Robust Determination of Protein Allosteric Signaling Pathways

To understand how protein function changes upon an allosteric perturbation, such as ligand binding and mutation, significant progress in characterizing allosteric network from molecular dynamics (MD) simulations has been made. However, determining which amino acid(s) play an essential role in the propagation of signals may prove challenging, even when the location of the source and sink is known for a protein or protein complex. This challenge is mainly due to the large fluctuations in protein dynamics that cause instability of the network topology within a single trajectory or between multiple replicas. To solve this problem, we introduce the current-flow betweenness scheme, originated from electrical network theory, to protein dynamical network analysis. To demonstrate the benefit of this new method, we chose a prototypic allosteric enzyme (IGPS or HisH-HisF dimer) as our benchmark system. Using multiple replicas of simulations and multiple network topology comparison metrics (edge ranking, path length, and node frequency), we show that the current-flow betweenness provides a significant improvement in the convergence of the allosteric networks. The improved stability of the network topology allows us to generate a delta-network between the apo and holo forms of the protein. We illustrated that the delta-network is a more rigorous way to capture the subtle changes in the networks that would otherwise be neglected by comparing node usage frequencies alone. We have also investigated the use of a linear smoothing function to improve the stability of the contact map. The methodology presented here is general and may be applied to other topology and weighting schemes. We thus conclude that, for determining protein signaling pathways between the pair(s) of source and sink, multiple MD simulation replicas are necessary, and the current-flow betweenness scheme introduced here provides a more robust approach than the geodesic scheme based on correlation edge weighting.