Bones from the mammalian cranial vault are formed by the process of intramembranous ossification where condensations of multipotent mesenchymal cells differentiate directly into functioning osteoblasts to form bone (Tubbs et al. (involving premature closure of cranial vault sutures and skull dysmorphology) as well as answer basic Iguratimod (T 614) IC50 questions in developmental biology and evolution. Initially undifferentiated mesenchymal cells migrate to future sites of bone formation situated on the brain and its meningeal layers (pia arachnoid dura mater). Over time the proliferation and differentiation are regulated by growth factor signaling pathways and their downstream transcription factors in order for these cells to become committed to an array of different fates. In a few cells the intracellular signaling pathways trigger differentiation Iguratimod (T 614) IC50 of mesenchymal cells into osteoblasts the cells that build bone tissue (Marie et al. 2002 Gordeladze et al. 2010 Tubbs et al. 2012 Differentiation of condensed sets of osteoblasts leads to the forming of ossification centers that type in tissues membranes surrounding the mind. Next osteoblasts commence to secrete a bone tissue matrix osteoid that is after that mineralized eventually developing a bone tissue from the cranial vault. For the mouse the procedure of cell migration starts around embryonic time 9 (E9) and skull bone tissue growth proceeds postnatally involving duration scales which range from the nanometer to millimeter as schematically proven in Figure ?Body11. To be able to understand the essential systems of skull development both computational and experimental strategies have already been employed. Many studies have got experimentally researched the roles of varied proteins in cranial bone tissue development (Holleville et al. 2003 Wan and Cao 2005 and development of cranial bone fragments (Martínez-Abadías et al. 2013 Motch Perrine et al. 2014 Percival and Richtsmeier 2013 and likened the craniofacial bone tissue development patterns of regular mice and the ones holding mutations that in human beings cause disease. Body ?Figure22 implies that cranial vault bone tissue components (frontal parietal and interparietal bone fragments) appear from embryonic time 14.5 (E14.5) and continue steadily to grow through postnatal time 0 (P0) and beyond. In addition it implies that the frontal bone tissue forms initial as well as the interparietal bone forms later forming sutures between individual bones while they grow. Experimental studies are extremely valuable but can be costly and only so many variations can be explored. Therefore it is useful to also examine the possibility of using computational methods to understand fundamental mechanisms of morphogenesis. Several computational studies have been conducted to model the process of skull bone formation. IL1B A mathematical model for reaction-diffusion controlled by two interacting chemical molecules proposed by Turing (1952) has been employed in the study of biological pattern formation and development of biological systems. Kondo and Shirota (2009) analyzed the mechanism of skin pattern formation of animals using the Turing model and (Marcon and Sharpe 2012 adopted the model to explain various biological development processes. Garzón-Alvarado et al. (2013) used the model to establish a computational framework for investigating bone formation in human cranial vault. The model commonly referred to as the reaction-diffusion model shows that through the regulatory loop of interacting molecules the concentration of the molecules forms an inhomogeneous special pattern in space. In this study we adopt an approach similar to that of Garzón-Alvarado et al. (2013) to study growth of the skull in a mouse style of individual disease and propose an expansion of the framework. As depicted on Physique ?Physique1 1 we subdivide the process into two stages: (1) initiation (differentiation) of main centers of ossification; and (2) bone growth. In the first stage we focus on differentiation of osteoblast lineage cells (OLCs) which leads to the initial main centers of ossification of the smooth Iguratimod (T Iguratimod (T 614) IC50 614) IC50 bones of the cranial vault. We presume that the conversation of extracellular molecules which are associated with the differentiation process of OLCs along an osteogenic path can be modeled using the reaction-diffusion model. Reaction-diffusion models can be further subdivided into activator-inhibitor and activator-substrate models according to how molecules interact with each other (Gierer and Meinhardt 1972 The primary difference between the two models Iguratimod (T 614) IC50 is the way.