Using Monoids for the Integration of Genomic and Metabolic Parameters in the Prediction of Phenotypes in Regulatory Cascades.

Molecular network modeling requires the use of mathematical and computational formalisms for a robust and accurate prediction of phenotypes. Furthermore, there is a need to extend these formalisms to be applied to large-scale molecular networks, thus helping in the understanding of biological complexity. In this work, we propose an extension to the modeling framework known as design principles, developed by M.A. Savageau, which is based on the Power Law Modeling. While valuable to understand several properties of molecular networks, the power law modeling cannot be used to infer kinetic orders, which are typically related to the number of binding sites present in molecules. We modified the traditional approach by incorporating the use of monoids generating a new methodological approach that we call Genotype Arithmetic. This approach solves local geometry, solving networks through monoids and varieties, reducing the computational complexity. The resulting combinatorial object contains a family of geometric points, whose fixed points in the exponent space define a set of constraints determining the correct kinetic order to be used in the power law modeling. This characteristic constitutes a prediction of the binding strength and/or the number of DNA binding sites in regulatory sequences, as well as the reaction orders in enzymatic kinetics. To show the applicability of the present approach, we show how the number of binding sites can be approximated in metabolic pathways formed by 3 to 9 reactions, in allosteric systems of end-product inhibition with intermediate catalytic reactions and one gene inhibition. Author summaryIn this work, was revised the Power Law Modeling to analyze and predict kinetic and genomic parameters in molecular networks. It was developed a new approach, called Genotype Arithmetic, which takes advantage from the properties of Monoids found within this formalism. Using this algebraic and geometric technique, were predicted the number of binding sites for various cases associated with the pathway length in the gene allosteric system for end-product inhibition.