Preservation of protein-protein interaction networks Simple simulated example

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1 Preservation of protein-protein interaction networks Simple simulated example Peter Langfelder and Steve Horvath May, 0 Contents Overview.a Setting up the R session Calculation of module preservation Analysis of module preservation statistics A Simulation of PPI networks Overview This document contains a simple illustration of the use of the function modulepreservation [] to study the preservation of complexes in protein-protein interaction (PPI) networks. We simulate two PPI networks. Each network contains complexes with sizes between and 0 proteins. Five of the complexes, labeled, are preserved between the two networks, while the other five complexes (labeled -) are not preserved. We encourage readers unfamiliar with any of the functions used in this tutorial to type, in an active R session, help(functionname) (replace functionname with the actual name of the function) to get a detailed description of what the functions does, what the input arguments mean, and what is the output..a Setting up the R session After starting R we execute a few commands to set the working directory and load the requisite packages: # Display the current working directory getwd(); # If necessary, change the path below to the directory where the data files are stored. # "." means current directory. On Windows use a forward slash / instead of the usual \. workingdir = "."; setwd(workingdir); # Load the package library(wgcna); # The following setting is important, do not omit. options(stringsasfactors = FALSE);

2 Calculation of module preservation We use simulated PPI networks that are generated using code provided in Appendix A. For simplicity, we simply load the networks saved there. load(file = "simulatedppinetworks.rdata"); The above command loads two object, PPInetwork and PPInetwork. Each of them is a list with two components: the component adjacency contains the network adjacency matrix, and the component labels contains the module (or protein complex) labels. The modules are labeled by numbers. Proteins that are not part of any complex carry the label 0. To get a basic idea of how big the network is, we can use dim(ppinetwork$adjacency) which will tell us that the network contains 0 proteins. Also note that the columns of the adjacency matrix must carry protein names. In our example we named the simulated proteins simply "Protein." "Protein.0": colnames(ppinetwork$adjacency) Column names for the adjacency matrices are important because they allow the module preservation function to match proteins between reference and test networks even though here we use the same proteins in the same order, in practice this may not be the case. We next create multi-adjacency and module multi-labels. These variables are lists with one component per data set. In this example we study two data sets, a reference set () and a test set (). Note that the components of the list must be named. The names are used as identifiers for the data set. multiadj = list( network = list(data = PPInetwork$adjacency), network = list(data = PPInetwork$adjacency)); multilabels = list(network = PPInetwork$labels); We now call the modulepreservation function to calculate network module preservation statistics. This calculation may take up to a few hours, depending on the available computational speed. mp = modulepreservation(multiadj, multilabels, dataisexpr = FALSE, referencenetworks =, restrictsummaryforgeneralnetworks = FALSE, npermutations = 0, calculatecor.kimall = FALSE, verbose = ); # Save the results save(mp, file = "mp.rdata"); We saved the results so the calculation only need to be run once. The results can be re-loaded using the following command: load(file = "mp.rdata"); Analysis of module preservation statistics We now isolate the medianrank and the Z statistics and plot them as a function of module size. stats = cbind(medianrank = mp$preservation$observed[[]][[]]$medianrank.pres[-c(,)], mp$preservation$z[[]][[]][-c(,), -]); modulesizes = mp$preservation$z[[]][[]][-c(,), ]; # Order rows by module label order = order(as.numeric(rownames(stats))) stats = stats[order, ] modulesizes = modulesizes[order] labels = as.numeric(rownames(stats)) # Indicate preserved modules by red color and non-preserved by black color preserved = c(:);

3 presind = match(preserved, labels); prescolor = rep(, length(labels)); prescolor[presind] = ; # Open a suitably sized graphics window or, alternatively, open a pdf file to hold the plot sizegrwindow(,); #pdf(file=spaste("plots/ppisimulation-halfpreserved"), wi=, he=) # Set sectioning and margins par(mfrow = c(,)) par(mar = c(.,.,, 0.)) par(mgp = c(.0, 0., 0)) # Plot the individual statistics for (s in :ncol(stats)) min = min(stats[, s], na.rm = TRUE); max = max(stats[, s], na.rm = TRUE); if (s > ) if (min > -max/) min = -max/; else tmp = min; min = max; max = tmp; plot(modulesizes, stats[, s], main = colnames(stats)[s], ylab = colnames(stats)[s], type = "n", xlab = "", cex.main =, ylim = c(min, max)) text(modulesizes, stats[, s], labels = labels, col = prescolor); box = par("usr"); if (s==) legend(x = box[], y = (max+min)/, xjust =, yjust = 0., legend = c("preserved", "Non-preserved"), fill = c(,), cex = 0.) if (s>) abline(h=0) abline(h=, col = "blue", lty = ); abline(h=, col = "darkgreen", lty = ); # If plotting into a file, close it. dev.off(); The resulting plot is shown in Figure. We note that in this example the composite statistics medianrank and Z summary work best at separating the preserved and non-preserved modules. While medianrank appears largely independent of module size, the Z statistics for preserved modules show a marked dependence on module size. This agrees with the intuition that it is more significant to observe a preservation of a pattern among 0 proteins than among proteins.

4 medianrank Z.propVarExplained Z.cor.kIM 0 0 medianrank Preserved Non preserved Z.propVarExplained Z.cor.kIM Zsummary Z.meanKIM Z.cor.kME Zsummary Z.meanKIM Z.cor.kME Zdensity Z.meanAdj Z.cor.adj Zdensity Z.meanAdj Z.cor.adj Zconnectivity Z.meanClusterCoeff Z.cor.clusterCoeff Zconnectivity Z.meanClusterCoeff Z.cor.clusterCoeff Figure : Module preservation statistics of simulated modules in this study. Each plot shows one of the preservation statistics (indicated in the title) as a function of the module size. Modules are labeled by their numeric labels; red color denotes preserved and black non-preserved modules. The blue and green dashed lines denote the thresholds Z = and Z =. The statistics medianrank and Z summary do the best job of distinguishing the preserved and non-preserved modules in this study.

5 A Simulation of PPI networks Here we generate the reference and test networks used in this tutorial. We start by defining two functions, one for simulating a protein complex (a group of densely interconnected proteins), and for simulating a network consisting of several complexes. simulatecomplex = function(nproteins, minscaledk, maxscaledk) k = seq(from = maxscaledk, to=minscaledk, length.out = nproteins) * nproteins; K = sum(k); adjacency = matrix(, nproteins, nproteins); pmat = matrix(na, nproteins, nproteins) for (i in :(nproteins-)) for (j in (i+):nproteins) p = k[i]*k[j] / (K - (k[i] + k[j])/); if (p >) p = ; pmat[i,j] = pmat[j,i] = p; adjacency[i,j] = adjacency[j,i] = sample(c(0,), size =, prob = c(-p, p)) adjacency; simulateproteinnetwork = function( complexsizes, nsigletons, minscaledk = 0., maxscaledk = 0., propmissinglinks = 0, propintercomplexlinks = 0) nproteins = sum(complexsizes) + nsingletons; adjacency = matrix(0, nproteins, nproteins); diag(adjacency) = ; labels = rep(0, nproteins); starts = c(, cumsum(complexsizes)+); ends = c(cumsum(complexsizes), nproteins); for (c in :ncomplexes) st = starts[c]; en = ends[c]; adj.complex = simulatecomplex(complexsizes[c], minscaledk, maxscaledk); adj.dst = as.dist(adj.complex); leaveout = sample(c(false, TRUE), size = length(adj.dst), prob = c(-propmissinglinks, propmissinglinks), replace = TRUE); adj.dst[leaveout] = 0; adj.complex = as.matrix(adj.dst); diag(adj.complex) = ; adjacency[st:en, st:en] = adj.complex; labels[st:en] = c; for (c in :(ncomplexes+)) if (c <= ncomplexes) cx = c + else

6 cx = c; for (c in cx:(ncomplexes + )) st = starts[c]; en = ends[c]; st = starts[c]; en = ends[c]; n = en - st + ; n = en - st + ; interadj = sample(c(0, ), size = n*n, prob = c(-propintercomplexlinks, propintercomplexlinks), replace = TRUE); dim(interadj) = c(n, n); if (c==c) interadj = as.matrix(as.dist(interadj)); diag(interadj) = ; adjacency[st:en, st:en] = interadj; adjacency[st:en, st:en] = t(interadj); colnames(adjacency) = spaste("protein.", c(:nproteins)); rownames(adjacency) = spaste("protein.", c(:nproteins)); list(adjacency = adjacency, labels = labels); We next define basic paramaters of the simulation. ncomplexes = ; npreserved = ; preserved = c(:npreserved) nnonpreserved = ncomplexes - npreserved; nonpreserved = c(:ncomplexes)[-preserved]; complexsizes = seq(from = 0, to =, length.out = npreserved); complexsizes = rep(complexsizes, ); nsingletons = 0; We call the simulation function twice, to generate two separate networks with the same complex structure, but details of the connections within complexes differ a bit. For simplicity we do not simulate any connections between proteins in different complexes although the above functions support it. set.seed(); PPInetwork = simulateproteinnetwork(complexsizes, nsingletons); PPInetwork = simulateproteinnetwork(complexsizes, nsingletons); The networks can be visualized, for example, using the heatmap function: sizegrwindow(,); #pdf(file = "Plots/networkImage.pdf", wi=, he=); image(ppinetwork$adjacency, xaxt = "none", yaxt = "none") dev.off(); The plot is shown in Figure. The network image verifies that we have simulated complexes of different sizes. We now permute the proteins in the non-preserved complexes in the test data set. starts = c(, cumsum(complexsizes)+); ends = cumsum(complexsizes); scramble = starts[ min(nonpreserved)]:ends[max(nonpreserved)]; neworder = sample(scramble); PPInetwork$adjacency[scramble, scramble] = PPInetwork$adjacency[newOrder, neworder];

7 Figure : Image of the simulated reference PPI network. Each row and column represents one protein; red color means not connected and white color means connected. Squares along the diagonal with dense connections correspond to simulated complexes. PPInetwork$labels[scramble] = PPInetwork$labels[newOrder]; Lastly, we save the networks for future use. save(ppinetwork, PPInetwork, file = "simulatedppinetworks.rdata"); The resulting file is used as input at the start of this tutorial.

8 References [] Peter Langfelder, Rui Luo, Michael C. Oldham, and Steve Horvath. Is my network module preserved and reproducible? PLoS Comput Biol, ():e0, 0 0.