Microglia are resident immune cells in the central nervous system, showing a regular distribution. Advancing microscopy and image processing techniques have contributed to elucidating microglia’s morphology, dynamics, and distribution. However, the mechanism underlying the regular distribution of microglia remains to be elucidated. First, we quantitatively confirmed the regularity of the distribution pattern of microglial soma in the retina. Second, we formulated a mathematical model that includes factors that may influence regular distribution. Next, we experimentally quantified the model parameters (cell movement, process formation, and ATP dynamics). The resulting model simulation from the measured parameters showed that direct cell–cell contact is most important in generating regular cell spacing. Finally, we tried to specify the molecular pathway responsible for the repulsion between neighboring microglia.

The median palatal suture serves as a growth center for the maxilla; inadequate growth at this site causes malocclusion and dental crowding. However, the pattern formation mechanism of palatal sutures is poorly understood compared with that of calvarial sutures such as the sagittal suture. In the present study, therefore, we compared the morphological characteristics of sagittal and palatal sutures in human bone specimens. We found that palatal suture width was narrower than sagittal suture width, and the interdigitation amplitude of the palatal suture was lower than that of the sagittal suture. These tendencies were also observed in the neonatal stage. However, such differences were not observed in other animals such as chimpanzees and mice. We also used a mathematical model to reproduce the differences between palatal and sagittal sutures. After an extensive parameter search, we found two conditions that could generate the difference in interdigitation amplitude and suture width: bone differentiation threshold $$v_c$$ v c and growth speed c. We discuss possible biological interpretations of the observed pattern difference and its cause.

Sutures, the thin, soft tissue between skull bones, serve as the major craniofacial growth centers during postnatal development. In a newborn skull, the sutures are straight; however, as the skull develops, the sutures wind dynamically to form an interdigitation pattern. Moreover, the final winding pattern had been shown to have fractal characteristics. Although various molecules involved in suture development have been identified, the mechanism underlying the pattern formation remains unknown. In a previous study, we reproduced the formation of the interdigitation pattern in a mathematical model combining an interface equation and a convolution kernel. However, the generated pattern had a specific characteristic length, and the model was unable to produce a fractal structure with the model. In the present study, we focused on the anterior part of the sagittal suture and formulated a new mathematical model with time–space-dependent noise that was able to generate the fractal structure. We reduced our previous model to represent the linear dynamics of the centerline of the suture tissue and included a time–space-dependent noise term. We showed theoretically that the final pattern from the model follows a scaling law due to the scaling of the dispersion relation in the full model, which we confirmed numerically. Furthermore, we observed experimentally that stochastic fluctuation of the osteogenic signal exists in the developing skull, and found that actual suture patterns followed a scaling law similar to that of the theoretical prediction.

Microglia are resident immune cells in the central nervous system (CNS), showing a regular distribution. Advancing microscopy and image processing techniques have contributed to elucidating microglia’s morphology, dynamics, and distribution. However, the mechanism underlying the regular distribution of microglia remains to be elucidated. First, we quantitatively confirmed the regularity of the distribution pattern of microglial soma. Second, we formulated a mathematical model that includes factors that may influence regular distribution. Next, we experimentally quantified the model parameters (cell movement, process formation, and ATP dynamics). The resulting model simulation from the measured parameters showed that direct cell-cell contact is most important in generating regular cell spacing. Finally, we tried to specify the molecular pathway responsible for the repulsion between neighboring microglia.

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