Gaussian Network Model Revisited: Effects of Mutation and Ligand Binding on Protein Behavior

The coarse-grained Gaussian Network model, GNM, considers only the alpha carbons of the folded protein. Therefore it is not directly applicable to the study of mutation or ligand binding problems where atomic detail is required. This shortcoming is improved by including the local effect of heavy atoms in the neighborhood of each alpha carbon into the Kirchoff Adjacency Matrix. The presence of other atoms in the coordination shell of each alpha carbon diminishes the magnitude of fluctuations of that alpha carbon. But more importantly, it changes the graph-like connectivity structure, i.e., the Kirchoff Adjacency Matrix of the whole system which introduces amino acid specific and position specific information into the classical coarse-grained GNM which was originally modelled in analogy with phantom network theory of rubber elasticity. With this modification, it is now possible to make predictions on the effects of mutation and ligand binding on residue fluctuations and their pair-correlations. We refer to the new model as all-atom GNM. Using examples from published data we show that the all-atom GNM applied to in silico mutated proteins and to their laboratory mutated structures gives similar results. Thus, loss and gain of correlations, which may be related to loss and gain of function, may be studied by using simple in silico mutations only.

Causality, Transfer Entropy and Allosteric Communication Landscapes in Proteins with Harmonic Interactions

A fast and approximate method of generating allosteric communication landscapes is presented by using Schreiber's entropy transfer concept in combination with the Gaussian Network Model of proteins. Predictions of the model and the allosteric communication landscapes generated show that information transfer in proteins does not necessarily take place along a single path, but through an ensemble of pathways. The model emphasizes that knowledge of entropy only is not sufficient for determining allosteric communication and additional information based on time delayed correlations has to be introduced, which leads to the presence of causality in proteins. The model provides a simple tool for mapping entropy sink-source relations into pairs of residues. Residues that should be manipulated to control protein activity may be determined with this approach. This should be of great importance for allosteric drug design and for understanding the effects of mutations on protein function. The model is applied to determine allosteric communication in two proteins, Ubiquitin and Pyruvate Kinase. Predictions are in agreement with detailed molecular dynamics simulations and experimental evidence.SignificanceProteins perform their function by an exchange of information within themselves and with their environments through correlated fluctuations of their atoms. Fluctuations of one atom may drive the fluctuations of another. Information transmitted in this way leads to allosteric communication which is described as the process in which action at one site of the protein is transmitted to another site at which the protein performs its activity. Disruption of allosteric communication by mutation for example leads to disease. The present paper incorporates information theoretic concepts into the well known Gaussian Network Model of proteins and allows for rapid characterization of allosteric communication landscapes for normal functioning as well as malfunctioning proteins.

Identification of Hot Spots in Protein Structures Using Gaussian Network Model and Gaussian Naive Bayes

Residue fluctuations in protein structures have been shown to be highly associated with various protein functions. Gaussian network model (GNM), a simple representative coarse-grained model, was widely adopted to reveal function-related protein dynamics. We directly utilized the high frequency modes generated by GNM and further performed Gaussian Naive Bayes (GNB) to identify hot spot residues. Two coding schemes about the feature vectors were implemented with varying distance cutoffs for GNM and sliding window sizes for GNB based on tenfold cross validations: one by using only a single high mode and the other by combining multiple modes with the highest frequency. Our proposed methods outperformed the previous work that did not directly utilize the high frequency modes generated by GNM, with regard to overall performance evaluated using F1 measure. Moreover, we found that inclusion of more high frequency modes for a GNB classifier can significantly improve the sensitivity. The present study provided additional valuable insights into the relation between the hot spots and the residue fluctuations.