Barycentric Algebras and Gene Expression

Authors:
Anna B. Romanowska;Jonathan D. Smith
Affiliations:
Faculty of Mathematics and Information Sciences, Warsaw University of Technology, Warsaw, Poland 00-661;Department of Mathematics, Iowa State University, Ames, USA 50011
Venue:
WILF '09 Proceedings of the 8th International Workshop on Fuzzy Logic and Applications
Year:
2009

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Abstract

Barycentric algebras have seen widespread application in the modeling of convex sets, semilattices, and quantum mechanics. Recently, they were developed further to encompass Boolean logic and if-then-else algebras. This paper discusses an application of barycentric algebras to systems biology. Here, they provide a calculus for the conversion from simplified Boolean models of gene transcription to fuzzy models that give a more realistic tracking of the biochemistry. Indeed, it appears that logic gates experimentally observed in cells actually follow the barycentric algebra format.