Identifying Anatomical Origins of Coexisting Oscillations in the Cortical Microcircuit

Abstract

Oscillations are omnipresent in neural population signals, like multi-unit recordings, EEG/MEG, and the local field potential. They have been linked to the population firing rate of neurons, with individual neurons firing in a close-to-irregular fashion at low rates. Using a combination of mean-field and linear response theory we predict the spectra generated in a layered microcircuit model of V1, composed of leaky integrate-and-fire neurons and based on connectivity compiled from anatomical and electrophysiological studies. The model exhibits low- and high-γ oscillations visible in all populations. Since locally generated frequencies are imposed onto other populations, the origin of the oscillations cannot be deduced from the spectra. We develop an universally applicable systematic approach that identifies the anatomical circuits underlying the generation of oscillations in a given network. Based on a theoretical reduction of the dynamics, we derive a sensitivity measure resulting in a frequency-dependent connectivity map that reveals connections crucial for the peak amplitude and frequency of the observed oscillations and identifies the minimal circuit generating a given frequency. The low-γ peak turns out to be generated in a sub-circuit located in layer 2/3 and 4, while the high-γ peak emerges from the inter-neurons in layer 4. Connections within and onto layer 5 are found to regulate slow rate fluctuations. We further demonstrate how small perturbations of the crucial connections have significant impact on the population spectra, while the impairment of other connections leaves the dynamics on the population level unaltered. The study uncovers connections where mechanisms controlling the spectra of the cortical microcircuit are most effective.

The Dynamics of Error Processing in the Human Brain as Reflected by High-Gamma Activity in Noninvasive and Intracranial EEG

“…shows that the network mechanism is here a subcircuit comprised of excitatory and 675 inhibitory neurons in layers 2/3 and 4 (Bos et al, 2016). The mathematical analysis of 676 these networks also exposes why the power of the oscillation is strongly influenced by 677 the tonic drive to the network, predominantly to layer 4.…”

Local Field Potentials: Myths and Misunderstandings

“…For example, recorded LFPs reflect some but not all inputs (Martín-Vázquez et al, 2016) and some, but not others, may be correlated with spike activity (de Cheveigné et al, 2013). In addition, age, experience, training and even ongoing activity modify the receptive fields (Arieli et al, 1996; Fiser et al, 2004), indicating that connectivity varies and hence, the physical structure of the sources too, which may provoke changes in the spatial spread of LFPs or in the relative contributions of network components (Bos et al, 2016). As suggested by many, volume-conduction may indeed play a role in the reported different spatial spread of cortical LFPs and spikes, and provided that all other factors remain the same, one could expect it to be stronger the larger the activated region (Fernández-Ruiz et al, 2013), thereby reaching other cortical and subcortical regions.…”

Integration of Continuous-Time Dynamics in a Spiking Neural Network Simulator

“…Networks of such noisy linear rate models have been investigated to explain features such as oscillations (Bos et al, 2016) or the smallness of average correlations (Tetzlaff et al, 2012; Helias et al, 2013). We here consider a prototypical network model of excitatory and inhibitory units following the linear dynamics given by Equation 9 with ϕ( x ) = ψ( x ) = x , μ = 0, and noise amplitude σ, $\tau d{X}^i(t)=\left(-X^i+{\displaystyle \sum _{j=1}^N{w}^{ij}}{X}^j(t)\right)dt+\sqrt{\tau }\sigma d{W}^i(t).$ Due to the linearity of the model, the cross-covariance between units i and j can be calculated analytically and is given by Ginzburg and Sompolinsky (1994); Risken (1996); Gardiner (2004); Dahmen et al (2016): $c(t)={\displaystyle \sum _{i,j}\frac{v^{i\text{T}}{\sigma }^2{v}^j}{{\lambda }_i+{\lambda }_j}}{u}^i{u}^{j\text{T}}\left(H(t)\frac{1}{\tau }{e}^{-{\lambda }_i\frac{t}{\tau }}+H(-t)\frac{1}{\tau }{e}^{{\lambda }_j\frac{t}{\tau }}\right),$ where H denotes the Heaviside function.…”

“…While the mean-field approach presented is strictly valid only in the thermodynamic limit, finite-size fluctuations around this state are accessible using the noisy linear-rate model (Section 3.3.1) as elaborated by Bos et al (2016) or within the population-density approach (Schwalger et al, 2016). …”