Phase response analysis during in vivo-like high conductance states; dendritic SK determines the mean and variance of responses to dendritic excitation

We generated high conductance states in the model by applying synaptic backgrounds composed of randomly-timed excitatory and inhibitory synaptic inputs at 1022 GABA synapses and 100 AMPA synapses distributed throughout the dendrite. By varying the synaptic gain and input frequency parameters across the physiological range for inputs to GP, we achieved a diverse set of high conductance states characterized by sub-threshold voltage fluctuations, irregular spiking, and elevated membrane conductance (Figure 1A &1B) and spanning the range of spike frequencies observed in vivo (15-45 Hz). For each synaptic background parameter set, we generated 100 single-trial PRCs by delivering a single 2.5 nS AMPA-synaptic input to either the soma or distal dendrite at each of 72 time-points (in separate simulations) within the first spike cycle of each of 100 control spike trains (Figure 1C &1D). We then averaged the single-trial PRCs for each synaptic background to evaluate the dependence of PRC shape on stimulus location, spike frequency, and dendritic SK conductance, in addition to the gain and input frequencies of synaptic backgrounds. Next, we analyzed on a trial-by-trial basis the interactions of PRC stimuli with transient fluctuations in the synaptic background leading to added or skipped spikes. We determined that dendritic SK underlies both the incidence of skipped spikes and the dependence of skipped spike events on stimulus phase. Interestingly, the input-phase dependence of skipped spike events mirrored the phase-dependent variance in the PRC itself (which we plotted as phase response-variance curves, PRVCs). This indicates that dendritic SK determines not only the mean response, but also the variance of responses, to excitatory dendritic inputs. Average somatic and dendritic PRCs were type I and type II, respectively, and are likely to represent the average behavior of populations of GP neurons in response to shared excitation. Furthermore, in-as-much as the GP model and simulated synaptic backgrounds are physiologically realistic, the variance in the model’s responses across trials directly reflects a major source of spike time variance across populations of GP neurons in vivo.