Competition between neurite branches in a complex morphology.

<p>(A) Example morphology of a reconstructed pyramidal neuron with apical and basal dendrites. (B) In the control case, starting from the reconstructed morphology, the neuron was allowed to grow out for 10 hours in the model. The simulation was then repeated with the same initial conditions, but with increased polymerization rate for one of the growth cones. The dendritic morphology obtained in this last simulation is represented by a dendrogram, colored according to the tubulin concentration in the branches. The gray vertical lines at the terminal segments indicate the starting morphology, and the black vertical lines show the neurite length after 10 hours in the control case. The black dot marks the growth cone with increased polymerization rate. (C) The competition between branches increases with increasing path distance to the soma. The graph shows the total retraction of all neurites, divided by the growth of the modified growth cone, as a function of path length between the modified growth cone and the soma.</p

Neurite outgrowth of a developing neuron in tissue culture.

<p>(A) Still shots of a time-lapse movie of a developing cerebellar neuron in tissue culture, revealing neurites that are growing out and retracting. The arrows point to the neurites' growth cones; color of arrows corresponds to colors used in panels B and C. Figure taken from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0086741#pone.0086741-DaFontouraCosta1" target="_blank">[3]</a>. (B) The red and green neurites are forced to grow out as in the experiment (dashed black lines), whereas the blue neurite is fully controlled by the tubulin dynamics of the model. The parameters of the model (diffusion constant, active transport rate, tubulin decay and tubulin soma concentration) were optimized so as to make the blue neurite grow as closely as possible to the experimental data. (C) Using the optimized parameter set from B, the green neurite is now fully governed by the model, whereas the red and blue neurites are forced to grow according to data recorded in the experiment. The errors in B and C are the square root of the summed squared deviation of the free growth cone from the experimentally measured location at each point in time.</p

Default and optimized values of the model parameters.

<p>Default and optimized values of the model parameters.</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

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

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

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 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

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