Synchronous and Asynchronous Response in Dynamically Perturbed Proteins

Dynamically driven correlations in elastic net models reveal sequence of events and causality in proteins

An explicit analytic solution is given for the Langevin equation applied to the Gaussian Network Model of a protein subjected to both a random and a deterministic periodic force. Synchronous and asynchronous components of time correlation functions are derived and an expression for phase differences in the time correlations of residue pairs is obtained. The synchronous component enables the determination of dynamic communities within the protein structure. The asynchronous component reveals causality, where the time correlation function between residues i and j differs depending on whether i is observed before j or vice versa, resulting in directional information flow. Driver and driven residues in the allosteric process of cyclophilin A and human NAD-dependent isocitrate dehydrogenase are determined by a perturbation-scanning technique. Factors affecting phase differences between fluctuations of residues, such as network topology, connectivity, and residue centrality, are identified. Within the constraints of the isotropic Gaussian Network Model, our results show that asynchronicity increases with viscosity and distance between residues, decreases with increasing connectivity, and decreases with increasing levels of eigenvector centrality.

Continuing progress in the field of two-dimensional correlation spectroscopy (2D-COS), part II. Recent noteworthy developments

This comprehensive survey review compiles noteworthy developments and new concepts of two-dimensional correlation spectroscopy (2D-COS) for the last two years. It covers review articles, books, proceedings, and numerous research papers published on 2D-COS, as well as patent and publication trends. 2D-COS continues to evolve and grow with new significant developments and versatile applications in diverse scientific fields. The healthy, vigorous, and diverse progress of 2D-COS studies in many fields strongly confirms that it is well accepted as a powerful analytical technique to provide an in-depth understanding of systems of interest.

Continuing progress in the field of two-dimensional correlation spectroscopy (2D-COS): Part III. Versatile applications

In this review, the comprehensive summary of two-dimensional correlation spectroscopy (2D-COS) for the last two years is covered. The remarkable applications of 2D-COS in diverse fields using many types of probes and perturbations for the last two years are highlighted. IR spectroscopy is still the most popular probe in 2D-COS during the last two years. Applications in fluorescence and Raman spectroscopy are also very popularly used. In the external perturbations applied in 2D-COS, variations in concentration, pH, and relative compositions are dramatically increased during the last two years. Temperature is still the most used effect, but it is slightly decreased compared to two years ago. 2D-COS has been applied to diverse systems, such as environments, natural products, polymers, food, proteins and peptides, solutions, mixtures, nano materials, pharmaceuticals, and others. Especially, biological and environmental applications have significantly emerged. This survey review paper shows that 2D-COS is an actively evolving and expanding field.

Mutual information analysis of mutation, nonlinearity, and triple interactions in proteins

Mutations are the cause of several diseases as well as the underlying force of evolution. A thorough understanding of their biophysical consequences is essential. We present a computational framework for evaluating different levels of mutual information (MI) and its dependence on mutation. We used molecular dynamics trajectories of the third PDZ domain and its different mutations. Nonlinear MI between all residue pairs are calculated by tensor Hermite polynomials up to the fifth order and compared with results from multivariate Gaussian distribution of joint probabilities. We show that MI is written as the sum of a Gaussian and a nonlinear component. Results for the PDZ domain show that the Gaussian term gives a sufficiently accurate representation of MI when compared with nonlinear terms up to the fifth order. Changes in MI between residue pairs show the characteristic patterns resulting from specific mutations. Emergence of new peaks in the MI versus residue index plots of mutated PDZ shows how mutation may change allosteric pathways. Triple correlations are characterized by evaluating MI between triplets of residues. We observed that certain triplets are strongly affected by mutation. Susceptibility of residues to perturbation is obtained by MI and discussed in terms of linear response theory.

Key Residues in δ Opioid Receptor Allostery Explored by the Elastic Network Model and the Complex Network Model Combined with the Perturbation Method

Opioid receptors, a kind of G protein-coupled receptors (GPCRs), mainly mediate an analgesic response via allosterically transducing the signal of endogenous ligand binding in the extracellular domain to couple to effector proteins in the intracellular domain. The δ opioid receptor (DOP) is associated with emotional control besides pain control, which makes it an attractive therapeutic target. However, its allosteric mechanism and key residues responsible for the structural stability and signal communication are not completely clear. Here we utilize the Gaussian network model (GNM) and amino acid network (AAN) combined with perturbation methods to explore the issues. The constructed fcfGNM_MD, where the force constants are optimized with the inverse covariance estimation based on the correlated fluctuations from the available DOP molecular dynamics (MD) ensemble, shows a better performance than traditional GNM in reproducing residue fluctuations and cross-correlations and in capturing functionally low-frequency modes. Additionally, fcfGNM_MD can consider implicitly the environmental effects to some extent. The lowest mode can well divide DOP segments and identify the two sodium ion (important allosteric regulator) binding coordination shells, and from the fastest modes, the key residues important for structure stabilization are identified. Using fcfGNM_MD combined with a dynamic perturbation-response method, we explore the key residues related to the sodium ion binding. Interestingly, we identify not only the key residues in sodium ion binding shells but also the ones far away from the perturbation sites, which are involved in binding with DOP ligands, suggesting the possible long-range allosteric modulation of sodium binding for the ligand binding to DOP. Furthermore, utilizing the weighted AAN combined with attack perturbations, we identify the key residues for allosteric communication. This work helps strengthen the understanding of the allosteric communication mechanism in δ opioid receptor and can provide valuable information for drug design.

Allosteric mechanism for SL RNA recognition by polypyrimidine tract binding protein RRM1: An atomistic MD simulation and network-based study

Polypyrimidine tract-binding protein (PTB), an RNA-binding protein, is involved in the regulation of diverse processes in mRNA metabolism. However, the allosteric modulation of its binding with RNA remains unclear. We explore the dynamic characteristics of PTB RNA recognition motif 1 (RRM1) in its RNA-free and wild-type/mutant RNA-bound states to understand the issues using molecular dynamics (MD) simulation, perturbation response scanning (PRS) and protein structure network (PSN) models. It is found that RNA binding strengthens RRM1 stability, while L151G mutation in α3 helix far away from the interface makes the complex unstable. The latter is caused by long-distance dynamic couplings, which makes intermolecular electrostatic and entropy energies unfavorable. The weakened couplings between interface β sheets and C-terminal parts upon mutation reveal RNA recognition is co-regulated by these regions. Interestingly, PRS analysis reveals the allostery caused by the perturbation on α3 helix has already been pre-encoded in the equilibrium dynamics of the protein structure. PSN analysis shows the details of the allosteric signal transmission, revealing the necessity of strong couplings between α3 helix and interface for maintaining the high binding affinity. This study sheds light on the mechanisms of PTB allostery and RNA recognition and can provide important information for drug design.

Prediction of Allosteric Communication Pathways in Proteins

MOTIVATION

Allostery in proteins is an essential phenomenon in biological processes. In this paper, 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 preexistence 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.

Information Flow and Allosteric Communication in Proteins

Based on Schreiber's work on transfer entropy, a molecular theory of nonlinear information transfer in proteins is developed. The joint distribution function for residue fluctuations is expressed in terms of tensor Hermite polynomials which conveniently separate harmonic and nonlinear contributions to information transfer. The harmonic part of information transfer is expressed as the difference between time dependent and independent mutual information. Third order nonlinearities are discussed in detail. Amount and speed of information transfer between residues, important for understanding allosteric activity in proteins, are discussed. While mutual information shows the maximum amount of information that may be transferred between two residues, it does not explain the actual amount of transfer nor the transfer rate of information. For this, dynamic equations of the system are needed. The solution of the Langevin equation and molecular dynamics trajectories are used in the present work for this purpose. Allosteric communication in Human NAD-dependent isocitrate dehydrogenase is studied as an example. Calculations show that several paths contribute collectively to information transfer. Important residues on these paths are identified. Time resolved information transfer between these residues, their amplitudes and transfer rates, which are in agreement with time resolved ultraviolet resonance Raman measurements in general, are estimated. Estimated transfer rates are in the order of 1-20 megabits per second. Information transfer from third order contributions are one to two orders of magnitude smaller than the harmonic terms, showing that harmonic analysis is a good approximation to information transfer.

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 all atom pairs within the coordination shell of each other into the Kirchoff Adjacency Matrix. Counting all contacts rather than only alpha carbon contacts diminishes the magnitude of fluctuations in the system. But more importantly, it changes the graph-like connectivity structure, i.e., the Kirchoff Adjacency Matrix of the protein. This change depends on amino acid type which introduces amino acid specific and position specific information into the classical coarse-grained GNM which was originally modelled in analogy with the phantom network model of rubber elasticity. With this modification, it is now possible to explain the consequences of mutation and ligand binding on residue fluctuations, their pair-correlations and mutual information (MI) shared by each pair. We refer to the new model as 'all-atom GNM'. Using examples from published data we show that the all-atom GNM gives B-factors that are in better agreement with experiment, can explain effects of mutation on long range communication in PDZ domains and can predict effects of GDP and GTP binding on the dimerization of KRAS.

Global Dynamics Renders Protein Sites with High Functional Response

Deep mutational scanning enables examination of the effects of many mutations at each amino acid position in a query protein, readily disclosing positions that are particularly sensitive. Mutations in these positions alter protein function the most. Here, on the premise that dynamics underlie function, we explore to what extent the measured sensitivity to mutations could be linked to-perhaps be explained by-the structural dynamics of the protein. We employ a minimalist perturbation-response approach based on the Gaussian Network Model (GNM) on a data set of seven proteins with deep mutational scanning data. The analysis shows that the mutation-sensitive positions are often of capacity to modulate the global dynamics and to intermediate allosteric interactions in the structure. With that, upon strain perturbation, these positions decrease residue fluctuations the most, affecting function via entropy changes. This is particularly relevant for positions that are distant from binding sites or other functional regions of the protein and are sensitive to mutations, nevertheless. Our results indicate that mutations in these positions allosterically manipulate protein function.