Polynucleotides encoding fluorescent indicators, which contain a sensor polypeptide inserted within a fluorescent moiety, are provided, as are polypeptides encoded by such polynucleotides. Also provided are circularly permuted fluorescent polypeptides and polynucleotides encoding the circularly permuted fluorescent polypeptides. In addition, methods of using the fluorescent indicators and the circularly permuted fluorescent polypeptides are provided.