Optical parameters of the tunable Bragg reflectors in squid

Abstract

Cephalopods (e.g. octopus, squid and cuttlefish) dynamically tune the colour and brightness of their skin for camouflage and communication using specialized skin cells called iridocytes. We use high-resolution microspectrophotometry to investigate individual tunable Bragg structures (consisting of alternating reflectin protein-containing, high-refractive index lamellae and low-refractive index inter-lamellar spaces) in live and chemically fixed iridocytes of the California market squid, Doryteuthis opalescens. This subcellular, single-stack microspectrophotometry allows for spectral normalization, permitting use of a transfer-matrix model of Bragg reflectance to calculate all the parameters of the Bragg stack-the refractive indices, dimensions and numbers of the lamellae and inter-lamellar spaces. Results of the fitting analyses show that eight or nine pairs of low- and high-index layers typically contribute to the observed reflectivity in live cells, whereas six or seven pairs of low- and high-index layers typically contribute to the reflectivity in chemically fixed cells. The reflectin-containing, high-index lamellae of live cells have a refractive index proportional to the peak reflectivity, with an average of 1.405 ± 0.012 and a maximum around 1.44, while the reflectin-containing lamellae in fixed tissue have a refractive index of 1.413 ± 0.015 suggesting a slight increase of refractive index in the process of fixation. As expected, incremental changes in refractive index contribute to the greatest incremental changes in reflectivity for those Bragg stacks with the most layers. The excursions in dimensions required to tune the measured reflected wavelength from 675 (red) to 425 nm (blue) are a decrease from ca 150 to 80 nm for the high-index lamellae and from ca 120 to 50 nm for the low-index inter-lamellar spaces. Fixation-induced dimensional changes also are quantified, leading us to suggest that further microspectrophotometric analyses of this iridocyte system can be used as a model system to quantify the effects of various methods of tissue fixation. The microspectrophotometry technique described can be expected to provide deeper insights into the molecular and physical mechanisms governing other biophotonically active cells and structures.

Keywords: Doryteuthis opalescens; iridescence; iridocyte; iridophore; reflectin; refractive index.

Figure 1.

(a) Schematic of the sample and microscope set-up. Illumination is from below through a microscope objective, and the light is shown as the yellow region. Note that the entire solid angle is used for both illumination and collection, and for all cases, the range of illumination and collection angles are the same. See details in §2. (b) Close-up schematic of the tissue with iridocytes. (c) A schematic of the detail in a single iridocyte. The optically distinct Bragg reflectors are indicated by the dashed black rectangles, and the normal to the surface of the Bragg stack is indicated by the corresponding arrow at the surface. The yellow triangle is of the same angle as in (a) and indicates the cone of illumination and collection. Note that for the far-right Bragg stack, the normal lies outside the cone of illumination and collection, so no light is collected from the stack and is indicated by the red cross mark. In contrast, the remaining Bragg stacks all have their surface normal within the cone of illumination/collection, and so spectra—always including the case for normal illumination—are collected from the remaining Bragg stacks (as indicated by the green check marks).

Figure 2.

(a) Microscopic image of five iridocytes (some only partially shown), with the one to be analysed marked by the white-dashed surrounding oval. The narrow rectangular area demarcated in white is the area within this single cell measured by the spectrometer. (b) The light from the rectangular area in (a) is dispersed along the x-axis on the spectrometer CCD, with the background signal subtracted. The y-dimension is the vertical dimension of the rectangular region, as indicated by the section of the image next to the y-axis. The vertical z-axis is the number of CCD counts measured. A few spectra corresponding to the bright regions in the rectangle in (a) (and laid out along the y-axis) are seen as peaks, with one of them highlighted in red. (c) The highlighted spectrum from (b), after nearest neighbour smoothing and normalization to a specular reflectivity standard (see §§2 and 4).

Figure 3.

Schematic of a multi-layer stack of a Bragg reflector, with low- and high-refractive indices of n_L and n_H, respectively, and corresponding thicknesses d_L and d_H, respectively. (Online version in colour.)

Figure 4.

Sample normalized reflectivity spectrum from a single multi-layer stack in an iridocyte (grey line). Data were fitted using the transfer-matrix method beginning with a starting fit (dashed black line) and ending with a best fit (solid black line) to the data, as decribed in §2. Inset text shows final parameters obtained from successive refinements.

Figure 5.

Peak reflectivity, R_max, as a function of peak wavelength, λ_max, obtained from the measured reflectivity data. Filled squares are data from live cells, and open circles are data from chemically fixed cells. There is no correlation between reflectivity and the wavelength at which this reflectivity is observed (Pearson's R = −0.13 and 0.09 for live and fixed cells, respectively) indicating absence of a relation between these two factors.

Figure 6.

Refractive index n_H of the reflectin-filled lamellae obtained from fits to individual multi-layer stacks, as a function of the peak wavelength, λ_max, of the corresponding reflection peaks. Filled squares are data from live cells, and open circles are data from chemically fixed cells. Values of n_H typically lie between 1.38 and 1.44, with rare high values up to n_H = 1.48. Average refractive index of the reflectin-containing lamellae from the live cells was and from the fixed cells was . There is no observed correlation between n_H and λ_max (Pearson's R = −0.06).

Figure 7.

n_H obtained from fits, as a function of peak reflectivity R_max of the corresponding peaks (obtained from the spectra of iridocytes). For each discrete number of pairs of layers N, n_H shows a strong linear correlation with the observed maximum reflectivity R_max, with Pearson's R values ranging from 0.90 to 0.99. (a) The data for live cells, and (b) the data for chemically fixed cells.

Figure 8.

The fraction of total occurrences in which fitted spectra yielded a particular number of pairs of layers in the best fit. Filled squares are data from live cells, and open circles are data from chemically fixed cells. More than 60% of the fits of live cells resulted in N values of 8 or 9, whereas in the case of chemically fixed cells, more than 60% of the fits resulted in N values of 6 or 7 layers.

Figure 9.

(a) Reflectin-containing layer thickness, and (b) inter-lamellar space thickness as a function of peak wavelength, λ_max. For both plots, filled squares are data from live cells, and open circles are data from chemically fixed cells. The thickness of both is higher for redder colours. Note the weak positive correlation for both the reflectin-containing layers and the inter-platelet layers—Pearson's R ≈ 0.59 for both d_H and d_L. (c) A sample TEM image used to obtain thickness measurements for the high- and low-index regions. The dark parallel stripes are the regions filled with reflectin; the intervening light regions are the inter-lamellar spaces.

Figure 10.

Bright-field microscopy images of two samples of cells before and after chemical fixation. (a,b) Live cells and (c,d) chemically fixed.