Presentation Information
[MS15-05]Predictions of the mechanisms for pinstripe and elliptical-leaf formations from analyses of mathematical models
*Akiko M Nakamasu1 (1. Meiji University (Japan))
Keywords:
Pattern formation,Morphogenesis,PDE
I will talk about two studies about fish pigmentation patterns and leaf shapes through analyses of respective mathematical models.
First, I focus on patterns composed of thin stripes and broad inter-stripes and call them “pinstripe”. Pinstripe formations have been explained by taxis-like mechanisms (Painter et al. 1999, Alessio & Gupta 2023). But I report that it can be derived by general diffusions. Cellular and molecular mechanisms of pigmentation pattern formation have been revealed empirically in zebrafish as a model organism. And one of connexin transgenics shows a pinstripe pattern (Watanabe & Kondo 2012). As mentioned above, connexin molecules are important for the pigmentation-pattern formation, and parameters of a reaction-diffusion model suggested by interactions of pigment cells were linked to functions of the connexins. However, there was a discrepancy between the patterns predicted from the assumption and obtained from the actual experiments (Nakamasu 2022). Here, I will show that the model could reproduce the pattern change with a reconsideration of the parameters affected by the connexin defects. And pinstripe patterns arise naturally using this model. When I analytically sought the reason for the sharpness of strips, difference in wave lengths of two pattern-formation motives in the model was found to be remarkable. Therefore, the present mechanism is considered to be characteristic to three-variable system and work in a linear way.
Second, I introduce a model-based prediction to generate diverse shape proportions of entire leaves (Nakamasu 2025). The way to read out positional information is key to shape diversification, because simple positional information likely falls into a similar shape production. Here, formations of entire leaves will be a good system to study outputs of simple positional information, on 2-dimentional morphogenesis with less cell’smotility. Aligned cells grow directionally (elongate) on the peripheral with a gradient and are assumed to work as a flame of the shape. In this situation, whether “cell divide or not” seems to be important to make peripheral curves. Therefore, I implemented two algorithms for contour deformations corresponding to the two growth modes. When the algorithms were combined as a model, leaf-like shapes were spontaneously obtained. In this model, a gradient-norm dependency of shape proportion was analytically confirmed in growth algorithm for without cell division. And growth with division was numerically confirmed to shorten the shape in a speed dependent manner.
First, I focus on patterns composed of thin stripes and broad inter-stripes and call them “pinstripe”. Pinstripe formations have been explained by taxis-like mechanisms (Painter et al. 1999, Alessio & Gupta 2023). But I report that it can be derived by general diffusions. Cellular and molecular mechanisms of pigmentation pattern formation have been revealed empirically in zebrafish as a model organism. And one of connexin transgenics shows a pinstripe pattern (Watanabe & Kondo 2012). As mentioned above, connexin molecules are important for the pigmentation-pattern formation, and parameters of a reaction-diffusion model suggested by interactions of pigment cells were linked to functions of the connexins. However, there was a discrepancy between the patterns predicted from the assumption and obtained from the actual experiments (Nakamasu 2022). Here, I will show that the model could reproduce the pattern change with a reconsideration of the parameters affected by the connexin defects. And pinstripe patterns arise naturally using this model. When I analytically sought the reason for the sharpness of strips, difference in wave lengths of two pattern-formation motives in the model was found to be remarkable. Therefore, the present mechanism is considered to be characteristic to three-variable system and work in a linear way.
Second, I introduce a model-based prediction to generate diverse shape proportions of entire leaves (Nakamasu 2025). The way to read out positional information is key to shape diversification, because simple positional information likely falls into a similar shape production. Here, formations of entire leaves will be a good system to study outputs of simple positional information, on 2-dimentional morphogenesis with less cell’smotility. Aligned cells grow directionally (elongate) on the peripheral with a gradient and are assumed to work as a flame of the shape. In this situation, whether “cell divide or not” seems to be important to make peripheral curves. Therefore, I implemented two algorithms for contour deformations corresponding to the two growth modes. When the algorithms were combined as a model, leaf-like shapes were spontaneously obtained. In this model, a gradient-norm dependency of shape proportion was analytically confirmed in growth algorithm for without cell division. And growth with division was numerically confirmed to shorten the shape in a speed dependent manner.