Finite Dimension: A Mathematical Tool to Analise Glycans

Abstract

There is a need to develop widely applicable tools to understand glycan organization, diversity and structure. We present a graph-theoretical study of a large sample of glycans in terms of finite dimension, a new metric which is an adaptation to finite sets of the classical Hausdorff "fractal" dimension. Every glycan in the sample is encoded, via finite dimension, as a point of Glycan Space, a new notion introduced in this paper. Two major outcomes were found: (a) the existence of universal bounds that restrict the universe of possible glycans and show, for instance, that the graphs of glycans are a very special type of chemical graph, and (b) how Glycan Space is related to biological domains associated to the analysed glycans. In addition, we discuss briefly how this encoding may help to improve search in glycan databases.