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Signaling networks regulate cellular responses to environmental stimuli through cascades of protein interactions. External signals can trigger cells to polarize and move in a specific direction and maintain spatially localized activity of proteins. To investigate the effects of morphological changes on intracellular signaling, we implement a numerical scheme consisting of a cut cell finite volume spatial discretization coupled with level set methods. Applications of this method to models of signaling networks in time-dependent geometries are then discussed. This is joint work with David Adalsteinsson and Timothy Elston.