8 (link), in directed networks and in weighted networks. Centralities for directed networks (see
As an example, in
The image, obtained using Cytoscape’s graphical tool, represents the different Stress values by using the colour and the size of the nodes. The size describes the value obtained by using the directed Stress: the bigger the node the higher the value; the colour describes the value obtained by using the undirected Stress: red is used for the highest value, blue for the lowest value. For example a large blue node requires particular attention because it is showing a node with a high centrality value if the network is considered as directed but with a very low value if the network is considered as undirected.
By analyzing the Oncogenes network we saw that the large red node, i.e. AKT1, shows how its Stress values are high using both algorithms. It plays a central role in different cell processes like metabolism, proliferation, cell survival, growth and angiogenesis. This role may highlight its high Stress value but, on the other hand, the high values suggest us to deeply investigate its characteristics; it is also involved in two different kind of cancer: breast and colorectal (see
Another interesting result is shown by the blue medium sized node RAF1. It shows how, using undirected Stress we obtained a low value, but by using the new algorithm we obtained an interesting Stress value. RAF1 was identified as a proto-oncogene with different and fundamental cellular functions (see
The opposite situation is found in the third highlighted node, the small green node, RB1 in the right bottom corner. In this case the value computed with undirected Stress is not very high, but the value computed with the directed Stress is very low. RB1 is a gene involved in coding a protein involved in the retinoblastoma and other type of cancer like bladder cancer and osteogenic sarcoma. It was the first tumor suppressor gene found (see
All the results shown and described must be considered as a possible direction for further lab experiments. The main goal of this kind of analysis is to give us a comprehensive view that could be useful in describing the role of each node involved in a specific biological process and to drive future insights and investigations.
Second important features of the new version of CentiScaPe is the possibility of computing centralities for weighted networks, that are networks in which the edges are provided with an attribute that can be interpreted as a distance between the two connected nodes.
In the network in
dist) attribute for each edge. The values are
dist(
A,
B) = 2,
dist(
B,
C) = 3 and
dist(
A,
C) = 7. Since A and C are connected by a single edge, in an unweighted computation, the distance from A to C is equal to one. But if the attributes of the edges are considered as distances, the shortest path between A and C is the one passing through B (= 2 + 3 = 5) since it is shorter, or
lighter, than the one connecting A directly to C (= 7). The computation of weighted shortest paths will result in completely different values from the case wherein the weight is not considered. The user should consider that the weight is used in the sense that close nodes are more important than distant nodes. Therefore depending on the meaning of the attributes, one can use the real value or its reciprocal. For example if the attribute represents the speed of a reaction instead of a distance, the reciprocal should be used. This is because the higher the value of the speed, the nearer the nodes are: an increasing speed determines a decreasing reciprocal and the distance decrease by consequence.
An example of usage of weighted networks centralities analysis, can be found in Holly
et al.9 (link) where an euclidean distance is given to each edge depending on the difference between the phosphorylation level of the proteins connected by that edge.
All the graphical features of the previous version of CentiScaPe, as the plot-by-node, the plot-by-centrality and the boolean-based result panel have been maintained in the new version. A complete guide can be found in Scardoni
et al.8 (link) or in the CentiScaPe userguide available from the website.