A c c e p t e d m a n u s c r i p t2 Abstract Several graph representations have been introduced for different data in theoretical biology. For instance, Complex Networks based on Graph theory are used to represent the structure and/or dynamics of different large biological systems such as protein-protein interaction networks. In addition, Randic, Liao, Nandy, Basak, and many others developed some special types of graph-based representations. This special type of graph includes geometrical constrains to node positioning in space and adopts final geometrical shapes that resemble lattice-like patterns. Lattice networks have been used to visually depict DNA and protein sequences but they are very flexible. However, despite the proved efficacy of new Lattice-like graph/networks to represent diverse systems, most works focus on only one specific type of biological data. This work proposes a generalized type of lattice and illustrates how to use it in order to represent and compare biological data from different sources. We exemplify the following cases: Protein sequence; Mass Spectra (MS) of protein Peptide Mass Fingerprints (PMF); Molecular Dynamic Trajectory (MDTs) from structural studies; mRNA Microarray data; Single Nucleotide Polymorphisms (SNPs); 1D or 2D-Electrophoresis study of protein Polymorphisms and Protein-research patent and/or copyright information. We used data available from public sources for some examples but for other, we used experimental results reported herein for the first time. This work may break new ground for the application of graph theory in theoretical biology and other areas of biomedical sciences.Keywords: Graph theory; Complex Networks; Proteomics; Mass Spectrometry; Leishmaniosis; 2D Electrophoresis; Parasite population Polymorphism; Single Nucleotide Polymorphism; Schizophrenia; Microarray; Cancer; Patents & Copyright studies.
A c c e p t e d m a n u s c r i p t 3
IntroductionSeveral graph representations have been introduced for different data in theoretical biology. For instance, Complex Networks based on Graph theory are used to represent the structure and/or dynamics of different large biological systems such as protein-protein interaction networks. Complex networks are made up of nodes and edges/arcs (node-node connections or links). Drugs, genes, RNAs, proteins, organisms, brain cortex regions, diseases, patients or environmental systems may play the role of nodes. In general, the edges represent similarity/dissimilarity relationships between the nodes. In Complex Networks, both nodes and edges are placed generally in space without any geometrical constrains; nodes do not need spatial coordinates and edges have not a specific length or shape (Barabasi and Oltvai, 2004;Boccaletti et al., 2006;Estrada, 2006). In addition, Randic, Nandy, Basak, Liao, and many others developed some special types of graph-based representations. This special type of graph includes geometrical constrains to node positioning in space and sometimes adopts final geometrical shapes that resemble lattice...