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 ????