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Flow of ions through voltage gated channels can be represented theoretically using stochastic differential equations where the gating mechanism is represented by a Markov model. The flow through a channel can be manipulated using various drugs, and the effect of a given drug can be reflected by changing the Markov model. These lecture notes provide an accessible introduction to the mathematical methods needed to deal with these models. They emphasize the use of numerical methods and provide sufficient details for the reader to implement the models and thereby study the effect of various drugs. Examples in the text include stochastic calcium release from internal storage systems in cells, as well as stochastic models of the transmembrane potential. Well known Markov models are studied and a systematic approach to including the effect of mutations is presented. Lastly, the book shows how to derive the optimal properties of a theoretical model of a drug for a given mutation defined in terms of a Markov model.

Mathematics - General --- Mathematics --- Physical Sciences & Mathematics --- Mathematics. --- Computer graphics. --- Computer mathematics. --- Computational Science and Engineering. --- Biomedicine general. --- Computer Imaging, Vision, Pattern Recognition and Graphics. --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Automatic drafting --- Graphic data processing --- Graphics, Computer --- Computer art --- Graphic arts --- Engineering graphics --- Image processing --- Math --- Science --- Digital techniques --- Computer science. --- Medicine. --- Computer vision. --- Machine vision --- Vision, Computer --- Artificial intelligence --- Pattern recognition systems --- Clinical sciences --- Medical profession --- Human biology --- Life sciences --- Medical sciences --- Pathology --- Physicians --- Informatics --- Health Workforce --- Optical data processing. --- Biomedicine, general. --- Optical computing --- Visual data processing --- Bionics --- Integrated optics --- Photonics --- Computers --- Optical equipment --- Life Sciences --- Pharmacology and Toxicology --- Economics --- Political Economy --- Development --- International Relations --- International Political Economy --- African Studies --- African Economics

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Flow of ions through voltage gated channels can be represented theoretically using stochastic differential equations where the gating mechanism is represented by a Markov model. The flow through a channel can be manipulated using various drugs, and the effect of a given drug can be reflected by changing the Markov model. These lecture notes provide an accessible introduction to the mathematical methods needed to deal with these models. They emphasize the use of numerical methods and provide sufficient details for the reader to implement the models and thereby study the effect of various drugs. Examples in the text include stochastic calcium release from internal storage systems in cells, as well as stochastic models of the transmembrane potential. Well known Markov models are studied and a systematic approach to including the effect of mutations is presented. Lastly, the book shows how to derive the optimal properties of a theoretical model of a drug for a given mutation defined in terms of a Markov model.

Mathematics --- Human biochemistry --- Computer science --- Artificial intelligence. Robotics. Simulation. Graphics --- Computer. Automation --- medische biochemie --- biochemie --- computers --- grafische vormgeving --- informatica --- wiskunde --- informaticaonderzoek --- KI (kunstmatige intelligentie) --- AI (artificiële intelligentie) --- Medicine. --- Optical data processing. --- Computational Science and Engineering. --- Biomedicine, general. --- Computer Imaging, Vision, Pattern Recognition and Graphics. --- Mathematics.