Multiple time scales and mixed mode oscillations in intracellular calcium dynamics
Emily Harvey, Mathematical Sciences, Montana State University (August 27, 2012)
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Calcium plays a crucial role in a huge range of cellular processes including muscle contraction, secretion, neuronal ring and many other functions. Of particular interest are the oscillations seen in free intracellular calcium concentration, which are known to act as intracellular messages, relaying information within cells to regulate cell activity.
A key feature of intracellular calcium dynamics is that some physiological processes occur much faster than others. This leads to models with variables evolving on very dierent time scales. Using geometric singular perturbation techniques (GSPT) it is possible to exploit this separation in time scales to analyse the models. These techniques can be used to explain the observed dynamics, including oscillatory patterns known as mixed-mode oscillations and complicated bifurcation structures.