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Article

Self-assembly of collagen on surfaces: the interplay ofcollagen-collagen and collagen-substrate interactions

Badri Narayanan, George H. Gilmer, Jinhui Tao, James J. De Yoreo, and Cristian V. CiobanuLangmuir, Just Accepted Manuscript • DOI: 10.1021/la4043364 • Publication Date (Web): 17 Jan 2014

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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, CO 80401, and Physical Sciences Division, Pacific Northwest National

Laboratory, Richland, WA 99352

E-mail: cciobanu@mines.edu

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

∗To whom correspondence should be addressed†Department of Mechanical Engineering and Materials Science Program, Colorado School of Mines,

Golden, CO 80401‡Physical Sciences Division, Pacific Northwest National Laboratory, Richland, WA 99352

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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 self-assemble 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 mm-long fibers form via specific cross-linkages.1,2

Such a hierarchical organization of collagen molecules provides superior mechanical prop-

erties 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.16–21 The scaffolds resulting from in vitro assembly of collagen have a

wide variety of bio-technological applications, such as platforms for tissue engineering,22,23

direct cellular processes (e.g., migration, differentiation),24,25 bone-regeneration,26,27 coat-

ings for improved bio-compatibility,28 patterning bio-functionalized 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-

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depth understanding of the factors governing self-assembly of collagen is of key importance

for bio-technological advances as well as for fundamental bio-medical 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 (Fig. 1) are

characterized by thickness or stiffness modulations due to 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

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is governed by the competition between the collagen-collagen (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 three-dimensional collagen bundles,

while strong c–s interactions lead to random monolayer networks.

Gap D = 67 nmOverlap

Figure 1: Schematic representation of axial arrangement of collagen molecules (shown asgreen rods) in a self-assembled microfibril.

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 Fig. 2(a)]. 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 crosslink with other chains; these regions, or groups of three type-2

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Figure 2: (a) Interactions describing the microscopic model. Each chain of 19 beads rep-resents a collagen molecule; there are two types of beads, labeled type 1 (yellow) and type2 (orange). Within a chain, each pair of adjacent beads are connected via FENE bondswhile the bond angles (and flexibility of the chain) are modeled by a cosine squared bendingpotential. Between two different chains, the 2-2 interactions are much stronger than the 1-1and 1-2 (see text). (b) Model single layer of collagen generated by staggering the chainsof beads along the vertical direction in the plane of the layer. The staggered arrangementresults in a hexagonal close-packing of the type 2 beads [magnified view in panel (b)].

Figure 3: Schematic representation of multilayer collagen structures produced by stackingsingle layers such that the gaps are staggered along the direction normal to the layers. Eachlayer is represented by a different color, i.e., red (layer 1), blue (layer 2), green (layer 3), andgold (layer 4).

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beads, are placed at the ends and in the middle of the chain, as shown in Fig. 2(a). Every

pair of beads of type i and j separated by a distance r interact through a 12–6 Lennard-Jones

(LJ) potential

Uij(r) =

4εij

[(σr

)12 − (σr

)6], r ≤ rc

0, r > rc

(1)

where εij is the depth of attractive minimum between beads of type i and j, and rc is the

cut-off distance. The value of rc is set to 2.5σ for all non-bonded 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

Ub(r) =

−0.5kbr20ln

[1−

(rr0

)2]

, 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.

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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 a collagen concentration of 36µg/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 12µg/ml; this excludes the possibility of liquid-crystallinity 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.

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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 Fig. 1], resulting in characteristic

D-bands with a periodicity D∼67 nm.3This 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 Fig. 2(b). 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 Fig. 2(b)] that arises from the in-plane staggering of the molecules.

Figure 4: Typical simulation cell used in the MD simulations of collagen assembly. Thecollagen molecules are described by the interactions shown in Fig. 2(a), and also experiencea downward constant acceleration and an attraction towards the substrate (i.e., the bottomface of the simulation cell.)

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In addition to the single layer assembly, we have also assessed the stability of configu-

rations 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 Fig. 2(b)

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 4-layer assembly are outlined in Fig. 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 (Fig. 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.

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 Fig. 4, consisted of a rectangular

block 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

ULJ(r) =

εs

[215

(σr

)9 − (σr

)3], r ≤ rc

0, r > rc

(4)

where εs defines the strength of the collagen–substrate interaction and rs is the cut-off

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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 micro-canonical ensemble (NVE) for 40,000τ with a timestep 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/τ 2 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 ∼ 300kDa.43 From these values and setting T = 300 K, we obtain σ =

15.8 nm, ε = 0.026 eV, m = 2.62×10−23kg and τ = 1.25 ns.

Fig. 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 300K, 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 [Fig. 5(d–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

[Fig. 5(d)] 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 forma-

tion of co-aligned fibrils at 200 mM KCl [Fig. 5(e)] and eventually 3D bundles at 300 mM

KCl [Fig. 5(f)]. 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 Fig.7(c)]; in contrast, at 200 mM K+ and pH 4.0 co-aligned fibrils

were obtained [Fig. 5(e)]. 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

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the basic principles that govern the assembly of collagen from solution onto on a flat sub-

strate. 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 [Fig. 5(a)] with a thickness ∼σ that agrees well with empirically

observed assemblies at low ionic strength [Fig. 5(d)]. 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 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 co-alignment [Fig. 5(b)]. This alignment

is consistent with the AFM results shown in [Fig. 5(e)]. Furthermore, at ε22 ≤ 0.305ε, the

molecules adsorb onto the substrate only within the initial ∼15,000τ time frame; afterwards,

the substrate coverage remains nearly constant while the remaining un-deposited 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

Fig. 5(c) at ε22 = 0.457ε]. This assembly is in excellent agreement with the configuration

observed using AFM at 300 mM K+ [see inset of Fig. 5(f)]. 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 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

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d

e

f

100 mM

200 mM

300 mM

200 nm

200 nm

200 nm

1 μm

Model AFM ε

22 = 0.085ε

ε22

= 0.305ε

ε22

= 0.457ε

a

c

b

Figure 5: Comparison of the morphology of collagen assembly predicted by our MD simula-tions (a–c) with those obtained by AFM experiments (d–f). The simulations were performedat εs = 0.7ε and different values of ε22 (a) 0.085ε, (b) 0.305ε, and (c) 0.457ε. For all thesimulations 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.

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t (×103 τ)〈[

r(t

) - r

(0)]

2〉

(×10

3 σ

2)

ε22

= 0.457εε

22= 0.406ε

Figure 6: Mean square displacement of beads on the substrate (〈[r(t)− r(0)]2〉) as a functionof time (t) after deposition at different values of ε22.

0

2

3

1

4

z (σ)

a b c d e

f g h i j

200 nm

200 mM K+

pH 9

εs = 0.7ε ε

s = 0.875ε ε

s = 1.05ε ε

s = 1.225ε ε

s = 1.4ε

Figure 7: Molecular dynamics study of the effect of the strength of c-s interaction on themorphology of the deposited collagen molecules during post-deposition heat treatment. Theheight variations of the molecules on the substrate at various values of εs are shown inthe top (a–e) while the corresponding equilibrium configurations are depicted in the panelsbelow (f–j). The periodic height bands predicted by our model at εs = 1.05ε [panel (c)] arein excellent agreement with AFM images obtained at 200 mM K+ ions and pH 9.0 [inset,panel(c)].

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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. Fig. 6 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 [Fig. 5(c)]. To obtain multiple bundles in the final

assembly at ε22 = 0.457ε [Fig. 5(c)], a substrate with an area four times larger than that

used for Figs. 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 to those used for Fig. 5(c) led to bundles with

similar thickness [as Fig. 5(c)] but at other locations and with different relative orientations.

A careful inspection of Figs. 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 in-plane 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 re-alignment 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 (Fig. 5)

shows that our model works well for room-temperature deposition of collagen coverages of

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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 Fig. 3, but simply to relieve the conformational frustration that occurs during the

rapid deposition. In the thermal treatment, the temperature is ramped to 600K over 5000τ

while simultaneously the c–s strength is ramped from 0.7ε to the values shown in the panels

of Fig. 7. Thereafter, the system was annealed at 600 K (50,000τ) and then cooled slowly

back to 300K (50,000τ). The resulting multilayer collagen morphologies are shown in Fig. 7.

Fig. 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

[Fig. 5(a,f)]. On increasing εs to 0.875ε, the tendency to bundle is reduced. At 1.05 ε,

the height variations are periodic, which is in agreement with AFM experiments [see inset

of Fig. 7(c)]. The thermal treatment has lead 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 Fig. 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 Fig. 7(c), but multiple domains can emerge

(Figs. 7(d,e)) because the molecules are to some extent pinned to the surface and do not

have sufficient mobility to completely re-align with same orientation throughout.

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Discussion

MD simulations based on the microscopic model of collagen molecules have shown that the

morphology of collagen assembly on 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 inter-molecular 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 [Fig. 5(a)]. This corresponds

to low K+ concentration regime (< 100 mM) and acidic conditions pH = 4 [Fig. 5(d)].

Doubling the concentration of K+ ions (200 mM) at constant pH, causes the collagen fibrils

formed on the substrate to co-align [Fig. 5(e)], which is also seen in MD simulations for

0.45 < ε22/εs < 0.6 [Fig. 5(b)]. 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 the mica

substrate,45 thus, neutralizing the negative charge on the surface. Using AFM, Leow and

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co-workers18 have inferred that the preferential binding of K+ on mica surface reduces the

affinity of collagen molecules towards 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.

Figure 8: Equilibrium configuration predicted by our MD simulations after post-depositionheat treatment of the collagen bundles shown in Fig. 5(c). This thermal treatment relievesthe conformational frustration in the bundles resulting in a ordered structure with D-bandsin excellent agreement with the experimentally observed ones.

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),

co-aligned fibrils were formed [Fig. 5(e)] while at pH = 9, an unidirectionally aligned 2D

array with native-like ordering (67 nm D-bands) was obtained [inset Fig. 7(c)]. In terms of

the microscopic model, this increase in the pH had the effect of increasing the ratio ε22/εs

from 0.4 (co-aligned molecules, Fig. 5(b)] 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 in-

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sights into understanding the hierarchical structure of collagenous scaffolds.19,46 Using AFM

imaging, Loo et al. showed that collagen bundles form via co-alignment 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, co-aligned 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 [Fig. 5(c)],

expectedly, lacks such ordering; this is an artifact of the fast deposition rates necessitated by

the limited timescales accessible to MD simulations, which leads to conformational frustra-

tion. To relieve this frustration, we employed a post- deposition thermal treatment identical

to the one used in Fig. 7. The resulting bundles exhibited the characteristic D-periodicity

[Fig. 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 bun-

dle, 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),

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

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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 [Figs. 7, 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 [Fig. 5(c)]; 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.

Conclusion

In conclusion, we have developed a microscopic model that incorporates the key features of

the interactions between collagen molecules and we used that model for molecular statics

tests of structure stability, as well as for analyzing the morphologies of collagen obtained via

deposition simulated by MD. Using MD simulations and AFM experiments, we have shown

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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 timescale restrictions in MD caused frustration between

layers and lead to the formation of some isolated islands of collagen. We circumvented this

timescale 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.

Acknowledgement

The research at Colorado School of Mines was supported by Lawrence Livermore National

Laboratory (Contract B601600) and by the National Science Foundation (Grant CMMI-

0846858). 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-AC02-05CH11231 and DE-AC52-07NA27344, respectively. Supercomputer time for the

MD calculations was provided by the Golden Energy Computing Organization at Colorado

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School of Mines.

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Graphical TOC Entry

Model AFMIn-vitro collagen self-assembly

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