Periodic neuronal activity has been observed in various areas of the brain, from lower sensory to higher cortical levels. Specific frequency components contained in this periodic activity can be identified by a neuronal circuit that behaves as a bandpass filter with given preferred frequency, or best modulation frequency (BMF). For BMFs typically ranging from 10 to 200 Hz, a plausible and minimal configuration consists of a single neuron with adjusted excitatory and inhibitory synaptic connections. The emergence, however, of such a neuronal circuitry is still unclear. In this letter, we demonstrate how spike-timing-dependent plasticity (STDP) can give rise to frequency-dependent learning, thus leading to an input selectivity that enables frequency identification. We use an in-depth mathematical analysis of the learning dynamics in a population of plastic inhibitory connections. These provide inhomogeneous postsynaptic responses that depend on their dendritic location. We find that synaptic delays play a crucial role in organizing the weight specialization induced by STDP. Under suitable conditions on the synaptic delays and postsynaptic potentials (PSPs), the BMF of a neuron after learning can match the training frequency. In particular, proximal (distal) synapses with shorter (longer) dendritic delay and somatically measured PSP time constants respond better to higher (lower) frequencies. As a result, the neuron will respond maximally to any stimulating frequency (in a given range) with which it has been trained in an unsupervised manner. The model predicts that synapses responding to a given BMF form clusters on dendritic branches.
Optical spike-timing-dependent plasticity with weight-dependent learning window and reward modulation
