Feedforward and feedback loops are key regulatory elements in cellular signaling and information processing. Synthetic biology exploits these elements for the design of molecular circuits that enable the reprogramming and control of specific cellular functions. These circuits serve as a basis for the engineering of complex cellular networks, opening the door for numerous medical and biotechnological applications. Here, a similar principle is applied. Feedforward and positive feedback circuits are incorporated into biohybrid polymer materials in order to develop signal-sensing and signal-processing devices. This concept is exemplified by the detection of the proteolytic activity of the botulinum neurotoxin A. To this aim, site-specific proteases are incorporated into receiver, transmitter, and output materials, and their release, diffusion, and/or activation are wired according to a feedforward or a positive feedback circuit. The development of a quantitative mathematical model enables analysis and comparison of the performance of both systems. The flexible design could be easily adapted to detect other toxins or molecules of interest. Furthermore, cellular signaling or gene regulatory pathways could provide additional blueprints for the development of novel biohybrid circuits. Such information-processing, material-embedded biological circuits hold great promise for a variety of analytical, medical, or biotechnological applications. © 2018 The Authors. Published by WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim