Going the Distance for Protein Function Prediction: A New Distance Metric for Protein Interaction Networks

Abstract

In protein-protein interaction (PPI) networks, functional similarity is often inferred based on the function of directly interacting proteins, or more generally, some notion of interaction network proximity among proteins in a local neighborhood. Prior methods typically measure proximity as the shortest-path distance in the network, but this has only a limited ability to capture fine-grained neighborhood distinctions, because most proteins are close to each other, and there are many ties in proximity. We introduce diffusion state distance (DSD), a new metric based on a graph diffusion property, designed to capture finer-grained distinctions in proximity for transfer of functional annotation in PPI networks. We present a tool that, when input a PPI network, will output the DSD distances between every pair of proteins. We show that replacing the shortest-path metric by DSD improves the performance of classical function prediction methods across the board.

RETRACTED ARTICLE: Detangling PPI networks to uncover functionally meaningful clusters

“…We showed in [8] for any fixed k , that DSD is a true distance metric, namely that it is symmetric, positive definite, and non-zero whenever u ≠ v , and it obeys the triangle inequality. Thus, one can use DSD to reason about distances in a network in a sound manner.…”

“…In 2013, Cao et al introduced a new distance measure called Diffusion State Distance, or DSD, designed to be a more fine-grained distance measure for protein-protein interaction networks [8]. In contrast to the typical shortest path metric, which measures distance between pairs of nodes by the number of hops on the shortest path that joins them in the network, DSD was shown to spread out the pairwise distances, making for a more fine-grained notion of graph local neighborhood.…”

New directions for diffusion-based network prediction of protein function: incorporating pathways with confidence

“…We set a global threshold D based on the average DSD of all pairs, specifically we set $D=\mu -c*\sigma$, where μ is the average, and σ is the standard deviation of the global set of DSD values among all pairs of nodes in the graph. As in (Cao et al , 2013), we set c = 1.5.…”

“…We first calculate He { k } ( A , B ) as the expected number of times that a random walk starting at node A and proceeding for k steps, will visit node B; then we further define a n -dimensional vector $H{e}^{\left\{k\right\}}(v_i),\forall v_i\in V$, where $H{e}^{\left\{k\right\}}(v_i)=(H{e}^{\left\{k\right\}}(v_i,v_1),H{e}^{\left\{k\right\}}(v_i,v_2),\mathrm{...},H{e}^{\left\{k\right\}}(v_i,v_n)).$ In what follows, the k -step DSD between two vertices u and $v,\forall u,v\in V$ is defined as ${\text{DSD}}^{\left\{k\right\}}(u,v)=||H{e}^{\left\{k\right\}}(u)-H{e}^{\left\{k\right\}}(v)|{false|}_1,$ where $||H{e}^{\left\{k\right\}}(u)-H{e}^{\left\{k\right\}}(v)|{false|}_1$ denotes the L 1 norm of the He vectors of u and v . As proved in (Cao et al , 2013), on the simple connected graph whose random walk one-step transition probability matrix is diagonalizable and ergodic as a Markov chain, the limit of DSD when k approaches infinity exists and can be calculated as $\underset{k\to \infty }{\lim }{\text{DSD}}^{\left\{k\right\}}(u,v)=||({\mathrm{bold-italicb}}_{\mathrm{bold-italicu}}{}^T-{\mathrm{bold-italicb}}_{\mathrm{bold-italicv}}{}^T){(I-P+C)}^{-1}|{false|}_1,$ where I is the identity ma...…”

Revealing protein functions based on relationships of interacting proteins and GO terms

“…In fact, it is commonplace in the PPI network that regulation relationship, upstreamdownstream relations between interacting proteins when they are involved in signal transduction, transcriptional regulation, cell cycle or metabolism [20]. Moreover, it is reported by recent studies [21][22][23] that GBA is the exception rather than the rule in the PPI network and protein functions are determined by specific and critical interactions. Hence the relationship between interacting proteins may affect their functions and should be considered in the process of predicting protein functions.…”