Ralston BN, Flagg LQ, Faggin E, Birmingham JT. Incorporating spike-rate adaptation into a rate code in mathematical and biological neurons. J Neurophysiol 115: 2501-2518, 2016. First published February 17, 2016 doi:10.1152/jn.00993.2015.-For a slowly varying stimulus, the simplest relationship between a neuron's input and output is a rate code, in which the spike rate is a unique function of the stimulus at that instant. In the case of spike-rate adaptation, there is no unique relationship between input and output, because the spike rate at any time depends both on the instantaneous stimulus and on prior spiking (the "history"). To improve the decoding of spike trains produced by neurons that show spike-rate adaptation, we developed a simple scheme that incorporates "history" into a rate code. We utilized this rate-history code successfully to decode spike trains produced by 1) mathematical models of a neuron in which the mechanism for adaptation (I AHP ) is specified, and 2) the gastropyloric receptor (GPR2), a stretch-sensitive neuron in the stomatogastric nervous system of the crab Cancer borealis, that exhibits long-lasting adaptation of unknown origin. Moreover, when we modified the spike rate either mathematically in a model system or by applying neuromodulatory agents to the experimental system, we found that changes in the rate-history code could be related to the biophysical mechanisms responsible for altering the spiking.decoding; integrate-and-fire; spike-rate adaptation; stomatogastric nervous system; stretch receptor OVER THE LAST CENTURY, considerable effort has been made to construct and understand mathematical codes that relate the time-varying stimuli presented to a neuron (or group of neurons) to the resulting spike trains