proper-
ties. The construction of such a full collagen fibril mechanics
model could be addressed in future work. However, computa-
tional challenges associated with such modeling are daunting as
the construction of such a model would involve billions of atoms
for protein and solvent, a size that is currently out of reach for
protein simulations.
A quantitative understanding of elastic moduli at varied scales
and deformation states is important in the context of mechanical
properties of collagen tissues for cell culture. It has been shown
that a cell's microenvironment is important in stem cell lineage
specification, where soft matrices that resemble brain tissuelike
moduli are neurogenic, stiffer matrices that mimic muscle are
myogenic, and rigid matrices that mimic bone prove to be
osteogenic.61Cells act at the micrometer scale, the scale of
collagenmicrofibrils,fibrils,andfibers,andtheirbehaviorislikely
directed by the complex hierarchical structure of their surround-
ing environment. However, current biomaterials used for scaf-
folding do not present a hierarchical structure such as that found
in natural ECM materials, which may affect the cell behavior and
differentiation. Indeed, a clear understanding of collagen's scale
andstraindependentstiffnessmayhelpindesigningbiomaterials
with appropriate mechanical characteristics and thus addresses
an immediate need for optimized matrix elasticity to foster
differentiation and enhanced performance for regenerative med-
icine applications based on stem cell therapies such as cardio-
myoplasty, muscular dystrophy, and neuroplasty.62,63
OurmodelofcollagenmicrofibrilmechanicsisbasedonX-ray
diffraction results and is limited by the range of molecular
conformation changes that can be observed at a molecular
dynamics time-scale. For example, even though the mechanical
analysisofthemodulus ofdehydratedcollagenmicrofibrilagrees
well with experimental findings (with similar Young's modulus
values asshown inTable 1),theRamachandrananalysissuggests
aheightenedlevelofdisorderinthesystem,perhapsindicativeof
molecular unfolding. Drastic changes in the molecular architec-
ture associated with such mechanisms could be explored via the
use of advanced computational methods, such as replica ex-
change molecular dynamics and may be combined with experi-
mental efforts.57The computational challenges associated with
these methods are, however, enormous. A limitation of the
collagen microfibril mechanics model is that it is based on the
periodic repetition of a crystallographic unit cell, necessitated by
thesignificantcomputationalcostassociatedwithsimulatingthis
large molecular structure. The periodic model also implies that
nocross-links betweenmoleculesare consideredand that sliding
between triple helical collagen molecules is not taken into
account. Despite these limitations, as confirmed in Table 1, the
model properly captures the mechanical behavior seen in experi-
ments, likely because the above listed constraints do not affect
the behavior at relatively small deformation below 20-30%
strain. Indeed, the effects of cross-links between molecules and
intermolecular sliding have been shown to dominate the proper-
ties primarily at larger deformation.64A microfibril model that
explicitly considers multiple molecules poses no fundamental
challenge; however, it would be rather challenging from a
computational point of view. As appropriate computational
resources become available, however, development of such
models should be straightforward by extending the work re-
ported here.
4. Materials and Methods. Existing collagen microfibril and
fibril models represent the supramolecular arrangement in
collagenous tissues in a simplified way, using a two-dimensional
lattice of mesoscopic beads45,46or extremely short collagen
peptides.36-41These models donotaccountfor the biochemical
details and are much smaller than the typical length-scales of
collagen molecules foundincollagen microfibrilsand fibrils. The
reason for these approximations is that up until now crystal-
lographic details (and in particular a full-atomistic geometry) of
the collagen molecule have been obtained only for short col-
lagen-like peptides with lengths below ≈10 nm.32-34The
method applied here overcomes these limitations and enables
us to develop a full atomistic model of the mechanics of collagen
microfibrils.
Homology Modeling. The structural model of the collagen
microfibril is generated starting from the in situ structure of full
length collagen type I molecule8(Protein Data Bank identifica-
tion code 3HR2). This structure, obtained by employing con-
ventional crystallographic techniques in X-ray fiber diffraction
experiments, resolved for the first time the specific three-dimen-
sional arrangement of collagen molecules in naturally occurring
fibrils, including the N- and C-telopeptides. Since the structure
reported in ref 8 includes only backbone R-carbons and the
primary sequence of Rattus norvegicus, we used homology
modelingtoobtainafull-atomstructurewiththehumancollagen
sequence.ThesequenceofthehumantypeIcollagenisobtained
from PubMed (entry number NP_000079 for R1(I) chain and
NP_000080 for the R2(I) chain). The 3HR2 structure and the
human collagen type I sequence are aligned, and ten homology
models are built and scored by the discrete optimized protein
energy(DOPE)usingtheModelerprogram(version9.6).65The
structure with the lowest DOPE value is chosen for building the
collagen microfibril model.
FibrilModelGeneration. Thecollagensupramolecularmodel
(microfibril) is generated using the information on the naturally
occurring crystallographic unit cell reported in ref 8, and in the
associated 3HR2 structure (a ≈ 40.0 Å, b ≈27.0 Å, c ≈ 678 Å,
R ≈ 89.2?, β ≈ 94.6?, γ ≈ 105.6?). The molecular packing
topology obtained by the periodic repetition of the unit cell lead
to quasi-hexagonally packed collagen molecules which interdigi-
tates with neighboring molecules to form a supertwisted right-
handed microfibril and to the well-known D-banding periodicity
seen in AFM images of collagen fibrils. The fibril model is
solvated using the solvate plug in of GROMACS by adding

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LETTER
SPC water molecules. Since the molecule at physiological pH
includes a net charge (positive net charge þ34), counterions
(Cl-) are added in order to keep the system neutral. The final
solvated all-atom system contains ≈57000 atoms, including
∼32000 water atoms. The first step of energy minimization is
performedbyasteepestdescentalgorithmusingtheGROMACS
4.0 code66and the GROMOS 43a1 force field, which includes
parameters for hydroxyproline amino acid (HYP) found in
collagen. This force field has been widely validated for a variety
of biochemical models of proteins including collagen.40,41
All-Atom Equilibration. Full atomistic simulations are carried
out using the GROMACS 4.0 code.66Rigid bonds are used to
constrain covalent bond lengths, thus allowing an integration
time step of 2 fs. Nonbonding interactions are computed using a
cutoff for the neighbor list at 1.35 nm with a switching function
between1.0and1.2nmforVanDerWaalsinteractions,whilethe
particle-mesh Ewald summation (PME) method is applied to
describe electrostatic interactions. The fibril model is equili-
brated through 8.5 ns NPT molecular dynamics simulations at a
temperature of 310 K (37 ?C) and with 1 bar pressure. We use a
velocity-rescaling thermostat with 1 ps coupling constant and a
Berendsenbarostatwith1pstimeconstant.Weensurestructural
convergence through a root mean square deviation (rmsd)
analysis, where convergence is confirmed when the slope of
the rmsd with respect to time approaches zero for all levels of
applied stress.
In Silico Mechanical Testing. To assess the mechanical
properties of the hydrated and dehydrated atomistic microfibril
models, we perform molecular dynamics simulations with in-
creasingconstantmechanicalstressintensionalongthefibrilaxis
whilemaintainingthepressureontheotheraxesconstantat1bar
(using a Berendsen barostat and 1 ps coupling constant).
Although the c axis (the long axis) of the periodic unit cell is
notperfectlyalignedparallelwiththemicrofibrildirection(byan
angle mismatch of about 1?), the effect on the mechanical
properties (the focus of this study) is very small since the
mechanical load is reasonably well aligned with the overall
direction of the microfibril. The mechanical loading implemen-
ted here reflects the setupthatis also usedfor mechanical testing
in experimental studies. The applied stresses are in the range
from 0 to 200 MPa, applied during 20 ns molecular dynamics
simulation for each load applied. We find that equilibrium of the
molecular structure is reliably reached within 10-15 ns of
molecular dynamics simulation, depending on the extent of the
deformation. Thus we use the last 5 ns of molecular dynamics
simulation for the mechanical analysis after the system has fully
converged. To ensure that equilibrium is obtained, we monitor
pressure equilibrium, protein rmsd, and confirm that the size of
the simulation cell reaches a steady value. The strain ε(σ) is
calculated as follows
εðσÞ ¼LðσÞ-L0
L0
ð1Þ
where L(σ) is the equilibrium cell length along the microfibril
axis when a strain σ is applied, while L0is the equilibrium cell
length along the fibril axis for σ = 0. From the fibril strains ε(σ)
resulting from each applied stress σ, we obtain the stress-strain
behavior as plotted in Figure 4.
Computational Method and Cost. Because of the size of the
model, all-atom simulations of the collagen microfibril with
explicit solvent are computationally very intense. The fully
solvated (full-atomistic model contains ≈57000 atoms
(≈25000 in the dehydrated [dry] model), requiring about 6 h
pernanosecondon32CPUsonaparallelmachine.Sincepheno-
mena involving the molecular (and supramolecular) scale are
often in the range of several nanoseconds or even microseconds,
molecular dynamics simulations of the full-atomistic collagen
fibril are at the limit of current computational capabilities.
’AUTHOR INFORMATION
Corresponding Author
*E-mail: mbuehler@MIT.EDU.
Notes
The authors declare no competing interests of any sort.
’ACKNOWLEDGMENT
The authors thank Joseph Orgel (Pritzker Institute of Biome-
dical Science and Engineering at the Illinois Institute of Tech-
nology and Argonne National Lab, U.S.A.), Sandra Shefelbine
(Department of Bioengineering at Imperial College, London,
U.K.), John Currey (University of York, U.K.) and Steve Cowin
(City College New York, U.S.A.) for their helpful suggestions
during the preparation of this manuscript. This research was
supported by NSF (Grant CMMI-0642545), ONR (Grant
N000141010562), by the MIT-Italy program “Progetto Rocca”
and by Politecnico di Milano (Grant “5 per mille junior 2009”).
High-performance computing resources have been provided by
Regione Lombardia and CILEA Consortium through a LISA
Initiative (Laboratory for Interdisciplinary Advanced Simula-
tion) 2010 grant and by CINECA under the ISCRA initiative
as well as NSF TeraGrid.
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’NOTE ADDED AFTER ASAP PUBLICATION
Due to a production error, this paper published January 5, 2011
with an incorrect abstract image. The correct version published
January 7, 2011.