Analysis Strategy of Protein–Protein Interaction Networks

Abstract

Protein interactions, as well as the networks they formed, play a key role in many cellular processes and the distortion of the protein interacting interfaces may lead to the development of many diseases. In this chapter, we will briefly introduce the background knowledge of the protein–protein interaction, followed by the detailed explanation of varied analysis—from basic to advanced, as well as related tools and databases. VisANT (http://visant.bu.edu)—a free Web-based software platform for the integrative visualization, mining, analysis, and modeling of the biological networks—will be used as a main tool for all examples used in this section.

Appendix

1.1 Mathematical Definition of Metagraph

A metagraph ${G_{\rm{m}}} = \{ V,E\}$ consists of a finite set V of the nodes and a finite set E of the edges. Nodes in a metagraph can be denoted as $V = \{ {V_{\rm{s}}},{V_{\rm{m}}}\}$ where ${V_{\rm{s}}}$ represents simple nodes as generally defined in simple graph and ${V_{\rm{m}}}$ represents the metanodes. The subscription s represents the simple node/edge and the subscription m represents metanode/metaedge. Each metanode ${v_{\rm{m}}} \in {V_{\rm{m}}}$ contains a subgraph consisting of child nodes and connected edges. In addition, each node $v \in V$ represents a set of its instance nodes, i.e., $v = \left\{ {{v_i}\left| {i > 0} \right.} \right\}$ where ${v_i}$ is the instance node of $v$. Instance nodes remains exact same identity between them but can have individual-specific properties. The statement that two metanodes share a node implies that each metanode contains an instance of the same node.

A metanode ${v_{\rm{m}}}$ has two states, expanded or contracted; the expanded state manifests the internal subgraph (that is, places all children nodes with their connections into the graph) while the contracted state replaces this subgraph with the single node. The combination of different states of the metanodes for a given metagraph results in multiple views that are abstract representations of the same underlying data. The change of the views for a given metagraph is defined as the dynamics of the metagraph, as shown in Fig. 1D, E.

Edges in a metagraph can be denoted as $E = \{ {E_{\rm{s}}},{E_{\rm{m}}}\}$where ${E_{\rm{s}}}$represents simple edges that are generally defined in the simple graph and ${E_{\rm{m}}}$ represents metaedges. Each metanode edge ${e_{\rm{m}}} \in {E_{\rm{m}}} = {e_{{{v_{\rm{m}}},v}}}$is associated with at least one contracted metanode ${v_{\rm{m}}}$and is transient: it appears when the metanode is contracted and disappears when one or two connected metanode nodes expanded, i.e., the metaedge is derived from the properties of two connected nodes. The most common derivation of the metaedge is the connection transfer. For example, when metanodes M1 and M2 are contracted in Fig. 1E, the connection between C and E is transferred to M1 and M2. However, metaedge can also be derived from other properties of the metanode. The metaedge shown in Fig. 1E is derived because two metanode M2 and M3 share the same node E. The derivation of the metaedge can be generalized as ${e_{{{v_{{{\rm{m}},v}}}}}} = g({v_{{{\rm{m}},}}}v)$, where g is the aggregation function and $v \in V$ can either be a metanode node or a simple node.

1.2 Download and Run VisANT as a Local Application

VisANT has four running modes in total, and two of them require a local copy of VisANT. Please visit http://visant.bu.edu and click the link “Run VisANT” for detailed instruction of other modes. It is recommended to run VisANT as a local application when handling large-scale network, such as the network with more than 100,000 nodes and edges because you will have the option to specify the memory size that VisANT can use. In addition, a local application allows VisANT to access local resources, such as load/save network files, directly; it also allows the user to develop VisANT plugins, as well as run a list of batch commands in the background without any user interface (batch mode).

The only drawback to run VisANT as a local application is that it easily becomes out of date because VisANT is under active development. Fortunately, VisANT provides a function to checks the update automatically and an icon will be shown near the Help menu if the update is available. Users can either click the icon, or corresponding menu to upgrade the VisANT to the latest version, as shown below:

• 1. If not already installed, download and install the Java 2 Platform, Standard Edition, version 1.4 or higher (http://java.sun.com/javase/downloads/index.jsp).

• 2. Go to http://visant.bu.edu and click on the link “Download,” then click the link “Latest Version of VisANT.”

• 3. Select a directory to save the file “VisAnt.jar”

  The VisAnt.jar is only about 400 K in size and the download shall take less than 1 min to finish. No installation is needed to run the VisANT.

• 4. To launch VisANT, double-clicking VisAnt.jar

• 5. To launch VisANT by an alternative mean: Open a Dos window in Win OS, or a shell window in other operation systems, and go to the directory where VisAnt.jar locates, and run the command:

  java -Xmx512M -classpath VisAnt.jar cagt.bu.visant.VisAntApplet

  where 512 M indicates the maximum size of the memory that VisANT can use. Increase this number if you have a large network or you get the “run out of memory” error.

• 6. The VisANT main window will appear (Fig. 4).

• 7. To exit VisANT, close the VisANT main window, or use the File → Exit menu option, or press the key combination ALT + X.

1.3 GO Term Enrichment Analysis

The four steps here describe how GOTEA works in VisANT. For illustration purposes, the following steps take only one metanode, G, into account and calculate only the enrichment score of one target GO term, T.

Step 1: Fully annotate all of the nodes in G with gene names and GO terms.

Step 2: Calculate density scores for each node based upon the topology and the GO term similarity to T. A vector D ^G of density scores of each gene in G is computed, with the element of D ^G for the ith gene denoted D _i . The density score is used to evaluate the impact of other genes in G on the ith gene, according to both the GO term similarity and the topological distance to the ith gene. D _i is defined as:

$$ {D_i} = \sum\limits_{{j \in G}} {{{\log }_2}\left[ {\left( {\frac{{{M_j}}}{\alpha }} \right)\Theta ({M_j} - \alpha ) + \Theta (\alpha - {M_j})} \right]} {{\text{e}}^{{ - \beta {d_{{ij}}}}}}, $$

where the step function,

$$ \Theta (x - y) = \left\{ {\begin{array}{ll} 1 \hfill & {x \geqslant y} \hfill \\0 \hfill & {x < y,} \hfill \\\end{array} } \right. $$

ensures that D _i  ≥ 0. M _j is a measure of the GO term similarity calculated based upon the graph structure of the GO term hierarchy [85]. A significance threshold, α, is used to control the contribution that gene j makes to D _i . For larger α, a greater number of less statistically significant (with M _j  < α) genes are filtered and they do not contribute to D _i . The shortest distance between genes i and j given the topology of G is denoted d _ij and was calculated with the Floyd–Warshall algorithm. We assume that shorter distances make an exponentially greater contribution to the density than do longer distances, with the steepness of the exponential determined by the parameter $\tilde{\beta }$When a bigger β is chosen, more distant genes can contribute to the density. Taken together, the parameters α and β are used to control the sensitivity and selectivity of the density.

Step 3: Another vector of density scores, D ^NG, is computed based upon a randomly chosen subset of genes representative of the background distribution. The background consists of all genes annotated by NCBI.

Step 4: Statistical significance for rejecting the null hypothesis is determined by a permutation test. For statistical robustness, step 3 is repeated n times. The number of times the average density score of randomly chosen genes is found to be larger than the average density score of genes in G is counted after n iterations and used to compute the final p-value (Fig. 23).

Fig. 23.

VisANT upgrade.

These four steps can be carried out for multiple testing by using multiple metanodes and multiple targeting GO terms. In this case, the p-values are corrected using FDR methods (79). Specifically,${\text{\ FDR}} = p \times {{m} \left/ {k} \right.}$, where m is the total number of GO terms tested and k is the rank of the GO terms under consideration. There is also an option for GOTEA to identify representative GO terms from all its discoveries based upon approaches that identify the most informative GO term (84).

1.4 Network Module Enrichment Analysis

NMEA is implemented in a manner similar to GOTEA. Where GOTEA used GO term similarities, NMEA uses p-values from T-tests on the expression values of two phenotypes.

Step 1: Fetch the expression profile of each gene in a given module (i.e., metanode, denoted M in the following context) from formatted user input. The input should include an adequate number of samples with comparable phenotypes (e.g., normal and disease).

Step 2: A vector D ^M of density scores of each gene is computed, with the element of D ^M for the ith gene denoted as D _i . D _i is defined as:

$$ {D_i} = \sum\limits_{{j \in G}} {{{\log }_2}\left[ {\left( {\frac{\alpha }{{{M_j}}}} \right)\Theta (\alpha - {M_j}) + \Theta ({M_j} - \alpha )} \right]} {{\text{e}}^{{ - \beta {d_{{ij}}}}}}, $$

where the step function,

$$ \Theta (x - y) = \left\{ {\begin{array}{ll} 1 \hfill & {x \geqslant y} \hfill \\0 \hfill & {x < y,} \hfill \\\end{array} } \right. $$

ensures that D _i  ≥ 0. M _j is the p-value from a two-tailed t-test of differential expression between two phenotypes (for example, normal and disease). The parameters α and β are used to control the sensitivity and selectivity of the density as described in the previous section.

The density score is used to evaluate the impact of other genes in M on the ith gene, according to both the p-value calculated by T-test (an indicator of differential expression) and their topological distances to the ith gene.

Step 3: Another vector of density scores, D ^NM, is computed by randomly shuffling the phenotypes to obtain a representative sampling of the background distribution.

Step 4: Statistical significance for rejecting the null hypothesis is determined by a permutation test. For statistical robustness, step 3 is repeated n times. The number of times the average density score of randomly chosen genes is found to be larger than the average density score of genes in M is counted after n iterations and used to compute the final p-value.

When applying NMEA to multiple metanodes, the p-value must be corrected by FDR in a manner similar to what was described above for GOTEA. In this case, ${\text{FDR}} = p \times {{m} \left/ {k} \right.}$ as before, but m is the total number of metanodes and k is the rank of the metanodes under consideration.