Calcium is a universal messenger that participates in a great variety of physiological functions including muscle contraction, neuronal plasticity and immune responses. There is now compelling evidence that transient changes in the intracellular calcium concentration are key for achieving such versatility.
To date, most of these findings have been obtained from constant stimulation or step change protocols. However, under physiological conditions, cells often experience time dependent stimuli such as transient changes in neurotransmitter or oscillations in hormone concentrations. How cells transduce such dynamic stimuli into an appropriate response is an open question. We exposed HEK293 cells and astrocytes to dynamically varying time courses of carbachol and ATP, respectively, and investigated the corresponding cellular calcium activity. While single cells generally fail to follow the applied stimulation due to their intrinsic stochasticity and heterogeneity, faithful signal reconstruction is observed at the population level. We provide a number of transfer functions that translate the extracellular stimuli into the ensemble calcium spike rates. By computing the mean root square error between the predicted responses (based on the transfer functions) and the actual responses, we identify a simple leaky integrator model as a a powerful approach. For this, we show how to invert the transfer function to estimate the stimulus that should be applied in order to achieve a specific response. Throughout the analysis we pay particular attention to the non-stationarity of both the applied stimuli and the calcium responses.