Self-Assembly of Collagen on Flat Surfaces: The Interplay of Collagen

Subscriber access provided by DUESSELDORF LIBRARIES

Article

Self-assembly of collagen on 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 Langmuir, Just Accepted Manuscript • DOI: 10.1021/la4043364 • Publication Date (Web): 17 Jan 2014 Downloaded from http://pubs.acs.org on January 21, 2014

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

Langmuir is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 26

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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, CO 80401, and Physical Sciences Division, Pacific Northwest National Laboratory, Richland, WA 99352 E-mail: [email protected]

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 †

1 ACS Paragon Plus Environment

Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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 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. 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 coatings for improved bio-compatibility, 28 patterning bio-functionalized surfaces, 21 templates for silicon nanowire growth, 29 and fabrication of novel biomimetic 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 in2 ACS Paragon Plus Environment

Page 2 of 26

Page 3 of 26

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

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


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 4 of 26

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

Overlap

D = 67 nm

Figure 1: Schematic representation of axial arrangement of collagen molecules (shown as green 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 4 ACS Paragon Plus Environment

Page 5 of 26

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

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)].

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).


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 6 of 26

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) =

 h¡ ¢ ¡ ¢i   4²ij σ 12 − σ 6 , r ≤ rc r r   0,

(1)

r > rc

where ²ij 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 21/6 σ so that the LJ interactions for these pairs are repulsive. In all our simulations, we have set ²11 = ²12 = 0.1², where ² 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) =

 · ³ ´2 ¸   −0.5kb r02 ln 1 − rr , r ≤ r0 0   ∞,

(2)

r > r0

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 = 30² and r0 = 1.5σ. To describe the flexibility of a molecule, we have imposed a bending potential between any three neighboring beads in a chain 39 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 = 75² and θ0 = 180◦ which gives largely straight molecules albeit flexible as expected from experiments.


Page 7 of 26

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

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 Na2 HPO4 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.


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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. 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 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. The collagen molecules are described by the interactions shown in Fig. 2(a), and also experience a downward constant acceleration and an attraction towards the substrate (i.e., the bottom face of the simulation cell.)


Page 8 of 26

Page 9 of 26

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

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 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 collagencollagen (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) =

 h ¡ ¢ ¡ ¢i   ²s 2 σ 9 − σ 3 , r ≤ rc 15 r r   0,

(4)

r > rc

where ²s defines the strength of the collagen–substrate interaction and rs is the cut-off 9 ACS Paragon Plus Environment

Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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 = ²/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/²)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 long 3,18,34 and has a molecular weight of ∼ 300kDa. 43 From these values and setting T = 300 K, we obtain σ = 15.8 nm, ² = 0.026 eV, m = 2.62×10−23 kg and τ = 1.25 ns. Fig. 5(a–c) illustrates the morphologies of the collagen assembly obtained at increasing the c–c interaction (²22 ) with respect to a constant c–s strength (²s ). 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 ²s kept constant at 0.7², 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 formation 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


Page 10 of 26

Page 11 of 26

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

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 ²22 , e.g. ²22 = 0.085², 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 studies 18,20,21 which report that at low concentrations, the K+ ions cannot effectively screen the c–s interactions. An increase in ²22 to 0.305² 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 ²22 ≤ 0.305², 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 ²22 , we found that the dominating interaction switches from c–s to c–c at ²22 ≥ 0.457². Such increase in ²22 leads to the formation of 3D-bundles [e.g., see Fig. 5(c) at ²22 = 0.457²]. 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 ²22 , ²22 ≤ 0.305². The dominating c–c interactions, however, enhance the mobility of the adsorbed molecules, which leads to


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Model a

Page 12 of 26

AFM

ε22 = 0.085ε d

100 mM

200 nm

b

ε22 = 0.305ε e

200 mM

200 nm

c

ε22 = 0.457ε

f

300 mM 200 nm

1 μm

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 ²s = 0.7² and different values of ²22 (a) 0.085², (b) 0.305², and (c) 0.457². 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.


2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

3 2 〈[r(t) - r(0)] 〉 (×10 σ )

Page 13 of 26

ε22= 0.457ε ε22= 0.406ε

t (×103 τ)

Figure 6: Mean square displacement of beads on the substrate (h[r(t) − r(0)]2 i) as a function of time (t) after deposition at different values of ²22 .

a

εs = 0.7ε b

εs = 0.875ε c

εs = 1.05ε d

εs = 1.225ε e

εs = 1.4ε

z (σ) 4 3

200 mM K+ pH 9

2 1

200 nm

f

g

h

0

i

j

Figure 7: Molecular dynamics study of the effect of the strength of c-s interaction on the morphology of the deposited collagen molecules during post-deposition heat treatment. The height variations of the molecules on the substrate at various values of ²s 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 ²s = 1.05² [panel (c)] are in excellent agreement with AFM images obtained at 200 mM K+ ions and pH 9.0 [inset, panel(c)].


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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 ²22 (0.457²), the molecules (chains) deposited on the substrate undergo higher mean square displacement h[r(t) − r(0)]2 i as compared to that at ²22 = 0.406²; this provides clear evidence that the surface diffusion of the collagen molecules is facilitated upon increasing ²22 . 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 ²22 = 0.457² [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 (²22 , ²s ) 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, ²22 = 0.406², ²s = 0.7², 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


Page 14 of 26

Page 15 of 26

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

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 0.7² 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 ²s = 0.7², 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 ²s to 0.875², the tendency to bundle is reduced. At 1.05 ², 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 ²s 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.


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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 (²22 and ²s ) 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 ²22 /²s , 0.1 < ²22 /²s < 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 < ²22 /²s < 0.6 [Fig. 5(b)]. Eventually, at very high K+ ion concentration (> 300 mM) in experiment and ²22 /²s > 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, ²22 ). The qualitative mapping between K+ ionic strength of the acidic buffer and the strength of the c–c interaction in our model (²22 ) 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 16 ACS Paragon Plus Environment

Page 16 of 26

Page 17 of 26

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

co-workers 18 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-deposition heat treatment of the collagen bundles shown in Fig. 5(c). This thermal treatment relieves the conformational frustration in the bundles resulting in a ordered structure with D-bands in 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 ²22 /²s 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 sidechains 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 in17 ACS Paragon Plus Environment

Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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 frustration. 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 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), 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


Page 18 of 26

Page 19 of 26

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

into the origin of the distribution in D-periodicity values. From their AFM studies, Leow and co-workers 18 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 ²s ≥ 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


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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., ²22 ≤ 0.305² and ²s = 0.7²), 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 ²22 ) or that show a preferred uniform orientation (at slightly higher values of ²22 ). At higher values of ²22 (> 0.457²), 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 ²22 and ²s [²22 = 0.406², ²s = 0.7²]. 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 ²s = 1.05² 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 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-AC02-05CH11231 and DE-AC52-07NA27344, respectively. Supercomputer time for the MD calculations was provided by the Golden Energy Computing Organization at Colorado 20 ACS Paragon Plus Environment

Page 20 of 26

Page 21 of 26

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

School of Mines.

References (1) Buehler, M. J. Nature designs tough collagen: explaining the nanostructure of collagen fibrils. Proc. Natl. Acad. Sci. USA 2006, 103, 12285–12290. (2) Gautieri, A.; Vesentini, S.; Redaelli, A.; Buehler, M. J. Hierarchical Structure and Nanomechanics of Collagen Microfibrils from the Atomistic Scale Up. Nano Lett. 2011, 11, 757–766. (3) Kadler, K. E.; Holmes, D. F.; Trotter, J. A.; Chapman, J. A. Collagen fibril formation. Biochem. J. 1996, 316, 1. (4) Shoulders, M. D.; Raines, R. T. Collagen Structure and Stability. Ann. Rev. Biochem. 2009, 78, 929–958. (5) Hulmes, D. J. Building collagen molecules, fibrils, and suprafibrillar structures. J. Struct. Biol. 2002, 137, 2. (6) Orgel, J. P.; Miller, A.; Irving, T. C.; Fischetti, R. F.; Hammersley, A. P.; Wess, T. J. The in situ supermolecular structure of type I collagen. Structure . Structure 2001, 9, 1061. (7) Wess, T. J.; Hammersley, A. P.; Wess, L.; Miller, A. Molecular packing of type I collagen in tendon. J. Mol. Biol. 1998, 275, 255. (8) Orgel, J. P. R. O.; Irving, T. C.; Miller, A.; Wess, T. J. Microfibrillar structure of type I collagen in situ. Proc. Natl. Acad. Sci. USA 2006, 103, 9001–9005. (9) Gale, M.; Pollanen, M. S.; Markiewicz, P.; Goh, M. C. Sequential assembly of collagen revealed by atomic force microscopy. Biophys. J. 1995, 68, 2124–2128.


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(10) Fratzl, P. Collagen: Structure and Mechanics; Springer: New York, 2008. (11) Cowin, S. C.; Doty, S. B. Tissue Mechanics; Springer: New York, 2007. (12) Holmes, D. F.; Gilpin, C. J.; Baldock, C.; Ziese, U.; Koster, A. J.; Kadler, K. E. Corneal collagen fibril structure in three dimensions: structural insights into fibril assembly, mechanical properties, and tissue organization. Proc. Natl. Acad. Sci. USA 2001, 98, 7307. (13) Akiyama, S. K.; Nagata, K.; Yamada, K. M. Cell surface receptors for extracellular matrix components. Biochim. Biophys. Acta 1990, 1031, 91. (14) Grinnell, F. Fibroblast biology in three-dimensional collagen matrices. Trends Cell Biol. 2003, 13, 264. (15) Myllyharju, J.; Kivirikko, K. I. Collagens and collagen-related diseases. Ann. Med. 2001, 33, 7. (16) Chernoff, E. A. G. Atomic force microscope images of collagen fibers. J. Vac. Sci. Tech. A Vac. Surf Films 1992, 10, 596. (17) Jiang, F.; H¨orber, H.; Howard, J.; Muller, D. J. Assembly of collagen into microribbons: effects of pH and electrolytes. J. Struct. Biol. 2004, 148, 268–278. (18) Leow, W. W.; Hwang, W. Epitaxially Guided Assembly of Collagen Layers on Mica Surfaces. Langmuir 2011, 27, 10907–10913. (19) Loo, R. W.; Goh, M. C. Potassium Ion Mediated Collagen Microfibril Assembly on Mica. Langmuir 2008, 24, 13276–13278. (20) Cisneros, D. A.; Hung, C.; Franz, C. M.; Muller, D. J. Observing growth steps of collagen self-assembly by time-lapse high-resolution atomic force microscopy. J. Struct. Biol. 2006, 154, 232–245. 22 ACS Paragon Plus Environment

Page 22 of 26

Page 23 of 26

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

(21) Cisneros, D. A.; Friedrichs, J.; Taubenberger, A.; Franz, C. M.; Muller, D. J. Creating Ultrathin Nanoscopic Collagen Matrices For Biological And Biotechnological Applications. Small 2007, 3, 956–963. (22) Maas, M.; Guo, P.; Keeney, M.; Yang, F.; Hsu, T. M.; Fuller, G. G.; Martin, C. R.; Zare, R. N. Preparation of Mineralized Nanofibers: Collagen Fibrils Containing Calcium Phosphate. Nano Lett. 2011, 11, 1383. (23) Fienberg, A. W.; Parker, K. K. Surface-Initiated Assembly of Protein Nanofabrics. Nano Lett. 2010, 10, 2184. (24) Poole, K.; Khairy, K.; Friedrichs, J.; Franz, C.; Cisneros, D. A.; Howard, J.; Mueller, D. Molecular-scale topographic cues induce the orientation and directional movement of fibroblasts on two-dimensional collagen surfaces. J. Mol. Biol. 2005, 349, 380. (25) Taubenberger, A. V.; Woodruff, M. A.; Bai, H.; Muller, D. J.; Hutmacher, D. W. The effect of unlocking RGD-motifs in collagen I on pre-osteoblast adhesion and differentiation. Biomaterials 2010, 31, 2827. (26) Stupp, S. I. Self-assembly and biomaterials. Nano Lett. 2010, 10, 4783. (27) Zhu, B.; Lu, Q.; Yin, J.; Hu, J.; Wang, Z. Alignment of osteoblast-like cells and cellproduced collagen matrix induced by nanogrooves. Tissue Eng. 2005, 11, 825. (28) Sinani, V. A.; Koktysh, D. S.; Yun, B.-G.; Matts, R. L.; Pappas, T. C.; Motamedi, M.; Thomas, S. N.; Kotov, N. A. Collagen Coating Promotes Biocompatibility of Semiconductor Nanoparticles in Stratified LBL Films. Nano Lett. 2003, 3, 1177. (29) Salhi, B.; Vaurette, F.; Grandidier, B.; Sti´evenard, D.; Coffinier, O. M. Y.; Boukherroub, R. The collagen assisted self-assembly of silicon nanowires. Nanotechnology 2009, 20, 235601.


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(30) Wu, S.; Liu, X.; Hu, T.; Chu, P. K.; Ho, J. P. Y.; Chan, Y. L.; Yeung, K. W. K.; Chu, C. L.; Hung, T. F.; Huo, K. F.; Chung, C. Y.; Lu, W. W.; Cheung, K. M. C.; Luk, K. D. K. A Biomimetic Hierarchical Scaffold: Natural Growth of Nanotitanates on Three-Dimensional Microporous Ti-Based Metals. Nano Lett. 2008, 8, 3803. (31) Fang, M.; Goldstein, E. L.; Matich, E. K.; Orr, B. G.; Holl, M. M. Type I collagen self-assembly: the roles of substrate and concentration. Langmuir 2013, 29, 2330. (32) Sun, M.; Stetco, A.; Merschrod S, E. F. Surface-Templated Formation of Protein Microfibril Arrays. Langmuir 2008, 24, 5418–5421. (33) Li, Y.; Asadi, A.; Monroe, M. R.; Douglas, E. P. pH effects on collagen fibrillogenesis in vitro: Electrostatic interactions and phosphate binding. Mat. Sci. Eng. C 2009, 29, 1643–1649. (34) Gautieri, A.; Russo, A.; Vesentini, S.; Redaelli, A.; Buehler, M. J. Coarse-Grained Model of Collagen Molecules Using an Extended MARTINI Force Field. J. Chem. Theor. Comput. 2010, 6, 1210–1218. (35) Schor, M.; Ensing, B.; Bolhuis, P. G. A simple coarse-grained model for self-assembling silk-like protein fibers. Faraday Discussions 2010, 144, 127–141. (36) Eyre, D. R.; Wu, J. J. Collagen cross-links. Top Curr. Chem. 2005, 247, 207–229. (37) Grest, G. S.; Kremer, K. Molecular dynamics simulation for polymers in the presence of a heat bath. Phys. Rev. A 1986, 33, 3628–3631. (38) Kremer, K.; Grest, G. S. Dynamics of entangled linear polymer melts: A molecular dynamics simulation. J. Chem. Phys. 1990, 92, 5057. (39) Plimpton, S. Fast parallel algorithms for short-range molecular dynamics. J. Comp. Phys. 1995, 117, 1.


Page 24 of 26

Page 25 of 26

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Langmuir

(40) Giraud-Guille, M. M.; Mosser, G.; Belamie, E. Liquid crystallinity in collagen systems in vitro and in vivo. Curr. Opin. Col. Inter. Sci. 2008, 13, 303. (41) Heine, D.; Grest, G.; Webb, E. Spreading dynamics of polymer nanodroplets. Phys. Rev. E 2003, 68, 061603. (42) Schneider, T.; Stoll, E. Molecular-dynamics study of a three-dimensional onecomponent model for distortive phase transitions. Phys. Rev. B 1978, 17, 1302. (43) Zhang, Z.; Li, G.; Shi, B. Physicochemical Properties of Collagen, Gelatin and Collagen Hydrolysate derived from bovine limed split wastes. J. Soc. Leather Tech. Chem. 2006, 90, 23–28. (44) Schlegel, M. L.; Nagy, K. L.; Fenter, P.; Cheng, L.; Sturchio, N. C.; Jacobsen, S. D. Cation sorption on the muscovite (001) surface in chloride solutions using highresolution X-ray reflectivity. Geochim. Cosmochim. Acta 2006, 70, 3549. (45) Heinz, H.; Castelijns, H. J.; Suter, U. W. Structure and Phase Transitions of Alkyl Chains on Mica. J. Am. Chem. Soc. 2003, 125, 9500. (46) Bozec, L.; van der Heijden, G.; Horton, M. Collagen Fibrils: Nanoscale Ropes. Biophys. J. 2007, 92, 70. (47) Fang, M.; Goldstein, E. L.; Turner, A. S.; Les, C. M.; Orr, B. G.; Fisher, G. J.; Welch, K. B.; Rothman, E. D.; Holl, M. M. B. Type I Collagen D-Spacing in Fibril Bundles of Dermis, Tendon, and Bone: Bridging between Nano- and Micro-Level Tissue Hierarchy. ACS Nano 2013, 6, 9503.


Langmuir

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Graphical TOC Entry In-vitro collagen self-assembly Model AFM


Page 26 of 26

Self-Assembly of Collagen on Flat Surfaces: The Interplay of Collagen

Recommend Documents