Anisotropic Raman scattering in collagen bundles

doi:10.1364/OL.35.002765

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Anisotropic Raman scattering in collagen bundles

Marek Janko, Polina Davydovskaya, Michael Bauer, Albert Zink, and Robert W. Stark »View Author Affiliations

Optics Letters, Vol. 35, Issue 16, pp. 2765-2767 (2010)
http://dx.doi.org/10.1364/OL.35.002765

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Abstract

Collagen is the main connective tissue protein of vertebrates and shows exceptional mechanical and optical properties. The alignment of collagen fibrils correlates to the function of a specific tissue and leads to optical anisotropy. The effect of the molecular alignment on Raman scattering, however, has barely been investigated. We found that the peak intensities of the $C ─ C$ , $C ═ O$ , and $N ─ H$ vibrational modes, which are typical for the Raman bands of the protein backbone, change with the orientation of the collagen fibrils. These observations demonstrate that Raman spectra contain specific information regarding molecular and fiber alignment.

Collagen is the most abundant structural protein of vertebrates and features unique properties. It is known for its exceptional durability [1

M. Janko, A. Zink, A. M. Gigler, W. M. Heckl, and R. W. Stark, Proc. R. Soc. London B 277, 2301 (2010). [CrossRef]

] and tensile strength, both of which result from the hierarchical structure [2

J. Gosline, M. Lillie, E. Carrington, P. Guerette, C. Ortlepp, and K. Savage, Philos. Trans. R. Soc. London B 357, 121 (2002). [CrossRef]

, 3

M. J. Buehler, Proc. Natl. Acad. Sci. USA 103, 12285 (2006). [CrossRef] [PubMed]

, 4

J. P. R. O. Orgel, T. C. Irving, A. Miller, and T. J. Wess, Proc. Natl. Acad. Sci. USA 103, 9001 (2006). [CrossRef] [PubMed]

] and fibril alignment. According to its specific function, it is organized in bundles or in a random meshwork, determining the tensile stress, elasticity, and geometry of skin, tendons, ligaments, and artery walls, or the organic matrix of bones. In tissue that is subject to unidirectional forces, such as tendons, single collagen fibrils are equally oriented and organized in bundles. The bundles are aligned with the direction of the load, thereby, leading to anisotropic mechanical properties.

Collagen also features remarkable optical properties. Optical anisotropy, such as birefringence or differences in light scattering and propagation [5

A. Kienle, F. K. Forster, and R. Hibst, Opt. Lett. 29, 2617 (2004). [CrossRef] [PubMed]

, 6

S. Nickell, M. Hermann, M. Essenpreis, T. J. Farrell, U. Kramer, and M. S. Patterson, Phys. Med. Biol. 45, 2873 (2000). [CrossRef] [PubMed]

], reflects the structure and alignment of the fibrils. Therefore, the collagen fibril orientation is an exceptional indicator of the properties of a biological tissue. For example, in the cornea, the regularly arranged collagen bundles are transparent [7

D. M. Maurice, J. Physiol. 136, 263 (1957). [PubMed]

, 8

G. B. Benedek, Appl. Opt. 10, 459 (1971). [CrossRef] [PubMed]

]. In diseased tissue, however, the molecular alignment can be disturbed, impairing the eye’s optical power [9

A. Daxer and P. Fratzl, Invest. Ophthalmol. Visual Sci. 38, 121 (1997).

, 10

K. M. Meek, S. J. Tuft, Y. Huang, P. S. Gill, S. Hayes, R. H. Newton, and A. J. Bron, Invest. Ophthalmol. Visual Sci. 46, 1948 (2005). [CrossRef]

Optical methods such as second-harmonic-generation microscopy [11

K. M. Hanson and C. J. Bardeen, Photochem. Photobiol. 85, 33 (2009). [CrossRef] [PubMed]

, 12

T. Yasui, Y. Tohno, and T. Araki, Appl. Opt. 43, 2861 (2004). [CrossRef] [PubMed]

, 13

J. C. Mansfield, C. P. Winlove, J. Moger, and S. J. Matcher, J. Biomed. Opt. 13, 044020 (2008). [CrossRef] [PubMed]

] can help to characterize the ori entation of the biopolymer. To this end, confocal Raman microscopy is also a promising high-resolution technique because the conformation and molecular order of (bio)polymers can be characterized spectroscopically [1

M. Janko, A. Zink, A. M. Gigler, W. M. Heckl, and R. W. Stark, Proc. R. Soc. London B 277, 2301 (2010). [CrossRef]

, 14

H. Kuzmany, J. F. Rabolt, B. L. Farmer, and R. D. Miller, J. Chem. Phys. 85, 7413 (1986). [CrossRef]

, 15

H. G. M. Edwards, D. W. Farwell, J. M. Holder, and E. E. Lawson, J. Mol. Struct. 435, 49 (1997). [CrossRef]

, 16

B. G. Frushour and J. L. Koenig, Biopolymers 14, 379 (1975). [CrossRef] [PubMed]

]. Here, we show that there is a strong dependency between the intensity of certain Raman bands (e.g., the amide bands around 1271 and

1668 {cm}^{- 1}

) and the orientation of aligned collagen fibrils with respect to the polarization of the incident laser light.

We investigated 2-μm-thick transverse sections of bovine Achilles tendon (Sigma-Aldrich) and human skin. The sections were processed following standard protocols [1

M. Janko, A. Zink, A. M. Gigler, W. M. Heckl, and R. W. Stark, Proc. R. Soc. London B 277, 2301 (2010). [CrossRef]

]. The samples were imaged with an atomic force microscope (AFM) to identify collagen-rich areas and to verify the orientation and the banding pattern of the fibrils (Veeco Dimension 3100, Cantilever; BS Tap 300 Budget Sensors,

D \sim 40 N / m

f_{res} \sim 300 kHz

). Type I collagen has a characteristic D-periodic banding pattern of

67 nm

. The measured values of

65.2 \pm 2.0 nm

in human skin or

65.7 \pm 2.0 nm

for the bovine tendon match the literature value. Both samples show highly ordered collagen structures with well-defined, uniaxial, parallel-aligned collagen fibrils (Fig. 1). Raman spectra were taken with a confocal Raman microscope (WITec alpha

300 R

532 nm

600 l / mm grating

). The laser power was set to

1.0 mW

to avoid denaturation. The confocal setup resulted in a focal depth of approximately

1 μm

with a diffraction-limited spot diameter of about

400 nm

. Although the laser had a polarization ratio of

100 ∶ 1

, all measurements can be regarded as unpolarized because no analyzer was used. Three single spectra were recorded, each with

180 s

of integration time. The samples were rotated in steps of

15 °

, and the measurements were repeated for each step.

The spectra shown in Fig. 2 were obtained on fibrils whose long fibril axes were aligned in parallel and perpendicular with respect to the polarization of the incident laser. The spectra were normalized to the most intense Raman band at around

2939 {cm}^{- 1}

, which features a steady intensity and peak center position throughout the measurements and is far away from the fingerprint region of collagen (700 to

1800 {cm}^{- 1}

; inset in Fig. 2). The spectra are consistent and feature the characteristic collagen bands [1

M. Janko, A. Zink, A. M. Gigler, W. M. Heckl, and R. W. Stark, Proc. R. Soc. London B 277, 2301 (2010). [CrossRef]

]. The first peaks exhibiting an orientation- dependent intensity are found at about 766 and

780 {cm}^{- 1}

ν (CCO)

[15

H. G. M. Edwards, D. W. Farwell, J. M. Holder, and E. E. Lawson, J. Mol. Struct. 435, 49 (1997). [CrossRef]

]. Their intensity nearly vanishes when rotating the sample by

90 °

. Such behavior could also be observed for the band at about

939 {cm}^{- 1}

(

C ─ C

stretch) that is typical for the protein backbone [16

B. G. Frushour and J. L. Koenig, Biopolymers 14, 379 (1975). [CrossRef] [PubMed]

, 17

M. Gniadecka, O. F. Nielsen, D. H. Christensen, and H. C. Wulf, J. Invest. Dermatol. 110, 393 (1998). [CrossRef] [PubMed]

]. The deformation band of the amide III

δ (NH)

[15

H. G. M. Edwards, D. W. Farwell, J. M. Holder, and E. E. Lawson, J. Mol. Struct. 435, 49 (1997). [CrossRef]

, 16

B. G. Frushour and J. L. Koenig, Biopolymers 14, 379 (1975). [CrossRef] [PubMed]

, 17

M. Gniadecka, O. F. Nielsen, D. H. Christensen, and H. C. Wulf, J. Invest. Dermatol. 110, 393 (1998). [CrossRef] [PubMed]

] at

1271 {cm}^{- 1}

also features anisotropic Raman scattering. However, the

1271 {cm}^{- 1}

band shows behavior that is inverse to that at 766, 780, and

939 {cm}^{- 1}

. It is less intense when the collagen fibrils are oriented in parallel and shows enhanced Raman scattering in the perpen dicular configuration. The strongest polarization de pendence appears in the range of 1580 to

1720 {cm}^{- 1}

, specifically at

1668 {cm}^{- 1}

, with the shoulder at about

1641 {cm}^{- 1}

corresponding to the

C ═ O

stretching vibration of amide I

ν (CO)

[15

H. G. M. Edwards, D. W. Farwell, J. M. Holder, and E. E. Lawson, J. Mol. Struct. 435, 49 (1997). [CrossRef]

, 16

B. G. Frushour and J. L. Koenig, Biopolymers 14, 379 (1975). [CrossRef] [PubMed]

, 17

M. Gniadecka, O. F. Nielsen, D. H. Christensen, and H. C. Wulf, J. Invest. Dermatol. 110, 393 (1998). [CrossRef] [PubMed]

]. Likewise, at about

3321 {cm}^{- 1}

, a peak appears that is located near the broad background peak of water. Leikin et al. [18

S. Leikin, V. A. Parsegian, W.-H. Yang, and G. E. Walrafen, Proc. Natl. Acad. Sci. USA 94, 11312 (1997). [CrossRef] [PubMed]

] reported that this band corresponds to the

N ─ H

vibration mode of amides in protein backbones.

The polar diagram in Fig. 3 outlines the peak intensities for a total rotation of

360 °

, illustrating the intensity as a function of the collagen orientation. The bands at about 766, 1246, 1271, 1451, 1668, and

3321 {cm}^{- 1}

are displayed. The intensities were determined by fitting a second-order polynomial to a narrow range (40 to

100 {cm}^{- 1}

) around the peak centers. The respective fitting ranges were maintained for all sample orientations. From the asymmetric intensity distribution, the alignment of the collagen fibrils in the specimen can be derived. The shape of the intensity distribution indicates strong anisotropic Raman scattering. The amide I and amide III bands, which represent the peptide bonds within proteins and in the collagen, indicate the stabilization of the subfibrillar triple helical structure by the formation of interchain hydrogen bonds between the

N ─ H

groups of glycines and the

C ═ O

groups of prolines in neighboring chains [19

R. D. B. Fraser, T. P. Macrae, and E. Suzuki, J. Mol. Biol. 129, 463 (1979). [CrossRef] [PubMed]

, 20

A. Rich and F. H. C. Crick, Nature 176, 915 (1955). [CrossRef] [PubMed]

]. The anisotropic Raman scattering at these amide groups indicates that they are oriented in the direction of the fibril backbone (long axis). The intensity distribution of the

766 {cm}^{- 1}

band is turned by

90 °

compared to those of the amide bands. This observation implies that the preferential polarizability of the molecular subunit CCO that is responsible for the

766 {cm}^{- 1}

peak could be perpendicular compared to those of the bands at 1271, 1668, and

3321 {cm}^{- 1}

. The polarizability typically varies if the electrical field is applied parallel or perpendicular to the molecular axis or in different directions relative to the molecule. This causes a variation in the induced dipole moment (

P = ε_{0} χ E = ε_{0} χ E_{0} e^{[i (k_{i} \cdot r - ω_{i} t)]}

). Hence, the Raman scattering in the collagen fibers depends on the fiber alignment and the orientation of the polarized laser. The anisotropy is expressed by the nonzero elements (

(\partial χ / \partial ω_{j})_{0} = χ^{(1)} \neq 0

) of the Taylor expanded susceptibility tensor (

χ = χ^{(0)} + \sum_{j} χ^{(1)} Q_{j} + \dots

) for Raman scattering. Therefore, a rotation of aligned collagen fibrils with respect to the incident laser causes intensity variations in several Raman bands. Thus, the orientation of the intensity distribution pattern in the polar diagrams characterizes the uniaxial orientation of the collagen bundles. The shape of these isointensities can act as an indicator for the fibril structure of bundles. For comparison, two bands (1246 and

1451 {cm}^{- 1}

) that are not affected by the rotation are also shown in Fig. 3. The

1246 {cm}^{- 1}

peak is related to the amide III band and is assigned to the

δ (NH)

vibration of the

N ─ H

groups. Compared to the amide III band at

1271 {cm}^{- 1}

, however, the Raman active

N ─ H

groups at

1246 {cm}^{- 1}

are in a disordered phase [15

H. G. M. Edwards, D. W. Farwell, J. M. Holder, and E. E. Lawson, J. Mol. Struct. 435, 49 (1997). [CrossRef]

]. The other isotropic Raman band at

1451 {cm}^{- 1}

is assigned to methyl

δ ({CH}_{3})

and methylene

δ ({CH}_{2})

deformation vibrations [16

B. G. Frushour and J. L. Koenig, Biopolymers 14, 379 (1975). [CrossRef] [PubMed]

, 17

M. Gniadecka, O. F. Nielsen, D. H. Christensen, and H. C. Wulf, J. Invest. Dermatol. 110, 393 (1998). [CrossRef] [PubMed]

]. Similar to the

N ─ H

groups at

1246 {cm}^{- 1}

, the

{CH}_{3}

and

{CH}_{2}

groups do not show a preferential orientation. Both bands correspond to the Raman scattering of molecules that are equally distributed across the collagen amino acid sequence and, thus, homogeneous Raman scattering occurred.

In summary, the conformation and orientation of hierarchical molecules can be characterized by Raman spectroscopy. Intensity variations of several Raman bands were observed while rotating aligned collagen fibrils with respect to the polarization of the incident laser beam. This result implies that the orientation of Raman active subunits of an ordered macromolecular protein in a tissue can be determined by Raman scattering. The orientation- dependent scattering not only enables the optical characterization of the alignment of collagen fibrils, but also has to be considered in the analysis of the spectra.

Acknowledgments

We gratefully acknowledge the Deutsche Forschungsgemeinschaft (DFG) clusters of excellence Nanosystems Initiative Munich and Center of Smart Interfaces Darmstadt for financial support.

References and links

1.	M. Janko, A. Zink, A. M. Gigler, W. M. Heckl, and R. W. Stark, Proc. R. Soc. London B 277, 2301 (2010). [CrossRef]
2.	J. Gosline, M. Lillie, E. Carrington, P. Guerette, C. Ortlepp, and K. Savage, Philos. Trans. R. Soc. London B 357, 121 (2002). [CrossRef]
3.	M. J. Buehler, Proc. Natl. Acad. Sci. USA 103, 12285 (2006). [CrossRef] [PubMed]
4.	J. P. R. O. Orgel, T. C. Irving, A. Miller, and T. J. Wess, Proc. Natl. Acad. Sci. USA 103, 9001 (2006). [CrossRef] [PubMed]
5.	A. Kienle, F. K. Forster, and R. Hibst, Opt. Lett. 29, 2617 (2004). [CrossRef] [PubMed]
6.	S. Nickell, M. Hermann, M. Essenpreis, T. J. Farrell, U. Kramer, and M. S. Patterson, Phys. Med. Biol. 45, 2873 (2000). [CrossRef] [PubMed]
7.	D. M. Maurice, J. Physiol. 136, 263 (1957). [PubMed]
8.	G. B. Benedek, Appl. Opt. 10, 459 (1971). [CrossRef] [PubMed]
9.	A. Daxer and P. Fratzl, Invest. Ophthalmol. Visual Sci. 38, 121 (1997).
10.	K. M. Meek, S. J. Tuft, Y. Huang, P. S. Gill, S. Hayes, R. H. Newton, and A. J. Bron, Invest. Ophthalmol. Visual Sci. 46, 1948 (2005). [CrossRef]
11.	K. M. Hanson and C. J. Bardeen, Photochem. Photobiol. 85, 33 (2009). [CrossRef] [PubMed]
12.	T. Yasui, Y. Tohno, and T. Araki, Appl. Opt. 43, 2861 (2004). [CrossRef] [PubMed]
13.	J. C. Mansfield, C. P. Winlove, J. Moger, and S. J. Matcher, J. Biomed. Opt. 13, 044020 (2008). [CrossRef] [PubMed]
14.	H. Kuzmany, J. F. Rabolt, B. L. Farmer, and R. D. Miller, J. Chem. Phys. 85, 7413 (1986). [CrossRef]
15.	H. G. M. Edwards, D. W. Farwell, J. M. Holder, and E. E. Lawson, J. Mol. Struct. 435, 49 (1997). [CrossRef]
16.	B. G. Frushour and J. L. Koenig, Biopolymers 14, 379 (1975). [CrossRef] [PubMed]
17.	M. Gniadecka, O. F. Nielsen, D. H. Christensen, and H. C. Wulf, J. Invest. Dermatol. 110, 393 (1998). [CrossRef] [PubMed]
18.	S. Leikin, V. A. Parsegian, W.-H. Yang, and G. E. Walrafen, Proc. Natl. Acad. Sci. USA 94, 11312 (1997). [CrossRef] [PubMed]
19.	R. D. B. Fraser, T. P. Macrae, and E. Suzuki, J. Mol. Biol. 129, 463 (1979). [CrossRef] [PubMed]
20.	A. Rich and F. H. C. Crick, Nature 176, 915 (1955). [CrossRef] [PubMed]

Fig. 1 AFM images of (a) human skin collagen (

2 μm \times 2 μm

) and (b) bovine Achilles tendon collagen (

3 μm \times 3 μm

). Fibrils in a parallel alignment with their characteristic banding pattern prevail. The insets display (a) a bundle of skin collagen and (b) a profile of the banding pattern of Achilles tendon collagen. Raman spectra were taken at the position marked by the crosshair.

Fig. 2 Normalized Raman spectra taken on collagen fibrils oriented parallel and perpendicular to the incident laser beam. The gray squares indicate the bands that show the strongest anisotropic Raman scattering. The inset outlines the fingerprint region of collagen.

Fig. 3 Polar diagrams of selected Raman bands displayed for a full sample rotation.

OCIS Codes
(170.1470) Medical optics and biotechnology : Blood or tissue constituent monitoring
(170.6510) Medical optics and biotechnology : Spectroscopy, tissue diagnostics
(190.4710) Nonlinear optics : Optical nonlinearities in organic materials
(300.6450) Spectroscopy : Spectroscopy, Raman
(170.6935) Medical optics and biotechnology : Tissue characterization

ToC Category:
Spectroscopy

History
Original Manuscript: May 26, 2010
Revised Manuscript: July 7, 2010
Manuscript Accepted: July 15, 2010
Published: August 12, 2010

Virtual Issues
Vol. 5, Iss. 13 Virtual Journal for Biomedical Optics

Citation
Marek Janko, Polina Davydovskaya, Michael Bauer, Albert Zink, and Robert W. Stark, "Anisotropic Raman scattering in collagen bundles," Opt. Lett. 35, 2765-2767 (2010)
http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-35-16-2765

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References

M. Janko, A. Zink, A. M. Gigler, W. M. Heckl, and R. W. Stark, Proc. R. Soc. London B 277, 2301 (2010). [CrossRef]
J. Gosline, M. Lillie, E. Carrington, P. Guerette, C. Ortlepp, and K. Savage, Philos. Trans. R. Soc. London B 357, 121(2002). [CrossRef]
M. J. Buehler, Proc. Natl. Acad. Sci. USA 103, 12285 (2006). [CrossRef] [PubMed]
J. P. R. O. Orgel, T. C. Irving, A. Miller, and T. J. Wess, Proc. Natl. Acad. Sci. USA 103, 9001 (2006). [CrossRef] [PubMed]
A. Kienle, F. K. Forster, and R. Hibst, Opt. Lett. 29, 2617(2004). [CrossRef] [PubMed]
S. Nickell, M. Hermann, M. Essenpreis, T. J. Farrell, U. Kramer, and M. S. Patterson, Phys. Med. Biol. 45, 2873(2000). [CrossRef] [PubMed]
D. M. Maurice, J. Physiol. 136, 263 (1957). [PubMed]
G. B. Benedek, Appl. Opt. 10, 459 (1971). [CrossRef] [PubMed]
A. Daxer and P. Fratzl, Invest. Ophthalmol. Visual Sci. 38, 121 (1997).
K. M. Meek, S. J. Tuft, Y. Huang, P. S. Gill, S. Hayes, R. H. Newton, and A. J. Bron, Invest. Ophthalmol. Visual Sci. 46, 1948 (2005). [CrossRef]
K. M. Hanson and C. J. Bardeen, Photochem. Photobiol. 85, 33 (2009). [CrossRef] [PubMed]
T. Yasui, Y. Tohno, and T. Araki, Appl. Opt. 43, 2861 (2004). [CrossRef] [PubMed]
J. C. Mansfield, C. P. Winlove, J. Moger, and S. J. Matcher, J. Biomed. Opt. 13, 044020 (2008). [CrossRef] [PubMed]
H. Kuzmany, J. F. Rabolt, B. L. Farmer, and R. D. Miller, J. Chem. Phys. 85, 7413 (1986). [CrossRef]
H. G. M. Edwards, D. W. Farwell, J. M. Holder, and E. E. Lawson, J. Mol. Struct. 435, 49 (1997). [CrossRef]
B. G. Frushour and J. L. Koenig, Biopolymers 14, 379(1975). [CrossRef] [PubMed]
M. Gniadecka, O. F. Nielsen, D. H. Christensen, and H. C. Wulf, J. Invest. Dermatol. 110, 393 (1998). [CrossRef] [PubMed]
S. Leikin, V. A. Parsegian, W.-H. Yang, and G. E. Walrafen, Proc. Natl. Acad. Sci. USA 94, 11312 (1997). [CrossRef] [PubMed]
R. D. B. Fraser, T. P. Macrae, and E. Suzuki, J. Mol. Biol. 129, 463 (1979). [CrossRef] [PubMed]
A. Rich and F. H. C. Crick, Nature 176, 915 (1955). [CrossRef] [PubMed]

Appl. Opt.

Biopolymers

B. G. Frushour and J. L. Koenig, Biopolymers 14, 379(1975). [CrossRef] [PubMed]

Invest. Ophthalmol. Visual Sci.

A. Daxer and P. Fratzl, Invest. Ophthalmol. Visual Sci. 38, 121 (1997).
K. M. Meek, S. J. Tuft, Y. Huang, P. S. Gill, S. Hayes, R. H. Newton, and A. J. Bron, Invest. Ophthalmol. Visual Sci. 46, 1948 (2005). [CrossRef]

J. Biomed. Opt.

J. C. Mansfield, C. P. Winlove, J. Moger, and S. J. Matcher, J. Biomed. Opt. 13, 044020 (2008). [CrossRef] [PubMed]

J. Chem. Phys.

H. Kuzmany, J. F. Rabolt, B. L. Farmer, and R. D. Miller, J. Chem. Phys. 85, 7413 (1986). [CrossRef]

J. Invest. Dermatol.

M. Gniadecka, O. F. Nielsen, D. H. Christensen, and H. C. Wulf, J. Invest. Dermatol. 110, 393 (1998). [CrossRef] [PubMed]

J. Mol. Biol.

R. D. B. Fraser, T. P. Macrae, and E. Suzuki, J. Mol. Biol. 129, 463 (1979). [CrossRef] [PubMed]

J. Mol. Struct.

H. G. M. Edwards, D. W. Farwell, J. M. Holder, and E. E. Lawson, J. Mol. Struct. 435, 49 (1997). [CrossRef]

J. Physiol.

D. M. Maurice, J. Physiol. 136, 263 (1957). [PubMed]

Nature

A. Rich and F. H. C. Crick, Nature 176, 915 (1955). [CrossRef] [PubMed]

Opt. Lett.

A. Kienle, F. K. Forster, and R. Hibst, Opt. Lett. 29, 2617(2004). [CrossRef] [PubMed]

Philos. Trans. R. Soc. London B

J. Gosline, M. Lillie, E. Carrington, P. Guerette, C. Ortlepp, and K. Savage, Philos. Trans. R. Soc. London B 357, 121(2002). [CrossRef]

Photochem. Photobiol.

K. M. Hanson and C. J. Bardeen, Photochem. Photobiol. 85, 33 (2009). [CrossRef] [PubMed]

Phys. Med. Biol.

S. Nickell, M. Hermann, M. Essenpreis, T. J. Farrell, U. Kramer, and M. S. Patterson, Phys. Med. Biol. 45, 2873(2000). [CrossRef] [PubMed]

Proc. Natl. Acad. Sci. USA

M. J. Buehler, Proc. Natl. Acad. Sci. USA 103, 12285 (2006). [CrossRef] [PubMed]
J. P. R. O. Orgel, T. C. Irving, A. Miller, and T. J. Wess, Proc. Natl. Acad. Sci. USA 103, 9001 (2006). [CrossRef] [PubMed]
S. Leikin, V. A. Parsegian, W.-H. Yang, and G. E. Walrafen, Proc. Natl. Acad. Sci. USA 94, 11312 (1997). [CrossRef] [PubMed]

Proc. R. Soc. London B

M. Janko, A. Zink, A. M. Gigler, W. M. Heckl, and R. W. Stark, Proc. R. Soc. London B 277, 2301 (2010). [CrossRef]

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