Weak phase-resetting in neural oscillators.

Phase-resetting experiments have frequently been employed to understand the input/output dynamics of oscillatory physiological systems, such as the respiratory and cardiovascular systems. Analogous techniques based on phase-oscillator models have often been used in computational studies of neuronal networks. These models are often simplified by assuming weak coupling between neurons. This assumption has powerful ramifications for both experimental and theoretical studies, yet it has never been demonstrated in living neurons. Here we examine phase response curves (PRCs) for neurons with different stimulus waveforms. Focusing on amplitude, we show that weak amplitude stimuli create PRCs that scale linearly with amplitude, while strong do not. This is the first step in demonstrating that weak coupling occurs in living neurons. We also show that this notion of weak coupling is more stringent than the geometric classification of weak coupling frequently associated with experimental PRC analysis.