Modeling and simulating networks of interdependent protein interactions

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/cpinsimandviaBioconda (https://bioconda.github.io).Author summaryProteins are the main molecular tools of cells. They do not act individually, but rather collectively in order to peform complex cellular actions. Recent years have led to a relatively good understanding about which proteins may interact, both in general and in specific conditions, leading to the definition of protein interaction networks. However, the reality is more complex, and protein interactions are not independent of each other. Instead, several potential interaction partners of a specific protein may compete for the same binding domain, making all of these interactions mutually exclusive. Additionally, a binding of a protein to another one can enable or prevent their interactions with other proteins, even if those interactions are mediated by different domains. Hence, understanding how the dependencies (or constraints) of protein interactions affect the behaviour of the system is an important and timely goal, as data is now becoming available. Here we present a mathematical framework to formalize such interaction constraints and incorporate them into the simulation of protein complex formation. With our framework, we are able to better understand how perturbations of single proteins (knockout or overexpression) impact other proteins in the network.