Total execution times in seconds.

<p>Total execution times in seconds.</p

Results of the application of network inference algorithms on the simulated dataset.

<p>PPV: Positive Predicted Value (or accuracy) defined as , where is true positive and is false positive; Se: Sensitivity defined as with false negative. : directed graph; : undirected graph. In bold are the results obtained by using our parallel implementation of the NIR algorithm which could not be obtained in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0010179#pone.0010179-Bansal2" target="_blank">[8]</a>. NIR performs significantly better than other software even for the 1000 gene networks.</p

Spatial macrodomains.

<p>The contact maps for Chr19 obtained at the end of the steered-MD simulations and inferred from HiC data are shown on the left and right, respectively. The grey bands mark entries involving the centromere region. The boundaries of the principal spatial domains, identified with a clustering analysis of the contact maps, are overlaid on the matrices. The consistency of the two macrodomain subdivisions is visually conveyed in the chromosome sketch at the center. The overlapping portions of the domain subdivisions are colored (different colors are used for different domains). Non-overlapping regions are shown in white, while the centromere region is shown in grey. The overlapping regions accounts for of the chromosome (centromere excluded).</p

Statistical analysis of mutual information.

<p>(A) Mutual information values for any pairs of probe sets on Chr19. The middle point of each probe set identifies its position along the chromosome. The gray stripes correspond to the centromere. (B) Histograms of values of mutual information for pairs of probe sets located at various intervals of their genomic separation. The black lines correspond to fitting the histograms with the theoretical (null case) MI distribution <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003019#pcbi.1003019-Goebel1" target="_blank">[36]</a>. The vertical black dashed lines correspond to the estimated threshold values (see next and main text). (C) Example of E-value (expected number of false positives) distribution for probe set pairs located at genomic separation in the range . The threshold is the value of mutual information at which the E-value is equal to . For different genomic separations, analogous curves were obtained. (D) Network of coregulated pairs of genes at separation. The analysis illustrated in (C) singles out significantly-high values of Mutual Information. These contributions corresponds to connections (<i>cyan links</i>) between coregulated gene pairs (<i>red dots</i>). The scale is in . (E) Networks of coregulated pairs of loci used to fix the spatial constraints between corresponding regions of the model chromosomes. For the sake of clarity, the whole network has been represented as three sub-networks for pairs of loci at genomic separations of 0–20 Mbp (<i>left</i>), 20–40 Mbp (<i>middle</i>) and 40–60 Mbp (<i>right</i>), respectively.</p

Variant systems subjected to the MD steering protocol.

<p>(A) Initial configuration of 6 random-walk like chains the linear size the model chromosome 19. (B) Model chromosomes were initially arranged as in the mitotic-like configuration of <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003019#pcbi-1003019-g001" target="_blank">Fig. 1B</a>, but the pairings between genes were randomized. The randomization preserved the number of pairs that each probe set takes part to. (C) Model chromosomes were initially arranged as in the mitotic-like configuration of <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003019#pcbi-1003019-g001" target="_blank">Fig. 1B</a>, but the gene positions along the chromosome were randomized. The randomization preserved the native pairings of the genes. In all panels chromosome regions involved in the native or randomized coregulatory network are highlighted in red. For all the three systems considered the same physical conditions of fiber density, stiffness and excluded volume interactions of the original system apply.</p

Increase of the percentage, , of Chr19 coregulated pairs which colocalize during the MD steering protocol, for the three variants of the native systems.

<p>The configurations reached at the end of the steering protocol are shown on the right. Chromosome regions that take part to the pairs of loci to be colocalized are highlighted in red.</p

Increase of the percentage, , of Chr19 coregulated pairs which colocalize during the MD steering protocol.

<p>The two curves reflect different initial conditions corresponding to the mitotic and the interphase conformations of panels (B) and (C) of <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003019#pcbi-1003019-g001" target="_blank">Fig. 1</a>. The final configurations, corresponding to are shown on the right. Chromosome regions involved in the coregulatory network are highlighted in red. These and other graphical representations of model chromosomes were rendered with the VMD graphical package <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003019#pcbi.1003019-Humphrey1" target="_blank">[47]</a>.</p

Mitotic and interphase configurations of the model system chromosomes.

<p>(A) Initial mitotic-like arrangement, constituted by 6 copies of model human chromosome 19. Following ref. <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003019#pcbi.1003019-Rosa1" target="_blank">[21]</a>, the chromatin fiber is helicoidally arranged into loops of each, and departing radially from a central axis. The six solenoidal arrangements were next placed in a random, but non-overlapping manner inside a cubic simulation box of side equal to and with periodic boundary conditions. (B) Chromosome spatial arrangement after short relaxation with a standard push-off protocol of MD time steps (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003019#s4" target="_blank">Materials and Methods</a>). (C) Interphase-like configuration obtained by evolving the initial mitotic configuration for MD time steps (approximately corresponding to hours in “real-time” <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003019#pcbi.1003019-Rosa1" target="_blank">[21]</a>). (<i>Inset</i>) The corresponding contact probabilities between <i>loci</i> of model interphase chromosomes decay as a power law of the genomic distance, , consistent with recent experimental observations <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003019#pcbi.1003019-LiebermanAiden1" target="_blank">[6]</a>,<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003019#pcbi.1003019-Rosa2" target="_blank">[29]</a>. In all panels, chromosome regions involved in the coregulatory network are highlighted in red.</p

Biological systems.

<p>(a): The Gfp protein was integrated downstream of the endogenous <i>GAL1</i> promoter (yeast strain courtesy of Prof. Botstein lab). (b): IRMA is composed of 5 genes encoding for transcription factors modulating the expression of each other. Both the transcription factors in the network and the promoters driving their expression are shown (adapted from <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003625#pcbi.1003625-Cantone1" target="_blank">[17]</a>). Solid lines model transcriptional interactions, while dashed lines are meant to represent protein-protein interactions.</p

<i>In-vivo</i> set point control experiments on the GAL1 promoter.

<p>(A–D) Four <i>in-vivo</i> set point control experiments were performed on the GAL1 promoter. The desired ( in blue) and experimentally quantified GFP fluorescence ( in green) in the cell population are shown for the whole duration of the experiments; the control action starts at time and lasts for . The fluctuations in fluorescence during the calibration phase are due to stress response after loading cells in the microfludics device. The input signal , computed in real-time by the control algorithm, is shown in red: a high signal corresponds to galactose-rich growth medium, a low signal to glucose growth medium. (Insets) Images taken during the experiments show the growing yeast populations at the beginning, at the half and at the end of each experiment.</p