Performances with the optimal and .

<p>Performances with the optimal and .</p

A Sparse Reconstruction Approach for Identifying Gene Regulatory Networks Using Steady-State Experiment Data

<div><p>Motivation</p><p>Identifying gene regulatory networks (GRNs) which consist of a large number of interacting units has become a problem of paramount importance in systems biology. Situations exist extensively in which causal interacting relationships among these units are required to be reconstructed from measured expression data and other a priori information. Though numerous classical methods have been developed to unravel the interactions of GRNs, these methods either have higher computing complexities or have lower estimation accuracies. Note that great similarities exist between identification of genes that directly regulate a specific gene and a sparse vector reconstruction, which often relates to the determination of the number, location and magnitude of nonzero entries of an unknown vector by solving an underdetermined system of linear equations <i>y</i> = Φ<i>x</i>. Based on these similarities, we propose a novel framework of sparse reconstruction to identify the structure of a GRN, so as to increase accuracy of causal regulation estimations, as well as to reduce their computational complexity.</p><p>Results</p><p>In this paper, a sparse reconstruction framework is proposed on basis of steady-state experiment data to identify GRN structure. Different from traditional methods, this approach is adopted which is well suitable for a large-scale underdetermined problem in inferring a sparse vector. We investigate how to combine the noisy steady-state experiment data and a sparse reconstruction algorithm to identify causal relationships. Efficiency of this method is tested by an artificial linear network, a mitogen-activated protein kinase (MAPK) pathway network and the <i>in silico</i> networks of the DREAM challenges. The performance of the suggested approach is compared with two state-of-the-art algorithms, the widely adopted total least-squares (TLS) method and those available results on the DREAM project. Actual results show that, with a lower computational cost, the proposed method can significantly enhance estimation accuracy and greatly reduce false positive and negative errors. Furthermore, numerical calculations demonstrate that the proposed algorithm may have faster convergence speed and smaller fluctuation than other methods when either estimate error or estimate bias is considered.</p></div

Comparison of the boundary of success phase at several values of indeterminacy <i>δ</i>.

<p>Comparison of the boundary of success phase at several values of indeterminacy <i>δ</i>.</p

Change point Detection Procedure.

<p>Change point Detection Procedure.</p

ROC and PR curves of .

<p>ROC and PR curves of .</p

Prediction Performances for the DREAM3 Networks Using Method Integrations.^†

†<p>As noted in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0031194#pone.0031194-Pinna1" target="_blank">[22]</a>, is obtained for after a comparison with the actual network. On the other hand, the optimal can hardly be obtained in actual estimations for each of , , . The purposes to include their inference results here are only to clarify estimation performance degradations when an empirical parameter is adopted.</p><p>*Due to the some reasons as those of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0031194#pone-0031194-t001" target="_blank">Table 1</a>, these -values can not be distinguished from zero in actual computations, which makes it impossible to compare scores of the adopted GRN topology estimation methods.</p

Performances with DREAM3 <i>in silico</i> size10 challenge.

<p>Performances with DREAM3 <i>in silico</i> size10 challenge.</p

Prediction Performances for the DREAM4 Networks.^†

<p>RPV-Z: relative performance variation with respect to the -score based method; RPV-B: relative performance variation with respect to the best team; ARPV: averaged relative performance variation of the 5 networks.</p>†<p>The purposes to include the inference results of are completely the same as those of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0031194#pone-0031194-t001" target="_blank">Table 1</a>. That is, to clarify that deviation of the parameter from its optimal value usually does not lead to significant estimation performance degradations.</p

Precision-recall curves of some typical estimations.

<p>Precision-recall curves of some typical estimations.</p

Variations of the AUROC and AUPR specifications with the threshold value

<p><b>.</b> To make the variations clearer, the specifications shown are their deviations from those respectively with (for the -score based method) and with (for the algorithm suggested in this paper).</p