MOTIVATION: Proteins are dynamic entities that undergo conformational changes critical for their functions. Understanding the communication pathways and information transfer within proteins is crucial for elucidating allosteric interactions in their mechanisms. This study utilizes mutual information (MI) analysis to probe dynamic allostery. Using two cases, Ubiquitin and PLpro, we have evaluated the accuracy and limitations of different approximations including the exact anisotropic and isotropic models, multivariate Gaussian model, isotropic Gaussian model, and the Gaussian Network Model (GNM) in revealing allosteric interactions. RESULTS: Our findings emphasize the required trajectory length for capturing accurate mutual information profiles. Long molecular dynamics trajectories, 1 ms for Ubiquitin and 100 µs for PLpro are used as benchmarks, assuming they represent the ground truth. Trajectory lengths of approximately 5 µs for Ubiquitin and 1 µs for PLpro marked the onset of convergence, while the multivariate Gaussian model accurately captured mutual information with trajectories of 5 ns for Ubiquitin and 350 ns for PLpro. However, the isotropic Gaussian model is less successful in representing the anisotropic nature of protein dynamics, particularly in the case of PLpro, highlighting its limitations. The GNM, however, provides reasonable approximations of long-range information exchange as a minimalist network model based on a single crystal structure. Overall, the optimum trajectory lengths for effective Gaussian approximations of long-time dynamic behavior depend on the inherent dynamics within the protein's topology. The GNM, by showcasing dynamics across relatively diverse time scales, can be used either as a standalone method or to gauge the adequacy of MD simulation lengths. AVAILABILITY AND IMPLEMENTATION: Mutual information codes are available at https://github.com/kemaldemirtas/prc-MI.git.

MOTIVATION: Allostery in proteins is an essential phenomenon in biological processes. In this article, we present a computational model to predict paths of maximum information transfer between active and allosteric sites. In this information theoretic study, we use mutual information as the measure of information transfer, where transition probability of information from one residue to its contacting neighbors is proportional to the magnitude of mutual information between the two residues. Starting from a given residue and using a Hidden Markov Model, we successively determine the neighboring residues that eventually lead to a path of optimum information transfer. The Gaussian approximation of mutual information between residue pairs is adopted. The limits of validity of this approximation are discussed in terms of a nonlinear theory of mutual information and its reduction to the Gaussian form. RESULTS: Predictions of the model are tested on six widely studied cases, CheY Bacterial Chemotaxis, B-cell Lymphoma extra-large (Bcl-xL), Human proline isomerase cyclophilin A (CypA), Dihydrofolate reductase (DHFR), HRas GTPase and Caspase-1. The communication transmission rendering the propagation of local fluctuations from the active sites throughout the structure in multiple paths correlate well with the known experimental data. Distinct paths originating from the active site may likely represent a multi functionality such as involving more than one allosteric site and/or pre-existence of some other functional states. Our model is computationally fast and simple and can give allosteric communication pathways, which are crucial for the understanding and control of protein functionality. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

It has recently been proposed by Gunasakaran et al. that allostery may be an intrinsic property of all proteins. Here, we develop a computational method that can determine and quantify allosteric activity in any given protein. Based on Schreiber's transfer entropy formulation, our approach leads to an information transfer landscape for the protein that shows the presence of entropy sinks and sources and explains how pairs of residues communicate with each other using entropy transfer. The model can identify the residues that drive the fluctuations of others. We apply the model to Ubiquitin, whose allosteric activity has not been emphasized until recently, and show that there are indeed systematic pathways of entropy and information transfer between residues that correlate well with the activities of the protein. We use 600 nanosecond molecular dynamics trajectories for Ubiquitin and its complex with human polymerase iota and evaluate entropy transfer between all pairs of residues of Ubiquitin and quantify the binding susceptibility changes upon complex formation. We explain the complex formation propensities of Ubiquitin in terms of entropy transfer. Important residues taking part in allosteric communication in Ubiquitin predicted by our approach are in agreement with results of NMR relaxation dispersion experiments. Finally, we show that time delayed correlation of fluctuations of two interacting residues possesses an intrinsic causality that tells which residue controls the interaction and which one is controlled. Our work shows that time delayed correlations, entropy transfer and causality are the required new concepts for explaining allosteric communication in proteins.

We concentrate on the temporal stochastic behavior of electronic and biological systems due to mainly intrinsic noise and fluctuation phenomena as opposed to extrinsic crosstalk-like interference or statistical variations in system parameters. We provide an overview of modeling and analysis techniques for noise and fluctuation phenomena in biological systems with comparisons to electronic systems. We present several examples where a synergistic cross-fertilization between the two disciplines seems promising. In particular, we discuss the characterization of conformational fluctuations in proteins, the simulation of stochastic behavior in intracellular processes, and the modeling of noise in biological neurons, neuronal networks, nervous system and the brain.

A statistical thermodynamics approach is proposed to determine structurally and functionally important residues in native proteins that are involved in energy exchange with a ligand and other residues along an interaction pathway. The structure-function relationships, ligand binding and allosteric activities of ten structures of HLA Class I proteins of the immune system are studied by the Gaussian Network Model. Five of these models are associated with inflammatory rheumatic disease and the remaining five are properly functioning. In the Gaussian Network Model, the protein structures are modeled as an elastic network where the inter-residue interactions are harmonic. Important residues and the interaction pathways in the proteins are identified by focusing on the largest eigenvalue of the residue interaction matrix. Predicted important residues match those known from previous experimental and clinical work. Graph perturbation is used to determine the response of the important residues along the interaction pathway. Differences in response patterns of the two sets of proteins are identified and their relations to disease are discussed.