Molecular dynamics simulation of the adhesive behavior of collagen on smooth and randomly rough TiO2 and Al2O3 surfaces

Computational Materials Science 71 (2013) 172–178

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Molecular dynamics simulation of the adhesive behavior of collagen on smooth and randomly rough TiO2 and Al2O3 surfaces S. Ebrahimi a, K. Ghafoori-Tabrizi b, H. Rafii-Tabar a,c,⇑ a

Computational Physical Sciences Research Laboratory, School of Nano-Science, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395- 5531, Tehran, Iran Department of Physics, Shahid Beheshti University, Evin, Tehran, Iran c Department of Medical Physics and Biomedical Engineering and Research Centre for Medical Nanotechnology and Tissue Engineering, Shahid Beheshti University of Medical Sciences, Evin, Tehran, Iran b

a r t i c l e

i n f o

Article history: Received 19 September 2012 Received in revised form 18 December 2012 Accepted 5 January 2013 Available online 24 February 2013 Keywords: Collagen Ceramic MD simulation Roughness surface Contact surface Tissue engineering

a b s t r a c t Molecular dynamics (MD) simulations are performed to investigate the adhesion energy of type I collagen on smooth and rough ceramic rutile TiO2 (1 0 0) and a-Al2O3 (0 0 0 1) surfaces. To generate almost real-like rough surfaces, the self affine fractal method is employed and the effect of degree of roughness on adhesion is investigated. By adopting an overlayer-substrate model, the variation of adhesion force with distance is computed. We show that when the surface roughness is increased, the adhesion energy and the adhesion force correspondingly increase. It is found that the adhesion to rutile TiO2 (1 0 0) surface is far stronger than that to the a-Al2O3 (0 0 0 1) surface. Furthermore, we show that the deformation of collagen layer is dependent on the degree of surface roughness. Ó 2013 Elsevier B.V. All rights reserved.

1. Introduction Ceramic alloys, such as titania (TiO2) [1,2] and alumina (Al2O3) [2,3], and metals, such as titanium and titanium foam [3–7], are used extensively in medical technology as materials for implants and prosthesis due to their good biocompatibility and absence of toxicity. Experimental investigations show that TiO2 and a-Al2O3 can form contact with various proteins in the tissues of human body [1,3,8]. Compared to metal implants, ceramic surfaces can provide a higher biocompatibility. Due to increasing use of implants in regenerative medicine and tissue engineering, extensive world-wide research has focused on developing biocompatible materials that possess suitable mechanical and adhesive properties, for immediate use in such fields as bone repair and dental reconstruction. Alumina and titania, as bioceramics, are used in artificial organs due to their high mechanical strength and their in vivo safety. Aluminum oxide has been used for years in medical applications [9]. Dental implant abutments made from alumina have shown both an improved esthetics and biocompatibility compared to metal abutments [10–12]. It is believed that the biocom⇑ Corresponding author at: Department of Medical Physics and Biomedical Engineering, and Research Center for Medical Nanotechnology and Tissue Engineering, Shahid Beheshti University of Medical Sciences, Evin, Tehran, Iran. Tel: +98 21 23872566; fax: +98 21 22439941. E-mail address: rafi[email protected] (H. Rafii-Tabar). 0927-0256/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.commatsci.2013.01.017

patibility of titanium stems from the property of the titanium oxide layer that is naturally formed on its surface [13]. There have also been studies concerning the interaction of blood constituents with titanium oxide layers. Two studies [14,15] have indicated that titanium oxide films, in both amorphous and crystalline forms, possess a better hemocompatibility than low temperature isotropic pyrolytic carbon (LTIC). There are a number of computational works that have focused on the adhesion of biological polymers, such as collagen, on titanium oxide [16–21]. Koppen and coworkers investigated the adsorption of type I collagen triple helices, in aqueous solution, on titanium oxide employing classical MD simulation. They showed that the proteins establish few contact points with the surface. They suggested that the contact area per molecule may increase with time, and hence the adsorption energy would also increase with time [16]. In another work [17] they found that the adhesion energy of peptides on titanium dioxide surface depends on the charges of the surface hydroxyl groups. Adhesion energies of between 40 and 190 kJ/mol for glutamic acid and lysine side chains to this surface were obtained. Chen and coworkers modeled the adsorption of Arg-Gly-Asp (RGD) on rutile TiO2 (1 1 0) surface, and their results show that the adsorption of RGD onto grooved rutile TiO2 (1 1 0) surface is more stable and rapid than that onto a perfect surface [18]. Solid surfaces are rough, and the structure of most surfaces appears to be randomly rough on nanoscopic scales. In order to study

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the adhesive properties of two rough surfaces, normally a tip-substrate geometry, together with finite element methods, MD simulation method, and even multiscale modeling approaches have been adopted [19–35]. To our knowledge, the adhesion energy of collagen on alumina and the effect of surface roughness on this adhesion energy has not been computationally evaluated. Furthermore, there are a few computational studies which have investigated the adhesion of proteins to ceramic surfaces [16–21]. In this paper, we have extended a contact-mechanic model [19], to derive the adhesion energy of type I collagen on a-Al2O3 (0 0 0 1) and rutile TiO2 (1 0 0) surfaces. Our motivation for choosing collagen is that it is an important constituent protein of skin, bone, tendon, cartilage, blood vessels and teeth. Collagen molecules are composed of three polypeptide chains with a length of 300 nm and a diameter of 1.5 nm formed in a staggered self-assembled fashion [29]. We use self-affine fractal method [19] to generate randomly rough surfaces on nanoscopic scales. The organization of this paper is as follows. In Section 2 details of the atomistic modeling, including the prescribed inter-atomic potentials and force fields employed to describe the energetics of the various systems, are provided. This section also includes the description of the method used to generate randomly rough surfaces on nanoscopic scales. Section 3 summarizes the results and their appropriate discussions.

2. Details of atomistic-based modeling 2.1. Generation of randomly rough surface via self-affine fractal method The self affine fractal surfaces were generated via the procedure described in references [27,30,31]. The rutile TiO2 (1 0 0) and aAl2O3 (0 0 0 1) surfaces used in this work have an initially flat geometry. The x, y plane lies parallel to the surface plane, and z = h(x) is the surface height profile, where x = (x, y) is the position vector within the surface plane. The surface roughness power spectrum is of the form [27,30,31],

CðqÞ ¼

1

Z

ð2pÞ2

2

d xhhðxÞhð0ieiqx

ð1Þ

where h...i denotes the ensemble average, q is the wave vector, and h(x) is the surface height written as,

hðxÞ ¼

X

BðqÞei½qxþuðqÞ

ð2Þ

q

with h(x) being real, and u(q) are independent random variables, uniformly distributed in the interval [0, 2p], and

Table 1 The Morse potential parameters for the Ti–O system [35].

Ti–Ti Ti–O O–O

De (eV)

a0 (A1)

r0(A1)

0.00567139 1.0279493 0.042117

1.5543 3.640737 1.1861

4.18784 1.88265 3.70366

Table 2 The Buckingham potential parameters for the Al-O system [36].

Al–O O–O

A (eV)

C (eV/A6)

r0(A1)

12201 1844

31.99 192.5

0.1956 0.3436

Fig. 1. Simulation snapshots showing: (a) the initial configuration of collagen-rutile TiO2 (1 0 0) surface before equilibration, (b) after equilibration, (c) the initial configuration of collagen-a-Al2O3 before equilibration and (d) after equlibration.

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smooth surface 50

Fz (eV/A)

0 -50 0

2

4

6

8

10

-100 -150 -200 -250 -300 -350 -400

Distance (A)

(a) H=0.95

50

0

0 -50 0

2

4

6

8

-50 0

10

-100

Fz (eV/A)

Fz (eV/A)

H=0.75

50

-150 -200 -250

4

-350 -400

Distance (A)

(b)

(c)

H=0.65

H=0.55

50

50

0 4

6

8

10

-50 0

Fz (eV/A)

Fz (eV/A)

0 2

-100 -150 -200 -250

6

8

10

-200 -250 -300 -350 -400

(d)

4

-150

-350

Distance (A)

2

-100

-300 -400

10

-250 -300

-50 0

8

-200

-350

Distance (A)

6

-150

-300 -400

2

-100

Distance (A)

(e)

Fig. 2. Variations of the simulated force of adhesion of type I collagen with distance from rutile TiO2 surface: (a) smooth surface, (b–e) for rough surfaces with H = 0.95, H = 0.75, H = 0.65, and H = 0.55 respectively. The broken and solid arrows respectively indicate the approach and the retraction phases.

BðqÞ ¼

  2p ½CðqÞ1=2 L

ð3Þ

where L is of the order of the inter-atomic bond distance. By assuming isotropic statistical properties of the surface, C(q) will only depend on the magnitude of wave vector q = |q|. The q in this work is in the range 2p=L 6 q 6 216  2p=L. The power spectrum for a self-affine surface has the power-law behavior [27]

CðqÞ  q2ðHþ1Þ

ð4Þ

where H is the Hurst exponent, and is related to the fractal dimension D via [30,31]

D ¼ 3  H:

2.2. Prescribed inter-atomic force fields 2.2.1. Non-bonding inter-atomic potential In our modeling, we have described the energetics of the nonbonding interactions between all pairs of collagen atoms, and collagen atoms and the substrate atoms (TiO2 and Al2O3) via Lennard pffiffiffiffiffiffiffi Jones potentials, and for the mixed state the rules eij ¼ ei ej and ri þrj rij ¼ 2 have been used, where eij and rij are the standard Lennard–Jones potential parameters describing the interaction of atoms i and j. The expression used for the cut-off distance was rcutij ¼ 21=6 rij , and its value was different for different atomic interactions. The corresponding potential parameters were taken from the Param file of the Tinker software package [34] for collagen atoms and from Ref. [35] for the ceramic atoms.

ð5Þ

It is evident from Eq. (5) that the smaller the parameter H, the larger is D, and hence the more irregular (or more rough) the surface becomes. When H > 1/2, the correlation in the successive steps is positive, whereas when H < 1/2 this correlation is negative. For H = 1/ 2, the successive steps in the trajectory are uncorrelated [32,33].

2.2.2. Collagen inter-atomic potentials For the bonding interactions three standard potentials namely, the harmonic bond-stretch, harmonic bond-bending, and the dihedral cosine potentials, were used. All potential parameters for bonding interactions were taken from the Param file of the Tinker software package [34].

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U TiO2 ðr ij Þ ¼ De ð½1  ea0 ðrij r0 Þ 2  1Þ U Al2 O3 ðrij Þ ¼ Aerij =r0 

ð6Þ

C r 6ij

ð7Þ

where rij is the separation distance between atoms i and j, and De is related to bond strength, r0 is the equilibrium inter-atomic separation, a0 is related to the curvature at the potential minimum, A and C scale the repulsive and attractive parts of interaction potential. In our simulations we have also used these potentials to describe the energetics of ceramic atoms. The Morse and Buckingham potential parameters for TiO2 and Al2O3 are listed in Tables 1 and 2, respectively. 2.3. Atomistic level structure of collagen-alumina and collagen-titania systems, and simulation data Fig. 3. The curve with square markers shows variations of equilibrium distance at contact for type I collagen for TiO2 surface with Hurst exponent (H) (left hand axis), and the curve with circle markers shows variations of adhesion energy with H (right hand axis).

2.2.3. Ceramics inter-atomic potentials The potentials that have been used for ceramics in previous MD simulations [36,37] were the Morse potential for rutile TiO2 and the Buckingham potential for a-Al2O3. These were of the form:

The molecular structure of the type I collagen on TiO2 and on aAl2O3 smooth surfaces is shown in Fig. 1. The initial configuration of collagen which we used in this work was a typical structure0 consisting of a triple-helix collagen molecule of length 116 Å A and 0 diameter 17.0 Å A, composed of 1299 atoms. The type chosen by us is computationally less expensive than the other type of collagen. The coordinates of this collagen were obtained from Protein Data Bank (PDB, 1CLG.pdb) [38]. This structure contains essentially only

Table 3 The adhesion energy, adhesion force at contact, and the equilibrium distance at contact for type I collagen on TiO2 smooth surface, and for surfaces with different degree of roughness. Type Smooth H = 0.55 H = 0.65 H = 0.75 H = 0.95

0

0

Maximum height of rough surface (Å A)

Equilibrium distance (Å A)

0 1.32 1.06 0.9 0.8

4.69 2.82 2.88 3.84 3.91

Force at contact (nN)

Adhesion energy (eV)

209.86 562.30 546.28 371.66 379.67

8.54 260.48 228.92 123.03 121.11

Fig. 4. Simulation snapshots of adhesion of type I collagen on TiO2 smooth surface (a–c), and rough surface with H = 0.55 (d–f). Complete cycle of approach (top), contact (center) and retraction (bottom) phases.

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GLY and PRO AA with an ideal structure. Here we discuss typical simulations dealing with the phenomenon of adhesion of collagen on rutile TiO2 (1 0 0) and a-Al2O3 with smooth and rough surfaces. The rutile TiO2 slab in all simulations consisted of 3745 atoms and the a-Al2O3 slab in all simulations consisted of 3850 atoms. Rough surfaces on slabs were generated by self-affine fractal method discussed in Section of 2.1. First, the collagen and the substrates (slabs) were equilibrated together within an NPT ensemble to find the optimum value of the volume of the simulation cell. The equilibration phase was performed for 150,000 up to 200,000 timesteps for different substrates. Following the equilibration, they were aligned in the z-direction and shifted with respect to each other, as shown in Figs. 1a, and c, and the system was again reequilibrated. The final equilibrated cell dimensions for various samples of collagen-TiO2 and collagen-a-Al2O3 were 26  41  118 Å3 and 15  20  118 Å3, respectively. Periodic boundary conditions were applied in x- and y-directions. Figs. 1b and d show respectively the collagen on TiO2 smooth surface and the collagen on a-Al2O3 smooth surface after equilibration. The actual simulation phase0 was conducted within an NVT ensemble. A displacement of 0.2 Å A was applied to all collagen atoms in the zdirection, away from and towards the substrate, and then the system was reequilibrated. By repeating this procedure, the force experienced by collagen atoms in the z-direction was obtained for various distances. In each simulation, the aim was to compute

the force of adhesion, which was defined as the negative force required to separate the adsorbent from the surface. To do this, following the initial contact between the collagen atoms and the substrate surface, the direction of motion of the collagen atoms was reversed and the force was computed during all stages, and the associated three dimensional structural transformations were recorded. The temperature was set at T = 300 K and the Nose–Hoover thermostat method [39–41] was employed to maintain the temperature constant during all phases of the simulation, with the instantaneous temperature reading as T = 300 ± 1 K during the equilibration phase. Following equilibration, the simulations were conducted within an NVT ensemble. The velocity Verlet algorithm [42] was used to integrate the equations of motion with the simulation time-step set at dt = 0.1 fs.

3. Results and discussion In this section the 10 simulation runs involving the adhesion of type I collagen on rutile TiO2 (1 0 0) and a-Al2O3 (0 0 0 1) substrates, with smooth and rough surfaces, are reported. In order to ascertain the effect of roughness on adhesion energy, rough alumina and titania surfaces with various Hurst exponent (H) were generated. As discussed before, a 0.2 Å displacement was applied to collagen atoms to displace them towards the ceramic surfaces until an equi-

Smooth surface

40

Fz (eV/A)

20 0 -20

4

4.5

5

5.5

6

6.5

7

-40 -60 -80

Distance (A)

(a) H=0.95

40 20

20

0 4

4.5

5

5.5

6

6.5

7

7.5

-20 -40

Fz (eV/A)

Fz (eV/A)

H=0.75

40

-60

0 4

4.5

5

-80

Distance (A)

7.5

Distance (A)

H=0.65

H=0.55 40

20

20

0 4.5

5

5.5

6

-40 -60

6.5

7

7.5

Fz (eV/A)

Fz (eV/A)

7

(b)

40

-80

6.5

-40

(c)

-20

6

-60

-80

4

5.5

-20

0 -20

4

4.5

5

5.5

6

6.5

7

7.5

-40 -60

Distance (A)

(e)

-80

Distance (A)

(d)

Fig. 5. Variations of the simulated force of adhesion with distance of type I collagen on a-Al2O3 surface for: (a) smooth surface, and rough surfaces with, (b) H = 0.95, (c) H = 0.75, (d) H = 0.65, (e) H = 0.55 respectively. The broken and solid arrows respectively indicate the approach and the retraction phases.

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177

librium contact distance was established. The force between the collagen and the substrate atoms was computed during the approach phase. Then the approach distance was further increased from its equilibrium value until a repulsive interaction set in. The direction of motion was then reversed, i.e., the retraction phase was started. By the equilibrium contact, we mean the distance at which the repulsive interaction begins. This is the standard definition of equilibrium contact point in such instruments as the Atomic Force Microscope. The results show that, PRO amino acids formed the surface contacts. Then by reversing the direction of motion, i.e. pulling away the collagen, in the z-direction, the force-distance curves for the collagen atoms were obtained. The hystereses in the force-distance curves were observed in all simulation runs. These hystereses were indicative of the deformation generated in the structure of collagen. Furthermore, the adhesion energy was computed via Fig. 6. The curve with square markers shows variations of the equilibrium distance at contact of type I collagen for a-Al2O3 surfaces with Hurst exponent (H) (left hand axis), and the curve with circle markers shows variations of adhesion with H (right hand axis).

Eadhesion ¼

Z

F z dz

ð8Þ

which is the integral of the force over the distance. 3.1. Collagen-TiO2 (1 0 0) contact

Table 4 The adhesion energy, adhesion force at contact, and the equilibrium distance at contact for type I collagen on a-Al2O3 smooth surface, and for surfaces with different degree of roughness. Type

Maximum height of

Equilibrium

0

Smooth H = 0.55 H = 0.65 H = 0.75 H = 0.95

0

rough surface (Å A)

distance (Å A)

0 1.32 1.06 0.9 0.8

5.57 4.23 4.63 4.46 4.46

Force at contact (nN)

Adhesion energy (eV)

34.44 107.97 77.54 65.68 66.0

4.36 28.95 27.97 23.15 22.91

In the case of collagen adsorption on TiO2 (1 0 0) surface, the variation of force with distance was obtained for smooth and rough surfaces. For the smooth surface, the hysteresis is too small (Fig. 2a), while by increasing the roughness, i.e., by decreasing H, the hysteresis increases (Figs. 2b–e). In the cases of H = 0.55 and H = 0.65 the sizes of the hystereses are considerably enhanced (Figs. 2d and e) and they are almost twice bigger than those corresponding to the cases of H = 0.75, and H = 0.95 (Figs. 2b and c). Therefore, the adhesion energy is enhanced when the roughness of the surface is increased. As can be seen from Fig. 3, for the cases with H 6 0:65 the adhesion energy increases significantly. Figs. 2 and 3 show that the contact equilibrium distance is in range of

Fig. 7. Simulation snapshots of adhesion of type I collagen on a-Al2O3 smooth surface (a–c), and rough surface with H = 0.55 (d–f). Complete cycle of approach (top), contact (center) and retraction (bottom) phases.

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2.82–4.69 Å A, which by increasing H, is increased. All results are listed in Table 3. We found that the force of rupture of collagen from various surfaces was in range of 209 to 562 nN, with the negative sign showing the direction of force. Experimental values range from 1 nN for smaller systems, such as bovine serum albumin [43], with only few contact points to 1.2 lN for collagen on titanium dioxide [44]. Our results are within the range of experimental data. In addition, the adhesion energy is in the range of 0.6 kJ/mol for smooth surface to 18 kJ/mol for a surface with H = 0.55. Chen et al. [18] have shown computationally that for RGD tripeptide adsorbed on rutile TiO2 (1 1 0) surface, groove surfaces provided higher reactive adsorption sites, and that the adsorption energy was in the range of 1179.22 to 377.21 kcal/ mol for groove and perfect surfaces, respectively. Fig. 4 shows the snapshots of the adhesion of collagen on rutile TiO2 (1 0 0). This figure shows that for a smooth surface the number of contact points is small, while by increasing the roughness, the number of contact points will increase. Furthermore, by increasing the surface roughness the collagen deformation increases as well.

experimental data. To our knowledge there is no experimental or computational data for adhesion energy of type I collagen on the a-Al2O3 surface. Our results show that by increasing the roughness, the number of contact points between the adsorbent and the surface increases, and the equilibrium distance between these two is reduced. Furthermore, the collagen deformation is depended on the surface roughness. In the case of a smooth surface, a minimum deformation of collagen is observed. The adhesion energy of type I collagen on rutile TiO2 (1 0 0) rough surface is much more enhanced compared with the adhesion of the same material on the a-Al2O3 (0 0 0 1) rough surface. The energy of adhesion of collagen on smooth surfaces is weak for both ceramics. Our results suggest that the rutile TiO2 (1 0 0), with a high rough surface, i.e., for H = 0.55, provides the maximum adhesion. This information would be very useful in the field of designing artificial ceramic-based implants wherein by manipulating the surface structure of the implant material, an optimal adhesive property can be achieved.

3.2. Collagen-a-Al2O3 (0 0 0 1) contact

[1] N. Huang, P. Yang, Y.X. Leng, J.Y. Chen, H. Sun, J. Wang, G.J. Wang, P.D. Ding, T.F. Xi, Biomaterials 24 (2003) 2177–2187. [2] T.J. Webster, R.W. Siegel, R. Bizios, Biomaterials 20 (1999) 1221–1227. [3] Y. Yokoyama, T. Tsukamotoa, T. Kobayashib, M. Iwaki, Surf. Coat. Technol. 196 (2005) 298–302. [4] T. Hanawa, Jpn. Dent. Sci. Rev. 46 (2010) 93–101. [5] B.S. Daniela, Bone 49 (2011) 463–472. [6] S. Rammelt, E. Schulze, R. Bernhardt, U. Hanisch, D. Scharnweber, H. Worch, H. Zwipp, J. Ortho. Res. 22 (2004) 1025–1034. [7] S. Glorius, B. Nies, J. Farack, P. Quadbeck, R. Hauser, G. Standke, S. Rößler, D. Scharnweber, G. Stephani, Adv. Mater. Eng. 13 (2011) 1019–1023. [8] H. Li, Y. Li, J. Jiao, H.-M. Hu, Nature Nanotechnol. 6 (2011) 645–650. [9] G. Heimke, Osseo-Integrated Implants, vol. 1, CRC Press, Boca Raton, FL, 1990. [10] V. Prestipino, A. Ingber, J. Esthet. Dent. 5 (1993) 29–36. [11] V. Prestipino, A. Ingber, J. Esthet. Dent. 8 (1996) 255–262. [12] G. Heydecke, M. Sierraalta, M.E. Razzoog, Int. J. Prosthodont. 15 (2002) 488– 493. [13] B. Kasemo, J. Prosthet. Dent. 49 (1983) 832–837. [14] N. Huang, P. Yang, X. Cheng, Y.X. Leng, X.L. Zheng, G.J. Cai, Z.H. Zhen, F. Zhang, Y.R. Chen, X.H. Liu, T.F. Xi, Biomaterials 19 (1998) 771–776. [15] F. Zhang, X.H. Liu, Y.G. Mao, N. Huang, Y. Chen, Z.H. Zheng, Z.Y. Zhou, A.Q. Chen, Z.B. Jiang, Surf. Coat. Technol. 103–104 (1998) 146–150. [16] S. Koppen, B. Ohler, W. Langel, Z. Phys. Chem. 221 (2007) 3–20. [17] S. Koppen, W. Langel, Langmuir 26 (2010) 15248–15256. [18] M. Chen, C. Wu, D. Song, W. Dong, K. Li, J. Mater. Sci: Mater. Med. 20 (2009) 1831–1838. [19] W. Friedrichs, B. Ohler, W. Langel, S. Montiand, S. Koppen, Adv. Eng. Mater. 13 (2011) B334–B342. [20] H. Chen, X. Su, K. Neoh, W. Choe, Langmuir 24 (2008) 6852–6857. [21] A.A. Skelton, T. Liang, T.R. Walsh, Appl. Mater. Interfaces 1 (2009) 1482–1491. [22] H. Rafii-Tabar, Phys. Rep. 325 (2000) 239–310. [23] L. Kogut, I. Etsion, ASME J. Appl. Mech. 69 (2002) 657–662. [24] T.H. Fang, C.I. Weng, Nanotechnology 11 (2000) 148–153. [25] Q.C. Hsu, C.D. Wu, T.H. Fang, Comput. Mater. Sci. 34 (2005) 314–322. [26] J.F. Lin, T.H. Fang, C.D. Wu, K.H. Houng, Comput. Mater. Sci. 40 (2007) 480–484. [27] C. Yang, U. Tartaglino, B.N.J. Persson, Eur. Phys. J. E 19 (2006) 47–58. [28] B.Q. Luan, S. Hyun, J.F. Molinari, N. Bernstein, M.O. Robbins, Phys. Rev. E 74 (2006) 046710. 11pp. [29] A. Rich, F.H.C. Crick, J. Mol. Biol. 3 (1961) 483–506. [30] B.N.J. Persson, O. Albohr, U. Tartaglino, A.I. Volokitin, E. Tossati, J. Phys. Condens. Mat. 17 (2005) R1–R62. [31] B.N.J. Persson, J. Chem. Phys. 115 (2001) 3840–3861. [32] H. Makse, S. Havlin, M. Schwartz, H.E. Stanley, Phys. Rev. E 53 (1996) 5445– 5449. [33] Sh. Behzadi, H. Rafii-Tabar, J. Mol. Graph. Modell. 27 (2008) 356–363. [34] J.W. Ponder, Tinker-Software Tools for Molecular Design Ver. 4.2. Washington University School of Medicine, St. Louis, MO, 2004. [35] L. Zhao, L. Liu, H. Sun, J. Phys. Chem. C 111 (2007) 10610–10617. [36] V. Swamy, J.D. Gale, L.S. Dubrovinsky, J. Phys. Chem. Solids 62 (2001) 887–895. [37] B.W.M. Thomas, R.N. Mead, G. Mountjoy, J. Phys.: Condens. Mat. 18 (2006) 4697–4708. [38] H.M. Berman, J. Westbrook, Z. Feng, G. Gilliland, T.N. Bhat, H. Weissig, I.N. Shindyalov, P.E. Bourne, Nucleic Acids Res. 28 (2000) 235–242. [39] S. Nose, Mol. Phys. 52 (1984) 255–268. [40] W.G. Hoover, Phys. Rev. A 31 (1985) 1695–1697. [41] W.G. Hoover, Phys. Rev. A 34 (1986) 2499–2500. [42] Loup. Verlet, Phys. Rev. 159 (1967) 98–103. [43] N. Schwender, K. Huber, F. Al Marrawi, M. Hannig, Ch. Ziegler, Appl. Surf. Sci. 252 (2005) 117–122. [44] G. Jänchen, M. Mertig, W. Pompe, Surf. Interface Anal. 27 (1999) 444–449.

In the case of collagen adhesion on the a-Al2O3 surface, the force-distance variations were obtained for the smooth surface. Fig. 5a shows that the hysteresis is too small. By increasing the roughness, i.e., decreasing H, the hysteresis increases, as seen in Figs. 5b–e. In cases of H = 0.55 and H = 0.65 the sizes of hystereses, shown in Figs. 5d and e, are larger than those corresponding to H = 0.75, and H = 0.95, shown in Figs. 5b and c. Compared to collagen-TiO2, the hystereses are insignificant for all cases. Compared with collagen-TiO2, the changes of equilibrium distance of contact point is low. The equilibrium distance of contact point is in range of 0 4.23–5.57 Å A (Fig. 6). Figs. 5 and 6 show the adhesion energy for the cases with H 6 0:65. As can be seen from these figures the adhesion energy is quite significant for higher values of H. All results are summarized in Table 4. The rupture force of collagen from various surfaces was computed to be in the range of 21.5 to 67.4 nN. In addition, the adhesion energy was in the range of 0.31 for a smooth surface to 2.02 kJ/mol for a surface with H = 0.55. Compared to collagen-TiO2 adhesion, the collagen-alumina adhesion energy is too weak. Fig. 7 shows the snapshots of adhesion of type I collagen on a-Al2O3 (0 0 0 1) surface, during the complete cycle of approach (top), contact (center) and retraction (bottom). This figure shows that for a smooth surface the number of contact points is small, while for the rough case the number of contact points is almost similar. This figure also shows that for a smooth surface, the collagen shape is almost undeformed, while for another case the deformation of collagen is increased when the surface roughness is increased. 4. Conclusion In this paper, we have investigated the adhesion of type I collagen on ceramics (rutile TiO2 (1 0 0) and a-Al2O3 (0 0 0 1)) smooth and rough surfaces. By using classical MD simulation, the variations of the adhesion force with distance of collagen from surface have been obtained for various types of surfaces. The equilibrium distance for contact, the adhesion force, and adhesion energy have been computed in all simulations. In order to find the effect of rough surfaces on adhesion, the self-affine fractal method was employed to generate randomly rough surfaces on nanoscopic scales. Our results show that by decreasing the Hurst exponent, i.e., by increasing the roughness, the adhesion energy is enhanced. This enhancement is considerable for a surface with H 6 0.65. Our computed adhesion energy for type I collagen on rutile TiO2 (1 0 0) surface is in the range of

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