Biomaterial Database

Speed of pattern appearance in reaction-diffusion models: implications in the pattern formation of limb bud mesenchyme cells. 2004

Takashi Miura, and Philip K Maini

Department of Human Anatomy and Genetics, University of Oxford, South Parks Road, Oxford OX1 3QX, UK. Miura@human-anatomy.oxford.ac.uk

It has been postulated that fibroblast growth factor (FGF) treatment of cultured limb bud mesenchyme cells reinforces the lateral inhibitory effect, but the cells also show accelerated pattern appearance. In the present study, we analyze how a small change in a specific parameter affects the speed of pattern appearance in a Turing reaction-diffusion system using linear stability analysis. It is shown that the sign of the change in appearance speed is qualitatively decided if the system is under the diffusion-driven instability condition, and this is confirmed by numerical simulations. Numerical simulations also show that a small change in parameter value induced easily detectable differences in the appearance speed of patterns. Analysis of the Gierer-Meinhardt model revealed that a change in a single parameter can explain two effects of FGF on limb mesenchyme cells-reinforcement of lateral inhibition and earlier appearance of pattern. These qualitative properties and easy detectability make this feature a promising tool to elucidate the underlying mechanisms of biological pattern formation where the quantitative parameters are difficult to obtain.

UI	MeSH Term	Description	Entries
D008954	Models, Biological	Theoretical representations that simulate the behavior or activity of biological processes or diseases. For disease models in living animals, DISEASE MODELS, ANIMAL is available. Biological models include the use of mathematical equations, computers, and other electronic equipment.	Biological Model,Biological Models,Model, Biological,Models, Biologic,Biologic Model,Biologic Models,Model, Biologic
D003198	Computer Simulation	Computer-based representation of physical systems and phenomena such as chemical processes.	Computational Modeling,Computational Modelling,Computer Models,In silico Modeling,In silico Models,In silico Simulation,Models, Computer,Computerized Models,Computer Model,Computer Simulations,Computerized Model,In silico Model,Model, Computer,Model, Computerized,Model, In silico,Modeling, Computational,Modeling, In silico,Modelling, Computational,Simulation, Computer,Simulation, In silico,Simulations, Computer
D005346	Fibroblast Growth Factors	A family of small polypeptide growth factors that share several common features including a strong affinity for HEPARIN, and a central barrel-shaped core region of 140 amino acids that is highly homologous between family members. Although originally studied as proteins that stimulate the growth of fibroblasts this distinction is no longer a requirement for membership in the fibroblast growth factor family.	DNA Synthesis Factor,Fibroblast Growth Factor,Fibroblast Growth Regulatory Factor,Growth Factor, Fibroblast,Growth Factors, Fibroblast
D000818	Animals	Unicellular or multicellular, heterotrophic organisms, that have sensation and the power of voluntary movement. Under the older five kingdom paradigm, Animalia was one of the kingdoms. Under the modern three domain model, Animalia represents one of the many groups in the domain EUKARYOTA.	Animal,Metazoa,Animalia
D047108	Embryonic Development	Morphological and physiological development of EMBRYOS.	Embryo Development,Embryogenesis,Postimplantation Embryo Development,Preimplantation Embryo Development,Embryonic Programming,Post-implantation Embryo Development,Postnidation Embryo Development,Postnidation Embryo Development, Animal,Pre-implantation Embryo Development,Prenidation Embryo Development, Animal,Development, Embryo,Development, Embryonic,Development, Postnidation Embryo,Embryo Development, Post-implantation,Embryo Development, Postimplantation,Embryo Development, Postnidation,Embryo Development, Pre-implantation,Embryo Development, Preimplantation,Embryonic Developments,Embryonic Programmings,Post implantation Embryo Development,Pre implantation Embryo Development
D051379	Mice	The common name for the genus Mus.	Mice, House,Mus,Mus musculus,Mice, Laboratory,Mouse,Mouse, House,Mouse, Laboratory,Mouse, Swiss,Mus domesticus,Mus musculus domesticus,Swiss Mice,House Mice,House Mouse,Laboratory Mice,Laboratory Mouse,Mice, Swiss,Swiss Mouse,domesticus, Mus musculus
D018878	Limb Buds	Distinct regions of mesenchymal outgrowth at both flanks of an embryo during the SOMITE period. Limb buds, covered by ECTODERM, give rise to forelimb, hindlimb, and eventual functional limb structures. Limb bud cultures are used to study CELL DIFFERENTIATION; ORGANOGENESIS; and MORPHOGENESIS.	Limb Bud,Bud, Limb,Buds, Limb
D019521	Body Patterning	The processes occurring in early development that direct morphogenesis. They specify the body plan ensuring that cells will proceed to differentiate, grow, and diversify in size and shape at the correct relative positions. Included are axial patterning, segmentation, compartment specification, limb position, organ boundary patterning, blood vessel patterning, etc.	Axial Patterning (Embryology),Embryonic Pattern Formation,Polarity of Development,Body Pattern Formation,Body Pattern Specification,Embryonic Pattern Specification,Development Polarity,Embryonic Pattern Formations,Formation, Embryonic Pattern,Pattern Formation, Body,Pattern Formation, Embryonic,Pattern Specification, Body,Pattern Specification, Embryonic,Patterning, Axial (Embryology),Patterning, Body,Specification, Body Pattern,Specification, Embryonic Pattern