Growth rate reduction

Figure 2. A weak but significant correlation between protein degree and gene knockout effect. Information on protein degrees shown here was obtained by pooling data from three independent sources, two large-scale protein interaction studies,38'42 and a public data base of protein interactions39 from which all interactions generated with the yeast two-hybrid assay had been eliminated. The horizontal axis shows the difference in the growth rate of a gene knock-out strain between the growth medium (among five different media) in which the strain grew at the highest rate, and the medium in which it grew at the lowest rate, as reported by Steinmetz and collaborators.28 Growth rates are measured relative to a large pool of yeast gene deletion strains.28 For most genes, the growth rate difference is an indicator of the largest gene knockout effect among the tested growth media. An analogous analysis using the growth rate change of a gene knockout mutation in only rich medium (YPD) yields the same results (not shown).

the network as a whole? The answer is yes.34 Such an explanation may still involve natural selection, but on a local instead of a global scale. For example, whenever a mutation causes a new interaction between two proteins to occur, natural selection may determine whether this interaction becomes fixed in a population or eliminated from it, depending on whether the interaction is beneficial, neutral, or deleterious. However, this is selection acting on individual interactions rather than global properties of an entire network.

In a previous contribution, I have proposed an explanation of the protein interaction networks degree distribution from purely local processes such as gene duplications and mutations that generate new interactions and cause others to disappear.34 The rate at which some of these processes occur can be roughly estimated from available protein interaction data, and based on these estimates, one can establish a quantitative mathematical model that explains the networks structure. This explanation falls within a class of models for network evolution that involve preferential attachment, that is, highly connected proteins are more likely to evolve new interactions than other proteins. Empirical data supports the notion that preferential attachment occurs in protein interaction networks, as shown in Figure 3. Others have also proposed models of protein network evolution,35 models that differ in important details but that have one key commonality: They do not require natural selection on a global network feature,


Figure 3. Preferential attachment in protein interaction networks. The horizontal axis shows protein degree d. The vertical axis shows the likelihood Pj that a protein of degree ┬┐evolves new interactions. This likelihood can be estimated from the number of newly evolved interactions between products of paralogous genes, as detailed in reference 34. For all member genes of a paralogous gene pair with a newly evolved interaction since their duplication, I determined the number Ij of those genes whose encoded proteins had d interactions to proteins different from its paralogue. To account for the fart that proteins of different degree occur at different frequencies in the network, I then divided this number by the relative frequency^ of proteins of degree d in the network, and normalized the resulting quantity to obtain Pj, i.e., P4 - (Ij/fjS)/Zd(IJfj). There is a strong, approximately linear association between protein degree and the likelihood to evolve new interactions. From Figure 5 in reference 34.

but they explain the network's structure from evolutionary events on the small, local scale of individual proteins.

Many models of network evolution based on preferential attachment predict that highly connected network nodes should be old nodes, nodes that were added very early in a networks history.36 They should have arisen early in the evolution of the network. Because the protein interaction network shows preferential attachment (Fig. 3), the question arises whether such an association between protein age and connectivity exists. Specifically, one can ask whether highly connected proteins are phylogenetically old. Phylogenetically old proteins should have a wider taxonomic distribution than more recendy arisen proteins. In two complementary analyses, I thus asked whether highly connected proteins have a wider phylogenetic distribution than less highly connected proteins.

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