• anatomical networks;
  • epigenetics;
  • Gabriel rule;
  • head development;
  • morphology


Craniofacial sutures and synchondroses form the boundaries among bones in the human skull, providing functional, developmental and evolutionary information. Bone articulations in the skull arise due to interactions between genetic regulatory mechanisms and epigenetic factors such as functional matrices (soft tissues and cranial cavities), which mediate bone growth. These matrices are largely acknowledged for their influence on shaping the bones of the skull; however, it is not fully understood to what extent functional matrices mediate the formation of bone articulations. Aiming to identify whether or not functional matrices are key developmental factors guiding the formation of bone articulations, we have built a network null model of the skull that simulates unconstrained bone growth. This null model predicts bone articulations that arise due to a process of bone growth that is uniform in rate, direction and timing. By comparing predicted articulations with the actual bone articulations of the human skull, we have identified which boundaries specifically need the presence of functional matrices for their formation. We show that functional matrices are necessary to connect facial bones, whereas an unconstrained bone growth is sufficient to connect non-facial bones. This finding challenges the role of the brain in the formation of boundaries between bones in the braincase without neglecting its effect on skull shape. Ultimately, our null model suggests where to look for modified developmental mechanisms promoting changes in bone growth patterns that could affect the development and evolution of the head skeleton.