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Description

(joint work with Vuk Milisic) In this talk I will present a general microscopic pde model (integro-differential) for the turnover of transiently remodeling elastic protein bonds. The purpose of this work is to relate such models to macroscopic, typically non-linear friction laws using asymptotic methods. Such nonlinear friction models are of interest in applications in biophysics . In the first part of the talk I will provide the asymptotic analysis of the microscopic model, both on a formal level and, and under assumptions, rigorously using a non-standard Liapunov functional for structured models and specific a-priori estimates. In a second part of the talk I will provide evidence for hysteresis numerically and by linear stability analysis when the off-rates of the protein bonds are load-dependent.