Cells use biochemical networks to translate environmental information into intracellular responses. These responses can be highly dynamic, but how the information is encoded in these dynamics remains poorly understood. Here, we investigate the dynamic encoding of information in the ATP-induced calcium responses of fibroblast cells, using a vectorial, or multi-time-point, measure from information theory. We find that the amount of extracted information depends on physiological constraints such as the sampling rate and memory capacity of the downstream network, and it is affected differentially by intrinsic versus extrinsic noise. By comparing to a minimal physical model, we find, surprisingly, that the information is often insensitive to the detailed structure of the underlying dynamics, and instead the decoding mechanism acts as a simple lowpass filter. These results demonstrate the mechanisms and limitations of dynamic information storage in cells.