Continual expression of coexistent oscillation frequencies.

<p>Shown are the Fourier transform (<b>a</b>), wavelet transform (<b>b</b>) and raster diagram of cell firing (<b>c</b>) from the excitatory population of the target network (the fast network). The inset in <b>a</b> shows the connectivity scheme from the slow to the fast network (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0100899#pone.0100899.s001" target="_blank">Fig. S1c</a>8), in which the iE connection had . The fast network co-expressed its own fast base frequency (32.4 Hz) and the base frequency of the slow network (20.4 Hz and corresponding harmonic and subharmonic frequencies). The power (amplitude) of both frequencies did not vary strongly over time.</p

Inter-Network Interactions: Impact of Connections between Oscillatory Neuronal Networks on Oscillation Frequency and Pattern

<div><p>Oscillations in electrical activity are a characteristic feature of many brain networks and display a wide variety of temporal patterns. A network may express a single oscillation frequency, alternate between two or more distinct frequencies, or continually express multiple frequencies. In addition, oscillation amplitude may fluctuate over time. The origin of this complex repertoire of activity remains unclear. Different cortical layers often produce distinct oscillation frequencies. To investigate whether interactions between different networks could contribute to the variety of oscillation patterns, we created two model networks, one generating on its own a relatively slow frequency (20 Hz; slow network) and one generating a fast frequency (32 Hz; fast network). Taking either the slow or the fast network as source network projecting connections to the other, or target, network, we systematically investigated how type and strength of inter-network connections affected target network activity. For high inter-network connection strengths, we found that the slow network was more effective at completely imposing its rhythm on the fast network than the other way around. The strongest entrainment occurred when excitatory cells of the slow network projected to excitatory or inhibitory cells of the fast network. The fast network most strongly imposed its rhythm on the slow network when its excitatory cells projected to excitatory cells of the slow network. Interestingly, for lower inter-network connection strengths, multiple frequencies coexisted in the target network. Just as observed in rat prefrontal cortex, the target network could express multiple frequencies at the same time, alternate between two distinct oscillation frequencies, or express a single frequency with alternating episodes of high and low amplitude. Together, our results suggest that input from other oscillating networks may markedly alter a network's frequency spectrum and may partly be responsible for the rich repertoire of temporal oscillation patterns observed in the brain.</p></div

Expression of a single oscillation frequency with strong fluctuations in power.

<p>Shown are the Fourier transform (<b>a, d</b>), wavelet transform (<b>b, e</b>) and raster diagram of cell firing (<b>c, f</b>) from the excitatory population of the target network (the slow network in <b>a–c</b> and the fast network in <b>d–f</b>). The inset in <b>a</b> shows the connectivity scheme from the fast to the slow network (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0100899#pone.0100899.s004" target="_blank">Fig. S4C</a>2), in which the Ie connection had . In the time interval shown, the slow network expressed its own base frequency (20.4 Hz) but with strong fluctuations in power. The inset in <b>d</b> shows the connectivity scheme from the slow to the fast network (see Fig. 5b2), in which the eI connection had . The fast network expressed the base frequency of the slow network with strong fluctuations in power.</p

Oscillatory activity in the slow and the fast network when they are unconnected or connected.

<p>Shown are the Fourier transform (<b>a, d, g</b>), wavelet transform (<b>b, e, h</b>) and raster diagram of cell firing (<b>c, f, i</b>) of the excitatory population in either the slow or the fast network. Color in the wavelet transforms indicates power of oscillation. The raster diagrams depict the firing times (indicated by dots). <b>a–c.</b> Activity of the slow network in isolation. The Fourier transform shows peaks at the base frequency (20.4 Hz) and at the first and second harmonics. Owing to the highly synchronized activity (making the signal effectively a comb function), the Fourier transform produced peaks at the harmonics, but there were no cells that actually fired at these frequencies (see panel c). <b>d–f</b>. Activity of the fast network in isolation. The Fourier transform shows peaks at the base frequency (32.4 Hz) and the first harmonic. <b>g–i.</b> Activity of the fast network when the excitatory cells of the slow network projected to the excitatory cells of the fast network (eE connection) with conductance factor (see Methods). With this connection strength, the slow network managed to impose its rhythm onto the fast network, in which the base frequency (20.4 Hz) of the slow network and its first harmonic were strongly expressed. Since there were no connections from the fast to the slow network, the activity of the slow network was not different from that in the unconnected situation.</p

Alternating expression of coexistent oscillation frequencies with fluctuations in power.

<p>Shown are the Fourier transform (<b>a</b>), wavelet transform (<b>b</b>) and raster diagram of cell firing (<b>c</b>) from the excitatory population of the target network (the fast network). The inset in <b>a</b> shows the connectivity scheme from the slow to the fast network (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0100899#pone.0100899.s001" target="_blank">Fig. S1c</a>5), in which the iE connection had . The base frequency of the fast network (32.4 Hz) and the base frequency of the slow network (20.4 Hz) appeared more or less intermittently in the fast network. When either frequency component was present, its power was not stable over time (e.g., the slow base frequency between t = 33.7 s and t = 33.9 s).</p

The connectivity schemes between the two model networks.

<p>In the slow network, the excitatory and inhibitory populations are labelled with lower case letters (e, i) and in the fast network with upper case letters (E, I). Each column (a–d, A–D) comprises what we call a connectivity class, consisting of eight different connectivity schemes. The strength of the connectivity type shown in red was varied in the simulations. A connectivity class is labelled with a lower or upper case letter depending on whether the slow or the fast network, respectively, is the network projecting to the other network. (See further Methods.)</p

Alternating episodes of high- and low-amplitude oscillations for two different values of AP randomness.

<p>Raster diagrams of cell firing (a, d), firing-rate histograms with interpolated spline polynomials (b, e) and wavelet transform of the firing-rate histograms (c, f) for the excitatory population for AP randomness 0.7 (a–c) and 0 (d–f) in the minimal stimulation protocol. For rand = 0, APs were simultaneously delivered to all I cells at regular intervals of 90 ms.</p

During a LAE, for both the excitatory and the inhibitory population, cell firing is less synchronous.

<p>This is revealed by the spread of activity over more time bins and the diminished overlap in membrane potential traces. In addition, fewer cells are firing during a LAE. Shown are the raster diagram of cell firing (a, d), the firing rate histogram with the spline polynomial (b, e), and the cell membrane potentials (c, f) of and interval of activity from <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002666#pcbi-1002666-g003" target="_blank">Fig. 3</a>. Horizontal dashed line, HAE threshold.</p

Amplitude fluctuations in carbachol-induced oscillations recorded in the infralimbic region of the PFC.

<p>(a) Extracellular field potential (top) at one of the 64 electrodes of a multi-electrode array, and wavelet transform (bottom). Episodes of high power are observed to alternate with episodes of low power. Color indicates power of oscillations. (b) Close up of the activity in (a).</p

The more random the AP train, the shorter the mean HAE duration and the longer the mean LAE duration.

<p>Mean HAE and LAE durations (SEM) in the excitatory population (a, b) and the inhibitory population (c, d) for different values of AP randomness. Red lines, exponential fits.</p