Improving evolutionary models of protein interaction networks.

Motivation: Theoretical models of biological networks are valuable tools in evolutionary inference. Theoretical models based on gene duplication and divergence provide biologically plausible evolutionary mechanics. Similarities found between empirical networks and their theoretically generated counterpart are considered evidence of the role modeled mechanics play in biological evolution. However, the method by which these models are parameterized can lead to questions about the validity of the inferences. Selecting parameter values in order to produce a particular topological value obfuscates the possibility that the model may produce a similar topology for a large range of parameter values. Alternately, a model may produce a large range of topologies, allowing (incorrect) parameter values to produce a valid topology from an otherwise flawed model. In order to lend biological credence to the modeled evolutionary mechanics, parameter values should be derived from the empirical data. Furthermore, recent work indicates that the timing and fate of gene duplications are critical to proper derivation of these parameters.

Results: We present a methodology for deriving evolutionary rates from empirical data that is used to parameterize duplication and divergence models of protein interaction network evolution. Our method avoids shortcomings of previous methods, which failed to consider the effect of subsequent duplications. From our parameter values, we find that concurrent and existing existing duplication and divergence models are insufficient for modeling protein interaction network evolution. We introduce a model enhancement based on heritable interaction sites on the surface of a protein and find that it more closely reflects the high clustering found in the empirical network.