Seeing the results of a mutation with a vertex weighted hierarchical graph.
Bottom Line:
We use this representation to model the effects of a mutation on the protein.Global graph-theoretic measures such as the number of triangles or the number of spanning trees can change as the result.Hence this method provides a way to visualize these global changes resulting from a small, seemingly inconsequential local change.
Affiliation: Department of Mathematics and Statistics, East Tennessee State University, Johnson City, TN 37614 ; Institute for Quantitative Biology, East Tennessee State University, Johnson City, TN 37614.
ABSTRACT
Background: We represent the protein structure of scTIM with a graph-theoretic model. We construct a hierarchical graph with three layers - a top level, a midlevel and a bottom level. The top level graph is a representation of the protein in which its vertices each represent a substructure of the protein. In turn, each substructure of the protein is represented by a graph whose vertices are amino acids. Finally, each amino acid is represented as a graph where the vertices are atoms. We use this representation to model the effects of a mutation on the protein. Methods: There are 19 vertices (substructures) in the top level graph and thus there are 19 distinct graphs at the midlevel. The vertices of each of the 19 graphs at the midlevel represent amino acids. Each amino acid is represented by a graph where the vertices are atoms in the residue structure. All edges are determined by proximity in the protein's 3D structure. The vertices in the bottom level are labelled by the corresponding molecular mass of the atom that it represents. We use graph-theoretic measures that incorporate vertex weights to assign graph based attributes to the amino acid graphs. The attributes of the corresponding amino acids are used as vertex weights for the substructure graphs at the midlevel. Graph-theoretic measures based on vertex weighted graphs are subsequently calculated for each of the midlevel graphs. Finally, the vertices of the top level graph are weighted with attributes of the corresponding substructure graph in the midlevel. Results: We can visualize which mutations are more influential than others by using properties such as vertex size to correspond with an increase or decrease in a graph-theoretic measure. Global graph-theoretic measures such as the number of triangles or the number of spanning trees can change as the result. Hence this method provides a way to visualize these global changes resulting from a small, seemingly inconsequential local change. Conclusions: This modelling method provides a novel approach to the visualization of protein structures and the consequences of amino acid deletions, insertions or substitutions and provides a new way to gain insight on the consequences of diseases caused by genetic mutations. No MeSH data available. Related in: MedlinePlus |
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Mentions: Using different subsets of the mutations in the sequence for dTIM we obtained different spanning trees, although some vertices in the top level graph were highly conserved across the collection of mutations. Figure 4 shows the minimum spanning tree of the top level graph of scTIM, while Figure 5 shows the minimum spanning tree for the all-mutations residue sequence dTIM. For Figures 4 and 5, we used a descriptor based on hydropathy [20]. In both cases, the minimum spanning tree is unique. Figure 6 shows the mean (point) and standard deviation (error bar) across a large number of mutation resamplings, where a mutation resampling was a random selection of mutations from the defective applied to the wild type. Sample size and number of samples were chosen so that each mutation was expected to occur 2.5 times. Figure 6 implies that the degrees of vertices D3, D8, D9, D11, and D18 are unaffected by mutations, whereas structure D4, D12, D17, and D19 are highly sensitive to mutations in the residue sequence. Subsets of the mutations allow individual structure to be studied independently. For example, Figure 7 shows that if mutations are allowed only in D3, then the minimum spanning tree is essentially that of the wild type graph. In contrast, Figure 8 shows that if mutations are only allowed in D9, then the minimum spanning tree is altered. |
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Affiliation: Department of Mathematics and Statistics, East Tennessee State University, Johnson City, TN 37614 ; Institute for Quantitative Biology, East Tennessee State University, Johnson City, TN 37614.
Background: We represent the protein structure of scTIM with a graph-theoretic model. We construct a hierarchical graph with three layers - a top level, a midlevel and a bottom level. The top level graph is a representation of the protein in which its vertices each represent a substructure of the protein. In turn, each substructure of the protein is represented by a graph whose vertices are amino acids. Finally, each amino acid is represented as a graph where the vertices are atoms. We use this representation to model the effects of a mutation on the protein.
Methods: There are 19 vertices (substructures) in the top level graph and thus there are 19 distinct graphs at the midlevel. The vertices of each of the 19 graphs at the midlevel represent amino acids. Each amino acid is represented by a graph where the vertices are atoms in the residue structure. All edges are determined by proximity in the protein's 3D structure. The vertices in the bottom level are labelled by the corresponding molecular mass of the atom that it represents. We use graph-theoretic measures that incorporate vertex weights to assign graph based attributes to the amino acid graphs. The attributes of the corresponding amino acids are used as vertex weights for the substructure graphs at the midlevel. Graph-theoretic measures based on vertex weighted graphs are subsequently calculated for each of the midlevel graphs. Finally, the vertices of the top level graph are weighted with attributes of the corresponding substructure graph in the midlevel.
Results: We can visualize which mutations are more influential than others by using properties such as vertex size to correspond with an increase or decrease in a graph-theoretic measure. Global graph-theoretic measures such as the number of triangles or the number of spanning trees can change as the result. Hence this method provides a way to visualize these global changes resulting from a small, seemingly inconsequential local change.
Conclusions: This modelling method provides a novel approach to the visualization of protein structures and the consequences of amino acid deletions, insertions or substitutions and provides a new way to gain insight on the consequences of diseases caused by genetic mutations.
No MeSH data available.