Training Signaling Pathway Maps to Biochemical Data with Constrained Fuzzy Logic: Quantitative Analysis of Liver Cell Responses to Inflammatory Stimuli

Right side: Workflow (Boxes A through G and Steps 1–6). The methodology requires a dataset that describes some species in the prior knowledge network (PKN; Box A). Based on the experimental design of the dataset (Box B), the map is compressed to contain only nodes measured (blue nodes), perturbed (green stimulated nodes and orange inhibited nodes), or necessary to maintain logical consistency between nodes (Step 1). The resultant compressed network (Box C) is then expanded to contain multiple possible logic descriptions of gates connecting more than one input node to a single output node (Step 2). The resultant expanded network (Box D) is trained to the data values (Box E) using several independent runs of a discrete genetic algorithm to minimize MSE (Step 3). Each independent run results in an unprocessed cFL model represented with a grey triangle. This results in a family of unprocessed cFL models (Box F). The result of each independent optimization run is now represented with a different colored triangle. Each individual unprocessed model is reduced with several reduction thresholds (Step 4), resulting in several reduced models (different triangles shadings). The parameters of each reduced model are then refined (Step 5), resulting in reduced-refined models (triangles outlined in black). Finally, one model is chosen to represent each original unprocessed model using a selection threshold (Step 6), resulting in a family of filtered models (Box G). Left side: Application to a toy model (panels a to e). A PKN was hypothesized from the Ingenuity Systems database (www.ingenuity.com) (a.i.) and compared to an in silico dataset generated by a simulation of a cFL model with known topology and parameters (a.ii.). The PKN contains 15 molecular species represented as nodes that are believed to positively (arrows) or negatively (blunt arrows) affect others species. These intermediate nodes summarize the possible paths between experimentally stimulated ligands (green) and measured (blue) or inhibited (orange) species. The model was compressed (b) as described in and then expanded (c) to contain all possible two-input AND gates. The expanded network was trained to the in silico dataset with twenty independent runs of the discrete genetic algorithm. The topologies of the resultant models (d) were identical except in the case of the gate describing activation of MEK, with sixteen models modeling this interaction with an activating gate (brown, dashed gate) and four models using an AND-NOT gate (green, dashed gate). The TNFα → JNK cFL gate was removed from all unprocessed models, reflecting that this interaction was inconsistent with the in silico data. The reduction process () showed that the AND-NOT gate could be described more simply without significantly affecting the MSE, resulting in a family of filtered models (e). We have labeled each gate with the sensitivity of the gate (defined in ), where sensitivity is scaled between zero and one and a higher sensitivity indicates that the output node is more active at lower input node values. All maps and the graphs of cFL models were generated by a CellNOpt routine using the graphviz visualization engine (www.graphviz.org) followed by manual annotation in Adobe Illustrator.

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Training Signaling Pathway Maps to Biochemical Data with Constrained Fuzzy Logic: Quantitative Analysis of Liver Cell Responses to Inflammatory Stimuli. (2011) Melody K. Morris, et al. PLoS Comput Biol. 2011 Mar;7(3):e1001099. Figure: F2. All organisms Homo sapiens Mus musculus Rattus norvegicus Drosophila melanogaster

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