Gökay Burak AKKUŞ 2003700717

1. Assessing Experimentally Derived Interactions in a Small WorldDebra S. Goldberg, Frederick P. RothHarvard Medical School Gökay Burak AKKUŞ 2003700717

2. Agenda • Experimentally determined networks • Small World networks • Watts & Strogatz model • Mutual Clustering Coefficients • Protein-protein interaction • Predictions without direct experimental evidence • Conclusions

3. Experimentally determined networks • “Experimentally derived networks are susceptible to errors” • True edges • False edges • From random graph • To regular lattice, • Small world Networks: By Watts & Strogatz

4. Small World Graphs • Three main attributes used to analyze Small World Graphs : • Average Vertex Degree (k) (Avg. of No. of Edges Incident on ‘v’ over all ‘v’) • Average Characteristic Path Length (L) (Shortest Dist. B/w 2 points Avg. over all connected pairs) • Average Clustering Coefficient (C) (Prob. Of 2 nodes with a “mutual” friend being connected)

5. Work of Watt and Strogatz • Asks why we see the small world pattern and what implications it has for the dynamical properties of social networks. • Their contribution is to show that the globally significant changes can result from locally insignificant network change.

6. Watts -Strogatz (WS) Model (1998)

7. Cohesive neighborhoods

8. Mutual Clustering Coefficients • Cohesiveness or “cliquishness” of a graph • Originally, neighborhood cohesiveness around each vertex • In the paper, the neighborhood cohesiveness around individual edges

9. Cvw • Cvw (mutual clustering coefficent) • For a pair of vertices v, w... • This coefficient is independent of the existence of an edge between v and w. • So, direct experimental evidence does not influence the assesment of neighborhood. • This measure is applied on edges, and on any pair of vertices.

10. Cvw • Used for hypothesis about missing edges • 4 alternative definitions of Cvw are considered. • N(x) represents the neighborhood of a vertex x. • Total represents the total number of proteins in the organism.

11. Cvw

12. P value • The cumulative hypergeometric distribution is frequently used to measure • Cluster enrichment • Significance of co-occurence • The summation in the formula can be intrepreted as p value: • Tye probability of obtaining a number of mutual neighbors between vertices v and w, at or above the observed number by chance

13. Protein-Protein interaction data • High-throughput, error-prone Y2H data • From CuraGen’s PathCallingYeast Interaction database • http://portal.curagen.com • For validation a more reliable conventional evidence used from PathCalling database. • Also Incyte Genomics’ Yeast Proteome Database is used for validation • http://www.incyte.com/proteome

15. Cvw and validity

16. Ranking by Cvw

17. P+ • Compute the probability of an interaction being true, given the experimental evidence (Y2H) and local network topology (Cvw) • Estimate the probability that there is a high confidence evidence that the two proteins interact • It is likely an under-estimate

18. P+ • This score can be computed by Bayes’ rule

19. Predictions

20. Pairs of proteins with high P+ score and no direct supporting evidence representr predicted interactions.

21. Conclusion • Data containing errors • Local topology gives clues about confidence in networks • This approach is used to predict protein function • Can be generalized for other small world networks... • For finding the missing parts, or confidence levels..

22. Thanx... • Questions ????