Inferring Cortical Variability from Local Field Potentials

Predicting MT responses from the stimulus and inferred network activity. A, Time–frequency analysis of the LFPs. Left, LFP signals and spiking activity were recorded with a 16-channel multielectrode array and used as inputs to a model that predicts a given single unit on the array (described below). Middle, To illustrate how each LFP was processed for use in the model, we show an LFP segment bandpassed in the gamma (30–70 Hz), alpha (8–12 Hz), and delta (1–4 Hz) bands. Right, To process each LFP for input to our model, we use a continuous wavelet transform to decompose the LFP signal into its amplitude and phase in each frequency band. To demonstrate how phase relates to a given bandpassed signal, the delta phase is shown below the delta band-filtered LFP (bottom middle); with times that phase is 180° (blue arrows) corresponding to local minima in the bandpassed signal. B, The phase-locking strength measured across frequency band and depth for an example neuron (top), demonstrating sensitivity in the delta and gamma bands. The phase-locking strength of simulated spikes generated by the LFP model (bottom) is nearly identical, demonstrating how the localized model components in D combine with correlations between LFP band and depth to result in empirical phase-locking measurements. C, Schematic of the LFP model, which includes a stimulus-processing component (from Fig. 1B), and the LFP-based component. D, Example LFP model component. Model weights (left) and preferred phases (right) are displayed as a function of both frequency bands (horizontal axis) and cortical depth (vertical axis). Phase values are depicted by hue, with the color brightness representing the corresponding weights to emphasize frequency bands and depths that are most important. E, To determine the effect of simultaneously fitting multiple model components, we measured the ratio of model weights for single-electrode LFP models fit with and without the stimulus-processing model. This shows that LFP models fit without the stimulus-processing component typically have much larger weights in low-frequency bands (<4 Hz, *p < 0.001, n = 108).

Dramatic improvement of model performance with the inclusion of the LFP component. A, LL_x values calculated for stimulus-processing models (left), and models that included either the LFP from the same electrode (middle) or all electrodes (right), for all neurons in the study. LL_x values were calculated at both 25 ms (left) and 5 ms (right) time resolution. To demonstrate the relative performance of each model across all neurons, we also normalized each LL_x value by that of the best model for that neuron (introduced below), and thus no model median reaches the (dashed) unity line here. The inclusion of the LFP component yields a more than threefold improvement in performance over the stimulus-processing model at 25 ms resolution (approximately the time course of the stimulus-locked rate). When considered at a higher time resolution (5 ms), the LFP model yields a median fivefold performance improvement, due to information about finer spike timing gained from the gamma-band LFP. B, The total variance of predicted firing rates from different models, normalized by the measured variance (left) or the variance of the best model for that neuron (right). C, Model performance improvement is tightly correlated with the increase in the variance of model outputs (r = 0.984, p < 10⁻⁶⁷). D, Improvements in model performance were greater for neurons that were less stimulus locked (r = −0.64, p < 10⁻¹⁰).

Frequency and phase preferences of MT neurons. A, There is a diverse array of tuning captured by the LFP components of different neurons, shown for six examples, with the red arrow designating the depth of the unit being modeled. Model weights (left) and preferred phases (right) are displayed as a function of both frequency bands (horizontal axis) and cortical depth (vertical axis) in the same way as in Figure 2C. B, While the absolute depth of the unit could not be determined in our experiments, we aligned model weights relative to the depth of the unit being modeled, and averaged these weights across neurons. This shows that model weights from the gamma band (30–70 Hz) are mostly localized in depth, whereas weights from the delta band (1–4 Hz) are distributed across multiple channels (n = 93). C, The relative impact of each LFP frequency band on model performance was computed by fitting each LFP model while omitting a given band. The effect on normalized LL_x is shown across all neurons (n = 93), showing that the removal of gamma (30–70 Hz) and delta (1–4 Hz) bands has the biggest impact on model performance. D, The consistency across neurons of phase preferences in each LFP band is demonstrated by a two-dimensional histograms of the preferred phase of each neuron in each frequency band from the single-electrode LFP model (n = 108).

Modeling MT neuron response with multiunit activity. A, Example multiunit spiking activity (MUA, top) and the resulting population firing rate (PR; bottom) recorded from the multielectrode array, with the red box highlighting the single unit being modeled (which was excluded from the model). B, Schematic of the population rate model, which sum the output of PR-based and stimulus-processing components, passing the result through a spiking nonlinearity. The contribution of the PR was modeled using a linear temporal filter applied to the recent history of PR. C, Left, A typical PR filter, showing coupling between the example neuron and PR as a function of time lag (horizontal axis). Right, Average of all PR model components across the population of recorded neurons (n = 93). D, Left, The LL_x of the PR and MUA models across the population of recorded neurons. Right, The same data, showing the normalized LL_x across all neurons (as in Fig. 3), where the LL_x of each model was normalized by the LL_x of the best model for that neuron (see below). The normalized LL_x is thus on the same scale as the LFP models considered earlier (Fig. 3), demonstrating that the PR-based models have less than half the performance of the LFP-based models. E, Schematic of the MUA model, where the MUA component replaces the PR component considered above (B). F, Left, A typical MUA model component, showing weights on MUA as a function of time lag (horizontal axis) and electrode depth (vertical axis) for the same neuron as the example in the top left panel in B. Right, Average of all MUA model components across the population of recorded neurons.

Network inputs predict trial-to-trial variability. A, Schematic of the full model, which includes a stimulus-processing component, and two “network-based” components: the LFP and MUA components. B, The model performance of the range of models considered, using the cross-validated log-likelihood relative to the “full” Stim–LFP–MUA model (normalized LL_x). This demonstrates that, while the addition of the MUA component can yield a nearly twofold improvement over the stimulus-processing (Stim) model, it has only a very small impact when added to the Stim–LFP model. C, The summed output of the three model components of the full model explains the spike response (red rasters) of the MT neuron on a trial-by-trial basis, as shown by the correspondence between observed spikes and model output. Colors are scaled such that blue is the most negative model output, and yellow is the most positive (arbitrary units). D, Spike raster across repeated trials (left), and the output of the three model components (right) across repeated trials of the same motion stimulus. The stimulus component output is identical across trials; the output of the LFP-dependent term is highly variable across trials, and the MUA component output has both stimulus-locked and trial-variable elements. The trial-averaged spike response and output of the three model components are shown on the bottom (black curve), together with an example trial in red. E, Variance of the model-predicted firing rate, normalized by the total amount of estimated firing-rate variance. F, The total variance of the model outputs are further separated into the contributions to the model firing rate of the stimulus-locked (left) and trial-variable (right) components, and are normalized by the corresponding measured stimulus-locked and estimated trial-variable variance. For example, the Stim model cannot predict any trial-variable variance (first column on right), while the full model (Stim–LFP–MUA, fourth column) predicts a median of 38% of the trial-variable variance of each neuron.