Abstract

Laser diffraction is commonly used in physiological research that explores single muscle fibers. Although variations in sarcomere morphological properties have often been observed, their effects on laser diffraction have not been studied in detail. In this study, we applied three-dimensional coupled wave theory to a physical sarcomere model to investigate the effects of inhomogeneous morphological profiles in muscle fibers. The simulation results were compared with several those of published experimental studies. Our results indicate that by incorporating various myofibril inhomogeneities such as skew and domain effect in the theoretical model, a variety of observations in single fiber diffraction under different experimental conditions can be reproduced in the simulation.

© 2008 Optical Society of America

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    [CrossRef] [PubMed]
  33. F. Carlsen, G. G. Knappeis, and F. Buchthal, “Ultrastructure of the resting and contracted striated muscle fiber at different degrees of stretch,” J. Biophys. Biochem. Cytol. 11, 95-117 (1961).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  37. A. F. Leung, Y. M. Cheung, and J. C. Hwang, “Light diffraction intensity from muscle fibers in different osmotic solutions: measurement of equilibrium time,” Eur. J. Physiol. 414, 676-682 (1989).
    [CrossRef]
  38. K. Burton and A. F. Huxley, “Identification of source of oscilations in apparent sarcomere length measured by laser diffraction,” Biophys. J. 68, 2429-2443 (1995).
    [CrossRef] [PubMed]
  39. Y. Yeh and R. J. Baskin, “Thory of optical ellipsometric measurements from muscle diffraction studies,” Biophys. J. 54, 205-218 (1988).
    [CrossRef] [PubMed]
  40. R. J. Baskin, R. L. Leiber, T. Oba, and Y. Yeh, “Intensity of light diffraction from striated muscle as a function of incident angle,” Biophys. J. 36, 759-773 (1981).
    [CrossRef] [PubMed]
  41. F. Buchthal and G. G. Knappeis, “Diffraction spectra and minute structure of the cross-striated muscle fiber,” Skand. Arch. Physiol. 83, 281-307 (1940).

2007 (2)

2003 (1)

P. K. Luther, R. Padron, S. Ritter, R. Craig, and J. M. Suire, “Hetrogenity of Z-band structure within a single muscle sarcomere: implications for sarcomere assembly,” J. Mol. Biol. 332, 161-169 (2003).
[CrossRef] [PubMed]

2002 (1)

W. Ding, H. Fujita, and M. Kawai, “The length of cooperative units on the filament in rabbit psoas muscle fibres,” Exp. Physiol. 87, 691-697 (2002).
[CrossRef] [PubMed]

1997 (1)

1995 (4)

1994 (1)

E. Sidick, R. J. Baskin, Y. Yeh, and J. Knoesen, “Rigorous analysis of light diffraction ellipsometry by striated muscle fibers,” Biophys. J. 66, 2051-2061 (1994).
[CrossRef] [PubMed]

1992 (1)

E. Sidick, J. Knoesen, K. Xian, Y. Yeh, and R. J. Baskin, “Rigorous analysis of light diffraction by a striated muscle fibre,” Proc. R. Soc. London, Ser. B 249, 247-256 (1992).
[CrossRef]

1991 (1)

R. A. Thornhill, N. Thomas, and N. Berovic, “Optical diffraction by well ordered muscle fibers,” Eur. Biophys. J. 20, 87-99 (1991).
[CrossRef] [PubMed]

1990 (1)

A. F. Huxley, “Theoretical treatment of diffraction light by a striated muscle fibre,” Proc. R. Soc. London, Ser. B 241, 65-71 (1990).
[CrossRef]

1989 (1)

A. F. Leung, Y. M. Cheung, and J. C. Hwang, “Light diffraction intensity from muscle fibers in different osmotic solutions: measurement of equilibrium time,” Eur. J. Physiol. 414, 676-682 (1989).
[CrossRef]

1988 (1)

Y. Yeh and R. J. Baskin, “Thory of optical ellipsometric measurements from muscle diffraction studies,” Biophys. J. 54, 205-218 (1988).
[CrossRef] [PubMed]

1986 (1)

C. L. Sundell, Y. E. Goldman, and L. D. Peachey, “Fine structure in near-field and far-field laser diffraction patterns from skeletal muscle fibers,” Biophys. J. 49, 521-530 (1986).
[CrossRef] [PubMed]

1985 (2)

S. Ishiwata, K. Muramatsu, and H. Higuchi, “Disassembly from both ends of thick filaments in rabbit skeletal muscle fibers,” Biophys. J. 47, 257-266 (1985).
[CrossRef] [PubMed]

B. Brenner, “Sarcomeric domain organization within single skinned rabbit psoas fibers and its effects on laser light diffraction patterns,” Biophys. J. 48, 967-982 (1985).
[CrossRef] [PubMed]

1984 (1)

R. L. Leiber, Y. Yeh, and R. J. Baskin, “Sarcomere length determination using laser diffraction,” Biophys. J. 45, 1007-1016 (1984).
[CrossRef]

1983 (1)

1982 (2)

A. F. Leung, “Calculation of the laser diffraction intensity of striated muscle by numerical methods,” Comput. Programs Biomed. 15, 169-174 (1982).
[CrossRef] [PubMed]

M. M. Judy, T. Summerour, R. Leconey, R. L. Roa, and G. H. Templeton, “Muscle diffraction theory,” Biophys. J. 37, 475-487 (1982).
[CrossRef] [PubMed]

1981 (2)

M. G. Moharam and T. K. Gaylord, “Rigorous coupled wave analysis of planar grating diffraction,” J. Opt. Soc. Am. 71, 811-818 (1981).
[CrossRef]

R. J. Baskin, R. L. Leiber, T. Oba, and Y. Yeh, “Intensity of light diffraction from striated muscle as a function of incident angle,” Biophys. J. 36, 759-773 (1981).
[CrossRef] [PubMed]

1980 (2)

R. Rudel and F. Zite-Ferenczy, “Efficiency of light diffraction by cross striated muscle fibers under stretch and during isometric contraction,” Biophys. J. 30, 507-516 (1980).
[CrossRef] [PubMed]

Y. Yeh, R. J. Baskin, R. L. Leiber, and K. P. Roos, “Theory of light diffraction by single skeletal muscle fibers,” Biophys. J. 29, 509-522 (1980).
[CrossRef] [PubMed]

1979 (3)

R. J. Baskin, K. P. Roos, and Y. Yeh, “Light diffraction study of single skeletal muscle fibers,” Biophys. J. 28, 45-64 (1979).
[CrossRef] [PubMed]

R. Rudel and F. Zite-Ferenczy, “Interpretation of light diffraction by cross-striated muscle as Bragg reflexion of light by the lattice of contractile proteins,” J. Physiol. (London) 290, 317-330 (1979).

R. L. Moss, “Sarcomere length-tension relations of frog skinned muscle fibers during calcium activation at short length,” J. Physiol. (London) 292, 177-192 (1979).

1978 (1)

S. Fujime and S. Yoshino, “Optical diffraction study of muscle fibers. I. A theoretical basis,” Biophys. Chem. 8, 305-315 (1978).
[CrossRef] [PubMed]

1976 (1)

P. J. Paolini, R. Sabbadini, K. P. Roos, and R. J. Baskin, “Sarcomere length dispersion in single muscle fibers and fiber bundles,” Biophys. J. 16, 919-930 (1976).
[CrossRef] [PubMed]

1975 (1)

S. Fujime, “Optical diffraction study of muscle fibers,” Biochim. Biophys. Acta 37, 227-238 (1975).

1973 (1)

M. Kawai and I. D. Kuntz, “Optical diffraction studies of muscle fibers,” Biophys. J. 13, 857-876 (1973).
[CrossRef] [PubMed]

1969 (1)

H. Kogelnik, “Coupled wave theory for thick hologram grating,” Bell Syst. Tech. J. 48, 2909-2943 (1969).

1963 (1)

S. G. Page and H. E. Huxley, “Filament lengths in striated muscle,” J. Cell Biol. 19, 369-390 (1963).
[CrossRef] [PubMed]

1962 (1)

G. G. Knappeis and F. Carlsen, “The ultrastructure of the Z disc in skeletal muscle,” J. Cell Biol. 13, 323-335 (1962).
[CrossRef] [PubMed]

1961 (1)

F. Carlsen, G. G. Knappeis, and F. Buchthal, “Ultrastructure of the resting and contracted striated muscle fiber at different degrees of stretch,” J. Biophys. Biochem. Cytol. 11, 95-117 (1961).
[CrossRef] [PubMed]

1958 (1)

A. F. Huxley and R. Niedergerke, “Measurement of the striations of isolated muscle fibers with the interference microscope,” J. Physiol. (London) 144, 403-425 (1958).

1957 (1)

H. E. Huxley and J. Hanson, “Quantitative studies on the structure of cross striated myofibrils.,” Biochim. Biophys. Acta 23, 229-249 (1957).
[CrossRef] [PubMed]

1940 (1)

F. Buchthal and G. G. Knappeis, “Diffraction spectra and minute structure of the cross-striated muscle fiber,” Skand. Arch. Physiol. 83, 281-307 (1940).

Baskin, R. J.

E. Sidick, R. J. Baskin, Y. Yeh, and J. Knoesen, “Rigorous analysis of light diffraction ellipsometry by striated muscle fibers,” Biophys. J. 66, 2051-2061 (1994).
[CrossRef] [PubMed]

E. Sidick, J. Knoesen, K. Xian, Y. Yeh, and R. J. Baskin, “Rigorous analysis of light diffraction by a striated muscle fibre,” Proc. R. Soc. London, Ser. B 249, 247-256 (1992).
[CrossRef]

Y. Yeh and R. J. Baskin, “Thory of optical ellipsometric measurements from muscle diffraction studies,” Biophys. J. 54, 205-218 (1988).
[CrossRef] [PubMed]

R. L. Leiber, Y. Yeh, and R. J. Baskin, “Sarcomere length determination using laser diffraction,” Biophys. J. 45, 1007-1016 (1984).
[CrossRef]

R. J. Baskin, R. L. Leiber, T. Oba, and Y. Yeh, “Intensity of light diffraction from striated muscle as a function of incident angle,” Biophys. J. 36, 759-773 (1981).
[CrossRef] [PubMed]

Y. Yeh, R. J. Baskin, R. L. Leiber, and K. P. Roos, “Theory of light diffraction by single skeletal muscle fibers,” Biophys. J. 29, 509-522 (1980).
[CrossRef] [PubMed]

R. J. Baskin, K. P. Roos, and Y. Yeh, “Light diffraction study of single skeletal muscle fibers,” Biophys. J. 28, 45-64 (1979).
[CrossRef] [PubMed]

P. J. Paolini, R. Sabbadini, K. P. Roos, and R. J. Baskin, “Sarcomere length dispersion in single muscle fibers and fiber bundles,” Biophys. J. 16, 919-930 (1976).
[CrossRef] [PubMed]

Berovic, N.

R. A. Thornhill, N. Thomas, and N. Berovic, “Optical diffraction by well ordered muscle fibers,” Eur. Biophys. J. 20, 87-99 (1991).
[CrossRef] [PubMed]

Brenner, B.

B. Brenner, “Sarcomeric domain organization within single skinned rabbit psoas fibers and its effects on laser light diffraction patterns,” Biophys. J. 48, 967-982 (1985).
[CrossRef] [PubMed]

Buchthal, F.

F. Carlsen, G. G. Knappeis, and F. Buchthal, “Ultrastructure of the resting and contracted striated muscle fiber at different degrees of stretch,” J. Biophys. Biochem. Cytol. 11, 95-117 (1961).
[CrossRef] [PubMed]

F. Buchthal and G. G. Knappeis, “Diffraction spectra and minute structure of the cross-striated muscle fiber,” Skand. Arch. Physiol. 83, 281-307 (1940).

Burton, K.

K. Burton and A. F. Huxley, “Identification of source of oscilations in apparent sarcomere length measured by laser diffraction,” Biophys. J. 68, 2429-2443 (1995).
[CrossRef] [PubMed]

Carlsen, F.

G. G. Knappeis and F. Carlsen, “The ultrastructure of the Z disc in skeletal muscle,” J. Cell Biol. 13, 323-335 (1962).
[CrossRef] [PubMed]

F. Carlsen, G. G. Knappeis, and F. Buchthal, “Ultrastructure of the resting and contracted striated muscle fiber at different degrees of stretch,” J. Biophys. Biochem. Cytol. 11, 95-117 (1961).
[CrossRef] [PubMed]

Cheung, Y. M.

A. F. Leung, Y. M. Cheung, and J. C. Hwang, “Light diffraction intensity from muscle fibers in different osmotic solutions: measurement of equilibrium time,” Eur. J. Physiol. 414, 676-682 (1989).
[CrossRef]

Craig, R.

P. K. Luther, R. Padron, S. Ritter, R. Craig, and J. M. Suire, “Hetrogenity of Z-band structure within a single muscle sarcomere: implications for sarcomere assembly,” J. Mol. Biol. 332, 161-169 (2003).
[CrossRef] [PubMed]

Ding, W.

W. Ding, H. Fujita, and M. Kawai, “The length of cooperative units on the filament in rabbit psoas muscle fibres,” Exp. Physiol. 87, 691-697 (2002).
[CrossRef] [PubMed]

Drew, A.

Fujime, S.

S. Fujime and S. Yoshino, “Optical diffraction study of muscle fibers. I. A theoretical basis,” Biophys. Chem. 8, 305-315 (1978).
[CrossRef] [PubMed]

S. Fujime, “Optical diffraction study of muscle fibers,” Biochim. Biophys. Acta 37, 227-238 (1975).

Fujita, H.

W. Ding, H. Fujita, and M. Kawai, “The length of cooperative units on the filament in rabbit psoas muscle fibres,” Exp. Physiol. 87, 691-697 (2002).
[CrossRef] [PubMed]

Gardiner, P. F.

B. R. Maclntosh, P. F. Gardiner, and A. J. McComas, Skeletal Muscle: Form and Function (Human Kinematics, 2006).

Gaylord, T. K.

Goldman, Y. E.

C. L. Sundell, Y. E. Goldman, and L. D. Peachey, “Fine structure in near-field and far-field laser diffraction patterns from skeletal muscle fibers,” Biophys. J. 49, 521-530 (1986).
[CrossRef] [PubMed]

Grann, E. B.

Hanson, J.

H. E. Huxley and J. Hanson, “Quantitative studies on the structure of cross striated myofibrils.,” Biochim. Biophys. Acta 23, 229-249 (1957).
[CrossRef] [PubMed]

Higuchi, H.

S. Ishiwata, K. Muramatsu, and H. Higuchi, “Disassembly from both ends of thick filaments in rabbit skeletal muscle fibers,” Biophys. J. 47, 257-266 (1985).
[CrossRef] [PubMed]

Huxley, A. F.

K. Burton and A. F. Huxley, “Identification of source of oscilations in apparent sarcomere length measured by laser diffraction,” Biophys. J. 68, 2429-2443 (1995).
[CrossRef] [PubMed]

A. F. Huxley, “Theoretical treatment of diffraction light by a striated muscle fibre,” Proc. R. Soc. London, Ser. B 241, 65-71 (1990).
[CrossRef]

A. F. Huxley and R. Niedergerke, “Measurement of the striations of isolated muscle fibers with the interference microscope,” J. Physiol. (London) 144, 403-425 (1958).

Huxley, H. E.

S. G. Page and H. E. Huxley, “Filament lengths in striated muscle,” J. Cell Biol. 19, 369-390 (1963).
[CrossRef] [PubMed]

H. E. Huxley and J. Hanson, “Quantitative studies on the structure of cross striated myofibrils.,” Biochim. Biophys. Acta 23, 229-249 (1957).
[CrossRef] [PubMed]

Hwang, J. C.

A. F. Leung, Y. M. Cheung, and J. C. Hwang, “Light diffraction intensity from muscle fibers in different osmotic solutions: measurement of equilibrium time,” Eur. J. Physiol. 414, 676-682 (1989).
[CrossRef]

Ishiwata, S.

S. Ishiwata, K. Muramatsu, and H. Higuchi, “Disassembly from both ends of thick filaments in rabbit skeletal muscle fibers,” Biophys. J. 47, 257-266 (1985).
[CrossRef] [PubMed]

Judy, M. M.

M. M. Judy, T. Summerour, R. Leconey, R. L. Roa, and G. H. Templeton, “Muscle diffraction theory,” Biophys. J. 37, 475-487 (1982).
[CrossRef] [PubMed]

Kawai, M.

W. Ding, H. Fujita, and M. Kawai, “The length of cooperative units on the filament in rabbit psoas muscle fibres,” Exp. Physiol. 87, 691-697 (2002).
[CrossRef] [PubMed]

M. Kawai and I. D. Kuntz, “Optical diffraction studies of muscle fibers,” Biophys. J. 13, 857-876 (1973).
[CrossRef] [PubMed]

Knappeis, G. G.

G. G. Knappeis and F. Carlsen, “The ultrastructure of the Z disc in skeletal muscle,” J. Cell Biol. 13, 323-335 (1962).
[CrossRef] [PubMed]

F. Carlsen, G. G. Knappeis, and F. Buchthal, “Ultrastructure of the resting and contracted striated muscle fiber at different degrees of stretch,” J. Biophys. Biochem. Cytol. 11, 95-117 (1961).
[CrossRef] [PubMed]

F. Buchthal and G. G. Knappeis, “Diffraction spectra and minute structure of the cross-striated muscle fiber,” Skand. Arch. Physiol. 83, 281-307 (1940).

Knoesen, J.

E. Sidick, R. J. Baskin, Y. Yeh, and J. Knoesen, “Rigorous analysis of light diffraction ellipsometry by striated muscle fibers,” Biophys. J. 66, 2051-2061 (1994).
[CrossRef] [PubMed]

E. Sidick, J. Knoesen, K. Xian, Y. Yeh, and R. J. Baskin, “Rigorous analysis of light diffraction by a striated muscle fibre,” Proc. R. Soc. London, Ser. B 249, 247-256 (1992).
[CrossRef]

Kogelnik, H.

H. Kogelnik, “Coupled wave theory for thick hologram grating,” Bell Syst. Tech. J. 48, 2909-2943 (1969).

Kuntz, I. D.

M. Kawai and I. D. Kuntz, “Optical diffraction studies of muscle fibers,” Biophys. J. 13, 857-876 (1973).
[CrossRef] [PubMed]

Lalanne, P.

Leconey, R.

M. M. Judy, T. Summerour, R. Leconey, R. L. Roa, and G. H. Templeton, “Muscle diffraction theory,” Biophys. J. 37, 475-487 (1982).
[CrossRef] [PubMed]

Leiber, R. L.

R. L. Leiber, Y. Yeh, and R. J. Baskin, “Sarcomere length determination using laser diffraction,” Biophys. J. 45, 1007-1016 (1984).
[CrossRef]

R. J. Baskin, R. L. Leiber, T. Oba, and Y. Yeh, “Intensity of light diffraction from striated muscle as a function of incident angle,” Biophys. J. 36, 759-773 (1981).
[CrossRef] [PubMed]

Y. Yeh, R. J. Baskin, R. L. Leiber, and K. P. Roos, “Theory of light diffraction by single skeletal muscle fibers,” Biophys. J. 29, 509-522 (1980).
[CrossRef] [PubMed]

Leung, A. F.

A. F. Leung, Y. M. Cheung, and J. C. Hwang, “Light diffraction intensity from muscle fibers in different osmotic solutions: measurement of equilibrium time,” Eur. J. Physiol. 414, 676-682 (1989).
[CrossRef]

A. F. Leung, “Calculation of the laser diffraction intensity of striated muscle by numerical methods,” Comput. Programs Biomed. 15, 169-174 (1982).
[CrossRef] [PubMed]

Luther, P. K.

P. K. Luther, R. Padron, S. Ritter, R. Craig, and J. M. Suire, “Hetrogenity of Z-band structure within a single muscle sarcomere: implications for sarcomere assembly,” J. Mol. Biol. 332, 161-169 (2003).
[CrossRef] [PubMed]

Maclntosh, B. R.

B. R. Maclntosh, P. F. Gardiner, and A. J. McComas, Skeletal Muscle: Form and Function (Human Kinematics, 2006).

Mattheij, R. M. M.

McComas, A. J.

B. R. Maclntosh, P. F. Gardiner, and A. J. McComas, Skeletal Muscle: Form and Function (Human Kinematics, 2006).

Moharam, M. G.

Moss, R. L.

R. L. Moss, “Sarcomere length-tension relations of frog skinned muscle fibers during calcium activation at short length,” J. Physiol. (London) 292, 177-192 (1979).

Muramatsu, K.

S. Ishiwata, K. Muramatsu, and H. Higuchi, “Disassembly from both ends of thick filaments in rabbit skeletal muscle fibers,” Biophys. J. 47, 257-266 (1985).
[CrossRef] [PubMed]

Niedergerke, R.

A. F. Huxley and R. Niedergerke, “Measurement of the striations of isolated muscle fibers with the interference microscope,” J. Physiol. (London) 144, 403-425 (1958).

Oba, T.

R. J. Baskin, R. L. Leiber, T. Oba, and Y. Yeh, “Intensity of light diffraction from striated muscle as a function of incident angle,” Biophys. J. 36, 759-773 (1981).
[CrossRef] [PubMed]

Padron, R.

P. K. Luther, R. Padron, S. Ritter, R. Craig, and J. M. Suire, “Hetrogenity of Z-band structure within a single muscle sarcomere: implications for sarcomere assembly,” J. Mol. Biol. 332, 161-169 (2003).
[CrossRef] [PubMed]

Page, S. G.

S. G. Page and H. E. Huxley, “Filament lengths in striated muscle,” J. Cell Biol. 19, 369-390 (1963).
[CrossRef] [PubMed]

Paolini, P. J.

P. J. Paolini, R. Sabbadini, K. P. Roos, and R. J. Baskin, “Sarcomere length dispersion in single muscle fibers and fiber bundles,” Biophys. J. 16, 919-930 (1976).
[CrossRef] [PubMed]

Peachey, L. D.

C. L. Sundell, Y. E. Goldman, and L. D. Peachey, “Fine structure in near-field and far-field laser diffraction patterns from skeletal muscle fibers,” Biophys. J. 49, 521-530 (1986).
[CrossRef] [PubMed]

Pommet, A.

Ranasinghesagara, J.

Ritter, S.

P. K. Luther, R. Padron, S. Ritter, R. Craig, and J. M. Suire, “Hetrogenity of Z-band structure within a single muscle sarcomere: implications for sarcomere assembly,” J. Mol. Biol. 332, 161-169 (2003).
[CrossRef] [PubMed]

Roa, R. L.

M. M. Judy, T. Summerour, R. Leconey, R. L. Roa, and G. H. Templeton, “Muscle diffraction theory,” Biophys. J. 37, 475-487 (1982).
[CrossRef] [PubMed]

Roos, K. P.

Y. Yeh, R. J. Baskin, R. L. Leiber, and K. P. Roos, “Theory of light diffraction by single skeletal muscle fibers,” Biophys. J. 29, 509-522 (1980).
[CrossRef] [PubMed]

R. J. Baskin, K. P. Roos, and Y. Yeh, “Light diffraction study of single skeletal muscle fibers,” Biophys. J. 28, 45-64 (1979).
[CrossRef] [PubMed]

P. J. Paolini, R. Sabbadini, K. P. Roos, and R. J. Baskin, “Sarcomere length dispersion in single muscle fibers and fiber bundles,” Biophys. J. 16, 919-930 (1976).
[CrossRef] [PubMed]

Rudel, R.

R. Rudel and F. Zite-Ferenczy, “Efficiency of light diffraction by cross striated muscle fibers under stretch and during isometric contraction,” Biophys. J. 30, 507-516 (1980).
[CrossRef] [PubMed]

R. Rudel and F. Zite-Ferenczy, “Interpretation of light diffraction by cross-striated muscle as Bragg reflexion of light by the lattice of contractile proteins,” J. Physiol. (London) 290, 317-330 (1979).

Sabbadini, R.

P. J. Paolini, R. Sabbadini, K. P. Roos, and R. J. Baskin, “Sarcomere length dispersion in single muscle fibers and fiber bundles,” Biophys. J. 16, 919-930 (1976).
[CrossRef] [PubMed]

Sidick, E.

E. Sidick, R. J. Baskin, Y. Yeh, and J. Knoesen, “Rigorous analysis of light diffraction ellipsometry by striated muscle fibers,” Biophys. J. 66, 2051-2061 (1994).
[CrossRef] [PubMed]

E. Sidick, J. Knoesen, K. Xian, Y. Yeh, and R. J. Baskin, “Rigorous analysis of light diffraction by a striated muscle fibre,” Proc. R. Soc. London, Ser. B 249, 247-256 (1992).
[CrossRef]

Suire, J. M.

P. K. Luther, R. Padron, S. Ritter, R. Craig, and J. M. Suire, “Hetrogenity of Z-band structure within a single muscle sarcomere: implications for sarcomere assembly,” J. Mol. Biol. 332, 161-169 (2003).
[CrossRef] [PubMed]

Summerour, T.

M. M. Judy, T. Summerour, R. Leconey, R. L. Roa, and G. H. Templeton, “Muscle diffraction theory,” Biophys. J. 37, 475-487 (1982).
[CrossRef] [PubMed]

Sundell, C. L.

C. L. Sundell, Y. E. Goldman, and L. D. Peachey, “Fine structure in near-field and far-field laser diffraction patterns from skeletal muscle fibers,” Biophys. J. 49, 521-530 (1986).
[CrossRef] [PubMed]

Templeton, G. H.

M. M. Judy, T. Summerour, R. Leconey, R. L. Roa, and G. H. Templeton, “Muscle diffraction theory,” Biophys. J. 37, 475-487 (1982).
[CrossRef] [PubMed]

Thomas, N.

R. A. Thornhill, N. Thomas, and N. Berovic, “Optical diffraction by well ordered muscle fibers,” Eur. Biophys. J. 20, 87-99 (1991).
[CrossRef] [PubMed]

Thornhill, R. A.

R. A. Thornhill, N. Thomas, and N. Berovic, “Optical diffraction by well ordered muscle fibers,” Eur. Biophys. J. 20, 87-99 (1991).
[CrossRef] [PubMed]

van der Aa, N. P.

Xian, K.

E. Sidick, J. Knoesen, K. Xian, Y. Yeh, and R. J. Baskin, “Rigorous analysis of light diffraction by a striated muscle fibre,” Proc. R. Soc. London, Ser. B 249, 247-256 (1992).
[CrossRef]

Yao, G.

Yeh, Y.

E. Sidick, R. J. Baskin, Y. Yeh, and J. Knoesen, “Rigorous analysis of light diffraction ellipsometry by striated muscle fibers,” Biophys. J. 66, 2051-2061 (1994).
[CrossRef] [PubMed]

E. Sidick, J. Knoesen, K. Xian, Y. Yeh, and R. J. Baskin, “Rigorous analysis of light diffraction by a striated muscle fibre,” Proc. R. Soc. London, Ser. B 249, 247-256 (1992).
[CrossRef]

Y. Yeh and R. J. Baskin, “Thory of optical ellipsometric measurements from muscle diffraction studies,” Biophys. J. 54, 205-218 (1988).
[CrossRef] [PubMed]

R. L. Leiber, Y. Yeh, and R. J. Baskin, “Sarcomere length determination using laser diffraction,” Biophys. J. 45, 1007-1016 (1984).
[CrossRef]

R. J. Baskin, R. L. Leiber, T. Oba, and Y. Yeh, “Intensity of light diffraction from striated muscle as a function of incident angle,” Biophys. J. 36, 759-773 (1981).
[CrossRef] [PubMed]

Y. Yeh, R. J. Baskin, R. L. Leiber, and K. P. Roos, “Theory of light diffraction by single skeletal muscle fibers,” Biophys. J. 29, 509-522 (1980).
[CrossRef] [PubMed]

R. J. Baskin, K. P. Roos, and Y. Yeh, “Light diffraction study of single skeletal muscle fibers,” Biophys. J. 28, 45-64 (1979).
[CrossRef] [PubMed]

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S. Fujime and S. Yoshino, “Optical diffraction study of muscle fibers. I. A theoretical basis,” Biophys. Chem. 8, 305-315 (1978).
[CrossRef] [PubMed]

Zite-Ferenczy, F.

R. Rudel and F. Zite-Ferenczy, “Efficiency of light diffraction by cross striated muscle fibers under stretch and during isometric contraction,” Biophys. J. 30, 507-516 (1980).
[CrossRef] [PubMed]

R. Rudel and F. Zite-Ferenczy, “Interpretation of light diffraction by cross-striated muscle as Bragg reflexion of light by the lattice of contractile proteins,” J. Physiol. (London) 290, 317-330 (1979).

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H. Kogelnik, “Coupled wave theory for thick hologram grating,” Bell Syst. Tech. J. 48, 2909-2943 (1969).

Biochim. Biophys. Acta (2)

H. E. Huxley and J. Hanson, “Quantitative studies on the structure of cross striated myofibrils.,” Biochim. Biophys. Acta 23, 229-249 (1957).
[CrossRef] [PubMed]

S. Fujime, “Optical diffraction study of muscle fibers,” Biochim. Biophys. Acta 37, 227-238 (1975).

Biophys. Chem. (1)

S. Fujime and S. Yoshino, “Optical diffraction study of muscle fibers. I. A theoretical basis,” Biophys. Chem. 8, 305-315 (1978).
[CrossRef] [PubMed]

Biophys. J. (14)

E. Sidick, R. J. Baskin, Y. Yeh, and J. Knoesen, “Rigorous analysis of light diffraction ellipsometry by striated muscle fibers,” Biophys. J. 66, 2051-2061 (1994).
[CrossRef] [PubMed]

Y. Yeh, R. J. Baskin, R. L. Leiber, and K. P. Roos, “Theory of light diffraction by single skeletal muscle fibers,” Biophys. J. 29, 509-522 (1980).
[CrossRef] [PubMed]

M. Kawai and I. D. Kuntz, “Optical diffraction studies of muscle fibers,” Biophys. J. 13, 857-876 (1973).
[CrossRef] [PubMed]

P. J. Paolini, R. Sabbadini, K. P. Roos, and R. J. Baskin, “Sarcomere length dispersion in single muscle fibers and fiber bundles,” Biophys. J. 16, 919-930 (1976).
[CrossRef] [PubMed]

R. J. Baskin, K. P. Roos, and Y. Yeh, “Light diffraction study of single skeletal muscle fibers,” Biophys. J. 28, 45-64 (1979).
[CrossRef] [PubMed]

R. Rudel and F. Zite-Ferenczy, “Efficiency of light diffraction by cross striated muscle fibers under stretch and during isometric contraction,” Biophys. J. 30, 507-516 (1980).
[CrossRef] [PubMed]

B. Brenner, “Sarcomeric domain organization within single skinned rabbit psoas fibers and its effects on laser light diffraction patterns,” Biophys. J. 48, 967-982 (1985).
[CrossRef] [PubMed]

C. L. Sundell, Y. E. Goldman, and L. D. Peachey, “Fine structure in near-field and far-field laser diffraction patterns from skeletal muscle fibers,” Biophys. J. 49, 521-530 (1986).
[CrossRef] [PubMed]

R. L. Leiber, Y. Yeh, and R. J. Baskin, “Sarcomere length determination using laser diffraction,” Biophys. J. 45, 1007-1016 (1984).
[CrossRef]

M. M. Judy, T. Summerour, R. Leconey, R. L. Roa, and G. H. Templeton, “Muscle diffraction theory,” Biophys. J. 37, 475-487 (1982).
[CrossRef] [PubMed]

S. Ishiwata, K. Muramatsu, and H. Higuchi, “Disassembly from both ends of thick filaments in rabbit skeletal muscle fibers,” Biophys. J. 47, 257-266 (1985).
[CrossRef] [PubMed]

K. Burton and A. F. Huxley, “Identification of source of oscilations in apparent sarcomere length measured by laser diffraction,” Biophys. J. 68, 2429-2443 (1995).
[CrossRef] [PubMed]

Y. Yeh and R. J. Baskin, “Thory of optical ellipsometric measurements from muscle diffraction studies,” Biophys. J. 54, 205-218 (1988).
[CrossRef] [PubMed]

R. J. Baskin, R. L. Leiber, T. Oba, and Y. Yeh, “Intensity of light diffraction from striated muscle as a function of incident angle,” Biophys. J. 36, 759-773 (1981).
[CrossRef] [PubMed]

Comput. Programs Biomed. (1)

A. F. Leung, “Calculation of the laser diffraction intensity of striated muscle by numerical methods,” Comput. Programs Biomed. 15, 169-174 (1982).
[CrossRef] [PubMed]

Eur. Biophys. J. (1)

R. A. Thornhill, N. Thomas, and N. Berovic, “Optical diffraction by well ordered muscle fibers,” Eur. Biophys. J. 20, 87-99 (1991).
[CrossRef] [PubMed]

Eur. J. Physiol. (1)

A. F. Leung, Y. M. Cheung, and J. C. Hwang, “Light diffraction intensity from muscle fibers in different osmotic solutions: measurement of equilibrium time,” Eur. J. Physiol. 414, 676-682 (1989).
[CrossRef]

Exp. Physiol. (1)

W. Ding, H. Fujita, and M. Kawai, “The length of cooperative units on the filament in rabbit psoas muscle fibres,” Exp. Physiol. 87, 691-697 (2002).
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J. Biophys. Biochem. Cytol. (1)

F. Carlsen, G. G. Knappeis, and F. Buchthal, “Ultrastructure of the resting and contracted striated muscle fiber at different degrees of stretch,” J. Biophys. Biochem. Cytol. 11, 95-117 (1961).
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G. G. Knappeis and F. Carlsen, “The ultrastructure of the Z disc in skeletal muscle,” J. Cell Biol. 13, 323-335 (1962).
[CrossRef] [PubMed]

S. G. Page and H. E. Huxley, “Filament lengths in striated muscle,” J. Cell Biol. 19, 369-390 (1963).
[CrossRef] [PubMed]

J. Mol. Biol. (1)

P. K. Luther, R. Padron, S. Ritter, R. Craig, and J. M. Suire, “Hetrogenity of Z-band structure within a single muscle sarcomere: implications for sarcomere assembly,” J. Mol. Biol. 332, 161-169 (2003).
[CrossRef] [PubMed]

J. Opt. Soc. Am. (2)

J. Opt. Soc. Am. A (4)

J. Physiol. (London) (3)

A. F. Huxley and R. Niedergerke, “Measurement of the striations of isolated muscle fibers with the interference microscope,” J. Physiol. (London) 144, 403-425 (1958).

R. L. Moss, “Sarcomere length-tension relations of frog skinned muscle fibers during calcium activation at short length,” J. Physiol. (London) 292, 177-192 (1979).

R. Rudel and F. Zite-Ferenczy, “Interpretation of light diffraction by cross-striated muscle as Bragg reflexion of light by the lattice of contractile proteins,” J. Physiol. (London) 290, 317-330 (1979).

Opt. Express (1)

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A. F. Huxley, “Theoretical treatment of diffraction light by a striated muscle fibre,” Proc. R. Soc. London, Ser. B 241, 65-71 (1990).
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E. Sidick, J. Knoesen, K. Xian, Y. Yeh, and R. J. Baskin, “Rigorous analysis of light diffraction by a striated muscle fibre,” Proc. R. Soc. London, Ser. B 249, 247-256 (1992).
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B. R. Maclntosh, P. F. Gardiner, and A. J. McComas, Skeletal Muscle: Form and Function (Human Kinematics, 2006).

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Figures (6)

Fig. 1
Fig. 1

Coordinates used in the 3DCW simulation of a sarco- meric grating structure.

Fig. 2
Fig. 2

Illustrations of (a) the sarcomere structure and (b) the optical sarcomere model. The distribution of refractive indices is also shown. W A C T , W A , W I , W A O , and W Z are the widths of the actin filament, A-band, I-band, overlap region, and Z-line, respectively. n A , n I , n A O , and n Z are the refractive indices of the A-band, I-band, overlap region, and Z-band, respectively.

Fig. 3
Fig. 3

Schematic illustration of muscle fibers of different morphologies. (a) Straight, (b) skew, (c) half-wave ripple, (d) full-wave ripple, (e) random slip.

Fig. 4
Fig. 4

Comparisons between experimental ω scans (curves of open circles) and theoretical results (solid curves) that were calculated for different myofibril parameters. Experimental results were obtained in rabbit pasos muscle fiber illuminated by TE polarized light. The sarcomere length was Λ = 3.04 μ m and the fiber thickness was d = 71 μ m . Other parameters were as stated in Subsection 2B. To conform to the experimental data, the refractive index outside the muscle fiber was 1.0. (a) Results obtained in straight fiber. (b) Effects of a positive (solid curve) or negative (dashed curve) skew ( α skew = 0.8 ° ) . (c) Effects of a random slip, δ slip = 1 % Λ. (d) Effects of half-wave ripple ( λ ripple = 2 d ) and full-wave ripple ( λ ripple = d ) with ripple amplitude u ripple = 0.5 μ m .

Fig. 5
Fig. 5

Domain effect on ω-scan profiles ( Λ = 2.6 μ m , d = 150 μ m ). Open circles were defined according to experimental data from Rudel and Zite-Ferenczy [4]. The skew domain effect applied was α ν = 5.9 ° and α μ = 0.0 ° . The default values discussed in Subsection 2B were used for all other sarcomere parameters.

Fig. 6
Fig. 6

Comparisons between simulated diffraction efficiencies (shown as solid curves) with experimental results (symbols) at different sarcomere lengths. (a) First-order diffraction measured by Paolini et al. [2] in single frog semitendinousus muscle fiber (circles). Also shown are the calculated results for a straight 48 - μ m -thick fiber (solid curve) and with 1.1° skew for a 65 - μ m -thick fiber (dashed curve). (b) First-order diffraction measured by Baskin et al. [3] in single frog semitendinousus muscle fiber (circles and triangles). The simulation results were obtained by considering a domain effect ( α ν = 0.75 × Λ ° and α μ = 0.75 ° ). (c) First-order diffraction measured by Kawai and Kuntz [9] in single frog semitendinousus muscle fiber (circles). The simulation results were obtained by introducing a domain effect ( α ν = 10 ° , α μ = 4.5 ° ). (d) Intensity ratio between the second and third diffraction orders measured by Fujime [7] in frog fascia of sartorius muscle fiber (circles). Theoretical values were calculated with a domain effect of skew using α ν = ( 0.5 Λ ) ° and α μ = 1.0 ° . TE polarization was used in all calculations. A common fiber thickness of 80 μ m was used for (b), (c), and (d). A value of 1.45 μ m was used as the A-band width for (d). The default values discussed in Subsection 2B were used for all other sarcomere parameters.

Tables (1)

Tables Icon

Table 1 Muscle Sarcomere Parameters of the Frog Semitendinosus and Rabbit Psoas Muscles Reported in Published Studies

Equations (13)

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E I = E 0 exp ( j k I r ) + i R i exp [ j k I i r ] ,
E III = i T i exp [ j k III i ( r d ) ] ,
E II = i [ S x i ( z ) x ̂ + S y i ( z ) y ̂ + S z i ( z ) z ̂ ] exp [ j σ i r ] ,
H II = ϵ 0 μ 0 i [ U x i ( z ) x ̂ + U y i ( z ) y ̂ + U z i ( z ) z ̂ ] exp [ j σ i r ] ,
× E II = j ω μ 0 H II ,
× H II = j ω ϵ 0 ϵ ( x ) E II ,
ϵ ( x ) = h ϵ ̂ h exp ( j h K x ) ,
ϵ ̂ h = 1 Λ 0 Λ ϵ ( x ) exp ( j h K x ) d x .
DE III i = Re ( k z III i k z ) T i 2 ,
u ( z ) = z tan α skew ,
u ( z ) = u ripple sin ( 2 π z λ ripple ) ,
u ( z ) = N ( 0 , δ slip 2 ) ,
α i = N ( α μ , α ν 2 ) ,

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