Article
pubs.acs.org/Langmuir
Self-Assembly of Collagen on Flat Surfaces: The Interplay of
Collagen−Collagen and Collagen−Substrate Interactions
Badri Narayanan,† George H. Gilmer,† Jinhui Tao,‡ James J. De Yoreo,‡ and Cristian V. Ciobanu*,†
†
Department of Mechanical Engineering and Materials Science Program, Colorado School of Mines, Golden, Colorado 80401, United
States
‡
Physical Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99352, United States
ABSTRACT: Fibrillar collagens, common tissue scaffolds in live
organisms, can also self-assemble in vitro from solution. While previous
in vitro studies showed that the pH and the electrolyte concentration in
solution largely control the collagen assembly, the physical reasons why
such control could be exerted are still elusive. To address this issue and to
be able to simulate self-assembly over large spatial and temporal scales, we
have developed a microscopic model of collagen with explicit interactions
between the units that make up the collagen molecules, as well as between
these units and the substrate. We have used this model to investigate
assemblies obtained via molecular dynamics deposition of collagen on a substrate at room temperature using an implicit solvent.
By comparing the morphologies from our molecular dynamics simulations with those from our atomic-force microscopy
experiments, we have found that the assembly is governed by the competition between the collagen−collagen interactions and
those between collagen and the substrate. The microscopic model developed here can serve for guiding future experiments that
would explore new regions of the parameter space.
■
INTRODUCTION
Collagen molecules represent the most prevalent structural
proteins in human beings and other vertebrates, and selfassemble in a complex hierarchical manner featuring structures
that range from molecular to macroscopic length scales.1−7
Each collagen molecule is ∼300 nm long and ∼1.5 nm in
diameter, and consists of three peptide chains spiraling around
each other.3,8 In their native state, the collagen molecules
organize in a longitudinally staggered arrangement forming
fibrils, which show a characteristic D-band periodicity (∼67
nm).6,9 At the next scale, ∼10 μm-thick, few millimeters-long
fibers form via specific cross-linkages.1,2 Such a hierarchical
organization of collagen molecules provides superior mechanical properties to connective tissues (e.g., ligaments, tendons
etc.),2,10 shapes extracellular matrices (e.g., cartilage, cornea
etc.),11,12 and is important for several biological functions such
as tissue-structuring, cell attachment, tissue repair, and control
of tissue-related diseases.13−15 Previous microscopy studies
have revealed that collagen molecules can also self-assemble on
inorganic substrates.9,16−21,31,32 The scaffolds resulting from in
vitro assembly of collagen have a wide variety of biotechnological applications, such as platforms for tissue engineering,22,23 direct cellular processes (e.g., migration, differentiation),24,25 bone-regeneration,26,27 coatings for improved
biocompatibility,28 patterning biofunctionalized surfaces,21
templates for silicon nanowire growth,29 and fabrication of
novel bio-mimetic functional materials.30 In most of the
applications that utilize the biological activity of collagen
molecules, it is crucial to mimic their native conformation on
the surface being functionalized.21 Therefore, an in-depth
© 2014 American Chemical Society
understanding of the factors governing self-assembly of collagen
is of key importance for biotechnological advances as well as for
fundamental biomedical research.
Significant insights into collagen self-assembly on substrates
(particularly, on mica) have come from atomic force
microscopy (AFM) experiments. Morphologies ranging from
random networks to ordered two-dimensional arrays with
native-like ordering can be obtained on mica by varying the
ionic strength and pH of the buffer solution.9,16−21,31,32 AFM
studies have shown that at certain ionic strengths and pH levels,
layers of unidirectionally aligned collagen molecules can form
with the D-band periodicity.17,33 The D bands (Figure 1) are
characterized by thickness or stiffness modulations due to
Figure 1. Schematic representation of axial arrangement of collagen
molecules (shown as green rods) in a self-assembled microfibril.
Received: November 14, 2013
Revised: January 10, 2014
Published: January 17, 2014
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staggered gaps in the layers and indicate native-like ordering.21
While a number of possible reasons have been proposed for the
formation of such collagen layers,17−19,32 the physical origins of
the effects of K+ and pH on the self-assembly are still not fully
understood, most likely because of many other factors present
in experimental investigations. A reduction in the number of
factors that affect the assembly in such a way that only the most
significant ones are considered should further our understanding of the assembly process. Such simplification will
elucidate how each of those factors, independently, affects the
final morphology.
Here, we propose a microscopic model of collagen that
incorporates only the key features of the interactions between
collagen molecules and the substrate, as well as those between
molecules themselves. Our model is informed by experiments
characterizing the formation of the D-bands on substrates: as
such, it is not a coarse-grained model per se because it is not
informed by all-atom simulations, as done recently by other
groups.34,35 In our microscopic description, a collagen molecule
is modeled as a chain of two types of bonded beads, which
interact either weakly or strongly with beads on another chain.
The former interaction simulates the overall weak attraction in
solution, while the latter simulates the strong chemical binding
that can occur when two collagen molecules are placed parallel
to one another. By comparing the morphologies from
molecular dynamics (MD) simulations based on our model
with those from our AFM experiments, we find that the
assembly is governed by the competition between the collagencollagen (c−c) interactions and the collagen-substrate (c−s)
interactions. In this microscopic model, one can readily vary the
strengths of the interactions independent of one another,
whereas such a decoupling of the control parameters may be
difficult to achieve experimentally.18,20,21 Our simulations show
that strong c−c interactions promote the formation of threedimensional collagen bundles, while strong c−s interactions
lead to random monolayer networks.
Figure 2. (a) Interactions describing the microscopic model. Each
chain of 19 beads represents a collagen molecule; there are two types
of beads, labeled type 1 (yellow) and type 2 (orange). Within a chain,
each pair of adjacent beads are connected via FENE bonds while the
bond angles (and flexibility of the chain) are modeled by a cosine
squared bending potential. Between two different chains, the 2−2
interactions are much stronger than the 1−1 and 1−2 (see text). (b)
Model single layer of collagen generated by staggering the chains of
beads along the vertical direction in the plane of the layer. The
staggered arrangement results in a hexagonal close-packing of the type
2 beads (magnified view in panel b).
where ϵij is the depth of attractive minimum between beads of
type i and j, and rc is the cutoff distance. The value of rc is set to
2.5σ for all nonbonded pairs. For bonded pairs, i.e., those
forming the individual chains, the cutoff is set at 21/6σ so that
the LJ interactions for these pairs are repulsive. In all our
simulations, we have set ϵ11 = ϵ12 = 0.1ϵ, where ϵ defines the
unit of energy or the characteristic energy scale. For bonded
pairs, i.e., those forming chains, an additional interaction is
employed using the finite extensible nonlinear elastic (FENE)
potential,37,38 given by
■
MICROSCOPIC MODEL
Our microscopic model is a bead−spring model in which a
single collagen molecule consists of N beads of identical
diameter σ and mass m, linked in a chain. The bead diameter
defines the excluded volume for interactions, while the springs
describe the connectivity between adjacent beads in a given
collagen molecule (chain of beads). Individual collagen
molecules cross-link via reactions between specific side
groups;36 to account for this behavior, we have chosen two
types of beads, type 1 and type 2, where the beads of the latter
type are assumed to contain the side groups responsible for
cross-linking (refer to Figure 2a). In our simplified model, each
collagen molecule is represented by a chain of N = 19 beads. To
render large-scale calculations more tractable, each chain has
only three regions (instead of five)20 along its length where it
can cross-link with other chains; these regions, or groups of
three type-2 beads, are placed at the ends and in the middle of
the chain, as shown in Figure 2a. Every pair of beads of type i
and j separated by a distance r interact through a 12−6
Lennard-Jones (LJ) potential
⎧ ⎡⎛ ⎞12 ⎛ ⎞6 ⎤
σ
σ
⎪
⎪ 4ϵij⎢⎜ ⎟ − ⎜ ⎟ ⎥ , r ≤ rc
⎝
⎠
⎝
r⎠ ⎦
Uij(r ) = ⎨ ⎣ r
⎪
⎪ 0,
r > rc
⎩
⎧
⎡
⎛ r ⎞2 ⎤
⎪
⎪−0.5k br02 ln⎢1 − ⎜ ⎟ ⎥ , r ≤ r0
⎢⎣
Ub(r ) = ⎨
⎝ r0 ⎠ ⎥⎦
⎪
⎪
r > r0
⎩∞ ,
(2)
where r is the distance between two adjacent beads, kb is the
bond stiffness constant, and r0 is the maximum length of an
unbroken bond. In all our simulations, we used kb = 30ϵ and r0
= 1.5σ. To describe the flexibility of a molecule, we have
imposed a bending potential between any three neighboring
beads in a chain39
Uθ = kθ(cos θ − cos θ0)2
(3)
where θ is the angle formed at a central bead by two adjacent
bonds, kθ is the angular stiffness, and θ0 is the equilibrium angle.
We have set kθ = 75ϵ and θ0 = 180°, which gives largely straight
molecules albeit flexible as expected from experiments.
■
EXPERIMENTAL SECTION
Sample Preparation. The collagen (brand name: Purecol) was
obtained from Advance Biomatrix Corporation. This as-obtained
solution contains 3.1 mg/mL of collagen [purified bovine Type I
(97%) and Type III collagen (3%)] at pH 2. This stock collagen
solution was diluted in a phosphate buffer (10 mM, pH 4.0) to obtain
(1)
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a collagen concentration of 36 μg/mL. To obtain the final sample with
a desired KCl concerntration (i.e., 100 mM, 200 mM, 300 mM), the
diluted collagen stock solution (36 μg/mL) was added to a buffer
containing 300 mM KCl and 10 mM Na2HPO4 in appropriate volume
ratios (i.e., collagen/buffer). The pH of the buffer solution was kept at
desired values (i.e., 4.0 and 9.0). In all these cases, the collagen
concentration was 12 μg/mL; this excludes the possibility of liquidcrystallinity controlled collagen assembly, which is known to occur in
tissues and at high collagen concentrations (>20 mg/mL).18,40 The
prepared collagen solutions were then applied to a freshly cleaved
muscovite mica disc (diameter 9.9 mm, Ted Pella, Inc.) and left in
contact for 10 min (for solution at pH 4.0) and 60 min (for solution at
pH 9.0), which is long enough for collagen adsorption onto the
substrate.
AFM Imaging. The ex-situ (in air) and in situ (in fluid) AFM
images were collected in tapping mode at room temperature (23 °C)
with a NanoScope IIIA AFM (Digital Instruments J scanner, Veeco)
using silicon tips (Nano World, FM-W, spring constant 2.8 N/m, tip
radius <8 nm and resonance frequency 75 kHz) and silicon nitride tips
(Asylum, TR400PSA, spring constant 0.08 N/m, tip radius <20 nm
and resonance frequency 34 kHz). The drive amplitude was 70 nm (in
air) and 20 nm (in fluid), and the signal-to-noise ratio was maintained
higher than 10. The scanning speed was 1 Hz. The amplitude set point
was tuned to minimize the forces (∼50 pN) loaded onto the collagen
surface. For imaging in air, unadsorbed collagen was then rinsed away
with water, and the substrate was dried with a stream of nitrogen gas.
Figure 3. Schematic representation of multilayer collagen structures
produced by stacking single layers such that the gaps are staggered
along the direction normal to the layers. Each layer is represented by a
different color, i.e., red (layer 1), blue (layer 2), green (layer 3), and
gold (layer 4).
To gain a better understanding of the self-assembly process
in terms of the collagen-collagen (c−c) and collagen-substrate
(c−s) interactions, we turn to MD simulations based on our
microscopic model. All simulations were performed using the
simulation package LAMMPS.39 The typical computational
supercell, shown in Figure 4, consisted of a rectangular block
■
RESULTS
To assess the suitability of our model for studying collagen
assemblies, we tested the stability of several empirically
observed configurations using this model. Type I human
collagen molecules stagger along the longitudinal direction
(refer to Figure 1), resulting in characteristic D-bands with a
periodicity D ∼ 67 nm.3 This staggered arrangement causes the
ends of two adjacent molecules in a fibril to be shifted laterally,
which in turn results in a gap region between them.5,7,20 In
accordance with these observations, we generated a layer of
collagen molecules (chains of 19 beads) using our bead−spring
model by staggering the molecules along the vertical direction
in the plane of the layer as illustrated in Figure 2b. Periodic
boundary conditions were employed in the plane of the layer.
Using conjugate gradient relaxation, we found that this
configuration is indeed a local energy-minimum; the stability
of this assembly is due to the hexagonal close-packing of the
strongly attracting type 2 beads (refer to the inset in Figure 2b)
that arises from the in-plane staggering of the molecules.
In addition to the single layer assembly, we have also assessed
the stability of configurations that contain multiple layers of
collagen molecules. The geometry for each assembly composed
of multiple layers was obtained by stacking copies of the layer
shown in Figure 2b one on top of the other such that
consecutive layers are off-registry with respect to each other by
(√3σ)/2 perpendicular to the chain direction, and by σ/2
along the chain direction. For example, the steps involved in
building a four-layer assembly are outlined in Figure 3, in which
each layer of molecules is shown in a different color for clarity.
It is worth noting that the protocol adopted here to create
multilayer assemblies results in a stagger of gaps along the
direction perpendicular to the layers, consistent with previous
microscopy studies. Furthermore, we have found that multilayer configurations of collagen molecules (Figure 3) are stable
regardless of the number of layers. This clearly demonstrates
that our description of collagen molecules is robust, so we can
employ it to understand their complex self-assembly process.
Figure 4. Typical simulation cell used in the MD simulations of
collagen assembly. The collagen molecules are described by the
interactions shown in Figure 2a, and also experience a downward
constant acceleration and an attraction toward the substrate (i.e., the
bottom face of the simulation cell).
with desired cross-section in which a thousand collagen
molecules (with N = 19 beads) were placed with random
orientations such that the end-to-end distance between any two
nearby molecules is ≥1.9σ. The bottom face (at z = 0) of the
simulation box was taken as an attractive flat substrate, which
interacts with every bead regardless of its type through a force
normal to the substrate. The interaction energy experienced by
the bead in the vicinity of the substrate is given by a 9−3 LJ
potential similar to previous other works on polymer
nanodroplets,41
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⎧ ⎡ ⎛ ⎞ 9 ⎛ ⎞3 ⎤
2 σ
σ
⎪ ϵs⎢ ⎜ ⎟ − ⎜ ⎟ ⎥ , r ≤ rc
⎝r⎠ ⎦
ULJ(r ) = ⎨ ⎣ 15 ⎝ r ⎠
⎪
⎪ 0,
r > rc
⎩
Article
(4)
where ϵs defines the strength of the collagen−substrate
interaction and rs is the cutoff distance for the c−s interactions
which is set to 2.5σ. Periodic boundary conditions were applied
in the plane of the substrate. The temperature (T = ϵ/kB, where
kB is the Boltzmann constant) was maintained by employing
Langevin thermostat.42 The equations of motions were
integrated in a microcanonical ensemble (NVE) for 40 000τ
with a time step of 0.005τ, where τ is the characteristic time
given by τ = σ(m/ϵ)1/2. The deposition of the molecules was
simulated by imparting every bead a constant acceleration of
0.001σ/τ2 along the negative z-direction. It is well-known that a
collagen molecule is ∼300 nm long3,18,34 and has a molecular
weight of ∼300 kDa.43 From these values and setting T = 300
K, we obtain σ = 15.8 nm, ϵ = 0.026 eV, m = 2.62 × 10−23 kg
and τ = 1.25 ns.
Figure 5(a−c) illustrates the morphologies of the collagen
assembly obtained at increasing the c−c interaction (ϵ22) with
respect to a constant c−s strength (ϵs). These morphologies are
compared with the experimental ones obtained at increasing K+
concentration (under constant pH), which effectively decreases
the influence of the c−s interactions relative to the c−c ones.18
The MD simulations were carried out at 300 K, with ϵs kept
constant at 0.7ϵ, for a time span of 40 000τ. We employed AFM
to image the self-assembled collagen on a flat muscovite mica
substrate under various conditions of electrolyte concentration
(KCl or K+ ions) and pH of the buffer solution (Figure 5d−f).
In an acidic environment (pH 4) and low concentration of
K+ ions in the buffer solution (100 mM), the collagen
molecules were observed to form a random monolayer-thick
network (Figure 5d) consistent with previous findings.17,19
Upon increasing the concentration of K+ ions, significant
ordering arises in the assembly of collagen molecules resulting
in the formation of coaligned fibrils at 200 mM KCl (Figure 5e)
and eventually 3D bundles at 300 mM KCl (Figure 5f).
Interestingly, we found that at basic pH (9.0) and intermediate
ionic strength (200 mM K+), the collagen molecules organize as
highly ordered 2D arrays with a thickness of ∼4 monolayers
(inset Figure 7c); in contrast, at 200 mM K+ and pH 4.0,
coaligned fibrils were obtained (Figure 5e). This demonstrates
the coupled effect of K+ ionic strength and pH on the
morphology of collagen assembly on mica, making it difficult to
empirically identify the basic principles that govern the
assembly of collagen from solution onto on a flat substrate.
Furthermore, the unidirectionally aligned 2D arrays obtained at
200 mM K+ and pH 9.0 were found to possess D-bands with
native-like in-plane ordering [periodicity ∼67 nm] of collagen
molecules.3,17,20
Our MD simulations show that at low values of ϵ22, e.g., ϵ22 =
0.085ϵ, the molecules form a random network (Figure 5a) with
a thickness of ∼σ that agrees well with empirically observed
assemblies at low ionic strength (Figure 5d). A close inspection
of the temporal evolution of the assembly simulation provides
the explanation for this random configuration. We found that
upon deposition, the molecules adsorb onto the substrate at
random locations, and most of them remain pinned at their
adsorption sites because the c−c interactions are too weak to
cause binding between them. In this regime, the assembly is
strongly governed by c−s interactions; this is consistent with
Figure 5. Comparison of the morphology of collagen assembly
predicted by our MD simulations (a−c) with those obtained by AFM
experiments (d−f). The simulations were performed at ϵs = 0.7ϵ and
different values of ϵ22 (a) 0.085ϵ, (b) 0.305ϵ, and (c) 0.457ϵ. For all
the simulations except those in panel (c), the substrate area was 99σ ×
99σ; for (c) it was 198σ × 198σ. The AFM images were obtained
using a buffer with pH 4.0 and varying ionic strength (d) 100 mM
KCl, (e) 200 mM KCl, and (f) 300 mM KCl.
previous studies18,20,21 which report that at low concentrations,
the K+ ions cannot effectively screen the c−s interactions.
An increase in ϵ22 to 0.305ϵ was found to significantly
increase the driving force for binding between collagen
molecules leading to their coalignment (Figure 5b). This
alignment is consistent with the AFM results shown in (Figure
5e). Furthermore, at ϵ22 ≤ 0.305ϵ, the molecules adsorb onto
the substrate only within the initial ∼15 000τ time frame;
afterward, the substrate coverage remains nearly constant while
the remaining undeposited molecules stay in the implicit
solvent.
Upon further increasing ϵ22, we found that the dominating
interaction switches from c−s to c−c at ϵ22 ≥ 0.457ϵ. Such
increase in ϵ22 leads to the formation of 3D-bundles (e.g., see
Figure 5c at ϵ22 = 0.457ϵ]. This assembly is in excellent
agreement with the configuration observed using AFM at 300
mM K+ (see inset of Figure 5f). Direct visualization of the
deposition process showed that all the available molecules in
the computational supercell adsorb onto the substrate within t
≤ 15 000τ. During this initial time period, the molecules adsorb
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at random locations, similar to the cases for low ϵ22, ϵ22 ≤
0.305ϵ. The dominating c−c interactions, however, enhance the
mobility of the adsorbed molecules, which leads to the
formation of 3D bundles. The surface diffusion, albeit present
during the deposition, was found to be particularly high at t >
15 000τ, which facilitated the growth of longer and thicker
bundles at the expense of nearby smaller ones. Figure 6
to those used for Figure 5c led to bundles with similar thickness
(as Figure 5c) but at other locations and with different relative
orientations.
A careful inspection of Figure 5(b,c) suggests that a region in
the parameter space (ϵ22, ϵs) must exist in which the mobility of
collagen molecules on the substrate is sufficiently large to form
ordered 2D-arrays but not so high as to form 3D bundles.
Indeed, our MD simulations show that at one such optimal
combination, ϵ22 = 0.406ϵ, ϵs = 0.7ϵ, the adsorbed collagen
molecules diffuse over the substrate leading to significant inplane ordering. In this case, we found that the deposited
collagen adsorb onto the substrate at random positions;
however, they align themselves such that all the adsorbed
molecules are oriented roughly along the same direction. This
realignment of the molecules along a preferred direction
continues via translation, rotation, and even “hopping” of
molecules until the entire substrate area is covered by a
unidirectionally aligned monolayer (at t ∼ 12 500τ).
The comparative analysis between the MD simulations and
the AFM images (Figure 5) shows that our model works well
for room-temperature deposition of collagen coverages of
approximately a monolayer (1 ML), on average. In addition,
our simulations help identify in what parameter regimes the
deposited collagen appears as a random network, as uniformly
oriented molecules, or as 3-D bundles. Encouraged by these
results, we have also performed multilayer deposition of
collagen at room temperature. We have found, expectedly,
that during the time-scale attainable in MD simulations, the
deposition rate is somewhat too fast and leads to frustration
between the layers and to formations of islands of collagen. In
order to mitigate this artifact, we have performed a post
deposition thermal treatment; we emphasize that the role of
this thermal treatment is not to reach the perfect structures
shown in Figure 3, but simply to relieve the conformational
frustration that occurs during the rapid deposition. In the
thermal treatment, the temperature is ramped to 600 K over
5000τ, while simultaneously the c−s strength is ramped from
0.7ϵ to the values shown in the panels of Figure 7. Thereafter,
Figure 6. Mean square displacement of beads on the substrate (⟨[r(t)
− r(0)]2⟩) as a function of time (t) after deposition at different values
of ϵ22.
illustrates that at higher values of ϵ22 (0.457ϵ), the molecules
(chains) deposited on the substrate undergo higher mean
square displacement ⟨[r(t) − r(0)]2⟩ as compared to that at ϵ22
= 0.406ϵ; this provides clear evidence that the surface diffusion
of the collagen molecules is facilitated upon increasing ϵ22. This
surface-diffusion assisted growth continues until t ≃ 30,000τ,
resulting in an equilibrium assembly consisting of multiple long
bundles ∼8σ thick along with single molecules adsorbed at
random locations on the substrate (Figure 5c). To obtain
multiple bundles in the final assembly at ϵ22 = 0.457ϵ (Figure
5c), a substrate with an area 4 times larger than that used for
Figure 5(a,b) was necessary. Furthermore, we found that the
position of the bundles formed and their relative orientation are
controlled only by the random thermal motion; another
simulation with the depositing molecules oriented differently in
the implicit solvent but with the rest of the parameters identical
Figure 7. Molecular dynamics study of the effect of the strength of c-s interaction on the morphology of the deposited collagen molecules during
postdeposition heat treatment. The height variations of the molecules on the substrate at various values of ϵs are shown in the top (a−e), while the
corresponding equilibrium configurations are depicted in the panels below (f−j). The periodic height bands predicted by our model at ϵs = 1.05ϵ
(panel c) are in excellent agreement with AFM images obtained at 200 mM K+ ions and pH 9.0 (inset, panel c).
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the mica substrate,45 thus, neutralizing the negative charge on
the surface. Using AFM, Leow and co-workers18 have inferred
that the preferential binding of K+ on mica surface reduces the
affinity of collagen molecules toward the surface by restricting
the number of available binding sites. Consequently, this
promotes diffusion of weakly adsorbed collagen molecules over
the mica substrate; in other words, it increases the c−c
attractive interactions consistent with our predictions from the
microscopic model.
It is interesting to note that at 200 mM of K+ ion
concentration, our AFM experiments showed different
morphologies depending on the pH value. At acidic conditions
(pH = 4), coaligned fibrils were formed (Figure 5e) while at pH
= 9, an unidirectionally aligned 2D array with native-like
ordering (67 nm D-bands) was obtained (inset Figure 7c). In
terms of the microscopic model, this increase in the pH had the
effect of increasing the ratio ϵ22/ϵs from 0.4 (coaligned
molecules, Figure 5b) to 0.58 (unidirectional ordered
monolayer); thus, using basic buffer enhances diffusion of
collagen molecules over the substrate. This is because at pH = 9
(close to the isoelectric point of collagen, pI = 9.3),17 most of
the amino acid side-chains of collagen become neutral; thereby,
the binding affinity of collagen on mica substrate is drastically
reduced.
Previous investigations on the self-assembly of type I
collagen have provided significant insights into understanding
the hierarchical structure of collagenous scaffolds.19,46 Using
AFM imaging, Loo et al. showed that collagen bundles form via
coalignment or intertwining of microfibrils (unit containing five
collagen molecules coiled around each other).19 In an earlier
study, Bozec and co-workers illustrated that collagen bundles
possess a rope-like structure in which the collagen molecules
intertwine around each other. Consistent with these reports,
our molecular dynamics (MD) simulations show that the
collagen molecules coil around each other in the various
assembly morphologies explored here, i.e., coaligned fibrils,
bundles, and unidirectional 2D arrays. Furthermore, by
employing a mechanical model of ropes, Bozec et al.
demonstrated that the D-bands observed in the bundles arise
due to the inherent twist in the individual collagen molecules,
and the periodic repetition of such a twist along the length of a
molecule.46 The collagen bundles predicted by our MD
simulations (Figure 5c), expectedly, lacks such ordering; this
is an artifact of the fast deposition rates necessitated by the
limited time scales accessible to MD simulations, which leads to
conformational frustration. To relieve this frustration, we
employed a post-deposition thermal treatment identical to
the one used in Figure 7. The resulting bundles exhibited the
characteristic D-periodicity (Figure 8) in excellent agreement
with the experimentally observed D-bands in collagen fibrils.
Furthermore, we found that such an ordering occurs regardless
of the diameter of the bundle, which is also consistent with
earlier reports.46 This illustrates that our model accurately
predicts the structural details of assembled collagen.
Recent experimental investigations of collagen fibrils grown
in vitro have shown that the periodicity of D-bands are
centered at ∼67 nm with a spread of ∼10 nm.31,47 This
distribution, which is also observed in biological tissues, was
found to occur regardless of the substrate employed and of
collagen concentration in the buffer solution.31,47 Indeed, our
MD simulations showed a distribution of D-spacings owing to
the intertwining of collagen molecules; the variations in the
value were found to be within a bead diameter, σ (15.8 nm),
the system was annealed at 600 K (50 000τ) and then cooled
slowly back to 300 K (50 000τ). The resulting multilayer
collagen morphologies are shown in Figure 7.
Figure 7 shows both the height variations for structures (a−
e), and their corresponding bead structures with the two bead
types identified by different colors (f−j). We note that the
height variations (a−f) correspond closely to the regions were
the strongly interacting type 2 beads are together. At ϵs = 0.7ϵ,
we find that the c−c interactions are still dominant, causing
formation of flattened bundles as evidenced by some parts of
the substrate left bare (Figure 5a,f). On increasing ϵs to 0.875ϵ,
the tendency to bundle is reduced. At 1.05ϵ, the height
variations are periodic, which is in agreement with AFM
experiments (see inset of Figure 7c). The thermal treatment has
led to the formation of a high-density phase in which the
molecules are approximately aligned along the same direction
(as opposed to the perfectly aligned arrangements in Figure 3),
because such configurations are significantly more probable
than the perfect structure without having much higher energies.
Structures formed at higher ϵs have same periodicity as those in
Figure 7c, but multiple domains can emerge (Figures 7d,e)
because the molecules are to some extent pinned to the surface
and do not have sufficient mobility to completely realign with
the same orientation throughout.
■
DISCUSSION
MD simulations based on the microscopic model of collagen
molecules have shown that the morphology of collagen
assembly on a flat substrate is determined by the competition
between the c−c and the c−s interactions. Experimentally, the
morphology on flat mica surfaces can be controlled via the ionic
strength (K+ ions) and the pH of the buffer solution. Since
these experimental parameters (i.e., K+ concentration, and pH)
affect both the c−c and c−s interactions,18,19,21 a one-to-one
correspondence between them and model parameters (ϵ22 and
ϵs) is not possible. Yet, one can identify qualitative trends
between the two sets of control parameters by comparing the
results of our AFM experiments and MD simulations. For
sufficiently low values of the ratio ϵ22/ϵs, 0.1 < ϵ22/ϵs < 0.4, the
intermolecular attractive forces are not high enough to
surmount the strong binding of collagen molecules to the
substrate, which leads to the formation of random networks
(Figure 5a). This corresponds to low K+ concentration regime
(<100 mM) and acidic conditions pH = 4 (Figure 5d).
Doubling the concentration of K+ ions (200 mM) at constant
pH causes the collagen fibrils formed on the substrate to
coalign (Figure 5e), which is also seen in MD simulations for
0.45 < ϵ22/ϵs < 0.6 (Figure 5b). Eventually, at very high K+ ion
concentration (>300 mM) in experiment and ϵ22/ϵs > 0.67 in
simulations, the collagen molecule assemble into 3-D bundles.
Thus, it can be inferred that under constant pH conditions,
increasing K+ concentration amounts to enhancing the
attraction between collagen molecules (i.e., ϵ22).
The qualitative mapping between K+ ionic strength of the
acidic buffer and the strength of the c−c interaction in our
model (ϵ22) is in agreement with the current understanding of
the role of K+ ions in collagen self-assembly on mica.17−19 It is
well-known that certain amino-acids side chains in the collagen
molecules are positively charged at pH = 4.17 On the other
hand, the mica surface possesses partially negative charge due
to the loss of certain K+ ions during cleavage of the mica crystal
that contained these K+ ions between the silicate sheets.44 The
K+ ions present in the buffer are known to bind preferentially to
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MD. Using MD simulations and AFM experiments, we have
shown that the morphology of collagen assembled on flat
substrates is dictated by the competition between the collagen−
collagen and collagen−substrate interactions. In the regime
where the c−s interactions dominate (i.e., ϵ22 ≤ 0.305ϵ and ϵs =
0.7ϵ), the motion of the as-deposited collagen molecules over
the substrate is strongly hindered, leading to the formation of
either random networks (at very low ϵ22) or that show a
preferred uniform orientation (at slightly higher values of ϵ22).
At higher values of ϵ22 (>0.457ϵ), the c−c interactions
dominate, which cause significant enhancement of the surface
mobility of collagen molecules. This increased mobility
facilitates translation, rotation, and hopping of the collagen
molecules over the substrate, resulting in the formation of 3-D
bundles. The entire substrate was found to be covered by a
monolayer of collagen molecules with significant in-plane
ordering at an optimum combination of ϵ22 and ϵs [ϵ22 =
0.406ϵ, ϵs = 0.7ϵ]. However, the fast deposition rates employed
in this study, owing to time scale restrictions in MD, caused
frustration between layers and led to the formation of some
isolated islands of collagen. We circumvented this time scale
problem via a post deposition thermal treatment. An increased
value of ϵs = 1.05ϵ during this treatment resulted in periodic
height variations that are in excellent agreement with the
observed bands in AFM experiments. This model can be used
in the future to predict new assembled morphologies for
regions of the parameter space that were not yet explored.
Figure 8. Equilibrium configuration predicted by our MD simulations
after postdeposition heat treatment of the collagen bundles shown in
Figure 5c. This thermal treatment relieves the conformational
frustration in the bundles, resulting in a ordered structure with Dbands in excellent agreement with the experimentally observed ones.
which is in order-of-agreement with experiments (∼10
nm).31,47 However, this qualitative agreement may be fortuitous
because the model, in its current form, does not provide
insights into the origin of the distribution in D-periodicity
values.
From their AFM studies, Leow and co-workers18 concluded
that the assembly of collagen molecules on mica occurs via a
pathway similar to assembly in solution. It consists of
adsorption of collagen molecules, surface diffusion, nucleation
of fibrils, and growth, in that order. Our MD simulations
confirm the experimental observations. Similar to experiments
at low concentrations of collagen molecules in the solution,18
the simulations show that collagen molecules have a high
affinity to bind to the flat substrate, as evidenced by absence of
any aggregates in the implicit solution for values of ϵs ≥ 0.3.
The previous AFM study with mica surfaces that possess
different crystal symmetries, namely, muscovite and phlogoptite, yielded distinct morphologies suggesting that the
anisotropy of underlying substrate guides the growth direction
of collagen molecules.18 In our MD simulations, we have found
that the ordering of collagen molecules (i.e., the formation of
D-bands in bundles or in unidirectional aligned 2D arrays)
occurs even on isotropic flat substrates (Figures 7 and 8). This
shows that the ordering of collagen molecules within a fibril
(bundle) is not controlled by the directional effects of the
substrate. The bundles do not align themselves along any
particular direction on isotropic substrates (Figure 5c); by
comparison, the collagen fibrils can align along specific
directions on an anisotropic muscovite mica surface.18,19 This
provides further confirmation that the crystallography of the
substrate controls the long-range alignment of the collagen
bundles on it, without influencing the ordering (D-band
formation) of the molecules within a bundle.
■
AUTHOR INFORMATION
Corresponding Author
*E-mail: cciobanu@mines.edu.
Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS
The research at Colorado School of Mines was supported by
Lawrence Livermore National Laboratory (Contract B601600)
and by the National Science Foundation (Grant CMMI0846858). The experimental part of this work was performed at
Lawrence Berkeley National Laboratory and Lawrence Livermore National Laboratory with support from the Office of
Science, Office of Basic Energy Sciences of the U.S.
Department of Energy under Contracts DE-AC0205CH11231 and DE-AC52-07NA27344, respectively. Supercomputer time for the MD calculations was provided by the
Golden Energy Computing Organization at Colorado School of
Mines.
■
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