Application of graph colouring to biological networks

Abstract

We explore the application of graph coloring to biological networks, specifically protein-protein interaction (PPI) networks. First, we find that given similar conditions (i.e. number of nodes, number of links, degree distribution and clustering), fewer colors are needed to color disassortative (high degree nodes tend to connect to low degree nodes and vice versa) than assortative networks. Fewer colors create fewer independent sets which in turn imply higher concurrency potential for a network. Since PPI networks tend to be disassortative, we suggest that in addition to functional specificity and stability proposed previously by Maslov and Sneppen (Science 296, 2002), the disassortative nature of PPI networks may promote the ability of cells to perform multiple, crucial and functionally diverse tasks concurrently. Second, since graph coloring is closely related to the presence of cliques in a graph, the significance of node coloring information to the problem of identifying protein complexes, i.e. dense subgraphs in a PPI network, is investigated. We find that for PPI networks where 1% to 11% of nodes participate in at least one identified protein complex, such as H. sapien (DIP20070219, DIP20081014 and HPRD070609), DSATUR (a well-known complete graph coloring algorithm) node coloring information can improve the quality (homogeneity and separation) of initial candidate complexes. This finding may help to improve existing protein complex detection methods, and/or suggest new methods.

Concurrency and Network Disassortativity

“…Closer examination of the independent sets generated for PPI networks is required. It may also be that a modified graph-coloring algorithm would produce more meaningful sets of nodes for analyzing PPI networks, for example, to identify protein complexes [1,6]. Nonetheless, we believe that our observations suggest an intriguing hypothesis: that concurrency concerns may be an additional factor exerting evolutionary pressure on the shape of biological networks.…”

A Modified Dna Computing Approach To Tackle The Exponential Solution Space Of The Graph Coloring Problem

“…Table 1. DNA strands used for solving the graph coloring problem shown in Figure 2 Color DNA strand Color DNA strand 3 TTTAGATGAAACTCGCGTTC r 9 CTCCGATTAATGCACATTTA g 3 TGGCACTCTTAAATCGAATA g 9 GTTCGCGGATAAGAAGTCGA b 3 TTGACAAGGAGGAGGATCCA b 9 GCGTCCTAGGATCGTTCATT r 4 TCGGGGTAAAGTGATTACTG r 10 TTCCCTTTCCGGACTCTTCG g 4 ACCGATCAGTAACTAAATTC g 10 GGCTACTTCTTGTTACTCCA b 4 CGATGAGCGCCCTGAGGGGC b 10 TAACTGAATCGTCCAATCAC r 5 CGCCGCGTAAGGAGCCCGGT r 11 CAAACTGCTACGTCGCCAAT g 5 ACTTATCTTATAAGCGCCGG g 11 GGCTCCGAAACGATGGAAGT b 5 GGTCCAGCCTAACTTTTCAT b 11 TTCTTGGGGCTTGGGCTATA r 6 ATCTTGACCGCCAATATAAG r 12 CTCACAGAATGCTGCGCAAA g 6 CCAATTGTGCCAGCACGTTA g 12 TAAATTTACTTCGGGACACC b 6 AGATACCCGTCTGGTTCACC b 12 TCTCAACAGCGTCTGGAAGT A typical DNA computing approach for coloring the graph shown in Figure 2 needs an initial test tube of 3 12 different DNA strands to encode all the solution space; but in our approach the solution space was searched step by step and the number of different DNA strands in a test never exceeded 180. The idea of reducing the number of DNA strands was already proposed by Xu et.…”

“…The graph coloring problem is defined as assigning colors to the vertices of a graph such a way that no two adjacent vertices have the same color and a minimum number of colors are used. This problem has many applications such as fault diagnosis [1], functional compression [2], broadcast scheduling [3], resource allocation [4] and biological networks [5].…”

Speaker-TTS voice mapping towards natural and characteristic robot storytelling

“…If the graph can be colored with k colors, the variables can be stored into k registers. There are a number of applications to other domains such as air traffic flow management, pattern matching of images, and an analysis of biological and archeological data [18,19,20].…”