Noise-induced scaling in skull suture interdigitation

Fractality of Cranial Sutures

It has long been known that skull suture has a typical fractal structure. Although the fractal dimension has been utilized to assess morphology, the mechanism of the fractal structure formation remains to be elucidated. Recent advances in the mathematical modeling of biological pattern formation provided useful frameworks for understanding this mechanism. This chapter describes how various proposed mechanisms tried to explain the formation of fractal structures in cranial sutures.

Mechanism of interdigitation formation at apical boundary of MDCK cell

It has been reported that the MDCK cell tight junction shows stochastic fluctuation and forms the interdigitation structure, but the mechanism of the pattern formation remains to be elucidated. In the present study, we first quantified the shape of the cell-cell boundary at the initial phase of pattern formation. We found that the Fourier transform of the boundary shape shows linearity in the log-log plot, indicating the existence of scaling. Next, we tested several working hypotheses and found that the Edwards-Wilkinson equation, which consists of stochastic movement and boundary shortening, can reproduce the scaling property. Next, we examined the molecular nature of stochastic movement and found that myosin light chain puncta may be responsible. Quantification of boundary shortening indicates that mechanical property change may also play some role. Physiological meaning and scaling properties of the cell-cell boundary are discussed.

Mathematical modeling of palatal suture pattern formation: morphological differences between sagittal and palatal sutures

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 [Formula: see text] and growth speed c. We discuss possible biological interpretations of the observed pattern difference and its cause.