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Thermodynamic Underpinnings of Cell Alignment on Controlled Topographies

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Yifu Ding , * Jirun Sun , Hyun Wook Ro , Zhen Wang , Jing Zhou , Nancy J. Lin , Marcus T. Cicerone , Christopher L. Soles , and Sheng Lin-Gibson *

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Surface topography is an important environmental cue for con-trolling cellular responses such as morphology, adhesion, align-ment, migration, and gene expression. [ 1–7 ] Surface topographies with feature sizes covering the range of cell and cell compo-nents, i.e., from a few nanometers to tens of micrometers, have been broadly investigated with respect to effects on cell contact guidance (CG). [ 2 , 8 ] Despite the signifi cant work done to date, there has not been a satisfactory general explanation for the phenomenon, although many hypothesize that it is related to a biological response. In this paper, we fabricate a platform with precisely controlled surface topography, and use it to per-form systematic cell studies that lead us to a new mechanistic understanding of CG under these conditions, which indicates that the response is rapid and largely physical rather than bio-logical in nature.

Below, we describe a two-step approach to fabricate sub-micrometer polymer gratings with continuous variations in grating height ( H ). First, large-area uniform gratings consisting of equally spaced lines were generated via nanoimprint lithog-raphy [ 9 , 10 ] on polystyrene (PS) and polymethylmethacrylate (PMMA). For each polymer, two sets of gratings were created with one-to-one line-to-space ratios, each with a pitch ( Λ ) of approximately 420 and 800 nm. Next, the uniformly patterned area was transformed to a continuous gradient in height by annealing on a thermal gradient stage for a fi xed time (see Sup-porting Information for details). A sketch of an annealed pat-tern with a height gradient is shown in the inset of Figure 1 . As indicated, the direction of the gradient is parallel to that of the polymer lines.

Figure 1 shows position-dependent grating heights for two PS gratings ( Λ = 420 and 800 nm). The grating heights were characterized by atomic force microscopy (AFM) and are nor-malized in Figure 1 by the maximum height, H 0 , at x = 0.

© 2011 WILEY-VCH Verlag GmAdv. Mater. 2011, 23, 421–425

Dr. Y. Ding , Dr. J. Sun ,[+] Dr. H. W. Ro , Dr. J. Zhou , Dr. N. J. Lin , Dr. M. T. Cicerone , Dr. C. L. Soles , Dr. S. Lin-Gibson Polymers Division, National Institute of Standards and Technology100 Bureau Dr. Gaithersburg, MD 20899, USA E-mail: slgibson@nist.gov Prof. Y. Ding , Z. Wang Department of Mechanical EngineeringUniversity of Colorado at BoulderBoulder, CO 80309, USA E-mail: Yifu.Ding@Colorado.Edu [+] Present address: American Dental Association Foundation, Paffenbarger Research Center, 100 Bureau Dr. Gaithersburg, MD 20899-8546, USA

DOI: 10.1002/adma.201001757

The abscissa is defi ned with its origin at the low-temperature side of the grating, where H is only slightly less than the ini-tial imprinted value. For all samples, H ( x ) continuously varies between approximately 320 and 0 nm across the 20 mm fi eld of the grating. The H ( x ) profi le was found to be in agreement with theoretical predictions based on a surface tension driven vis-cous fl ow of the polymer during annealing. [ 11 , 12 ] The details of the theoretical prediction and gradient grating data for PMMA are described in the Supporting Information, Figure S3b.

Standard procedures [ 13 ] were used to culture and image MC3T3-E1 murine preosteoblast cells on all PS and PMMA gradient gratings. Cell orientation, measured as a function of time, indicates that alignment occurs during the initial cell spreading ( Figure 2 a and b) and is dominated by passive wet-ting behaviors rather than the more active biological processes required for focal adhesion complex formation or cytoskeletal rearrangement. No statistical differences were observed in the orientation angle of the cells at the incipient point of attachment (20 min culture) compared to longer time points (up to 20 h), although the aspect ratio of the cells continues to increase until 3 h ( Figure 2 b). Figure 2 c displays representative fl uorescence

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Figure 1 . AFM measured grating height ( H(x) , normalized by the height at x = 0) as a function of position ( x , with 0 at the tall pattern side) for annealed PS gratings with 420 nm (black symbols) and 800 nm (red sym-bols) pitch. Symbols and error bars represent experimental data averaged from 3 samples and the corresponding standard deviations. The lines represent theoretical predictions for H x ∼ x , according to the mechanism of surface tension driven viscous fl ow (see Supporting Information).

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Figure 2 . a) Representative optical microscopy image taken at 20 min after seeding shows that cells develop strong alignment along the grating direction ( H ≈ 300 nm, Λ = 800 nm). b) Optical images of the same four cells at 20, 40, and 120 min are shown. The average orientation angle for a statistical population of cells ( n ≥ 30) does not change as the cells continue to elongate along the grating. c) Representative fl uorescence microscopy images of cells seeded on a grating ( Λ = 800 nm) at three positions along the height gradient show decreasing alignment with decreasing height: (top, c) cells at H ≈ 300 nm, (middle, c) cells at H ≈ 150 nm, and (bottom, c) cells at H ≈ 0 nm. d) The population of aligned cells is plotted as a function of grating height on PS gratings with Λ = 420 nm (solid circles) and Λ = 800 nm (open circles). Aligned cells are defi ned as cells with orientation angle ( α ) within 10 ° of the grating direction. In all images, the scale bars denote 100 μ m and the grating axis is horizontal.

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images of MC3T3-E1 cells seeded at three positions along a PS grating ( Λ = 800 nm). As expected, a larger proportion of cells are oriented parallel to the grating direction at higher H . The population of cells aligned with the grating direction for both 420 and 800 nm pitch samples is plotted as a func-tion of H in Figure 2 d for PS gratings (Supporting Informa-tion, Figure S4a for PMMA gratings). The cells are considered to be “aligned” with the direction of the grating if the angle ( α ) between the semimajor axis of the cell and the grating direction is < 10 ° ( Figure 2 d, inset). Note that by this defi nition, 11% of cells would be considered aligned in a randomly oriented cell population. For both values of Λ and both materials investi-gated, the population of the aligned cells increased from ≈ 12% (random) at H = 0 to ≥ 40% at H ≈ 300 nm. Similar enhanced alignment of cells with surface patterns has been reported by

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many groups. [ 2 , 8 , 14–16 ] This phenomenon is often attributed to cell-specifi c mechanisms such as an induced orientation of the fi lopodia or microfi lament attachment. [ 4 , 17 , 18 ] However, we show that in our system, alignment occurs during the initial cell con-tact and spreading processes; cell-specifi c biological interactions at later time points result in cell elongation but do not affect the cell orientation. Further, we show below that the alignment phenomenon is quantitatively similar to that seen for simple liquids on patterned surfaces, and can be largely accounted for using basic interfacial thermodynamics.

A small amount of water in contact with a grating-pat-terned surface will spread anisotropically to form an elongated droplet with its long axis parallel to the grating lines as shown in Figure 3 a. [ 19–21 ] The elongated shape is accompanied by a difference in the static water contact angles ( θ ) of the sessile

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Figure 3 . Experimental and calculated contact-angle anisotropy on grating patterns. a) Optical image of a water droplet on a PS 420 nm grating with H = 320 nm, illustrating the differences in θ // and θ ⊥ ; scale bar represents 500 μ m. b) Calculated free energy ( Δ G ) using the J–D model of a wetting water droplet as a function of apparent contact angle ( θ ) at α = 90 ° on a representative PS grating ( Λ = 420 nm) with H = 320 nm (red), and on a fl at PS fi lm (black). Inset shows an expanded view of the region near θ a . c) Advancing water contact angles in the wetting directions parallel ( θ // , red) or perpendicular ( θ ⊥ , blue) to grating lines, as a function of grating height on PS gratings. Solid and dashed lines correspond to θ a calculated using the J–D model for Λ = 420 nm (•) and Λ = 800 nm (�), respectively.

droplet in the wetting directions parallel ( θ // ) and perpendicular ( θ ⊥ ) to the grating lines. For example, water on a PS grating with Λ = 420 nm and H = 320 nm had a θ ⊥ – θ // ≈ 38 ° ( Figure 3 a).

© 2011 WILEY-VCH Verlag GmAdv. Mater. 2011, 23, 421–425

Anisotropic wetting can be understood in terms of a differ-ence in the free-energy ( Δ G ) landscape along the orthogonal directions of spreading. In Figure 3 b, we show Δ G values calcu-lated as a function of contact angle for a fl at surface, the equiva-lent of water spreading parallel to the grating direction, and for a water droplet spreading perpendicular to a grating with Λ = 420 nm and H = 320 nm. The calculation, based on the model of Johnson–Dettre (J–D), [ 22 , 23 ] shows Δ G to be a smooth func-tion of the contact angle parallel to the direction of the grating or for a fl at surface, but it is a signifi cantly corrugated function of contact angle along the direction perpendicular to the grating lines. Thus, water spreading on a fl at surface (or, equivalently, parallel to the grating direction) will fi nd the global minimum free-energy and display the associated contact angle (90 ° in this case). On the other hand, water spreading in a direction per-pendicular to the grating direction will become trapped in a local free-energy well at a value of θ ⊥ much different from the global equilibrium value. Furthermore, the particular value of θ ⊥ at which the system becomes trapped depends on whether the water is advancing or receding. θ a and θ r in Figure 3 b rep-resent the extreme angles at which the corrugated free-energy landscape has local minima, and thus the maximum and min-imum wetting angles that may be observed upon advancing and receding, respectively. These theoretically extreme values may not be observed experimentally. As an expanded view of the region around θ a shows ( Figure 3 b, inset), the free-energy well at θ a is very shallow, and the system may easily escape to a subsequent, deeper well before becoming trapped at a value of θ ⊥ that is closer to the global free-energy minimum. The theo-retical values of θ a and θ r are dependent on the height of the gratings. We point out that the J–D model assumes that water and substrate are in full contact or in the “noncomposite state”, which is appropriate for shallow gratings. With the increase of H , the water wetting may transition to an incomplete contact, or “composite state” depending on the interfacial energy, causing θ a to become less sensitive to changes in H. [ 24 ]

In Figure 3 c we plot the theoretical H dependence of θ a , both perpendicular to and parallel to the grating direction for PS gratings with Λ = 420 and 800 nm. We also plot the measured values of θ // and θ ⊥ for water on PS gratings (see Supporting Information, Figure S4 for PMMA grating data). In all cases, θ ⊥ are smaller than θ a , consistent with our discussion above. The radius of the water droplet used in the contact angle measure-ments is ≈ 1 mm, so a single drop covers a range of different H values on the gradient grating. To avoid this problem, we pre-pared a series of PS and PMMA gratings with uniform heights over large areas by isothermally annealing identical imprinted gratings for varying durations. [ 10 , 25 ]

Here, we note the similarity between the trends in Figure 2 d for cell alignment and Figure 3 c for the water contact angle. The similarity suggests a possible relationship between cell alignment and the behavior of a simple liquid on the same substrate. While the ordinate axes of these two graphs are not identical, they are related. Below, we explain the relationship and describe how the liquid wetting and cell orientation phe-nomena appear to have similar origins.

A work of adhesion ( W ad ), can be derived from the free-energy functions of Figure 3 b through W ad ( H, α ) = γ [cos θ α ( H, α )–cos θ γ ( H, α )] where γ is the interfacial free energy. [ 26 ] In Figure 4 a

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Figure 4 . Comparison of experimental and calculated orientation angles using W ad of water. a) Work of adhesion ( W ad ) of water droplet on a PS grating ( Λ = 420 nm) as a function of orientation angle ( α ) and grating height ( H ). b) Experimentally determined mean orientation angle of cells ( "̄exp ) as a function of calculated mean orientation angle ( "̄cal ), based on the probability of the orientation distribution determined by W ad of water. Solid and open symbols correspond to 420 and 800 nm pitch gratings, respectively, for PS (blue squares) and PMMA (red circles). A reference line indicates complete agreement between "̄exp and "̄cal .

we plot W ad , calculated as a function of α and H for water on a PS grating with Λ = 420 nm. Although Figure 4 a is calculated for water wetting the grating, a similar plot could be made for any fl uid body (including cells) interacting with a patterned interface, and would have the same generic features, in that the function would be minimized when the semimajor axis of the droplet (or cell) is aligned parallel to the grating axis, and that the free-energy cost of misalignment would become greater with increasing values of H . Using W ad , we calculate the proba-bility of a liquid droplet spreading along a grating with its semi-major axis aligned at an angle α with respect to the grating as,

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P(H, α ) ∼ P 0 exp[( − W ad ( H , α )/ kT ] α , where P 0 is a normalization constant, k is the Boltzmann constant, and T is temperature. This function indicates that depending on the profi le of the sur-face topography and the value of the interfacial free energy, a distribution of droplet orientations may be observed, as is the case with cells on grating patterns.

We can make a quantitative comparison between the observed cell alignment behavior and expectations from these thermody-namic considerations by comparing the experimental mean cell orientation angle, "̄exp , with a calculated value for "̄ based on the probability of the orientation distribution determined by W ad (H, α ) of water, ̄"cal = 90

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0 d"∫ . For a randomly oriented distribution of cells, "̄cal = 45 ° , and it approaches 0 ° as cells are progressively aligned parallel to the grating lines. A plot of "̄exp versus "̄cal ( Figure 4 b) shows two distinct features. The fi rst is that a striking correlation exists between the experi-mental and the calculated values. The second is that all the experimentally measured values of "̄ fall below the naively cal-culated value. The former feature indicates that, within a con-stant factor, the cell alignment response behaves like a simple fl uid wetting on a patterned surface. The parameter that most likely varies between the water case and the cell case is γ . In the case of the cell, the effective interfacial tension would be comprised of a sum of specifi c and nonspecifi c cell-substrate interactions (analogous to γ water-substrate ) and the cortical tension (analogous to γ water ). [ 27–29 ] The latter feature indicates that the interfacial tension between the cell and substrate is lower than that between water and the substrate. This difference makes sense since, for the cell spreading case, the difference between the cell-substrate interfacial tension and the water-substrate interfacial tension is sensed, whereas for the water spreading case, the difference between the water-substrate interfacial ten-sion and the air-substrate interfacial tension drives the wetting behavior. This could be confi rmed by directly modeling W ad of cells, similar to what was done for water in Figure 4 a. However, these would be challenging measurements because the equilib-rium Young’s contact angle ( θ Y , a necessary parameter for the modeling) of cells is diffi cult to determine due to the dynamic nature of cell spreading.

In summary, we show that the behavior of cell orientation on gratings is consistent with an underlying driving force for cell CG being the energetic barriers (or work of adhesion) that cells experience during spreading. This conclusion is supported by a quantitative correlation between the degree of cell alignment and the expected alignment based on anisotropic wetting of water droplets on polymer gratings with a height gradient. The results suggest that, despite complexity in both structure and dynamics, cells can be described as a simple viscous liquid during initial contact and spreading, a notion very much in accordance with a recent discovery that cells spread universally as a bilayer vis-cous liquid. [ 28 ] We note that our analysis does not suggest that cell-matrix specifi c interactions such as integrin attachment and focal adhesion formation are unimportant, but that they occur at later time points, after cell orientation has been established. The approach described here could facilitate noninvasive quan-tifi cation of thermodynamic contributions from surface inter-actions with individual cellular components. It also provides a framework for criteria one might use in designing surfaces or 3D environments to guide specifi c cell morphology.

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Supporting Information Supporting Information is available from the Wiley Online Library or from the author.

Acknowledgements Y. D. and J. S. contributed equally to the work. Offi cial contribution of the National Institute of Standards and Technology; not subject to copyright in the United States. Y. D. acknowledges the funding support from the National Science Foundation under Grant No. CMMI-0928067. This work is partially funded by the NIST Offi ce of Microelectronic Programs, and by National Institute of Dental and Craniofacial Research (NIDCR) through an Interagency Agreement (Y1-DE-7005-01). We acknowledge the nanofabrication laboratory of the Center for Nanoscale Science and Technology (CNST) at NIST for providing facilities for the nanoimprint process, and acknowledge the use of the NIST Combinatorial Methods Center equipment. We are thankful for helpful discussion with Claudio Migliaresi (University of Trento). This article is part of a Special Issue on Materials Science at the National Institute of Standards and Technology (NIST).

Received: May 12, 2010Published online: August 17, 2010

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