Sketches of two typical output networks.

<p>These two networks are constructed for <i>n</i>₁ = 100, <i>n</i>₂ = 1000, and <i>δ</i> = <i>π</i>. The nodes of the original graph are depicted in black, the forcing nodes are depicted in blue. The left (right) network corresponds to a case in which the forcing nodes are unable (able) to lock the phases of the oscillators in G₀.</p

Ensemble average of the final degree distribution in the parameter space.

<p>(a)–(c): Log-log plots of (see text for definition) <i>vs. k.</i> obtained after an ensemble average over 50 different realizations of the growing process (<i>n</i>₁ = 1000, <i>n</i>₂ = 10000, <i>d</i>₁ = 0.2). In all cases, solid (dashed) lines correspond to the locked (non locked) regime, obtained for high (low) values of <i>d_p</i>, and solid red lines indicate the best power-law fits. (d): final number of connections <i>k_i</i>(<i>t_fin</i>) acquired by each node as a function of its initial frequency <i>ω</i>_0<i>i</i> = 0.5 for, <i>δ</i> = <i>π</i>, and <i>d_p</i> = 0.2 (upper plot, unlocked case) and <i>d_p</i> = 0.5 (lower plot, locked case).</p

Time averaged phase synchronization order parameter <i>R</i> in the parameter space <i>ω_p</i>−<i>d_p</i>.

<p>Time averaged phase synchronization order parameter <i>R</i> (see text for definition) as a function of both the pacemaker frequency <i>ω_p</i> and the coupling strength <i>d_p</i>. Parameters: <i>n</i>₁ = 100, <i>d</i>₁ = 0.2, <i>m</i>₀ = 2, <i>n</i>₂ = 200, <i>δ</i> = <i>π</i> and each point is an average over 10 different realizations of the growing process.</p

Time evolution of the entrainment process.

<p>Time evolution of the mean frequency (upper row), frequency dispersion (middle row) and phase synchronization order parameter (lower row) for three pacemaker frequencies (<i>ω_p</i> = 0.1 red-dotted line, <i>ω_p</i> = 0.5 blue-solid line, and <i>ω_p</i> = 0.9 black-dashed line) and coupling strengths <i>d_p</i> = 0.5 (left column) and <i>d_p</i> = 5.5 (right column). See text for the definition of all reported quantities. The two vertical lines in the upper row denote the instants at which the growth process starts (dashed) and ends (continuous). Same parameters as in the caption of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0002644#pone-0002644-g001" target="_blank">Figure 1</a>.</p

Growth model.

<p>(A) Schematic representation of how cells get connected. At DIV 0, 4 cells of radius are located at random positions. The first iteration of the algorithm, DIV 1, assigns to each cell a disk of radius (green shade). At the next iteration, DIV 2, the disk's growth rate decreases, , and a link between two cells is established when their disks intersect (DIV 3). This process continues until steps. (B) Force diagram explaining cell migration and clustering. Tension forces , , and are acting on the central cluster composed of two cells, whose vector sum (red arrow) exceeds the adhesion to the substrate (green arrow). As a result, a new equilibrium state is produced with new tension forces , , and , being the central cluster pulled in the direction of the net force approaching the largest cluster.</p

Comparison between model and experiment.

<p>Legends in each panel clarifies on the topological quantities measured in experiments (dashed curves), and the corresponding trends of the simulated networks (solid curves). Simulation parameters are the same as in the caption of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0085828#pone-0085828-g007" target="_blank">Fig. 7</a>, and each point is the ensemble average over 50 independent runs of the growth algorithm.</p

Density of the network as a function of culture age.

<p>(A) Mean number of nodes (blue circles), including neurons and clusters of neurons, and links connecting them (red squares), calculated for the 6 cultures vs. age (DIV). Inset: the link density (green triangles) quantifies the actual number of links divided by that of an all-to-all configuration [, being the number of connected nodes at each age]. (B) Log-linear plot of the mean number of nodes having at least one connection (blue circles), of the mean size of the giant connected component (red squares) and of the second largest connected component (green triangles). In all plots, error bars stand for the standard errors of the mean (sem).</p

Schematic illustration of the network self-organization at three different instants of the automata generations.

<p>(A) DIV 3, (B) DIV 6, and (C) DIV 12. Simulation parameters: , , and .</p

Degree distribution and degree-degree correlation.

<p>(A) Cumulative node degree distributions on a semi-log scale for the state of the same culture at DIVs 3, 6, 7, and 12 (see legend for the symbol coding). Solid lines correspond to the best exponential fitting , with the mean degrees at DIV 3, 6, 7, and 12 respectively. (B) Degree correlation exponent (blue circles) measuring the network assortativity and the corresponding Pearson coefficient (red squares). Both quantities are averaged for the set of 6 cultures at each day of measure (DIV) and error bars represent the sem.</p

Extraction of the adjacency matrix defining the neural network connectivity.

<p>(A) Image cut taken from a 6 DIV culture and (B) the layer on top showing the identification of neurons and clusters of neurons (red), neurites connecting them (green) and neurite branching points (blue). (C) Mapping of the neuronal network into a graph where blue dots represent the nodes and green lines the links of the graph.</p