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Noise-induced scaling in skull suture interdigitation
- Source :
- PLoS ONE, PLoS ONE, Vol 15, Iss 12, p e0235802 (2020)
- Publication Year :
- 2020
- Publisher :
- Cold Spring Harbor Laboratory, 2020.
-
Abstract
- 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.Author summarySkull sutures (thin, undifferentiated tissue between bones) act as the growth centers for the skull. Sutures are straight at birth but later develop an interdigitated pattern that ultimately becomes a fractal structure. While our previous mathematical model of sutures generated a periodic pattern, the mechanism underlying the fractal structure formation remained to be elucidated. Here, we focused only on the anterior part of the sagittal suture and formulated a reduced model representing the initial linear phase of pattern formation with the addition of a time–space-dependent noise term. We showed analytically that the model generates patterns with a scaling law. This result was confirmed numerically and experimentally.
- Subjects :
- Cell signaling
Physics::Medical Physics
Geometry
Signal transduction
ERK signaling cascade
Mice
0302 clinical medicine
Mathematical and Statistical Techniques
Osteology
Osteogenesis
Morphogenesis
Medicine and Health Sciences
Musculoskeletal System
Physics
Fibrous joint
0303 health sciences
Multidisciplinary
Genetically Modified Organisms
Signaling cascades
Classical Mechanics
White noise
Sagittal suture
Fractals
medicine.anatomical_structure
Physical Sciences
Medicine
Engineering and Technology
Anatomy
Genetic Engineering
Research Article
Biotechnology
Cell biology
Characteristic length
Science
Pattern formation
Bioengineering
Fluid Mechanics
Research and Analysis Methods
Models, Biological
Continuum Mechanics
03 medical and health sciences
Fractal
medicine
Animals
Humans
Surface Tension
Scaling
Skeleton
030304 developmental biology
Genetically Modified Animals
Skull
Infant, Newborn
Biology and Life Sciences
Cranial Sutures
Models, Theoretical
Noise
White Noise
Signal Processing
030217 neurology & neurosurgery
Mathematics
Subjects
Details
- Database :
- OpenAIRE
- Journal :
- PLoS ONE, PLoS ONE, Vol 15, Iss 12, p e0235802 (2020)
- Accession number :
- edsair.doi.dedup.....e3a89e1d9be1ed1e97cb2a380076a658