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Assessing Experimentally Derived Interactions in a Small World Debra S. Goldberg, Frederick P. Roth Harvard Medical School. Gökay Burak AKKUŞ 2003700717. Agenda. Experimentally determined networks Small World networks Watts & Strogatz model Mutual Clustering Coefficients - PowerPoint PPT Presentation
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Assessing Experimentally Derived Interactions in a Small World
Debra S. Goldberg, Frederick P. RothHarvard Medical School
Gökay Burak AKKUŞ2003700717
Agenda Experimentally determined networks Small World networks Watts & Strogatz model Mutual Clustering Coefficients Protein-protein interaction Predictions without direct experimental
evidence Conclusions
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
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)
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.
Watts -Strogatz (WS) Model (1998)
Cohesive neighborhoods
Mutual Clustering Coefficients Cohesiveness or “cliquishness” of a graph Originally, neighborhood cohesiveness around
each vertex In the paper, the neighborhood cohesiveness
around individual edges
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.
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.
Cvw
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
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
Cvw and validity
Ranking by Cvw
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
P+ This score can be computed by Bayes’ rule
Predictions
Pairs of proteins with high P+ score and no direct supporting evidence representr predicted interactions.
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..
Thanx...
Questions ????