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Cephalopod Coloration Model. I. Squid Chromatophores and Iridophores

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Cephalopod Coloration Model. I. Squid Chromatophores and Iridophores 588 J. Opt. Soc. Am. A/Vol. 25, No. 3/March 2008 Sutherland et al. Cephalopod coloration model. I. Squid chromatophores and iridophores Richard L. Sutherland,1,2,* Lydia M. Mäthger,3 Roger T. Hanlon,3 Augustine M. Urbas,1 and Morley O. Stone1 1Air Force Research Laboratory, 3005 Hobson Way, Wright-Patterson Air Force Base, Ohio 45433-7707, USA 2Science Applications International Corporation, 4031 Colonel Glenn Highway, Dayton, Ohio 45431, USA 3Marine Resources Center, Marine Biological Laboratory, 7 MBL Street, Woods Hole, Massachusetts 02543, USA *Corresponding author: [email protected] Received September 11, 2007; revised November 28, 2007; accepted December 3, 2007; posted December 21, 2007 (Doc. ID 87405); published February 7, 2008 We have developed a mathematical model of skin coloration in cephalopods, a class of aquatic animals. Cepha- lopods utilize neurological and physiological control of various skin components to achieve active camouflage and communication. Specific physical processes of this coloration are identified and modeled, utilizing avail- able biological materials data, to simulate active spectral changes in pigment-bearing organs and structural iridescent cells. Excellent agreement with in vitro measurements of squid skin is obtained. A detailed under- standing of the physical principles underlying cephalopod coloration is expected to yield insights into the be- havioral ecology of these animals. © 2008 Optical Society of America OCIS codes: 000.1430, 050.7330, 160.1435, 240.0310, 260.3160, 330.1690. 1. INTRODUCTION experimental spectra or combined to illustrate coloration effects in different environments. Color is an important and ubiquitous property in biology. Our objective is to provide answers to questions such as Although animal pigments have long been studied, struc- the following: Given a particular light source, what does a tural coloration in biology has become a subject of recent intense interest, with many examples of exotic photonic patch of cephalopod skin look like to an observer? Particu- structures discovered in both aquatic and terrestrial sys- larly, what is the color rendition of the skin in a spatial tems [1–3]. Since most animals are visual, color plays a resolution element (i.e., a pixel)? What are the physical significant role in, for example, predator–prey relation- properties of the skin that lead to this coloration? In an- ships, mating, and the generation of visual signals be- swering such questions we must consider the multiple op- tween conspecific or interspecific animals. A crucial de- tical interactions of various skin components (pigments fense mechanism for many animals is camouflage. and structural elements), which can undergo physiologi- Cephalopods—a class of aquatic invertebrates (Phylum cal or neurological modification, and the fact that within Mollusca) that includes squid, octopus, and cuttlefish— an aquatic environment the nature of ambient light can have developed a highly sophisticated system of dynamic range from highly collimated to diffuse. Results of this camouflage [4,5]. They adapt their color and body pattern study should enhance our understanding of how these to various visual features of the immediate background. animals employ dynamic camouflage to adapt to their Color is controlled through a combination of both pig- background. ments and photonic structures in an elaborate skin con- We have developed a model of the reflective properties figuration. This produces a rich repertoire of spectra and for a generic cephalopod skin consisting of any number of patterns that is highly adaptive to changing backgrounds layers with various optical elements, both structural and and situations. Current biological research is focused on pigmented. The model incorporates multiple internal re- understanding how cephalopods neurologically perform flections among the various skin components and consists these adaptations [6–9]. also of various submodels describing the optical proper- Although cephalopod skin has been widely studied and ties of each skin element individually. In this paper we characterized biologically, there has been relatively little present these submodels for two components, namely, the work done in modeling its optical properties. Masthay pigmented chromatophores and the structural iri- presented a quantitative model of pigment absorption in dophores, for which the spectral reflectance and transmit- animals, including cephalopods, based solely on Beer’s tance can be changed by the animal, either neurologically law, but did not include scattering or diffuse reflection or physiologically, to achieve dynamic camouflage. We [10]. Denton and Land discussed the mechanism of irides- compare these models with in vitro experimental mea- cent reflections from fish and cephalopods in terms of surements of skin components in squid. Materials proper- quarter-wave thin-film stacks [11], and Mäthger and Den- ties, such as index of refraction, absorption and scattering ton described theoretical calculations of spectra that they coefficients, and dispersion are obtained either from the related qualitatively to the iridescence of loliginid squid literature or through comparison of the models with ex- [12]. In none of these previous works, however, were de- perimental data. A future paper will combine these re- tailed calculations of spectra compared quantitatively to sults with those of submodels for static skin components 1084-7529/08/030588-12/$15.00 © 2008 Optical Society of America Sutherland et al. Vol. 25, No. 3/March 2008/J. Opt. Soc. Am. A 589 to investigate multilayer effects on the total animal re- scattering, we introduce the forward scattering ratio ␰, flectance with a generic cephalopod skin. which is defined as the ratio of light scattered into the for- ward hemisphere to the total scattered light [16]. We treat the chromatophore ideally as a disk of uni- 2. THEORY form thickness d and elliptical cross section. Electron mi- The topmost layers of a squid skin are pigment-bearing croscopy data for an expanded chromatophore indicate ϳ organs called chromatophores. Each chromatophore com- that a typical pigment granule size is 300 nm and the Ͼ prises a sacculus containing pigment granules of a spe- mean center-to-center spacing of granules is 300 nm cific color (brown, red, or yellow) and surrounded by a se- [17]. Applying the standard Rayleigh criterion, the chro- ␦ Ͻ␭ ries of radial muscles. When the muscles contract, the matophore would be optically smooth if h /8n, where ␦ sacculus is expanded, thus spreading out the pigment h is the root-mean-square roughness height measured ␦ granules. The sacculus is elastic so that when the muscles from some reference plane, which would imply h Ͻ ␭ relax, the chromatophore retracts. The pigment colors are 55 nm for =600 nm and n=1.33. Since the surface is ordered, going from yellow to red to brown in skin depth not optically smooth, we make the simplifying assump- Ϸ [9]. Subjacent to the chromatophores are structural color tion that Rcc 0. Although this does not entirely rule out elements called iridophores. These consist of several iri- the presence of a specular component, it is likely to be dosomes that have a multilayer structure consisting of small and not contribute significantly to the total skin re- thin, transparent protein platelets [13] sandwiched be- flectance. Hence we consider a model for the isolated chro- tween spacers of cytoplasm. The iridophores produce iri- matophore as illustrated in Fig. 1. Let a prime symbol in- descent colors upon illumination by white light. The in- dicate the derivative with respect to z, where z is the tensity and color of iridophores can change in the distance measured from the front of the chromatophore presence of the neuromodulator acetylcholine [14]. (see Fig. 1). Designating I as the forward flux and J as the Ultimately, we wish to relate the various components of backward flux, the radiation transport equations may radiant flux (both collimated and diffuse) at the bound- then be written as [16] aries of the various skin layers. To this end we define the Ј ͑␣ ␴͒ ͑ ͒ I =− + Ic, 1a partial reflectances and transmittances for each layer. By c partial we mean the reflectance or transmittance that Ј ␩␣ ␩͑ ␰͒␴ ␩͑ ␰͒␴ ␰␴ ͑ ͒ would be measured in an experiment for a completely iso- Id =− Id − 1− Id + 1− Jd + Ic, 1b lated layer using either pure collimated or pure diffuse Ј ␩␣ ␩͑ ␰͒␴ ␩͑ ␰͒␴ ͑ ␰͒␴ ͑ ͒ light, and separately detecting specularly and diffusely Jd = Jd + 1− Jd − 1− Id − 1− Ic, 1c reflected or transmitted light. For example, if we desig- which is a variant of the Kubelka–Munk model [18]. In nate Jd←c as the diffuse component of the total reflected light for a purely collimated input I , then the ratio R Eqs. (1b) and (1c) we have introduced the effective path c cd length coefficient ␩ for diffuse light, defined by ␩ =J ← /I is the partial reflectance. A similar definition d c c =͗1/cos ␪͘, where ␪ is an angle of propagation with re- holds for the partial transmittance Tcd. We also define partial reflectance and transmittance for collimated light spect to the z axis and the brackets indicate an average produced from collimated light (R and T ) and diffuse over the full solid angle in the forward direction weighted cc cc by the angular distribution of the diffuse radiation light produced from diffuse light (Rdd and Tdd). For the models presented here we have made some sim- [16,18]. Note that Ic represents the flux of ballistic (un- plifying assumptions. All elements, as well as the entire scattered) photons and thus has an effective path length skin itself, are embedded in a watery environment. Hence coefficient of one. we can ignore interfacial Fresnel reflections except those This system of coupled differential equations consti- that arise from components of interest. These include tutes what is known as a three-flux model and may be specular reflections from iridophores and scattering from solved exactly. The solutions are similar in many respects pigment granules.
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