Mathematics Colloquia and Seminars

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Muscle contraction is a fundamental biological process that spans physiological size scales across nearly eight orders of magnitude. The exact mechanisms behind contraction are unclear, in part because unique behavior occurs at each size scale. Thus, to fully understand muscle function and disease, we must develop a comprehensive mathematical theory of contraction.

With this objective, we aim to develop a model of muscle, based in well-defined molecular mechanisms, that has predictive power at larger physiological scales. To do so, we focus on three features of muscle contraction that have unexplained molecular mechanisms, including 1) the effects of low pH and increased Pi, which are characteristic of muscle fatigue at the fiber scale, 2) the transient force response of a muscle fiber to rapid, small-amplitude stretch, which includes the phenomenon of stretch-activation, and 3) the behavior of muscle lengthened to large amplitudes, which displays an unexplained yielding regime. By developing our model to describe these measurements, we provide specific insight into the molecular mechanisms behind cellular phenomena and make explicit connections across physiological scales. In this talk, I will discuss these research projects, detail the mathematical techniques used in muscle models, and highlight both the challenges and benefits of developing such a theory.