Abstract

A recent study showed that the rod photoreceptor cell nuclei in the retina of nocturnal and diurnal mammals differ considerably in architecture: the location of euchromatin and heterochromatin in the nucleus is interchanged. This inversion has significant implications for the refractive index distribution and the light scattering properties of the nucleus. Here, we extend previous two-dimensional analysis to three dimensions (3D) by using both a numerical finite-difference time-domain and an analytic Mie theory approach. We find that the specific arrangement of the chromatin phases in the nuclear core-shell models employed have little impact on the far-field scattering cross section. However, scattering in the near field, which is the relevant regime inside the retina, shows a significant difference between the two architectures. The “inverted” photoreceptor cell nuclei of nocturnal mammals act as collection lenses, with the lensing effect being much more pronounced in 3D than in two dimensions. This lensing helps to deliver light efficiently to the light-sensing outer segments of the rod photoreceptor cells and thereby improve night vision.

© 2010 Optical Society of America

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2010

A. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

2009

I. Solovei, M. Kreysing, C. Lanctôt, S. Kösem, L. Peichl, T. Cremer, J. Guck, and B. Joffe, Cell 137, 356 (2009).
[CrossRef] [PubMed]

2007

K. Franze, J. Grosche, S. N. Skatchkov, S. Schinkinger, C. Foja, D. Schild, O. Uckermann, K. Travis, A. Reichenbach, and J. Guck, Proc. Natl. Acad. Sci. USA 104, 8287 (2007).
[CrossRef] [PubMed]

P. Fraser and W. Bickmore, Nature 447, 413 (2007).
[CrossRef] [PubMed]

2005

J. Postberg, O. Alexandrova, T. Cremer, and H. J. Lipps, J. Cell Sci. 118, 3973 (2005).
[CrossRef] [PubMed]

1997

1994

J. P. Berenger, J. Comput. Phys. 114, 185 (1994).
[CrossRef]

1993

1988

1966

K. Yee, IEEE Trans. Antennas Propagat. 14, 302 (1966).
[CrossRef]

Alexandrova, O.

J. Postberg, O. Alexandrova, T. Cremer, and H. J. Lipps, J. Cell Sci. 118, 3973 (2005).
[CrossRef] [PubMed]

Barton, J.

Berenger, J. P.

J. P. Berenger, J. Comput. Phys. 114, 185 (1994).
[CrossRef]

Bermel, P.

A. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

Bickmore, W.

P. Fraser and W. Bickmore, Nature 447, 413 (2007).
[CrossRef] [PubMed]

Bohren, C. F.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Cremer, T.

I. Solovei, M. Kreysing, C. Lanctôt, S. Kösem, L. Peichl, T. Cremer, J. Guck, and B. Joffe, Cell 137, 356 (2009).
[CrossRef] [PubMed]

J. Postberg, O. Alexandrova, T. Cremer, and H. J. Lipps, J. Cell Sci. 118, 3973 (2005).
[CrossRef] [PubMed]

Foja, C.

K. Franze, J. Grosche, S. N. Skatchkov, S. Schinkinger, C. Foja, D. Schild, O. Uckermann, K. Travis, A. Reichenbach, and J. Guck, Proc. Natl. Acad. Sci. USA 104, 8287 (2007).
[CrossRef] [PubMed]

Franze, K.

K. Franze, J. Grosche, S. N. Skatchkov, S. Schinkinger, C. Foja, D. Schild, O. Uckermann, K. Travis, A. Reichenbach, and J. Guck, Proc. Natl. Acad. Sci. USA 104, 8287 (2007).
[CrossRef] [PubMed]

Fraser, P.

P. Fraser and W. Bickmore, Nature 447, 413 (2007).
[CrossRef] [PubMed]

Goodman, J.

J. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

Gouesbet, G.

Gréhan, G.

Grosche, J.

K. Franze, J. Grosche, S. N. Skatchkov, S. Schinkinger, C. Foja, D. Schild, O. Uckermann, K. Travis, A. Reichenbach, and J. Guck, Proc. Natl. Acad. Sci. USA 104, 8287 (2007).
[CrossRef] [PubMed]

Guck, J.

I. Solovei, M. Kreysing, C. Lanctôt, S. Kösem, L. Peichl, T. Cremer, J. Guck, and B. Joffe, Cell 137, 356 (2009).
[CrossRef] [PubMed]

K. Franze, J. Grosche, S. N. Skatchkov, S. Schinkinger, C. Foja, D. Schild, O. Uckermann, K. Travis, A. Reichenbach, and J. Guck, Proc. Natl. Acad. Sci. USA 104, 8287 (2007).
[CrossRef] [PubMed]

Huffman, D. R.

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

Ibanescu, M.

A. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

Joannopoulos, J.

A. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

Joffe, B.

I. Solovei, M. Kreysing, C. Lanctôt, S. Kösem, L. Peichl, T. Cremer, J. Guck, and B. Joffe, Cell 137, 356 (2009).
[CrossRef] [PubMed]

Johnson, S. G.

A. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

Kösem, S.

I. Solovei, M. Kreysing, C. Lanctôt, S. Kösem, L. Peichl, T. Cremer, J. Guck, and B. Joffe, Cell 137, 356 (2009).
[CrossRef] [PubMed]

Kreysing, M.

I. Solovei, M. Kreysing, C. Lanctôt, S. Kösem, L. Peichl, T. Cremer, J. Guck, and B. Joffe, Cell 137, 356 (2009).
[CrossRef] [PubMed]

Lanctôt, C.

I. Solovei, M. Kreysing, C. Lanctôt, S. Kösem, L. Peichl, T. Cremer, J. Guck, and B. Joffe, Cell 137, 356 (2009).
[CrossRef] [PubMed]

Lipps, H. J.

J. Postberg, O. Alexandrova, T. Cremer, and H. J. Lipps, J. Cell Sci. 118, 3973 (2005).
[CrossRef] [PubMed]

Maheu, B.

Oskooi, A.

A. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

Peichl, L.

I. Solovei, M. Kreysing, C. Lanctôt, S. Kösem, L. Peichl, T. Cremer, J. Guck, and B. Joffe, Cell 137, 356 (2009).
[CrossRef] [PubMed]

Piket-May, M. J.

Postberg, J.

J. Postberg, O. Alexandrova, T. Cremer, and H. J. Lipps, J. Cell Sci. 118, 3973 (2005).
[CrossRef] [PubMed]

Reichenbach, A.

K. Franze, J. Grosche, S. N. Skatchkov, S. Schinkinger, C. Foja, D. Schild, O. Uckermann, K. Travis, A. Reichenbach, and J. Guck, Proc. Natl. Acad. Sci. USA 104, 8287 (2007).
[CrossRef] [PubMed]

Rodieck, R.

R. Rodieck, First Steps in Seeing (Sinauer, 1998).

Roundy, D.

A. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

Schild, D.

K. Franze, J. Grosche, S. N. Skatchkov, S. Schinkinger, C. Foja, D. Schild, O. Uckermann, K. Travis, A. Reichenbach, and J. Guck, Proc. Natl. Acad. Sci. USA 104, 8287 (2007).
[CrossRef] [PubMed]

Schinkinger, S.

K. Franze, J. Grosche, S. N. Skatchkov, S. Schinkinger, C. Foja, D. Schild, O. Uckermann, K. Travis, A. Reichenbach, and J. Guck, Proc. Natl. Acad. Sci. USA 104, 8287 (2007).
[CrossRef] [PubMed]

Skatchkov, S. N.

K. Franze, J. Grosche, S. N. Skatchkov, S. Schinkinger, C. Foja, D. Schild, O. Uckermann, K. Travis, A. Reichenbach, and J. Guck, Proc. Natl. Acad. Sci. USA 104, 8287 (2007).
[CrossRef] [PubMed]

Solovei, I.

I. Solovei, M. Kreysing, C. Lanctôt, S. Kösem, L. Peichl, T. Cremer, J. Guck, and B. Joffe, Cell 137, 356 (2009).
[CrossRef] [PubMed]

Taflove, A.

Travis, K.

K. Franze, J. Grosche, S. N. Skatchkov, S. Schinkinger, C. Foja, D. Schild, O. Uckermann, K. Travis, A. Reichenbach, and J. Guck, Proc. Natl. Acad. Sci. USA 104, 8287 (2007).
[CrossRef] [PubMed]

Troy, J. B.

Uckermann, O.

K. Franze, J. Grosche, S. N. Skatchkov, S. Schinkinger, C. Foja, D. Schild, O. Uckermann, K. Travis, A. Reichenbach, and J. Guck, Proc. Natl. Acad. Sci. USA 104, 8287 (2007).
[CrossRef] [PubMed]

Yee, K.

K. Yee, IEEE Trans. Antennas Propagat. 14, 302 (1966).
[CrossRef]

Appl. Opt.

Cell

I. Solovei, M. Kreysing, C. Lanctôt, S. Kösem, L. Peichl, T. Cremer, J. Guck, and B. Joffe, Cell 137, 356 (2009).
[CrossRef] [PubMed]

Comput. Phys. Commun.

A. Oskooi, D. Roundy, M. Ibanescu, P. Bermel, J. Joannopoulos, and S. G. Johnson, Comput. Phys. Commun. 181, 687 (2010).
[CrossRef]

IEEE Trans. Antennas Propagat.

K. Yee, IEEE Trans. Antennas Propagat. 14, 302 (1966).
[CrossRef]

J. Cell Sci.

J. Postberg, O. Alexandrova, T. Cremer, and H. J. Lipps, J. Cell Sci. 118, 3973 (2005).
[CrossRef] [PubMed]

J. Comput. Phys.

J. P. Berenger, J. Comput. Phys. 114, 185 (1994).
[CrossRef]

J. Opt. Soc. Am. A

Nature

P. Fraser and W. Bickmore, Nature 447, 413 (2007).
[CrossRef] [PubMed]

Opt. Lett.

Proc. Natl. Acad. Sci. USA

K. Franze, J. Grosche, S. N. Skatchkov, S. Schinkinger, C. Foja, D. Schild, O. Uckermann, K. Travis, A. Reichenbach, and J. Guck, Proc. Natl. Acad. Sci. USA 104, 8287 (2007).
[CrossRef] [PubMed]

Other

C. F. Bohren and D. R. Huffman, Absorption and Scattering of Light by Small Particles (Wiley, 1983).

R. Rodieck, First Steps in Seeing (Sinauer, 1998).

J. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

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Figures (3)

Fig. 1
Fig. 1

Far-field scattering properties of photoreceptor cell nuclei obtained with the coated-sphere Mie theory model. (a) Scattering cross sections of conventional and inverted nuclei (and a homogeneous sphere for comparison) as a function of wavelength for plane wave incidence. (b) Scattered power (i.e., intensity multiplied with the area element of the scattering arc) averaged over the visible spectrum (400 to 700 nm ) for illumination with a plane wave. (c) Scattered power for incidence of a single plane wave ( λ = 500 nm ) and (d) for a symmetrically incident Gaussian beam ( λ = 500 nm , w 0 = 2.5 μm ).

Fig. 2
Fig. 2

Scattering of an incident plane wave by conventional and inverted nuclei in the optical near field. Nuclei (not shown; for parameters see text) are centered on the coordinate origin. Light propagates along the positive z axis (see arrow). Mie theory results for the scattering from the (a) conventional (b) and inverted nuclear architecture. FDTD simulations for the scattering from a conventional (c) and (d) inverted nucleus.

Fig. 3
Fig. 3

Comparison of the FDTD results for the near-field scattering intensities in 2D and 3D for incidence of a plane wave ( λ = 500 nm ; propagation from left to right) on a nucleus of inverted architecture with 5 μm outer diameter. The focusing effect in (b) 3D is much more pronounced than in (a) 2D and is also insensitive to relatively large deviations from (c) a spherical shape (cross section through the center of the nucleus is shown on the left). The two-dimensional results were generated using the code from [1].

Equations (1)

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E r ( r , θ , φ ) = n = 1 m = n m = n + 1 P m n N r , m n ( r , θ , φ ) .

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