We report that GABA(A) receptors in a patch-clamped biological cell form a short-term memory circuit when integrated with a scanning-probe microfluidic device. Laminar patterns of receptor activators (agonists) provided by the microfluidic device define and periodically update the data input which is read and stored by the receptors as state distributions (based on intrinsic multistate kinetics). The memory is discharged over time and lasts for seconds to minutes depending on the input function. The function of the memory can be represented by an equivalent electronic circuit with striking similarity in function to a dynamic random access memory (DRAM) used in electronic computers. Multiplexed biohybrid memories may form the basis of large-scale integrated biocomputational/sensor devices with the curious ability to use chemical signals including odorants, neurotransmitters, chemical and biological warfare agents, and many more as input signals.