Describing the connectivity of chemical and/or biological systems using networks is a straight gate for the introduction of mathematical tools in proteomics. Networks, in some cases even very large ones, are simple objects that are composed at least by nodes and edges. The nodes represent the parts of the system and the edges geometric and/or functional relationships between parts. In proteomics, amino acids, proteins, electrophoresis spots, polypeptidic fragments, or more complex objects can play the role of nodes. All of these networks can be numerically described using the so-called Connectivity Indices (CIs). The transformation of graphs (a picture) into CIs (numbers) facilitates the manipulation of information and the search for structure-function relationships in Proteomics. In this work, we review and comment on the challenges and new trends in the definition and applications of CIs in Proteomics. Emphasis is placed on 1-D-CIs for DNA and protein sequences, 2-D-CIs for RNA secondary structures, 3-D-topographic indices (TPGIs) for protein function annotation without alignment, 2-D-CIs and 3-D-TPGIs for the study of drug-protein or drug-RNA quantitative structure-binding relationships, and pseudo 3-D-CIs for protein surface molecular recognition. We also focus on CIs to describe Protein Interaction Networks or RNA co-expression networks. 2-D-CIs for patient blood proteome 2-DE maps or mass spectra are also covered.

Proteomics, networks and connectivity indices.

Based on all kinds of adjacent amino acids (AAA), we map each protein primary sequence into a 400 by ($(L-1)$) matrix $({\schmi M})$. In addition, we further derive a normalized 400-tuple mathematical descriptors $({\schmi D})$, which is extracted from the primary protein sequences via singular values decomposition (SVD) of the matrix. The obtained 400-D normalized feature vectors (NFVs) further facilitate our quantitative analysis of protein sequences. Using the normalized representation of the primary protein sequences, we analyze the similarity for different sequences upon two data sets: 1) ND5 sequences from nine species and 2) transferrin sequences of 24 vertebrates. We also compared the results in this study with those from other related works. These two experiments illustrate that our proposed NFV-AAA approach does perform well in the field of similarity analysis of sequence.

Normalized Feature Vectors: A Novel Alignment-Free Sequence Comparison Method Based on the Numbers of Adjacent Amino Acids

6.8. Protein Profiles 823 7. Spectrum-like Representation of Proteins 824 8. Graphical Approach to Protein Alignment 825 9. Nongraphical Representation of Proteins 828 9.1. Representation of Proteins as Walks in Space 828 9.2. Protein Descriptors 829 10. Most Recent Results 830 10.1. Amino Acid Adjacency-Count Matrix 830 10.2. Higher-Order AA Adjacency-Count Matrices 834 10.3. Simplified Graphical Representations of Proteins 834

Graphical representation of proteins.

New 3D graphical representation of DNA sequence based on dual nucleotides

A 2D graphical representation of protein sequence and its numerical characterization

Over the last few years several authors have presented various methods to assign mathematical descriptors to DNA sequences in order to quantitatively compare the sequences and determine similarities and dissimilarities between them. The plethora of different methods used have made it necessary to compare them and determine which one(s), if any, best meet the needs required to characterize DNA sequences. With the very rapid rise in available DNA sequence data and the strong need for robust quantitative techniques to determine regions of interest in these sequences, numerical characterization of DNA and RNA sequences will be of great importance in filling a part of this need.

Marissa Harle

Papers

Mathematical descriptors of DNA sequences: development and applications