Inverse problems in neuronal calcium signaling

Calcium is the most important of the brain’s second messengers. Thanks to engineered fluorescent indicators and caged compounds we have an excellent qualitative picture of its regulation and impact. With the advent of new scanning technology that permits one to observe the calcium signal throughout a highly branched neuron the potential exists for functional, single cell, quantitative calcium imaging. To help realize that potential we analyze a sequence of four inverse problems that infer the parameters of the cytosolic calcium buffers and plasma membrane calcium pumps and channels from the light shed by fluorescent indicators following specific stimulus protocols. Our analyses lead in each case to practical algorithms that we illustrate and test on synthetic data.