Protein interaction networks in plants

Abstract

Protein–protein interactions are fundamental to virtually every aspect of cellular functions. With the development of high-throughput technologies of both the yeast two-hybrid system and tandem mass spectrometry, genome-wide protein-linkage mapping has become a major objective in post-genomic research. While at least partial “interactome” networks of several model organisms are already available, in the plant field, progress in this respect is slow. However, even with comprehensive protein interaction data still missing, substantial recent advance in the graph-theoretical functional interpretation of complex network architectures might pave the way for novel approaches in plant research. This article reviews current progress and discussions in network biology. Emphasis is put on the question of what can be learned about protein functions and cellular processes by studying the topology of complex protein interaction networks and the evolutionary mechanisms underlying their development. Particularly the intermediate and local levels of network organization—the modules, motifs and cliques—are increasingly recognized as the operational units of biological functions. As demonstrated by some recent results from systematic analyses of plant protein families, protein interaction networks promise to be a valuable tool for a molecular understanding of functional specificities and for identifying novel regulatory components and pathways.

Appendix Biological networks and graph theory: some basics

Biological networks are graphical visualizations of elements such as proteins or genes, depicted in the graph as nodes or vertices, connected to each other by links or edges representing their functional interactions. The most basic characteristic of a node in a network is its degree k, which is defined as the number of links it has to other nodes. In protein interaction networks, links usually are undirected. In other complex networks, like for example gene regulatory networks, links can be directional; here the degree of a node is divided into incoming degree, comprising the links that point towards that node, and outgoing degree, denoting links pointing away from it. An elementary measure to characterize a network’s topology is the degree distribution P(k), obtained by counting the number of nodes having the same degree N(k) divided by the total number of nodes (N). P(k) gives the probability of a node having exactly the degree k. The degree distribution can be used to classify networks. A Poisson distribution, for example, is indicative of random networks. An intriguing finding of recent years is that in very different “real” complex networks like the Internet, co-authorships, the road map of the USA and a number of biological networks, the degree distribution follows a power law (P(k)∼k ^−γ). Here the degree distribution P(k) is proportional to k ^−γ with the degree exponent γ ranging between 2 and 3. This means that the large majority of nodes have only one or very few links, while a small but significant number of nodes, the so-called “hubs”, are connected to many other nodes. According to Barabasi and Albert (1999), this type of networks is called “scale-free”. Hubs play a crucial role in the large-scale organization of scale-free networks and contribute to their special properties like the remarkable robustness against random perturbations (Jeong et al. 2001; Han et al. 2004).

Another elementary feature used to describe and classify network architecture and the relative position of particular nodes in the network is the path length, which is defined as the number of steps that have to be taken to reach from one node to another. The shortest path and the mean path length, defined as the average over the shortest paths of every node to every other node, are of special interest and are measures of the diameter of a network. Scale-free networks have ultra-short mean path lengths and therefore have so-called “small-world” properties, a characteristic of random networks.

Analysis of biological and other complex networks revealed, in addition to the scale-free characteristic, a high degree of clustering which is not found in random networks but rather is an attribute of regular networks. In order to mathematically quantify clustering, Watts and Strogatz (1998) introduced a clustering coefficient C _i , defined as the number of links existing between the neighbours of a node i divided by the maximum number of links possible between these neighbours: C _i =2n _i /k(k−1), where n is the number of links connecting the k neighbours. A high clustering coefficient means that, if for example a node A is connected to B and C, there is a high probability that B has a direct link to C or, in other words, A, B and C form a triangle.

A high clustering coefficient or likewise a high density of triangles is indicative of a “community structure” or a modular organization, which is another general property of complex networks. Modules emerging from network representations are clusters of nodes highly interconnected amongst each other, while being only loosely connected to the rest of the network. In biological networks, functional annotation of these separable subgraphs supports the view that these structures reflect the modularity of cellular functions. The basic building blocks of such functional modules are small patterns termed network motifs that recur at frequencies significantly higher than those found in equivalent randomized networks. These motifs are simple geometrical figures like triangles, squares or pentagons with a certain degree of internal connections. Completely connected subgraphs/motifs, i.e. geometrical structures in which every node is linked to every other node, is called clique. Significant overrepresentation of certain motifs or cliques has been shown to be of functional relevance and might be used to functionally distinguish different types of networks.