The Time Constant Rule for Neural Change Detection

Sensory pathways differ widely across species and modalities in anatomy and function. Yet many solve variants of the same ancient, pervasive problem: quickly detecting meaningful changes in the world. Sometimes animals need to make these detections from noisy signals with millisecond precision to survive. We suggest how a single spiking neuron can address this selection pressure for quick detection. We present a simple relationship linking neural voltage dynamics to online hypothesis testing that we call the time constant rule. Assume that a neuron's membrane time constant equals the inverse of a change in its input rate. We show that this rule is then necessary and sufficient for its subthreshold membrane potential to represent a likelihood ratio of that rate change. Thresholding that likelihood ratio makes the neuron an online detector of input rate increases and, by extension, stimulus onset when rapid reaction is required. We tested the time constant rule by reanalyzing published recordings from eight second-order sensory neurons spanning olfaction, mechanoreception, electroreception, and audition, across both insects and vertebrates. In all cases, the measured membrane time constants were consistent with the predicted inverse relationship. These examples are intended as cross-system and cross-phyla consistency checks rather than a population-level validation study. When the time constant rule holds, it yields a direct and intuitive interpretation of neural computation. A neuron's voltage is an online likelihood ratio: its time constant sets the decay of statistical evidence, its threshold is a decision line, and each output spike is a time-stamped declaration that its input statistics have changed. The rule links membrane biophysics with the statistical computation and ecological function of a neuron. Its falsifiability invites direct experimental tests to determine whether it extends more broadly across sensory pathways and neuron classes.