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. Crowther Audrey audrey.crowther@huskers.unl.edu University of Nebraska-Lincoln 2016-07-21T21:32:19Z 2017-02-13T13:39:00Z

Bmp2 derived from neighboring tissue

 2016-08-03T20:27:14Z

T-box transcription factor TBX5

Gene Name: TBX5

UniProt ID: Q99593

Gene ID: 6910

FHF transcription factor

 2017-02-08T19:11:12Z

This node representsMesp1 and Mesp2.

Gene Name: MESP1/MESP2

UniProt ID: Q9BRJ9/Q0VG99

Mesoderm posterior protein 1/ Mesoderm posterior protein 2

Gene ID: 55897/145873

transcription factor

 2017-02-13T13:39:00Z

Time delay of Bmp2 derived from neighboring tissue

 2017-02-13T13:39:00Z

Insulin gene enhancer protein ISL-1

SHF transcription factor

Gene Name: ISL1

UniProt ID: P61371

Gene ID: 3670

 2016-07-22T10:07:55Z

Dickkopf-related protein 1

Gene Name: DKK1

UniProt ID: O94907

Gene ID: 22943

Signaling factor

 2017-02-08T18:17:49Z

Fibroblast growth factor 8

Gene Name: FGF8

UniProt ID: P55075

Gene ID: 2253

SHF transcription factor

 2016-08-03T15:19:40Z

Time delay of canonical Wnt derived from neighboring tissue

 2016-07-22T10:25:19Z

This node represents Foxc1 and Foxc2.

Forkhead box protein C1/ Forkhead box protein C2 SHF transcription factor

Gene Name: FOXC1/FOXC2

UniProt ID: Q12948/Q99958

Gene ID: 2296/2303

 2016-07-22T10:21:04Z

T-box transcription factor TBX1

Gene Name: TBX1

UniProt ID: O43435

Gene ID: 6899

SHF transcription factor

 2016-08-03T15:19:40Z

Canonical Wnt derived from neighboring tissue

 2016-07-22T10:25:19Z

Homeobox protein Nkx-2.5

Gene Name: NKX2-5

UniProt ID: P52952

Gene ID: 1482

transcription factor

 2017-02-08T19:11:12Z

canonical Wnt signaling

 2017-02-13T13:39:00Z

Gene Name: BMP2

Bone morphogenetic protein 2

UniProt ID: P12643

Gene ID: 650

Signaling factor

 2016-12-19T14:24:15Z

This node represents GATA4, GATA5, and GATA6.

Transcription factor GATA-4/ Transcription factor GATA-5/Transcription factor GATA-6

Gene Name: GATA4/GATA5/GATA6

UniProt ID: P43694/Q9BWX5/Q92908

Gene ID: 14463/140628/2627

 2016-12-19T14:24:15Z

Mesp1 activates Tbx5.

Tbx1 inhibits Tbx5.

Tbx5 activates Tbx5.

Dkk1 inhibits Tbx5 when Mesp1 and Tbx5 are inactive.

canWnt inhibits Tbx5.

Nkx2.5 activates Tbx5.

Dkk1 downregulates Tbx5 expression.

canWnt downregulates Tbx5.

Mesp1 upregulates Tbx5 expression.

Tbx5 upregulates Tbx5 expression.

Tbx1 downregulates Tbx5 expression.

Nkx2.5 upregulates Tbx5 expression.

 S_12 1 S_10 1 S_5 1 S_2 1 S_1 1 S_13 1 S_2 1 S_10 1 S_5 1 S_2 1 S_1 1 S_13 1 S_1 1 S_10 1 S_5 1 S_2 1 S_1 1 S_13 1

canWnt activates Mesp1.

exogen_BMP2_II inhibits Mesp1.

After mesoderm formation, which is dependent on canWnt signaling, cardiogenic precursor cells express the transcription factor Mesp1.

BMP2 signaling inhibits Mesp1 expression.

 S_13 1 S_3 1

exogen_BMP2_I activates exogen_BMP2_II.

exogen_BMP2_I activates exogen_BMP2_II. This interaction ensures proper network timing.

 S_8 1

Mesp1 activates IsI1.

Fgf8 activates IsI1.

canWnt in conjunction with exogen_CanWnt activates Isl1.

Tbx1 activates IsI1.

exogen_CanWnt in conjunction with canWnt upregulates of IsI1 expression.

Decreased Fgf8 expression leads to aberrant production of Isl1, indicating Fgf8 is responsible for upregulating IsI1 expression.

Mesp1 upregulates IsI1 expression.

exogen_CanWnt in conjunction with canWnt upregulates of IsI1 expression.

Isl1 is downregulated in Tbx1 knockout embryos, indicating that Tbx1upregulates IsI1 expression.

 S_2 1 S_13 1 S_7 1 S_10 1 S_6 1

Mesp1 activates Dkk1.

exogen_BMP_II inhibits Dkk1.

canWnt activates Dkk1.

canWnt indirectly upregulates Dkk1.

Mesp1 upregulates Dkk1 gene expression.

exogen_BMP_II downregulates Dkk1 gene expression.

 S_2 1 S_13 1 S_3 1

Mesp1 inhibits Fgf8.

Tbx1 activates Fgf8.

Foxc1.2 activates Fgf8.

Mesp1 downregulates Fgf8 gene expression.

Foxc1.2 upregulates Fgf8 expression in the mesenchyme.

Tbx1 upregulates Fgf8 gene expression.

 S_10 1 S_2 1 S_9 1 S_2 1

exogen_CanWnt_I activates exogen_CanWnt_II.

exogen_CanWnt_I activates exogen_CanWnt_II. This interaction ensures proper network timing.

 S_11 1

canWnt with exogen_CanWnt activates Foxc1.2.

canWnt upregulates Foxc1.2 gene expression through β-catenin binding to conserved regions upstream of Foxc1.

Endodermal canWnt signaling (represented as exogen_CanWnt) activates Foxc1.2 gene expression.

 S_13 1 S_7 1

Foxc1.2 activates Tbx1.

Foxc1.2 bind to the Fox site #1 of Tbx1 to activate Tbx1 transcription.

 S_9 1

exogen_CanWnt_1 positively regulates itself.

exogen_CanWnt_1 positively regulates itself.

 S_11 1

Bmp2 in conjunction with GATAs activates Nkx2.5.

IsI1 in conjunction with GATAs activates Nkx2.5.

Tbx5 activates Nkx2.5.

Mesp1 in conjunction with DKK1 activates Nkx2.5.

Tbx1 activates Nkx2.5.

Mesp1 upregulates Nkx2.5 gene expression via Dkk-1-mediated blockade of canonical Wnt-signalling.

GATA binds to the Nkx2.5 enhancer region.

Bmp2 upregulates Nkx2.5 gene expression through the induction of Gata4 expression.

Mesp1 upregulates Nkx2.5 gene expression via Dkk-1-mediated blockade of canonical Wnt-signalling.

Tbx5 upregulates Nkx2.5 gene expression.

IsI1 binds to the Nkx2.5 enhancer region located adjacent to the Gata binding site

Tbx1 upregulates Nkx2.5 gene expression.

 S_2 1 S_5 1 S_15 1 S_14 1 S_1 1 S_4 1 S_15 1 S_10 1

canWnt is activated by exogen_CanWnt_II.

canWnt signally starts from the endoderm (represented as exogen_CanWnt_II) before reaching the mesoderm.

 S_7 1

canWnt inhibits Bmp2.

Bmp2 is activated by exogen_BMP2_II.

canWnt downregulates Bmp2 gene expression.

Bmp2 signally starts from the endoderm (represented as exogen_BMP2_II) before reaching the mesoderm.

 S_3 1 S_13 1

Mesp1 activates GATA4.

Nkx2.5. activates GATA6.

Tbx5 activates GATAs.

Mesp1 upregulates GATA4 expression.

Expression of GATA4 is reduced in Tbx5 knockout embroys, indicating that Tbx5 upregulates GATA4 expression.

Nkx2.5 binds to the GATA6 enhancer region.

 S_2 1 S_1 1 S_12 1