Mathematical Modeling of Neuroglial Communication
Mathematical modelling is being used in many areas of the biological sciences to gain a deeper understanding of the complex mechanisms governing the natural world. No field has more to gain from this type of analysis than the most complex object known, the brain. Glia cells coordinate chemical signalling within the brain. There is great variation in how this is performed, with intercellular communication via gap junctions and extracellular communication via diffusion participating to different degrees within different types of glial cells. Using this as a base, this book draws together existing experimental data and theoretical concepts and develops a new mathematical model that incorporates many aspects of this cellular behaviour. The development of the model is tracked as it is contrasted with other models and applied to a real life scenario. The implementation of the equations into a program is considered and simulation results displayed. The application of the model to real problems is emphasized, though there is consideration of more advanced theoretical concepts for the interested reader."
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astrocytes ATP and Ca2+ ATP concentration ATP production ATP release ATP wave basin of attraction Bennett biological Ca2+ concentration Ca2+ wave calculations cell wall central cell chemical concentration of IP3 cytosol decreases degradation rate demonstrated determined diffusion of ATP dimensional dissociation constant effect elevated endoplasmic reticulum equations experimental results extracellular ATP extracellular communication extracellular diffusion extracellular messenger extracellular pathway extracellular space Fink G-protein cascade gap junction coupling gap junctions glia glial cells grid square hemichannels Hofer ICWs increase infinitely regenerative initial release intercellular and extracellular intercellular pathway IP3 and Ca2+ IP3 concentration IP3 degradation IP3 diffuses IP3 receptors IP3 sensitive mechanisms mediated Miiller cells neurons Newman P2Y receptors parameter values peak concentration permeability Pip3 PLCd preferential pathways present model processes produced production rates purinergic receptors regeneration release of ATP replicate retina signalling simulation Sneyd somata structure suramin theoretical models velocity Wang wave radius wave spread