I will introduce some mathematical models for cell motion and model based inverse problems for extracting information from single cell movement. Inverse problems in the context of cell motility is a novel approach we have been developing. These models define mathematical diagnostic techniques for the analysis of single cell movements.
Cells are living organisms, and it is natural to think that behavioral or shape changes of a cell bear information about the underlying mechanisms that generate these changes. Reading the cell motion, namely, understanding these underlying biophysical and mechanochemical mechanisms of behavioral and shape changes is of paramount importance. This is analogous to the examination of patients, analysis of their symptoms, behavioral changes by physicians for possible causes behind their pathologies. The mathematical models we developed play the role of physicians or physical exams in diagnosis of the pathologies for cells instead of human subjects. Thus, the technique transforms the simplest physical information, i.e. cell position, into practical and clinically usable form.