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Hayashi T, Tomomizu T, Sushida T, Akiyama M, Ei SI, Sato M. Tiling mechanisms of the Drosophila compound eye through geometrical tessellation. Curr Biol 2022; 32:2101-2109.e5. [PMID: 35390281 DOI: 10.1016/j.cub.2022.03.046] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/02/2021] [Revised: 02/16/2022] [Accepted: 03/15/2022] [Indexed: 11/29/2022]
Abstract
Tiling patterns are observed in many biological structures. The compound eye is an interesting example of tiling and is often constructed by hexagonal arrays of ommatidia, the optical unit of the compound eye. Hexagonal tiling may be common due to mechanical restrictions such as structural robustness, minimal boundary length, and space-filling efficiency. However, some insects exhibit tetragonal facets.1-4 Some aquatic crustaceans, such as shrimp and lobsters, have evolved with tetragonal facets.5-8 Mantis shrimp is an insightful example as its compound eye has a tetragonal midband region sandwiched between hexagonal hemispheres.9,10 This casts doubt on the naive explanation that hexagonal tiles recur in nature because of their mechanical stability. Similarly, tetragonal tiling patterns are also observed in some Drosophila small-eye mutants, whereas the wild-type eyes are hexagonal, suggesting that the ommatidial tiling is not simply explained by such mechanical restrictions. If so, how are the hexagonal and tetragonal patterns controlled during development? Here, we demonstrate that geometrical tessellation determines the ommatidial tiling patterns. In small-eye mutants, the hexagonal pattern is transformed into a tetragonal pattern as the relative positions of neighboring ommatidia are stretched along the dorsal-ventral axis. We propose that the regular distribution of ommatidia and their uniform growth collectively play an essential role in the establishment of tetragonal and hexagonal tiling patterns in compound eyes.
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Affiliation(s)
- Takashi Hayashi
- Mathematical Neuroscience Unit, Institute for Frontier Science Initiative, Kanazawa University, 13-1 Takaramachi, Kanazawa, Ishikawa 920-8640, Japan.
| | - Takeshi Tomomizu
- Graduate School of Frontier Science Initiative, Kanazawa University, 13-1 Takaramachi, Kanazawa, Ishikawa 920-8640, Japan
| | - Takamichi Sushida
- Department of Computer Science and Technology, Salesian Polytechnic, 4-6-8 Oyamagaoka, Machida, Tokyo 194-0215, Japan
| | - Masakazu Akiyama
- Faculty of Science, Academic Assembly, University of Toyama, 3190 Gofuku, Toyama 930-8555, Japan
| | - Shin-Ichiro Ei
- Department of Mathematics, Faculty of Science, Hokkaido University, Kita 10, Nishi 8, Kita-Ku, Sapporo, Hokkaido 060-0810, Japan
| | - Makoto Sato
- Mathematical Neuroscience Unit, Institute for Frontier Science Initiative, Kanazawa University, 13-1 Takaramachi, Kanazawa, Ishikawa 920-8640, Japan.
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Nakatani M, Kobayashi Y, Ohno K, Uesaka M, Mogami S, Zhao Z, Sushida T, Kitahata H, Nagayama M. Temporal coherency of mechanical stimuli modulates tactile form perception. Sci Rep 2021; 11:11737. [PMID: 34083558 PMCID: PMC8175693 DOI: 10.1038/s41598-021-90661-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/04/2020] [Accepted: 05/11/2021] [Indexed: 11/09/2022] Open
Abstract
The human hand can detect both form and texture information of a contact surface. The detection of skin displacement (sustained stimulus) and changes in skin displacement (transient stimulus) are thought to be mediated in different tactile channels; however, tactile form perception may use both types of information. Here, we studied whether both the temporal frequency and the temporal coherency information of tactile stimuli encoded in sensory neurons could be used to recognize the form of contact surfaces. We used the fishbone tactile illusion (FTI), a known tactile phenomenon, as a probe for tactile form perception in humans. This illusion typically occurs with a surface geometry that has a smooth bar and coarse textures in its adjacent areas. When stroking the central bar back and forth with a fingertip, a human observer perceives a hollow surface geometry even though the bar is physically flat. We used a passive high-density pin matrix to extract only the vertical information of the contact surface, suppressing tangential displacement from surface rubbing. Participants in the psychological experiment reported indented surface geometry by tracing over the FTI textures with pin matrices of the different spatial densities (1.0 and 2.0 mm pin intervals). Human participants reported that the relative magnitude of perceived surface indentation steeply decreased when pins in the adjacent areas vibrated in synchrony. To address possible mechanisms for tactile form perception in the FTI, we developed a computational model of sensory neurons to estimate temporal patterns of action potentials from tactile receptive fields. Our computational data suggest that (1) the temporal asynchrony of sensory neuron responses is correlated with the relative magnitude of perceived surface indentation and (2) the spatiotemporal change of displacements in tactile stimuli are correlated with the asynchrony of simulated sensory neuron responses for the fishbone surface patterns. Based on these results, we propose that both the frequency and the asynchrony of temporal activity in sensory neurons could produce tactile form perception.
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Affiliation(s)
- Masashi Nakatani
- Faculty of Environment and Information Studies, Keio University, Tokyo, Japan.
| | - Yasuaki Kobayashi
- Research Institute for Electronic Science, Hokkaido University, Sapporo, Japan
| | - Kota Ohno
- Research Institute for Electronic Science, Hokkaido University, Sapporo, Japan
| | - Masaaki Uesaka
- Graduate School of Mathematical Sciences, The University of Tokyo, Tokyo, Japan
| | - Sayako Mogami
- Faculty of Policy and Management, Keio University, Tokyo, Japan
| | - Zixia Zhao
- Research Institute for Electronic Science, Hokkaido University, Sapporo, Japan
| | - Takamichi Sushida
- Department of Computer Science and Technology, Salesian Polytechnic, Machida, Japan
| | | | - Masaharu Nagayama
- Research Institute for Electronic Science, Hokkaido University, Sapporo, Japan.
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Ishida-Ishihara S, Akiyama M, Furusawa K, Naguro I, Ryuno H, Sushida T, Ishihara S, Haga H. Osmotic gradients induce stable dome morphogenesis on extracellular matrix. J Cell Sci 2020; 133:jcs.243865. [PMID: 32576662 DOI: 10.1242/jcs.243865] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/10/2020] [Accepted: 06/11/2020] [Indexed: 01/04/2023] Open
Abstract
One of the fundamental processes in morphogenesis is dome formation, but many of the mechanisms involved are unexplored. Previous in vitro studies showed that an osmotic gradient is the driving factor of dome formation. However, these investigations were performed without extracellular matrix (ECM), which provides structural support to morphogenesis. With the use of ECM, we observed that basal hypertonic stress induced stable domes in vitro that have not been seen in previous studies. These domes developed as a result of ECM swelling via aquaporin water transport activity. Based on computer simulation, uneven swelling, with a positive feedback between cell stretching and enhanced water transport, was a cause of dome formation. These results indicate that osmotic gradients induce dome morphogenesis via both enhanced water transport activity and subsequent ECM swelling.
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Affiliation(s)
- Sumire Ishida-Ishihara
- Department of Advanced Transdisciplinary Sciences, Faculty of Advanced Life Science, Hokkaido University, N10-W8, Kita-ku, Sapporo 060-0810, Japan
| | - Masakazu Akiyama
- Meiji Institute for Advanced Study of Mathematical Sciences, Meiji University, Nakano 4-21-1, Nakano-ku, Tokyo 164-8525, Japan
| | - Kazuya Furusawa
- Department of Advanced Transdisciplinary Sciences, Faculty of Advanced Life Science, Hokkaido University, N10-W8, Kita-ku, Sapporo 060-0810, Japan.,Faculty of Environmental and Information Sciences, Fukui University of Technology, Gakuen 3-6-1, Fukui 910-8505, Japan
| | - Isao Naguro
- Graduate School of Pharmaceutical Sciences, University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-0033, Japan
| | - Hiroki Ryuno
- Graduate School of Pharmaceutical Sciences, University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-0033, Japan
| | - Takamichi Sushida
- Department of Computer Science and Technology, Salesian Polytechnic, Oyamagaoka 4-6-8, Machida City, Tokyo 194-0215, Japan
| | - Seiichiro Ishihara
- Department of Advanced Transdisciplinary Sciences, Faculty of Advanced Life Science, Hokkaido University, N10-W8, Kita-ku, Sapporo 060-0810, Japan.,Soft Matter GI-CoRE, Hokkaido University, N21W11, Kita-ku, Sapporo 001-0021, Japan
| | - Hisashi Haga
- Department of Advanced Transdisciplinary Sciences, Faculty of Advanced Life Science, Hokkaido University, N10-W8, Kita-ku, Sapporo 060-0810, Japan .,Soft Matter GI-CoRE, Hokkaido University, N21W11, Kita-ku, Sapporo 001-0021, Japan
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Sushida T, Yamagishi Y. Geometrical study of phyllotactic patterns by Bernoulli spiral lattices. Dev Growth Differ 2017; 59:379-387. [PMID: 28702954 DOI: 10.1111/dgd.12378] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/28/2017] [Revised: 04/29/2017] [Accepted: 05/09/2017] [Indexed: 11/30/2022]
Abstract
Geometrical studies of phyllotactic patterns deal with the centric or cylindrical models produced by ideal lattices. van Iterson (Mathematische und mikroskopisch - anatomische Studien über Blattstellungen nebst Betrachtungen über den Schalenbau der Miliolinen, Verlag von Gustav Fischer, Jena, 1907) suggested a centric model representing ideal phyllotactic patterns as disk packings of Bernoulli spiral lattices and presented a phase diagram now called Van Iterson's diagram explaining the bifurcation processes of their combinatorial structures. Geometrical properties on disk packings were shown by Rothen & Koch (J. Phys France, 50(13), 1603-1621, 1989). In contrast, as another centric model, we organized a mathematical framework of Voronoi tilings of Bernoulli spiral lattices and showed mathematically that the phase diagram of a Voronoi tiling is graph-theoretically dual to Van Iterson's diagram. This paper gives a review of two centric models for disk packings and Voronoi tilings of Bernoulli spiral lattices.
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Affiliation(s)
- Takamichi Sushida
- Research Institute for Electronic Science, Hokkaido University, Sapporo, 060-0812, Japan
| | - Yoshikazu Yamagishi
- Department of Applied Mathematics and Informatics, Ryukoku University, Seta, Otsu, 520-2194, Japan
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Akiyama M, Sushida T, Ishida S, Haga H. Mathematical model of collective cell migrations based on cell polarity. Dev Growth Differ 2017; 59:471-490. [DOI: 10.1111/dgd.12381] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2017] [Revised: 05/26/2017] [Accepted: 05/26/2017] [Indexed: 12/23/2022]
Affiliation(s)
- Masakazu Akiyama
- Research Institute for Electronic Science Hokkaido University N12‐W7, Kita‐ku Sapporo Hokkaido 060‐0812 Japan
| | - Takamichi Sushida
- Research Institute for Electronic Science Hokkaido University N12‐W7, Kita‐ku Sapporo Hokkaido 060‐0812 Japan
| | - Sumire Ishida
- Division of Life Science Graduate School of Life ScienceHokkaido UniversityN10‐W8, Kita‐ku Sapporo Hokkaido 060‐0810 Japan
| | - Hisashi Haga
- Transdisciplinary Life Science Course Faculty of Advanced Life Science Hokkaido University N10‐W8, Kita‐ku Sapporo Hokkaido 060‐0810 Japan
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