Local field potentials primarily reflect inhibitory neuron activity in human and monkey cortex

The local field potential (LFP) is generated by large populations of neurons, but unitary contribution of spiking neurons to LFP is not well characterised. We investigated this contribution in multi-electrode array recordings from human and monkey neocortex by examining the spike-triggered LFP average (st-LFP). The resulting st-LFPs were dominated by broad spatio-temporal components due to ongoing activity, synaptic inputs and recurrent connectivity. To reduce the spatial reach of the st-LFP and observe the local field related to a single spike we applied a spatial filter, whose weights were adapted to the covariance of ongoing LFP. The filtered st-LFPs were limited to the perimeter of 800 μm around the neuron, and propagated at axonal speed, which is consistent with their unitary nature. In addition, we discriminated between putative inhibitory and excitatory neurons and found that the inhibitory st-LFP peaked at shorter latencies, consistently with previous findings in hippocampal slices. Thus, in human and monkey neocortex, the LFP reflects primarily inhibitory neuron activity.


Validation of the whitening technique
To validate the whitening method and, specifically, to show that it recovers the post-synaptic contribution to the LFP from a spike of a single neuron (the unitary LFP), we tested it on a model LFP signal. The LFP is modelled as a linear superposition of the trans-membrane currents generating the LFP (LFP sources).
For simplicity, we test the method on LFP signals recorded using only two electrodes, but this approach can be extended to multi-electrode arrays (Utah arrays). The LFP sources are modelled as post-synaptic currents triggered by a population of neurons. The contribution of these current to the LFP signal is quantified as the spatio-temporal LFP kernel, k(t − t , x − x ), where x − x is the distance of the electrode from the spiking neuron and t − t is the time from a spike. LFP source at given position x is then calculated as a sum of such kernels centered on all neurons and all spikes: where t ik (k = 1 . . . K) are K spikes of neuron i, x i is the position of neuron i.
The contribution from the local population decays exponentially in time and space, k The rationale for the assumption is that the probability of connections between neurons decays very fast in the close neighbourhood of the neuron, but for distances above 1 mm it stays at small and constant level (Peyrache et al. 2012). The size of the remote population is large (it covers much larger area that the local population within the radius of < 1 mm), so that it's contribution can be significant, even if single neurons contribute little. Alternatively, the contribution from far population can be indirect, i.e., mediated by common inputs or modulations of excitability rather than direct connections.
We generate spikes of local population with constant rate using Bernoulli process. The spikes of remote population are modelled using Poisson process. The contributions to the LFP sources of both populations are summed together. Finally, we obtain the LFP by a linear superposition of the sources using a mixture matrix, L, with elements l xx (also called a lead matrix in the EEG literature). This mixing operation is often referred to as the volume conduction. Using Einstein summation notation it can be represented as following: Note that for simplicity we assumed linear, homogeneous and ohmic medium, but it's possible to generalise to non-ohmic media.
We estimate the LFP kernel using only the simulated LFP signal and spikes of local population. We calculated the spike-triggered LFP (st-LFP) the standard way (see Methods) and compare it with the original LFP kernel (which normally would not be available to the experimentalist). We found that the st-LFP is broader spatially than the kernel, i.e. its amplitude decays slower with distance than the model LFP kernel (Supplementary Figure 1, left). This broadening is due to passive spread of electric field (the volume conduction), which is parametrised by the mixing (lead) matrix.
To recover the LFP kernel we might apply a spatial filtering. The optimal spatial filter is given by the inverse of the mixing matrix, Application of this filter to the st-LFP allows to recover the LFP kernel with the same spatial and temporal dependence (Supplementary Figure 1B): In practice, we do not know the mixing matrix, so we can not estimate the optimal unmixing filter. Therefore, we resort to the whitening technique, which allows to estimate the best filter directly from the data. To this end, we use a regularised pseudo-inverse of the ongoing LFP covariance matrix, W (see Methods). We find that this technique allows to recover the LFP kernels, which are very close to the ones obtained using the optimal unmixing matrix, but also the original LFP kernel (Supplementary Figure 1C).   Figure 1D in main text). Small negative deflections survive the averaging whereas other fluctuations only present in single electrodes are averaged out.

Supplementary Tables
Supplementary