A Network-based Approach for Predicting Missing Pathway Interactions

1. A Network-based Approach for Predicting Missing Pathway Interactions AnkushBansal 658347261

2. Outline • Protein-Protein Interactions and Signaling pathway • Problem statement and variations of problem • Shortest distance algorithm • Greedy approach to predict missing edges • Other approaches • Results • Future Applications

3. Protein-Protein Interaction

4. Signaling Pathway • Sub-networks of proteins that communicate via a series of interactions • Contains upstream proteins • Source proteins transmit information to a set of target proteins

5. Problem Statement Searching for missing edges that will maximally decrease the shortest-path distances between sources & targets

6. 1. Shortcuts Given a weighted digraph G = (V, E) and set of sources s  V and t  V, finding k edges that will minimize the total shortest distance between all source-target pairs.

7. 2. Shortcuts-X (restricted) Given a weighted digraph G = (V, E) and set of sources s  V and t  V and maximum allowable hops are r, then finding k edges that will minimize the total shortest distance between all source-target pairs.

8. 3. Shortcut-SS (Single Source) Given a weighted digraph G = (V, E) and set of sources s  V and t  V, then finding k edges that will minimize the total shortest distance between each target and its single closet source.

9. 4. Shortcuts-X-SS (Restricted, Single Source) Given a weighted digraph G = (V, E) and set of sources s  V and t  V and maximum allowable hops are r, then finding k edges that will minimize the total shortest distance between each target and its single closet source.

10. Example

11. Dijkstra’s Algorithm • Greedy algorithm to solve single source shortest-path problem • Doesn’t work for non-negative weights • Time complexity O(|E|+|V|log|V|), where |E| is # of edges and |V| is # of vertices

12. Dijkstra’s Algorithm

13. Dijkstra’s Algorithm

14. Dijkstra’s Algorithm

15. Dijkstra’s Algorithm

16. Dijkstra’s Algorithm

17. Dijkstra’s Algorithm

18. Dijkstra’s Algorithm

19. Dijkstra’s Algorithm

20. Dijkstra’s Algorithm

21. Dijkstra’s Algorithm

22. Bellman-Ford Algorithm • Another algorithm to find shortest-distance from one source node • Can handle negative weight in the graph • Time complexity is O(|V|.|E|), where | V | and | E | are the number of vertices and edges respectively

23. Bellman-Ford Algorithm

24. Bellman-Ford Algorithm

25. Bellman-Ford Algorithm

26. Greedy Algorithm to predict pathway-consistent edges • Selects k edges to add iteratively in each step that maximally reduces the cost function • # of non-existent edges are n(n-1) – m, where n and m are # of nodes and directed edges • Require recalculation of the shortest path length to each source to each target just to add a 1 edge

27. Greedy Algorithm to predict pathway-consistent edges (cont’d) • Trick is to pre-compute the shortest-path distance from every source to every other node, and from every node to every target • Then, check following condition: dprev(s,u) + d(u,v) + dprev(v,t) < dprev(s,t)

28. Greedy Algorithm to predict pathway-consistent edges (cont’d)

29. Complexity Improved from O(n2)O(|E|+|V|log|V|) for each step to O(n2)O(1) + (O(|E|+|V|log|V|) for each step

30. Hop-Restricted Greedy Algorithm • Used modified version of Bellman-ford algorithm that calculate shortest path using atmost r edges • r is generally 5 edges between a target and its closet source • Time complexity is O(n2)O(1) + O(r|E|) for each step

31. Hop-Restricted Greedy Algorithm (cont’d)

32. Other Algorithms to predict missing interaction • Direct-ST • predicts direct edges from sources to targets • reduces cost function maximally • Betweenness • Predict highly “central” to the sources and targets • Number of all-pair shortest paths that use the edge is “betweenness centrality” • Consider only source-target pairs

33. Other Algorithms to predict missing interaction (cont’d) • Jaccard • Add an edge between the two proteins with the highest weighted Jaccard coefficient J(u,v) =

34. Results (Criteria for evaluation) • Ability to reduce the cost function • Ability to predict edges that lie within the STRING potential edges • Ability to predict edges that lie within the STRING potential edges and HOG-related nodes

35. Results (Source-Target Distances)

36. Results (Prediction accuracy)

37. Summary • A new framework for predicting missing edges that lie “in-between” given sets of sources and targets • Greedy Algorithm substantially reduced source-target distance between by adding only few edges • Shortcut edges formed alternate path for signal flow which provides greater degree of robustness in the pathway

38. Summary • For Shortcuts, adding 3 edges reduced distance for 27 out of 55 • Similarly, for Shortcuts-X, adding 3 edges reduced distance for 18 pairs • Hop-restricted objectives tend to select central nodes through with much signal flows

39. Future Applications • Reducing routing lags or increasing information flow between entities in a network • This pathway-specific context can be applied to other species with such data

40. Thank you