8/6/2019 Specificity and Stability in Topology of Protein Networks(1)

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Specificity and stability in topology of protein networks

Sergei Maslov and Kim Sneppen

This paper analyzes the topological properties of interaction as well as transcriptionregulatory networks in yeast Saccharomyces cerevisiae, the interaction network consisting of 4549

physical interactions between 3278 yeast proteins as measured in two-hybrid screen of yeast

proteins, while the genetic regulatory network is formed by 1289 directed positive or negative direct

transcriptional regulations within a set of 682 proteins as listed in the YPD database. The number of

nodes with a given number of neighbors (connectivity) K scales as a power law in a protein

interaction network i.e. K 1/K^ ; where = 2.5 0.3 for K ranging from 2 to 100 in the resultant

histogram. The interaction between nuclear proteins was visualized and the graph obtained showed

the abundance of highly connected proteins that are mostly connected to those with low

connectivity, and thus well separated from each other. The correlations in connectivities of nodes

for each of the two networks is tested by calculating the likelihood P (K0 , K1 ) that two proteins

with connectivities K0 and K1 are connected to each other by a link and compared it to the samequantity Pr (K0 , K1 ) measured in a randomized version (null model) of the same network where

there is random choice of interaction parteners.

The transcription regulatory network is naturally directed, while the interaction network

among proteins is undirected. Randomized versions of these two networks were constructed by

randomly reshuffling links using a convenient algorithm, keeping the in- and out-degree of each

node constant, eliminating the chance of including multiple edges connecting same pair nodes.The

average expectation and the standard deviation for any particular property of the random network is

calculated by multiple sampling.Correlations in connectivities is found to be systematic deviations

of the ratio P (K0, K1 )/Pr (K0 , K1 ) from 1 which is calculated for both the networks. The

combination of plots of P (K0, K1 ), and the statistical significance Z(K0 , K1 )reveals the regions

on the K0 K1 plane, where connections between proteins in the real network are significantly

enhanced or suppressed, compared to the null model depicting tendency of highly connected nodes

(hubs) to associate with nodes of low connectivity and the reduced likelihood that two hub centers

are directly linked to each other. An enhanced affinity of proteins with between 4 and 9 interaction

partners to physically interact with each other is also seen which is attributed to the tendency of

members of multiprotein complexes to interact with other proteins from the same complex.

The correlation patterns in both networks when quantifed and compared with the average

connectivity K1 of nearest neighbors of a node, as a function of its own connectivity K0 shows a

gradual decline with K0 , fitted with 0.60.1 a power law K1 1/K0 .. This observation gives an

additional credit to the affinity between correlation patterns in these two protein networks similar to

the Internet, an another scale -free network. In short, molecular networks in a living cell have

organized themselves in an interaction pattern that is both robust and specific. Topologically the

specificity of different functional modules can be enhanced by limiting interactions between hubs

and suppressing the average connectivity of their neighbor.