Fig 1.
Simulated spike trains and results of model fitting.
(A) Simulated spike trains in response to a fluctuating stimulus and oscillatory drive. (B,C,D) Ground truth (red) and fitted results (blue) for different terms in the firing-rate probability model. For each fitted result, we used a parametric bootstrap to determine the 95% confidence band (cyan). (B) Effect of auto-history λ2(t − t*) on output firing rate. (C) Effect of stimulus λ1(t) on output firing rate. (D) Phase modulation curve λ3(ϕ) of firing rate.
Fig 2.
Estimation of LFP phase modulation by spike phase histogram and GLM methods.
(A,B,D,E) Point process regression using the GLM (B,E) yields estimates of the LFP phase modulation with comparable variance but substantially lower bias than estimates made using the spike phase histogram method (A,D). (C) Comparison of the MISE between the estimated and true LFP phase modulation using the spike phase histogram and GLM methods, across different sample sizes. (F) Comparison of the variance and bias in the LFP phase modulation estimated by the two methods.
Fig 3.
LFP phase modulation estimated by the spike phase histogram method is inherently biased for non-Poisson firing.
(A,D) Auto-history effects for Poisson (A) and non-Poisson (D) firing. (B,C,E,F) Theoretical and simulated estimations of the LFP phase modulation for Poisson (B,C) and non-Poisson (E,F) firing at low (B,E) and high (C,F) mean firing rates. Note that, for non-Poisson firing, the spike phase histogram estimation of the LFP phase modulation introduces a firing rate-dependent bias.
Fig 4.
LFP phase modulation estimated by the GLM method does not depend on firing rate.
(A,C), In three simulations, we keep λ3(ϕ) = 1 + 0.4cos(ϕ+π) while varying mean firing rates. The SFC method (A) reports three distinct results, while the GLM method (C) showed that the LFP phase modulations are the same. (B, D), Different combinations of firing rate and LFP phase modulation λ3(ϕ) = 1 + a ⋅ cos(ϕ + π) can yield the same SFC (B), while the GLM method can distinguish the differences in LFP phase modulation (D). For each parameter set (a,firing rate), we had 200 runs. The shaded area is the 95% confidence band.
Fig 5.
Schematic illustration of the contribution of a network-wide oscillation to synchronous spiking between two neurons.
The firing probability of each neuron is influenced by three factors: stimulus, auto-history and an oscillatory drive. The oscillatory drive is shared by the two neurons, but each neuron exhibits a unique phase modulation curve. Spike trains of the two neurons are observed and synchronized spikes are counted (red circles).
Fig 6.
Network-wide oscillations can enhance or suppress the predicted levels of spike synchrony.
(A) Dependence of on the difference in preferred phases between two neurons, as computed using models with and without an oscillatory factor. Purple and cyan arrows indicate two different Δ(Φpref)s. (B) Bootstrap-generated distribution of
values under the null hypothesis of logζ12 = 0. Arrowhead shows the value of
computed by the simplified model. Thus, a significantly larger number of synchronous spikes is observed than predicted by the model lacking an oscillatory factor (
, p value = 0.0025). (C) Including an oscillatory factor in the model yields an accurate prediction of the observed number of synchronous spikes (
, p value = 0.6775). (D, E) Same as (B,C) for different preferred phases that lead to significantly lower synchrony than predicted when an oscillatory factor is not included in the model (D:
, p value = 0.0025; E:
, p value = 0.2700). (F) Dependence of the power on number of trials and ζ. The mean firing rate is 25 Hz. The red and green lines indicate choices of ζ and N for which the power equals 0.8, based on simulation and theory respectively. (G) Same as (F), but the mean firing rate is 10 Hz.
Fig 7.
Shared oscillations contribute to spike synchrony between hippocampal CA1 pyramidal cells in vitro.
(A, B) Reconstructed morphologies (left) and raster plots of spike trains (right) evoked in two CA1 pyramidal cells by an arbitrary stimulus waveform with a shared oscillatory signal (“Exp. 2”). Red circles show synchronized spikes between the two neurons. (C) Estimated phase modulation of the two recorded neurons in response to a shared oscillatory signal simulating a network-wide oscillation. (D) In the absence of a shared oscillatory signal, the simplified model (stimulus, or PSTH effects [P] + spike or auto-history effects [H]) lacking an oscillatory factor accurately predicts the observed number of synchronous spikes between the two neurons. (E,F) In the presence of a shared oscillatory signal, the simplified model (P + H) fails to explain the observed number of synchronous spikes (E) while the full model (stimulus, or PSTH effects [P] + spike or auto-history effects [H] + an oscillatory factor [O]) containing an oscillatory factor accurately predicts the observed number of synchronous spikes (F).
Fig 8.
Shared oscillations contribute to spike synchrony between V4 neurons in vivo.
(A,D) Raster plot of spike trains from two neurons recorded simultaneously. Red circles show synchronized spikes between the two neurons. (B,E) Raw (blue) and 4–25 Hz filtered (red) surrounding LFP related with each neuron for a single trial. (C,F) The simplified model failed to explain the observed number of synchronous spikes (C), while the full model containing an oscillatory factor fully accounts for the observed number of synchronous spikes.