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Licensed Unlicensed Requires Authentication Published by De Gruyter July 30, 2015

Node sampling for protein complex estimation in bait-prey graphs

  • Denise M. Scholtens EMAIL logo and Bruce D. Spencer

Abstract

In cellular biology, node-and-edge graph or “network” data collection often uses bait-prey technologies such as co-immunoprecipitation (CoIP). Bait-prey technologies assay relationships or “interactions” between protein pairs, with CoIP specifically measuring protein complex co-membership. Analyses of CoIP data frequently focus on estimating protein complex membership. Due to budgetary and other constraints, exhaustive assay of the entire network using CoIP is not always possible. We describe a stratified sampling scheme to select baits for CoIP experiments when protein complex estimation is the main goal. Expanding upon the classic framework in which nodes represent proteins and edges represent pairwise interactions, we define generalized nodes as sets of adjacent nodes with identical adjacency outside the set and use these as strata from which to select the next set of baits. Strata are redefined at each round of sampling to incorporate accumulating data. This scheme maintains user-specified quality thresholds for protein complex estimates and, relative to simple random sampling, leads to a marked increase in the number of correctly estimated complexes at each round of sampling. The R package seqSample contains all source code and is available at http://vault.northwestern.edu/~dms877/Rpacks/.


Corresponding author: Denise M. Scholtens, PhD, Northwestern University Feinberg School of Medicine, Division of Biostatistics, Department of Preventive Medicine, 680 N. Lake Shore Drive Suite 1400, Chicago, IL 60611, USA, e-mail:

Appendix A

According to equation (3), if we choose a number of baits bh,SEQGNm+1 to be sampled from generalized node h in round m+1 such that

phmbh,SEQGNm+1bhm+phm(1f),

where bhm and phm are the number of baits and prey in h, respectively, then we know the following for any set ℐ of generalized nodes: phmbh,SEQGNmN(1f)×(bhm+phm)h(phmbh,SEQGNmN)(1f)h(bhm+phm)pmb,SEQGNmNbm+pm(1f)(pmb,SEQGNmN)2(bm+pm)2(1f)

where pm=hphm,bm=hbhm and b,SEQGNm+1=hbh,SEQGNm+1. And since

(pmb,SEQGNmN)(pmb,SEQGNmN1)(bm+pm)(bm+pm1)(pmb,SEQGNmN)2(bm+pm)2,

the desired bound in equation (4) from the manuscript is established.

Appendix B

Let [(Y+1)Cm] be a binary vector with entries of 1 indicating use as bait or adjacency to at least one bait, i.e. detection as prey, at some point during sampling up to and including sampling round m. Consider two nodes i and j that are members of the same generalized node h such that Xih=Xjh=1. By the definition of generalized node, Y·i+I·i=Y·j+I·j. Suppose Cim=1, but Cjm=0. Node j would be eligible for selection as bait in the next round of sampling; let the vector S*j indicate its potential selection with jth value equal to 1 and all other values equal to 0. Since

[(Y+I)(Cm+Sj)]=[(Y+I)Cm+Y.j+I.j]=[k:Ckm=1(Y.k+I.k)+Y.j+I.j]=[k:Ckm=1(Y.k+I.k)+Y.i+I.i]=[k:Ckm=1(Y.k+I.k)]=[(Y+I)Cm],

it follows that selection of a bait from a generalized node for which another member has already been used as bait will not change the set of detected prey. New prey will only be incorporated into the assayed graph when baits are selected from previously unsampled generalized nodes.

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Published Online: 2015-7-30
Published in Print: 2015-8-1

©2015 by De Gruyter

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