Shared neighbors of Ifit1 in three inferred networks.

a<p>Numbers indicate that the indicated gene is in the first order (1) or second order (2) network of Ifit1 for each network.</p

Condensed networks of bottlenecks and functional clusters.

<p>A network was inferred from the macrophage innate immune compendium (A), or the blood- (B) or brain-(C) derived transcriptome from the stroke study. Bottlenecks (circles) were identified based on topological betweenness and clusters (squares) were assessed for statistical enrichment in gene ontology functional categories versus genes in the rest of network using the hypergeometric test. Shared functions are indicated by cluster color: orange, immune related/stress response; pink, signaling; green, cell cycle/mitosis. Clusters are labeled with most enriched functional category followed by the negative exponent of the p-value for enrichment. Edges are colored red to indicate that the bottleneck is a member of the cluster that it links to, and red to indicate that the bottleneck is linked to the cluster. Note that not all bottlenecks, clusters or relationships between the two are present in this representation (see text).</p

Shared bottlenecks between three inferred networks.

<p>Shared bottlenecks between three inferred networks.</p

Overview of abstract dynamic modeling approach.

<p>1) Inferelator 1.1 infers a parsimonious set of potential regulatory influences whose expression can explain the expression of the target cluster maximally, but does so independently for each cluster. 2) The actual structure of the inferred network would consider that the regulators are members of clusters and that the network structure is complex and cyclical. 3) The regulatory influence model can be represented by a regulatory influence matrix and used to simulate the closed system of ordinary differential equations over time. 4) The optimization process (see text) is used to improve the ability of the model to simulate the system over time (i.e. calibrate to temporal data). 5) The resulting optimized model retains much of the structure of the initial model.</p

An Inferelator-based influence model provides statistically significant performance when treated as a system of ordinary differential equations (ODEs).

<p>The Inferelator-based influence model was treated as a system of ODEs and simulated over time. Expression levels of the simulation were compared with observed values of expression by correlation (Y axis) for the initial model (red dot) or for 100 randomized matrices. The matrices were randomized by replacing all non-zero values with other non-zero values (resampled) or from a uniform distribution (uniform), or the locations of all values in the matrix were reassigned (scramble). The results (as a box and whiskers plot) show that the Inferelator-based initial matrix produces simulation over time with a performance that is significantly better than that using random permutations of the matrix.</p

Modeling Dynamic Regulatory Processes in Stroke

<div><p>The ability to examine the behavior of biological systems <em>in silico</em> has the potential to greatly accelerate the pace of discovery in diseases, such as stroke, where <em>in vivo</em> analysis is time intensive and costly. In this paper we describe an approach for <em>in silico</em> examination of responses of the blood transcriptome to neuroprotective agents and subsequent stroke through the development of dynamic models of the regulatory processes observed in the experimental gene expression data. First, we identified functional gene clusters from these data. Next, we derived ordinary differential equations (ODEs) from the data relating these functional clusters to each other in terms of their regulatory influence on one another. Dynamic models were developed by coupling these ODEs into a model that simulates the expression of regulated functional clusters. By changing the magnitude of gene expression in the initial input state it was possible to assess the behavior of the networks through time under varying conditions since the dynamic model only requires an initial starting state, and does not require measurement of regulatory influences at each time point in order to make accurate predictions. We discuss the implications of our models on neuroprotection in stroke, explore the limitations of the approach, and report that an optimized dynamic model can provide accurate predictions of overall system behavior under several different neuroprotective paradigms.</p> </div

Correlation of gene expression between pretreatment time courses.

<p>Correlation of gene expression between pretreatment time courses.</p

The optimized model performs significantly better than randomly perturbed models.

<p>The best optimized model was simulated over time to provide predictions of expression levels for clusters. Correlation (Y axis) of the simulated versus observed data is shown for the best optimized model (red dot) and for 100 randomized matrices (boxes). The matrices were randomized by replacing all non-zero values with other non-zero values (resampled) or from a uniform random distribution (uniform), or the locations of all values in the matrix were reassigned (scramble). The results (as a box and whiskers plot) show that the optimized model is capable of simulation over time with a performance that is significantly better than randomized versions.</p

Functional coherence of clusters defines functional modules.

<p>To ascertain a reasonable number of clusters to consider in our model abstraction we calculated the normalized functional modularity (Y axis) for varying numbers of clusters (X axis) from the same hiearachical tree derived from the expression data. Functional modularity was defined as the number of genes annotated with a biological process gene ontology category that was functionally enriched in the gene's parent cluster with a p-value less than the threshold indicated (colored lines). The results show that 25 clusters provides a peak of functional modularity, especially for more coherent functional categories with lower p-values.</p

Optimization results.

a<p>Performance of the Inferelator-based model in steady-state prediction.</p>b<p>Performance of the Inferelator-based model in dynamic prediction.</p>c<p>Performance of the best optimized model for that pretreatment.</p>d<p>Performance of the best model optimized to another pretreatment.</p