LASSIM inferred a robust minimal and full-scale non-linear transcription factor—Target dynamic system describing naïve T-cells towards Th2 cells.

<p>(A) We identified 12 core Th2 driving TFs from the literature, and inferred their putative targets using DNase-seq data from ENCODE. In total, these interactions constituted of 63 core TF-TF interactions and 64,872 core-to-peripheral gene regulations. These interactions were assumed to follow a sigmoid function, as described in the Methods section. The complete prior network was, together with Th2 differentiation dynamics and siRNA mediated knock down data of each TF measured by microarray profiling, used by LASSIM to infer a Th2 core system. As can be seen in the core network, there are feedback loops between several of the TFs. (B) Microarray time series experiments (red dots) and respective state simulated by the LASSIM model (blue solid lines) of the core TFs. On the x-axis is time, and the y-axis denotes gene expression in arbitrary units. (C) Heat map of the data fit of the Th2 model to the siRNA perturbation data, i.e. the siRNA part of <i>V</i>(<b><i>p</i></b><i>*</i>). Each siRNA knock-down experiment is represented as a separate column. For example, the model fits the response of a siRNA knock-down on IRF4 well for all TFs except MAF well. (D) Box-plot representing the ranking of each removed parameter from multiple stochastic optimizations of the core model. All edges that had a median selection rank over 40 were included in the final model. Model selection was based on prediction error variation, see section <i>model selection</i> and <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005608#pcbi.1005608.s003" target="_blank">S3 Fig</a>.</p

The edges from the naïve Th2 model were better refitted to total Th2 differentiation than the prior network.

<p>(A) We refitted the core network to new time-series data from total Th2-cells by keeping the signs of the inferred minimal Th2 model. (B) The fit of the core model to the total T-cell data is shown. The y-axis has arbitrary units of expression, and the x-axis is time. The model output is denoted by the blue curves, and the data are shown by the red points. (C) The fit of the peripheral genes. The figure follows the same style as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005608#pcbi.1005608.g003" target="_blank">Fig 3B</a>. The black band in the cost bar denotes the 0.95 rejection limit of the corresponding χ²-test, with all rejected models above the band. (D) We resampled our prior matrix with the same number of parameters and signs as the Th2 model 10,000 times, and compared the random models with the output from LASSIM. The ability of the inferred core network structure to fit novel gene expression data of total T-activation was considered. A total of 1 000 random core model structures were drawn from the prior network, and refitted to the data. The distribution of the fit is shown by the blue curve. The core network identified from LASSIM was shown to be significantly better for fitting the novel data, as marked by the black arrow. Moreover, most of the core models could be rejected by a χ²-test, and are represented in red.</p

General workflow of the LArge-Scale SIMulation (LASSIM) high performance toolbox.

<p>As <b>Input</b> LASSIM take four basic components, <i>core and peripheral prior networks</i> (optional), <i>experimental data</i> and <i>dynamic equations</i> to fit a large-scale non-linear dynamic system based on the fully parallel PyGMO toolbox. <b>Step 1</b>, LASSIM performs pruning and data fitting on the core system. <b>Step 2</b>, LASSIM expands the core model by inferring outgoing interactions with peripheral genes, with each gene solved in parallel using a computer cluster. The LASSIM functions are fully modular, and have been built so that the functions describing the optimization procedure, dynamic equations, cost function and data pruning are modular and can easily be changed by the user. The <b>Output</b> is either the core network defined in <b>Step 1</b> or a genome wide regulatory network if <b>Step 2</b> is run, with ranked interactions based on selection order, as well as kinetic parameters for the dynamic equations.</p

LASSIM inferred a genome-wide model of 35,900 core-to-peripheral gene interactions.

<p>(A) These peripheral genes do not have any feedbacks to the core system, nor any crosstalk among themselves. (B) The measured mRNA profiles of the 10,543 peripheral genes (blue/yellow represent relative low/high expression), sorted by the model cost (<i>V</i>(<b><i>p</i></b><i>*</i>)) on the y-axis, and time points on the x-axis. As can be seen, genes that display a peak in expression at the second or third time points are generally associated with a higher cost. (C) The results from the ChIP-seq analysis of inferred to-gene interactions, where the y-axis shows the—log₁₀(p). The red line denotes the significance level (Bootstrap P < 0.05).</p