Synchrony tendency of coupled oscillators or neurons is predicted by the phase response curve (PRC) of a neuron that describes an amount of advance or delay by synaptic input given at a specific phase in an interspike interval. It is intriguing to know how this useful theory based on the fixed coupling strength between neurons generalizes to the cases where synaptic strength varies as observed in the real brain. A number of experiments have established that synaptic strength changes depending on pre- and postsynaptic spike times and theoretical implications of such spike-timing-dependent plasticity (STDP) have been extensively studied. Since the PRC and STDP both refer to the timings of spikes, a natural question is how these two properties of a neuronal network interact each other to carve a functional network in the brain.

To answer this question, we use a neuron model whose PRC can be systematically controlled (Izhikevich, 2004) unlike the simpler leaky integrate-and-fire (LIF) model. The model neurons favors either asynchronous (Model A) or synchronous (Model B) firing depending on the values of the model parameters. Our simulations show that STDP working on the network of Model A neurons converts an asynchronously firing neurons into three or more cyclically activated clusters of neurons. Interestingly, Model A neurons can synchronize within a cluster despite their preference to asynchrony because, as we see later, STDP selectively disrupts intra-cluster connections, nullifying the asynchrony preference. If STDP works on the network of Model B neurons, however, the neurons simply get synchronized globally, analogous to what was observed in (Karbowski and Ermentrout, 2002), and nothing peculiar happens.

Thus, the PRC influences the way STDP works. Importantly, STDP in turn changes the network structure and influences the way how PRC is readout to decide the network activity. Before the STDP learning begins, the initial slope of an effective PRC (defined later) determines the stability of the global synchrony. After the STDP learning forms cyclic activity of n clusters , the slope at 2pi(1-1/n) determines its stability. In this way, the two key features of a network of spiking neurons, the PRC and STDP, work synergetically to organize functional networks in the brain.