Study of Proteome Maps Using Partial Ordering

5 STUDY OF PROTEOME MAPS USING PARTIAL ORDERING 

Proteome maps (or proteomics maps) are arrived at by an experimental approach, which simultaneously combines electrophoresis and chromatography, and separates thousands of different proteins from cellular material by charge and by mass. The results are obtained as collection of spots on 2-D films, from which one can extract the (x, y) coordinates of the protein spots and, by measuring the density of the spot, their abundance. Snch results one can use to construct a bubble diagram, 2-D map in which the size of the bubbles represents the abundance of proteins, and 

A close look at Table 7.2 shows that spot 1 and spot 2 cannot be ordered or, in the terminology of partial ordering, are not comparable because although spot 1 has bigger mass (coordinate y), spot 2 has greater charge (coordinate x). Neither are spots 2 and 3 comparable because X2 X3 while y2 ys- However, if one compares the X, y coordinates of spot 1 and spot 3, one find that Xj X3 and yj y -, thus, spot 1 dominates spot 3. 

Partial ordering consists of finding all relationships X Xj andy y, (i,j = 1-20). Observe that the condition x, Xj and y y, geometrically corresponds, if the points (x x and (y yp are connected by a line, to lines with a positive slope. To be more precise, one should allow for the condition X x, and y y, but the equality cannot be simultaneously satisfied because that corresponds to the same spot. Thus, equalities of the more general condition correspond to vertical and horizontal connecting lines, respectively. By knowing these, and also knowing that the relationships X x, 

FIGURE 7.6 Schematic representation of the proteome map of Table 7.2 as a set of points in 2-D determined by their position as separated by electrophoresis (charge) and chromatography (mass). 

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M. Randic, M. Novid, M. Vradko, and D. Plavsic, Study of proteome maps using partial ordering, J. Theor. Biol. 266 (2010) 21-28. 

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