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.

Finite dimension of the ion pathway networks in conducting glasses

“…A Glycan Space (GS) is an easy finite dimension graphical representation [28], where the finite dimension (dimf) is related to the diameter (Dia) by a plane.…”

Glycosylation and the global virome

“…Glycosylation could be represented as data in several ways, ranging from simple (e.g., the presence or absence of a specific set of glycan structures) to complex (generating quantitative features using graph representations of the glycan structure (39)). These data can then be used several ways.…”

Glycosylation and the global virome

“…Glycosylation could be represented as data in several ways, ranging from simple (e.g., the presence or absence of a specific set of glycan structures) to complex (generating quantitative features using graph representations of the glycan structure (Alonso et al, 2018)). These data can then be used several ways.…”