Robust Determination of Protein Allosteric Signaling Pathways

Abstract

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.

Investigating Protein-Protein Allosteric Network using Current-Flow Scheme

“…Changes in edge usage appear much more consistent than changes in node usage when comparing all three gain-of-function mutants vs. wild type. This observation is in agreement with our previous statement that the edge usage is a more reliable metric than the node usage for comparing changes or perturbations in allosteric network topology 11 .…”

“…Next, current-flow betweenness for the FKBP12-R375 network was computed using the same protocol as previously described 11 . Briefly, to compute current-flow betweenness, one must first construct the associated adjacency and Laplacian matrices.…”

“…Same as in graph theory, a protein network topology is usually defined by a set of nodes, representing certain atoms in amino acids or centers of mass of amino acid side chains, and a set of edges connecting the nodes. Various edges weighting schemes have been previously discussed 11 . To assess the importance of a given node or edge with respect to signal propagation within a protein or between proteins, a common approach is to make use of betweenness centrality, also known as geodesic centrality, which measures the number of shortest paths that crosses a given node or utilizes a given edge in the studied network.…”

“…This method is more appropriate and more robust when only the transmission between a pair of residues or domains is of interest. Using a classic example of an allosteric enzyme imidazole glycerol phosphate synthase (IGPS), we calculated the current-flow betweenness network between an allosteric effector binding site and a remote catalytic site 2 0 A apart and demonstrated a significant improvement in the convergence of the allosteric network topology between independent replicas of simulations 11 .…”

“…In current study, we seek to expand the current-flow betweenness approach to a broader range of allosteric regulations involving protein-protein binding. Different from our previous studies 10,11 , which used a single pair of amino acids as the source and sink for current-flow betweenness calculation, here we report the usage of the current-flow scheme to multiple source/sink pairs in order to study the network change from protein-protein binding interface to the kinase catalytic site. More specifically, we conducted MD simulations of the FKBP12-ALK2 WT protein complex, and three gain-of-function mutants at ALK2-FKBP12 binding interface.…”