A Novel Mathematical Approach to Define the Genes/SNPs Conferring Risk or Protection in Sporadic Amyotrophic Lateral Sclerosis Based on Auto Contractive Map Neural Networks and Graph Theory.

Background. Complex diseases like amyotrophic lateral sclerosis (ALS) implicate phenotypic and genetic heterogeneity. Therefore, multiple genetic traits may show differential association with the disease. The Auto Contractive Map (AutoCM), belonging to the Artificial Neural Network (ANN) architecture, "spatializes" the correlation among variables by constructing a suitable embedding space where a visually transparent and cognitively natural notion such as "closeness" among variables reflects accurately their associations. Results. In this pilot case-control study single nucleotide polymorphism (SNP) in several genes has been evaluated with a novel data mining approach based on an AutoCM. We have divided the ALS dataset into two dataset: Cases and Control dataset; we have applied to each one, independently, the AutoCM algorithm. Six genetic variants were identified which differently contributed to the complexity of the system: three of the above genes/SNPs represent protective factors, APOA4, NOS3, and LPL, since their contribution to the whole complexity resulted to be as high as 0.17. On the other hand ADRB3, LIPC, and MMP3, whose hub relevancies contribution resulted to be as high as 0.13, seem to represent susceptibility factors. Conclusion. The biological information available on these six polymorphisms is consistent with possible pathogenetic pathways related to ALS.