The process of GSD is poorly characterized at the quantitative level, i.e., kinetic information regarding the interactions of the elements of this regulatory network is still lacking, therefore the implementation of the GSD network as a continuous model is, at this moment, out of reach. Given this, we decided to model the network as a discrete dynamical system so as to describe the qualitative observations that are experimentally reported. Specifically, we used a Boolean approach where every node might have one of two possible states; 1 (ON) or 0 (OFF), indicating that a given node within the network model is active or inactive, respectively.
To determine the activation state of each node in the GSD model we translated the experimental regulatory interactions into a set of Boolean functions with the use of the logical operators AND, OR and NOT (Table 1). The logical operator AND is used if two nodes named A and B are required to activate a third node named C. The logical operator OR is used if two nodes named A or B can activate, by its own, node C. The logical operator NOT is used if node A is an inhibitor of node B. Thus, the state of a given node over time is determined by the activation state of its regulators. We integrated to the model additional regulatory interactions not reported by observational or experimental studies (Table 2). These interactions were inferred from analysis of the dynamics of the Boolean model and might be considered as model predictions that deserve further experimentation to be validated. Interactions of model predictions are shown in Fig. 1 as orange dashed lines.

Set of functions for the Boolean model of gonadal sex determination

UGR, UGR & ! (NR5A1 ∣ WNT4)
CBX2, UGR & ! (NR0B1 & WNT4 & CTNNB1)
GATA4, (UGR ∣ WNT4 ∣ NR5A1 ∣ SRY)
WT1mKTS, (UGR ∣ GATA4)
WT1pKTS, (UGR ∣ GATA4) & ! (WNT4 & CTNNB1)
NR5A1, (UGR ∣ CBX2 ∣ WT1mKTS ∣ GATA4) & ! (NR0B1 & WNT4)
NR0B1, (WT1mKTS ∣ (WNT4 & CTNNB1)) & ! (NR5A1 & SOX9)
SRY, ((NR5A1 & WT1mKTS & CBX2) ∣ (GATA4 & WT1pKTS & CBX2 & NR5A1) ∣ (SOX9 ∣ SRY)) & ! (CTNNB1)
SOX9, ((SOX9 & FGF9) ∣ (SRY ∣ PGD2) ∣ (SRY & CBX2) ∣ (GATA4 & NR5A1 & SRY)) & ! (WNT4 ∣ CTNNB1 ∣ FOXL2)
FGF9, SOX9 & ! WNT4
PGD2, SOX9
DMRT1, (SRY ∣ SOX9) & ! (FOXL2)
DHH, SOX9
DKK1, (SRY ∣ SOX9)
AMH, ((SOX9 & GATA4 & NR5A1) ∣ (SOX9 & NR5A1 & GATA4 & WT1mKTS)) & ! (NR0B1 & CTNNB1)
WNT4, (GATA4 ∣ (CTNNB1 ∣ RSPO1 ∣ NR0B1)) & ! (FGF9 ∣ DKK1)
RSPO1, (WNT4 ∣ CTNNB1) & ! (DKK1)
FOXL2, (WNT4 & CTNNB1) & ! (DMRT1 ∣ SOX9)
CTNNB1, (WNT4 ∣ RSPO1) & ! (SRY ∣ (SOX9 & AMH))

Set of regulatory interactions inferred from analysis of the dynamics of the Boolean model, colored in orange, that deserve further experimentation to be validated

We performed an initial exhaustive evaluation of the dynamic behavior of the wild type model, simulating all possible initial activation states. Three fixed-point attractors were obtained, and we performed a search focused in finding the state transitions corresponding to both male and female pathways. To recover the wild type “male pathway”, we initiated the simulations with the UGR node in ON. In contrast, to created a wild type “female pathway”, without the SRY node, we set the UGR and WNT4 nodes as active at the beginning of simulations. Besides the wild type model, we simulated all possible loss and gain of function of single mutants, so as to describe alterations in activation states that might be interpreted as alterations in gene expression. Loss and gain of function single mutants were simulated by fixing the relevant node to 0 or 1, respectively. All simulations were carried out under the synchronous updating scheme with the use of BoolNet [33 (link)].
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