Inverse problems in ion channel modelling

This paper reviews several inverse problems related to biological ion channels and polymer nanopores. Different problems arise at different scales and thus lead to different inversion tasks, which can be modelled as parameter identification in systems of partial differential equations, ordinary differential equations, or as the solution of integral equations. Due to the high potential for future developments, we will not only discuss the previous results and approaches, but in particular highlight a variety of open issues and unsolved inverse problems, as well as biological questions that could be modeled as inverse problems and might lead to interesting future developments.