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  • Code and example simulations of phase-field crystal model (for cone mosaic formation)

    work
    Creator:
    Nunley, Hayden, Nagashima, Mikiko, Martin, Kamirah, Lorenzo Gonzalez, Alcides, Suzuki, Sachihiro C., Norton, Declan A., Wong, Rachel O. L., Raymond, Pamela A., and Lubensky, David K.
    Description:
    The most important part of this deposit is the code necessary for simulating the anisotropic phase-field crystal on a cone geometry. The second most important is the code for analyzing the simulation results, including the spatial distribution of Y-junctions in the simulated retinae. Included are simulation results in which we systematically scan both the undercooling parameters and the strength of noise in the initial conditions. Finally, we include an additional simulation example (as in Figure 7D). Please see readme file for description of main (MATLAB) functions used for simulating and analyzing simulations.
    Keyword:
    zebrafish cone mosaic, topological defects, grain boundaries, and phase-field crystal model
    Citation to related publication:
    Nunley, H., Nagashima, M., Martin, K., Gonzalez, A. L., Suzuki, S. C., Norton, D. A., Wong, R. O. L., Raymond, P. A., & Lubensky, D. K. (2020). Defect patterns on the curved surface of fish retinae suggest a mechanism of cone mosaic formation. PLOS Computational Biology, 16(12), e1008437.  https://doi.org/10.1371/journal.pcbi.1008437 and Defect patterns on the curved surface of fish retinae suggest mechanism of cone mosaic formation Hayden Nunley, Mikiko Nagashima, Kamirah Martin, Alcides Lorenzo Gonzalez, Sachihiro C. Suzuki, Declan Norton, Rachel O. L. Wong, Pamela A. Raymond, David K. Lubensky bioRxiv 806679; doi:  https://doi.org/10.1101/806679
    Discipline:
    Science

  • Defect patterns on the curved surface of fish retinae suggest a mechanism of cone mosaic formation

    User Collection
    collection
    Creator:
    Nunley, Hayden, Nagashima, Mikiko, Martin, Kamirah, Lorenzo Gonzalez, Alcides, Suzuki, Sachihiro C., Norton, Declan A., Wong, Rachel O. L., Raymond, Pamela A., and Lubensky, David K.
    Description:
    The outer epithelial layer of zebrafish retinae contains a crystalline array of cone photoreceptors, called the cone mosaic. As this mosaic grows by mitotic addition of new photoreceptors at the rim of the hemispheric retina, topological defects, called “Y-Junctions”, form to maintain approximately constant cell spacing. The generation of topological defects due to growth on a curved surface is a distinct feature of the cone mosaic not seen in other well-studied biological patterns like the R8 photoreceptor array in the _ Drosophila compound eye. Since defects can provide insight into cell-cell interactions responsible for pattern formation, here we characterize the arrangement of cones in individual Y-Junction cores (see Set of images for Figures 1 and 2 and 6 and Supplementary Figure 7) as well as the spatial distribution of Y-junctions across entire retinae (see Dataset for analyzing spatial distribution of Y-junctions in flat-mounted retinae). We find that for individual Y-junctions, the distribution of cones near the core corresponds closely to structures observed in physical crystals (see Set of images for Figures 1 and 2 and 6 and Supplementary Figure 7). In addition, Y-Junctions are organized into lines, called grain boundaries, from the retinal center to the periphery (see Dataset for analyzing spatial distribution of Y-junctions in flat-mounted retinae and Dataset for measuring tendency of Y-junctions to line up into grain boundaries during incorporation into retinae). In physical crystals, regardless of the initial distribution of defects, defects can coalesce into grain boundaries via the mobility of individual particles. By imaging in live fish, we demonstrate that grain boundaries in the cone mosaic instead appear during initial mosaic formation, without requiring defect motion (see Dataset for measuring tendency of Y-junctions to line up into grain boundaries during incorporation into retinae and Dataset for analyzing Y-junction motion in live fish retinae). Motivated by this observation, we show that a computational model of repulsive cell-cell interactions generates a mosaic with grain boundaries (see Code and example simulations of phase-field crystal model (for cone mosaic formation)). In contrast to paradigmatic models of fate specification in mostly motionless cell packings (see Code and accompanying input data for simulating lateral inhibition on motionless cell packing), this finding emphasizes the role of cell motion, guided by cell-cell interactions during differentiation, in forming biological crystals. Such a route to the formation of regular patterns may be especially valuable in situations, like growth on a curved surface, where the resulting long-ranged, elastic, effective interactions between defects can help to group them into grain boundaries.
    Keyword:
    zebrafish cone mosaic, lattice vectors, topological defects, tissue patterning, grain boundaries, lateral inhibition, photoconversion, phase-field crystal model, and defect motion
    Discipline:
    Science
    7Works