The Topological Profile of a Model of Protein Network Evolution Can Direct Model Improvement

Biological networks are an attractive construct for studying evolution. One method for inferring evolutionary mechanics is to construct models which generate networks sharing topological characteristics with their empirical counterparts. It remains a challenge to assess, modify, and improve a model based on the topological values it generates. A large range of parameter values may produce a similar topology, and topological properties may vacillate in unexpected ways, frustrating attempts to determine whether the model is flawed or model parameter values are incorrect. We introduce a new method for evaluating the fidelity of an evolutionary network model with respect to topological characteristics by driving topological characteristics towards empirical values concurrently with network generation. From this we compute a topological profile which defines the ability of the network model to produce a desired topology. The topological profile also measures the volatility of characteristics, and the interrelationships among topological characteristics. Our method shows that a top-rated protein interaction network model cannot produce the empirical number of triangles. As triangle count is driven to the empirical value, additional characteristics are propelled towards empirical values. These findings suggest that new model mechanics that increase the number of triangles produced will best enhance the existing model. By providing systematic evaluation of the ability of model mechanics to produce desired topological properties, our framework can help to focus the search for biologically plausible and relevant processes important to network evolution.