A key justification for molecular communications is low energy consumption and limited complexity. However, this is only the case if effective architectures for transmitting and receiving devices exist, which is not the case for most modulation and coding schemes at present. One approach to implementing these devices is to use biological circuits, based on chemical reaction networks and DNA transcription processes. In this paper, we develop a biological circuit to demodulate a class of molecular shift keying modulation schemes. A feature of our scheme is that only a single kind of receptor is required to which either of the signaling molecules can bind. We analyze our scheme to tune parameters and compare it to an optimal demodulation scheme. This reveals tradeoffs between performance and complexity in biological circuit implementations.