Broadband Spectral Change: Evidence for a Macroscale Correlate of Population Firing Rate?

A heuristic model for how broadband spectral increases might emerge from increases in presynaptic AP firing rate. A, Poisson-distributed presynaptic APs arrive at a neighboring neuron. The PSD of these AP events over time has a flat, frequency-independent form (i.e., a “white noise” shape, with spikes coming with equal probability at every frequency; blue trace in G). B, At the synapse between the two neurons, each arriving AP triggers release of a neurotransmitter and postsynaptic current influx. As shown in the central schematic neuron, this results in a gradient of charge density within the dendritic arbor. C, The temporal shape of the postsynaptic current smears out the PSD, giving it a 1/f² form, with a “kink” at a particular frequency determined by the decay time, τ, of the postsynaptic current (here ∼70 Hz), shown with a gray arrow in G. D, In this model, the inputs from 6000 such synaptic currents are integrated over time and space, simulating the time-dependent change in transmembrane charge concentration. The associated transmembrane potential produces a time-dependent current across the dendritic membrane. E, The combined effect of synaptic and transdendritic current influx/efflux induces a gradient of current–source density in the surrounding medium. The time dependence of transmembrane potentials are mimicked by the LFP (Okun et al., 2009), and likely by the macroscale (ECoG) potential as well. F, The PSD shifts associated with changes in mean firing rate from presynaptic inputs are broadband in nature (spread across all frequencies), with a characteristic P ∼ 1/f^χ form (i.e., the power in the PSD falls off with increasing frequency according to the exponent, χ). G, The P ∼ 1/f^χ PSD structure might emerge from the combinations of three simple processes. The first is Poisson-distributed input spikes [as in A, reflected in the rate measured by Manning et al. (2009)]. The second is a characteristic postsynaptic current with exponential decay, which produces a 1/f² form following a kink (gray arrow) at a frequency determined by the decay time at the synapse. The last process to shape the PSD is the integration of inward currents over time in the dendrite (as in D and E). This model demonstrates how the relationship between firing rate and broadband change observed by Manning et al. (2009) might arise. Model adopted from Bédard et al. (2006) and Miller et al. (2009b).