Protein interactions are fundamental building blocks of biochemical reaction systems underlying cellular functions. The complexity and functionality of these systems emerge not only from the protein interactions themselves but also from the dependencies between these interactions, e.g., allosteric effects, mutual exclusion or steric hindrance. Therefore, formal models for integrating and using information about such dependencies are of high interest. We present an approach for endowing protein networks with interaction dependencies using propositional logic, thereby obtaining constrained protein interaction networks ("constrained networks"). The construction of these networks is based on public interaction databases and known as well as text-mined interaction dependencies. We present an efficient data structure and algorithm to simulate protein complex formation in constrained networks. The efficiency of the model allows a fast simulation and enables the analysis of many proteins in large networks. Therefore, we are able to simulate perturbation effects (knockout and overexpression of single or multiple proteins, changes of protein concentrations). We illustrate how our model can be used to analyze a partially constrained human adhesome network. Comparing complex formation under known dependencies against without dependencies, we find that interaction dependencies limit the resulting complex sizes. Further we demonstrate that our model enables us to investigate how the interplay of network topology and interaction dependencies influences the propagation of perturbation effects. Our simulation software CPINSim (for Constrained Protein Interaction Network Simulator) is available under the MIT license at http://github.com/BiancaStoecker/cpinsim and via Bioconda (https://bioconda.github.io).
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