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. 2015 Jul 24;10(7):e0131832.
doi: 10.1371/journal.pone.0131832. eCollection 2015.

Predicting Variabilities in Cardiac Gene Expression With a Boolean Network Incorporating Uncertainty

Free PMC article

Predicting Variabilities in Cardiac Gene Expression With a Boolean Network Incorporating Uncertainty

Melanie Grieb et al. PLoS One. .
Free PMC article


Gene interactions in cells can be represented by gene regulatory networks. A Boolean network models gene interactions according to rules where gene expression is represented by binary values (on / off or {1, 0}). In reality, however, the gene's state can have multiple values due to biological properties. Furthermore, the noisy nature of the experimental design results in uncertainty about a state of the gene. Here we present a new Boolean network paradigm to allow intermediate values on the interval [0, 1]. As in the Boolean network, fixed points or attractors of such a model correspond to biological phenotypes or states. We use our new extension of the Boolean network paradigm to model gene expression in first and second heart field lineages which are cardiac progenitor cell populations involved in early vertebrate heart development. By this we are able to predict additional biological phenotypes that the Boolean model alone is not able to identify without utilizing additional biological knowledge. The additional phenotypes predicted by the model were confirmed by published biological experiments. Furthermore, the new method predicts gene expression propensities for modelled but yet to be analyzed genes.

Conflict of interest statement

Competing Interests: The authors have declared that no competing interests exist.


Fig 1
Fig 1. Phenotype analysis using the Boolean Network Extension (BNE).
The application of the BNE to a given Boolean network (BN) can be divided into three basic steps: Model extension (top), identification of stable structures (middle) and mapping to phenotypes (bottom). In the model extension step (top) the rules of the BN are transformed to the rules of the BNE by converting the rules of the BN to canonical disjunctive normal form (DNF) and then to product-sum fuzzy logic (DNF product-sum extension, details see section Extension of Boolean networks). In the “identification of stable structures”-step (middle) the extended BNE is simulated for a large number of random inputs. The resulting approximated attractors can either be fixed points approximated by point clouds, fixed points depending on one or multiple parameters or different dependencies. Finally, new phenotypes are identified step (bottom) by mapping the fixed points to their nearest hypothetical phenotype.
Fig 2
Fig 2. Parametric fixed points.
An example of parametric dependency of fixed points is shown. Table 1 shows the BNE.
Fig 3
Fig 3. Schematic drawing of cardiac tissue in Xenopus laevis at stage 24—Expression of genes in heart fields (left) and RT–PCR analysis of selected genes (right).
Panels adapted from Gessert and Kühl [19]. The left panel shows the genes expressed in different domains of the first heart field (FHF) and second heart field (SHF). The SHF is shown at the top and the FHF is shown at the bottom. Common genes expressed in all regions of the FHF and SHF, respectively, are shown on the left. Genes expressed in particular domains are shown on the right. Colors indicate different domains and corresponding expressed genes. The right figure shows the results of single cell RT–PCR analysis of gene expression for the four genes Nkx2.5, Isl1, Tbx1, and Tbx5. Values (0 and 1) and colors red/green represent inactive or active genes. The panel shows the gene expression of different single cell samples (numbered and named at the bottom). FHF and SHF are distinguished by the expression of the Isl1.
Fig 4
Fig 4. Phenotypes predicted by the BNE.
The phenotype profile used for the mapping is based on the 11 genes present in both the Boolean model and the Xenopus analysis. The figure in the left panel shows the distance curves for the nearest phenotypes and fixed points. The x-axis denotes the values of the parameter exogen_canWnt_I and the phenotypes to which the fixed points were mapped. The y-axis shows the actual distance. The phenotypes are ordered by increasing exogen_canWnt_I expression propensity (right panel). Activated genes are shown in green and deactivated genes are shown in red. The framed box shows the gene expression propensity pattern for the four genes Isl1, Nkx2.5, Tbx1, and Tbx5 that corresponds to the the RT–PCR phenotypes of the FHF and SHF from the Fig 3. The FHF_BOOL and SHF_BOOL phenotypes correspond to the phenotypes found in the Boolean model [16]. The SHF1 phenotype is split in three sub-phenotypes PH-1076, PH-564, and PH-692 that differ by the gene expression propensity of canWnt, Bmp2, and Fgf8. The expression of the Fgf8 gene was not reported in Xenopus. Its activation pattern is a prediction of the BNE.

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Grant support

This work was funded in part by the German federal ministry of education and research (BMBF) within the framework GERONTOSYS II (Forschungskern SyStaR, Project ID 0315894A to MK and HAK), European Community’s Seventh Framework Programme (FP7/2007-2013) under grant agreement no. 602783 (to HAK), and the International Graduate School in Molecular Medicine at Ulm University (GSC270). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.