The voltage and spiking responses of subthreshold resonant neurons to structured and fluctuating inputs: resonance, loss of resonance and variability

The communication of oscillatory activity between neurons in a network result from the interplay of the subthreshold oscillatory properties of the participating neurons, when they exist, the properties of the synaptic connectivity and modulatory effects (e.g., oscillatory, deterministic and stochastic fluctuations) capturing identified external activity and unidentified background activity. A necessary step to address the underlying mechanisms is to understand how the response of neurons to period inputs, and external inputs in general, depends on the interplay of the neuronal intrinsic properties and the properties of the input. We address this issues in a systematic manner in the context of the response of neurons to oscillatory and synaptic-like inputs, and we extend our investigation to fluctuating spiking inputs with more realistic distributions of spike times. We use relatively simple neuronal models subject to additive current-based inputs and multiplicative conductance-based synaptic inputs, and we use two types of chirp-like inputs, one consisting of a sequence of cycles with discretely increasing frequencies over time, and the other consisting of the same cycles arranged in an arbitrary order. We develop a number of voltage response metrics to capture the different aspects of the voltage response, including the standard impedance profiles (curves of the impedance amplitude as a function of the input frequency) and the peak-to-trough amplitude envelope (VENV) profiles. We show that Z-resonant cells (cells that exhibit subthreshold resonance in response to sinusoidal inputs) also show VENV-resonance in response to sinusoidal inputs, but generally do not (or very mildly) in response to square-wave and synaptic-like inputs. We also show that responses to conductance-based synaptic-like inputs are attenuated as compared to the response to current-based synaptic-like inputs. These response patterns were strongly dependent on the intrinsic properties of the participating neurons, in particular whether the unperturbed Z-resonant cells had a stable node or a focus. In addition, we show that variability emerges in response to chirp-like inputs with arbitrarily ordered patterns where all signals (trials) in a given protocol have the same frequency content and the only source of uncertainty is the subset of all possible permutations of cycles chosen for a given protocol. This variability is the result of the multiple different ways in which the autonomous transient dynamics is activated across cycles in each signal (different cycle orderings) and across trials. We extend our results to include high-rate Poisson distributed current- and conductance-based synaptic inputs and compare them with similar results using additive Gaussian white noise. We show that the responses to both Poisson-distributed synaptic inputs are attenuated with respect to the responses to Gaussian white noise. For cells that exhibit oscillatory responses to Gaussian white noise (band-pass filters), the response to conductance-based synaptic inputs are low-pass filters, while the response to current-based synaptic inputs may remain band-pass filters, consistent with experimental findings. Our results shed ling on the mechanisms of communication of oscillatory activity among neurons in a network in a network via subthreshold oscillations and resonance and the generation of network resonance.