Analysis and Practical Guideline of Constraint-Based Boolean Method in Genetic Network Inference

Boolean-based method, despite of its simplicity, would be a more attractive approach for inferring a network from high-throughput expression data if its effectiveness has not been limited by high false positive prediction. In this study, we explored factors that could simply be adjusted to improve the accuracy of inferring networks. Our work focused on the analysis of the effects of discretisation methods, biological constraints, and stringency of Boolean function assignment on the performance of Boolean network, including accuracy, precision, specificity and sensitivity, using three sets of microarray time-series data. The study showed that biological constraints have pivotal influence on the network performance over the other factors. It can reduce the variation in network performance resulting from the arbitrary selection of discretisation methods and stringency settings. We also presented the master Boolean network as an approach to establish the unique solution for Boolean analysis. The information acquired from the analysis was summarised and deployed as a general guideline for an efficient use of Boolean-based method in the network inference. In the end, we provided an example of the use of such a guideline in the study of Arabidopsis circadian clock genetic network from which much interesting biological information can be inferred

The effect of the number of (A) data-points and (B) amplitude on Boolean network inference.

<p>The constraint-based Boolean network was applied to the three distinct characteristics microarray time-series data, whose resulting networks were compared at a setting scenario: mean discretisation method and stringency at 100 percent. The studied datasets included (1) Galactose system (data from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030232#pone.0030232-DeRisi1" target="_blank">[13]</a>), (2) circadian clock system under constant light (data from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030232#pone.0030232-Covington1" target="_blank">[14]</a>), and (3) circadian clock system under light/dark cycle (data from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030232#pone.0030232-Blasing1" target="_blank">[15]</a>).</p

Overall methodology.

<p>In this study, the methods can be divided into 4 parts described in the Boxes 1–4; Box 1 – discretisation methods, Box 2 - constraint-based Boolean method, Box 3 – network evaluation, and Box 4 – master network concept.</p

The effect of constraints and stringency on the Boolean network inference regime among the observed datasets.

<p>The performances of Boolean networks were evaluated and compared under the (A) constrained and (B) varied stringency conditions. The studied datasets included (1) Galactose system (Gal: data from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030232#pone.0030232-DeRisi1" target="_blank">[13]</a>), (2) circadian clock system under constant light (Clock1: data from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030232#pone.0030232-Covington1" target="_blank">[14]</a>), and (3) circadian clock system under light/dark cycle (Clock2: data from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030232#pone.0030232-Blasing1" target="_blank">[15]</a>).</p

The effect of constraints on the Boolean network inference regime.

<p>The performances of constraint-based Boolean network for Galactose system (data from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030232#pone.0030232-DeRisi1" target="_blank">[13]</a>) were compared with those of the classical Boolean network inference: (A) accuracy; (B) precision; (C) sensitivity; (D) specificity; and black – non-constrained; hatch – constrained).</p

Evaluation of Boolean network performance for Galactose system (data from [<b>13</b>]).

<p>The results were obtained from the constraint-based Boolean network slightly modified from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030232#pone.0030232-Bumee1" target="_blank">[12]</a>: (A) accuracy; (B) precision; (C) sensitivity; (D) specificity.</p

The effect of level of stringency of Boolean function assignment on the Boolean network inference regime.

<p>The performances of constraint-based Boolean network for Galactose system (data from <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030232#pone.0030232-DeRisi1" target="_blank">[13]</a>) (right; A,C,E,G) were compared with those of the classical Boolean network (left; B,D,F,H) inference under different levels of stringency of Boolean function assignment: black – 100, hatch – 80, and grey – 50 percent).</p

Classical and constraint-based Boolean networks of the galactose system.

<p>The figure depicts the galactose networks inferred by (A) the classical and (B) constraint-based Boolean network. The <i>master Boolean networks</i> (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030232#s2" target="_blank">Methods</a>) presented were the results of combining 24 individual networks of using 24 discretisation varieties at the highest level of stringency (100 percent).</p

Boolean networks of circadian clock systems.

<p>Microarray data measured under different light conditions were analysed by the constraint-based Boolean approach resulting in the inferred networks of circadian clock system (A) under constant light (LL; <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030232#pone.0030232-Covington1" target="_blank">[14]</a>) and (B) under constant light (LD; <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030232#pone.0030232-Blasing1" target="_blank">[15]</a>). The <i>master Boolean networks</i> (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0030232#s2" target="_blank">Methods</a>) presented were the results of combining 23 individual networks of using 23 discretisation varieties at the highest level of stringency (100 percent).</p