To study biological signalling, great effort goes into designing sensors whose fluorescence follows the concentration of chemical messengers as closely as possible. However, the binding kinetics of the sensors are often overlooked when interpreting cell signals from the resulting fluorescence measurements. We propose a method to reconstruct the spatiotemporal concentration of the underlying chemical messengers in consideration of the binding process. Our method fits fluorescence data under the constraint of the corresponding chemical reactions and with the help of a deep-neural-network prior. We test it on several GCaMP calcium sensors. The recovered concentrations concur in a common temporal waveform regardless of the sensor kinetics, whereas assuming equilibrium introduces artifacts. We also show that our method can reveal distinct spatiotemporal events in the calcium distribution of single neurons. Our work augments current chemical sensors and highlights the importance of incorporating physical constraints in computational imaging.