Horacio G. Rotstein
Department of Mathematical Sciences
New Jersey Institute of Technology
Behavioral Neuroscience Program
Rutgers University (NWK) and
Federated Department of Biological Sciences
September 22, 2015
Inhibition-based theta resonance in a hippocampal network: a modeling study
Network rhythmic oscillations result from the cooperative activity of the participating neurons and synaptic connectivity. Several neuron types exhibit subthreshold (membrane potential) resonance (a peak in the voltage amplitude response to oscillatory current inputs at a preferred, resonant, frequency). Whether and how the individual neurons’ preferred subthreshold responses translate to the spiking and network regimes are still open questions.
We use mathematical modeling and numerical simulations to address these issues in the context of the in vivo experimental results reported in Stark et al (Neuron, 2013). In these experiments, pyramidal cells (PYR) and parvalbumin immunoreactive interneurons (INT) were optogenetically stimulated using wide-band (WB) oscillatory signals. Dependence of spiking activity on input frequency was measured by the spectral coherence between the input and output signals. While PYR have been shown to exhibit theta subthreshold resonance in vitro (Hu et al., J Physiol, 2002), in vivo responses of individual directly stimulated PYR were not predominantly at theta, but WB as INT were. In contrast, PYR exhibited theta band-limited rebound spiking induced through direct stimulation of INT, which exhibited a WB response.
We present a minimal biophysical (conductance-based) model of a CA1 hippocampal network that captures these experimental results. The basic model includes PYR and INT. The extended models include also OLM (orients-lacunosum moleculare cells) and synaptic depression. PYR and OLM included h-currents. The presence of subthreshold resonance in isolated PYR is not communicated to the spiking regime mainly due to the strong effect of the oscillatory input amplitude. PYR theta-band response results instead from a combination of rebound spiking and a timing mechanism. Rebound spiking is responsible for the generation of spikes at input frequencies that are low enough for the voltage response to be above threshold. The timing mechanisms are responsible for ”erasing” spikes generated by input frequencies lower that theta. We implemented two such mechanisms: (i) network-mediated inhibition from OLM or (ii) synaptic depression of INT synapses. Overall, these results provide a mechanistic understanding of network resonance at theta frequencies.