Novel membranes comprising various polymers containing heterocyclic nitrogen groups are described. These membranes are usefully employed in electrochemical sensors, such as amperometric biosensors. More particularly, these membranes effectively regulate a flux of analyte to a measurement electrode in an electrochemical sensor, thereby improving the functioning of the electrochemical sensor over a significant range of analyte concentrations. Electrochemical sensors equipped with such membranes are also described.