Network models are a fundamental tool for the visualization and analysis of molecular interactions occurring in biological systems. While broadly illuminating the molecular machinery of the cell, graphical representations of protein interaction networks mask complex patterns of interaction that depend on temporal, spatial, or condition-specific contexts. In this paper, we introduce a novel graph construct called a biological context network that explicitly captures these changing patterns of interaction from one biological context to another. We consider known gene ontology biological process and cellular component annotations as a proxy for context, and show that aggregating small process-specific protein interaction sub-networks leads to the emergence of observed scale-free properties. The biological context model also provides the basis for characterizing proteins in terms of several context-specific measures, including 'interactive promiscuity,' which identifies proteins whose interacting partners vary from one context to another. We show that such context-sensitive measures are significantly better predictors of knockout lethality than node degree, reaching better than 70% accuracy among the top scoring proteins.