A new modelling approach for Gli transcription factor network in hepatocytes

Morphogenetic pathways, like the Wnt and Hedgehog are complex systems which organize important processes during development and adulthood. In most of these pathways, positive and negative feedback loops are of considerable importance, because they influence and/or modulate the dynamic behaviour of these pathways. Usually, feedback loops are part of the signalling pathway itself based on the interaction of downstream components (e.g. target gene products) with upstream components in circuits of variable length.

In the case of vertebrate Hh signalling the 3 Gli proteins Gli1, Gli1 and Gli3 act as transcriptional activators or, in truncated form, as repressors (Gli2, Gli3) of signalling target genes when Hh is present or absent, respectively.

To get more insight into the activity of Hh signalling in the adult liver we performed RNA interference experiments to knock-down the expression of Gli1, Gli2 and Gli3 in cultured hepatocytes. Each Gli siRNA significantly depleted its respective mRNA. Surprisingly, Gli1 siRNA also caused an increase in Gli2 and Gli3 mRNAs, suggesting a negative feedback loop in the regulation of Gli factors in hepatocytes. Gli3 siRNA caused a decrease in Gli1 reflecting a target response rather than an off-target effect. This was also found by Dai et al. 1999, who described that in response to Shh, Gli3 can directly bind to the Gli1 promoter and induce Gli1 mRNA transcription. Thus, the Gli factors seem to form a self-stabilizing network in adult hepatocytes.

In order to verify this hypothesis a fuzzy logic based gene regulatory network was created. The network model was represented as a system of difference equations, whereby the time dependent changes of the system are calculated by fuzzy inference systems (FIS). The FIS is a modelling approach mapping the input space of a system (current state) to the output space (alteration of the system in the next time step) using the fuzzy set theory. The FIS uses membership functions of the state variables and rules in order to perform the mapping from input to output variables. The number of membership functions per state variable is present to 3 (low, medium, high). The location of the maximum and the spread of the membership functions were calculated using fuzzy-c-means clustering. The rules describing the input-output behavior were learned with the fuzzy a-priori algorithm. A minimal set of rules with a preset maximum number is chosen under the following criteria that most of the data of training samples could be simulated by the FIS.

A total of 11 siRNA knockdown experiments were used to infer the gene regulatory network of the Gli factors in hepatocytes. The inferred gene regulatory network contains a negative feedback regulation between Gli1 and Gli3 and, thus, can confirm the experimental finding by Dai et al. 1999, that Gli3 induce the Gli1 transcription. Furthermore, evidence has been found that a similar network motif also exists between Gli2 and Gli3. A further result of this study indicates slight evidence that there is double positive feedback loop between Gli1 and Gli2.

Corresponding author: Matz-Soja, Madlen

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