Although neuromodulation of synapses is extensively documented, its consequences in the context of network oscillations are not well known. We examine the modulation of synaptic strength and short-term dynamics in the crab pyloric network by the neuropeptide proctolin. Pyloric oscillations are driven by a pacemaker group which receives feedback through the inhibitory synapse from the lateral pyloric (LP) to pyloric dilator (PD) neurons. We show that proctolin modulates the spike-mediated and graded components of the LP to PD synapse. Proctolin enhances the graded component and unmasks a surprising heterogeneity in its dynamics where there is depression or facilitation depending on the amplitude of the voltage waveform of the presynaptic LP neuron. The spike-mediated component is influenced by the baseline membrane potential and is also enhanced by proctolin at all baseline potentials. In addition to direct modulation of this synapse, proctolin also changes the shape and amplitude of the presynaptic voltage waveform which additionally enhances synaptic output during ongoing activity. During ongoing oscillations, proctolin reduces the variability of cycle period but only when the LP to PD synapse is functionally intact. Using the dynamic clamp technique we find that the reduction in variability is a direct consequence of modulation of the LP to PD synapse. These results demonstrate that neuromodulation of synapses involves complex and interacting influences that target different synaptic components and dynamics as well as the presynaptic voltage waveform. At the network level, modulation of feedback inhibition can result in reduction of variability and enhancement of stable oscillatory output.

1. Using a rabbit cerebellar slice preparation, we stimulated a classical conditioning procedure by stimulating parallel fiber inputs to Purkinje cells with the use of a brief, high-frequency train of eight constant-current pulses 80 ms before climbing fiber inputs to the same Purkinje cell were stimulated with the use of a brief, lower frequency train of three constant-current pulses. In all experiments, we assessed the effects of stimulation by measuring the peak amplitude of Purkinje cell excitatory postsynaptic potentials (EPSPs) to single parallel fiber test pulses. 2. Intradendritically recorded Purkinje cell EPSPs underwent a long-term (> 20 min) reduction in peak amplitude (30%) after paired stimulation of the parallel and climbing fibers but not after unpaired or parallel fiber alone stimulation. We call this phenomenon pairing-specific long-term depression (PSD). 3. Facilitation of the peak amplitude of a second EPSP elicited by a parallel fiber train occurred both before and after paired stimulation suggesting that the locus of depression was not presynaptic. Depression of the peak amplitude of a depolarizing response to focal application of glutamate following pairings of parallel and climbing fiber stimulation added support to a suggested postsynaptic locus of the PSD effect. 4. The application of aniracetam potentiated EPSP peak amplitude by 40%, but these values returned to baseline as a result of pairings. With the removal of aniracetam from the bath 20 min after pairings, normal levels of pairing-specific EPSP depression were observed, indicating that the effect did not result from direct desensitization of alpha-amino-3-hydroxy-5-methyl-4-isoxazole-proprionic acid (AMPA) receptors. 5. Incubation of slices in the protein kinase inhibitor H-7 potentiated EPSP peak amplitudes slightly (9%), but peak amplitudes returned to baseline levels after pairings. The net reduction in EPSP peak amplitude of < 10% after pairings suggested that H-7 partially blocked PSD and that, in turn, PSD involved protein kinases. 6. The means of induction and the specificity of those means suggest that the phenomenology of PSD is fundamentally different from that of long-term depression. PSD only occurs with pairings of trains of parallel fiber and climbing fiber stimulation; it occurs without the need for bicuculline; and it can overcome the blocking effects of aniracetam. 7. Nevertheless, the involvement of protein kinases and the potential role of calcium suggest that the mechanisms involved in the induction of PSD and long-term depression have a number of features in common. 8. Because of the pairing-specific nature of the long-term synaptic depression observed in these experiments, PSD provides a mechanism that may contribute to the role of the cerebellar cortex in classical conditioning.

Synchronization of excitable cells coupled by reciprocal inhibition is a topic of significant interest due to the important role that inhibitory synaptic interaction plays in the generation and regulation of coherent rhythmic activity in a variety of neural systems. While recent work revealed the synchronizing influence of inhibitory coupling on the dynamics of many networks, it is known that strong coupling can destabilize phase-locked firing. Here we examine the loss of synchrony caused by an increase in inhibitory coupling in networks of type-I Morris-Lecar model oscillators, which is characterized by a period-doubling cascade and leads to mode-locked states with alternation in the firing order of the two cells, as reported recently by Maran and Canavier (J Comput Nerosci, 2008) for a network of Wang-Buzsáki model neurons. Although alternating-order firing has been previously reported as a near-synchronous state, we show that the stable phase difference between the spikes of the two Morris-Lecar cells can constitute as much as 70% of the unperturbed oscillation period. Further, we examine the generality of this phenomenon for a class of type-I oscillators that are close to their excitation thresholds, and provide an intuitive geometric description of such "leap-frog" dynamics. In the Morris-Lecar model network, the alternation in the firing order arises under the condition of fast closing of K( + ) channels at hyperpolarized potentials, which leads to slow dynamics of membrane potential upon synaptic inhibition, allowing the presynaptic cell to advance past the postsynaptic cell in each cycle of the oscillation. Further, we show that non-zero synaptic decay time is crucial for the existence of leap-frog firing in networks of phase oscillators. However, we demonstrate that leap-frog spiking can also be obtained in pulse-coupled inhibitory networks of one-dimensional oscillators with a multi-branched phase domain, for instance in a network of quadratic integrate-and-fire model cells. Finally, for the case of a homogeneous network, we establish quantitative conditions on the phase resetting properties of each cell necessary for stable alternating-order spiking, complementing the analysis of Goel and Ermentrout (Physica D 163:191-216, 2002) of the order-preserving phase transition map.